Broken Thing in teh website
I deleted the broken things
This commit is contained in:
Lucas Kent
parent
42f2aaac3e
commit
a701a6c770
@ -1,99 +0,0 @@
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||||
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File generated automatically on Fri, 28 Oct 2022 20:29:21, do NOT edit
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|
||||
and is used for updating this website.
|
||||
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|
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||||
DO NOT delete this folder unless you do not want to update the mirror in the future!!
|
||||
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|
||||
|
||||
note: the hts-log.txt file, and hts-cache folder, may contain sensitive information,
|
||||
such as username/password authentication for websites mirrored in this project
|
||||
do not share these files/folders if you want these information to remain private
|
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|
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HTTrack3.49-2+htsswf+htsjava launched on Fri, 28 Oct 2022 20:29:21 at https://www.mathsisfun.com/math-tools.html +*.png +*.gif +*.jpg +*.jpeg +*.css +*.js -ad.doubleclick.net/* -mime:application/foobar
|
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(winhttrack -qwC2%Ps2u1%s%uN0%I0p3DaK0H0%kf2A25000%f#f -F "Mozilla/4.5 (compatible; HTTrack 3.0x; Windows 98)" -%F "<!-- Mirrored from %s%s by HTTrack Website Copier/3.x [XR&CO'2014], %s -->" -%l "en, *" https://www.mathsisfun.com/math-tools.html -O1 "C:\My Web Sites\mathisfun" +*.png +*.gif +*.jpg +*.jpeg +*.css +*.js -ad.doubleclick.net/* -mime:application/foobar )
|
||||
|
||||
Information, Warnings and Errors reported for this mirror:
|
||||
note: the hts-log.txt file, and hts-cache folder, may contain sensitive information,
|
||||
such as username/password authentication for websites mirrored in this project
|
||||
do not share these files/folders if you want these information to remain private
|
||||
|
||||
20:32:35 Error: "Not Found" (404) at link https://www.mathsisfun.com/mathsisfun/ (from https://www.mathsisfun.com/main4.js)
|
||||
20:32:35 Error: "Not Found" (404) at link https://www.mathsisfun.com/localhost/ (from https://www.mathsisfun.com/main4.js)
|
||||
20:32:35 Error: "Not Found" (404) at link https://www.mathsisfun.com/POST (from https://www.mathsisfun.com/main4.js)
|
||||
20:32:35 Error: "Not Found" (404) at link https://www.mathsisfun.com/mathsisfun/images/style/320x60.jpg (from https://www.mathsisfun.com/main4.js)
|
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20:39:36 Error: "Not Found" (404) at link https://www.mathsisfun.com/datas/wiki/blue_info.png (from https://www.mathsisfun.com/images/style/info.svg)
|
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20:39:36 Error: "Not Found" (404) at link https://www.mathsisfun.com/home/cats/Documents/Fun/hands.png (from https://www.mathsisfun.com/images/style/activity-div.svg)
|
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20:48:53 Error: "Not Found" (404) at link https://www.mathsisfun.com/algebra/sets/game-theory.html (from https://www.mathsisfun.com/algebra/index.html)
|
||||
20:48:53 Error: "Not Found" (404) at link https://www.mathsisfun.com/algebra/sets/logic-gates.html (from https://www.mathsisfun.com/algebra/index.html)
|
||||
20:48:53 Error: "Not Found" (404) at link https://www.mathsisfun.com/algebra/sets/boolean-algebra.html (from https://www.mathsisfun.com/algebra/index.html)
|
||||
20:59:11 Error: "Not Found" (404) at link https://www.mathsisfun.com/numbers/localhost/ (from https://www.mathsisfun.com/main3.js)
|
||||
20:59:11 Error: "Not Found" (404) at link https://www.mathsisfun.com/numbers/POST (from https://www.mathsisfun.com/main3.js)
|
||||
20:59:34 Warning: Link https://www.mathsisfun.com/cdn-cgi/l/email-protection not scanned (follow robots meta tag)
|
||||
21:00:06 Error: "Not Found" (404) at link https://www.mathsisfun.com/Images/SVG/inkscape_pasted_image_20101001_094421.png (from https://www.mathsisfun.com/geometry/images/circle-area-ex.svg)
|
||||
21:00:07 Warning: Retry after error -5 (Unable to open local file) at link file:///C:/Images/SVG/inkscape_pasted_image_20101001_094421.png (from https://www.mathsisfun.com/measure/images/square-m-vs-m-square.svg)
|
||||
21:00:18 Error: "Not Found" (404) at link https://www.mathsisfun.com/geometry/images/nocdn/polyhedra.swf (from https://www.mathsisfun.com/geometry/polyhedron-models-flash.html)
|
||||
21:00:50 Error: "Not Found" (404) at link https://www.mathsisfun.com/switch-1.gif (from https://www.mathsisfun.com/binary-digits.html)
|
||||
21:00:51 Error: "Not Found" (404) at link https://www.mathsisfun.com/calculus/local.css (from https://www.mathsisfun.com/calculus/integration-definite.html)
|
||||
21:01:49 Error: "Not Found" (404) at link https://www.mathsisfun.com/coordinate.html (from https://www.mathsisfun.com/links/b-3to6-algebra.html)
|
||||
21:02:00 Error: "Not Found" (404) at link https://www.mathsisfun.com/activity/random-or-not.html (from https://www.mathsisfun.com/links/b-3to6-data.html)
|
||||
21:02:20 Error: "Not Found" (404) at link https://www.mathsisfun.com/definitions/contruction-geometry-.html (from https://www.mathsisfun.com/links/c-7to9-geometry.html)
|
||||
21:02:24 Error: "Not Found" (404) at link https://www.mathsisfun.com/definitions/imaginary-numbers.html (from https://www.mathsisfun.com/links/d-10up-numbers.html)
|
||||
21:03:55 Error: "Not Found" (404) at link https://www.mathsisfun.com/index.html (from https://www.mathsisfun.com/builders-math.html)
|
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21:06:21 Warning: Retry after error -4 (No data (connection closed)) at link https://www.mathsisfun.com/physics/images/telescope-bure-plateau.jpg (from https://www.mathsisfun.com/physics/reflection.html)
|
||||
21:08:26 Error: "Not Found" (404) at link https://www.mathsisfun.com/home/gps/documents/images/svg/foundit/YAFFr2prev.jpeg (from https://www.mathsisfun.com/measure/images/beaker.svg)
|
||||
21:08:33 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/connect.svg (from https://www.mathsisfun.com/games/images/connect.js?mode=4)
|
||||
21:08:35 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/GET (from https://www.mathsisfun.com/games/images/hex-drums.js)
|
||||
21:08:36 Error: "Not Found" (404) at link https://www.mathsisfun.com/numbers/images/407.323 (from https://www.mathsisfun.com/numbers/images/prime-composite.svg)
|
||||
21:08:36 Error: "Not Found" (404) at link https://www.mathsisfun.com/numbers/images/58.323 (from https://www.mathsisfun.com/numbers/images/factor-tree-48.svg)
|
||||
21:08:36 Error: "Not Found" (404) at link https://www.mathsisfun.com/numbers/images/10.323 (from https://www.mathsisfun.com/numbers/images/factor-tree-48.svg)
|
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21:08:36 Error: "Not Found" (404) at link https://www.mathsisfun.com/GET (from https://www.mathsisfun.com/images/player.js)
|
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21:08:36 Error: "Not Found" (404) at link https://www.mathsisfun.com/numbers/images/427.323 (from https://www.mathsisfun.com/numbers/images/real-number-line.svg)
|
||||
21:08:36 Error: "Not Found" (404) at link https://www.mathsisfun.com/numbers/images/392.323 (from https://www.mathsisfun.com/numbers/images/real-number-line.svg)
|
||||
21:08:37 Error: "Not Found" (404) at link https://www.mathsisfun.com/measure/images/335.323 (from https://www.mathsisfun.com/measure/images/temp-freeze-boil.svg)
|
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21:08:39 Error: "Not Found" (404) at link https://www.mathsisfun.com/sets/images/function-sin-sinh.svg (from https://www.mathsisfun.com/sets/images/function-sinh-sin.svg)
|
||||
21:08:39 Error: "Not Found" (404) at link https://www.mathsisfun.com/sets/images/function-cos-cosh.svg (from https://www.mathsisfun.com/sets/images/function-cosh-cos.svg)
|
||||
21:08:39 Error: "Not Found" (404) at link https://www.mathsisfun.com/sets/images/function-tan-tanh.svg (from https://www.mathsisfun.com/sets/images/function-tanh-tan.svg)
|
||||
21:08:40 Error: "Not Found" (404) at link https://www.mathsisfun.com/geometry/images/circle-area-arcs1.svg (from https://www.mathsisfun.com/geometry/images/circle-area-lines.svg)
|
||||
21:08:40 Warning: Retry after error -5 (Unable to open local file) at link file:///C:/Images/SVG/inkscape_pasted_image_20101001_094421.png (from https://www.mathsisfun.com/measure/images/square-m-vs-m-square.svg)
|
||||
21:08:40 Error: "Not Found" (404) at link https://www.mathsisfun.com/geometry/images/406.323 (from https://www.mathsisfun.com/geometry/images/cone-sphere-cylinder-vol.svg)
|
||||
21:08:40 Error: "Not Found" (404) at link https://www.mathsisfun.com/geometry/images/199.323 (from https://www.mathsisfun.com/geometry/images/cone-sphere-cylinder-vol.svg)
|
||||
21:08:40 Error: "Not Found" (404) at link https://www.mathsisfun.com/geometry/images/165.323 (from https://www.mathsisfun.com/geometry/images/cone-sphere-cylinder-vol.svg)
|
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21:08:41 Error: "Not Found" (404) at link https://www.mathsisfun.com/sets/not gate (from https://www.mathsisfun.com/sets/logic-gates.html)
|
||||
21:08:42 Warning: Retry after error 500 (Internal Server Error) at link https://www.mathsisfun.com/worksheets/print.php?w=34175&ID=16155 (from https://www.mathsisfun.com/numbers/addition-column.html)
|
||||
21:08:42 Warning: Retry after error 500 (Internal Server Error) at link https://www.mathsisfun.com/worksheets/print.php?w=34170&ID=5450 (from https://www.mathsisfun.com/numbers/addition-column.html)
|
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21:08:48 Error: "Not Found" (404) at link https://www.mathsisfun.com/numbers/local.css (from https://www.mathsisfun.com/numbers/choose-larger-block.html)
|
||||
21:08:50 Error: "Not Found" (404) at link https://www.mathsisfun.com/puzzles/images/pencils.svg (from https://www.mathsisfun.com/pencilsandjars.html)
|
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21:08:51 Error: "Not Found" (404) at link https://www.mathsisfun.com/data/images/line-graph-temp.svg (from https://www.mathsisfun.com/data/images/line-graph-deg.svg)
|
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21:08:51 Error: "Not Found" (404) at link https://www.mathsisfun.com/images/style/smiley.svg (from https://www.mathsisfun.com/images/style/smile.svg)
|
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21:08:51 Error: "Not Found" (404) at link https://www.mathsisfun.com/media/sda2/storage/dir/programs/gimp/svg/match.png (from https://www.mathsisfun.com/activity/images/match-no-head.svg)
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21:08:51 Error: "Not Found" (404) at link https://www.mathsisfun.com/geometry/images/symboli-right-angle.svg (from https://www.mathsisfun.com/geometry/images/symbol-right-angle.svg)
|
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21:08:51 Error: "Not Found" (404) at link https://www.mathsisfun.com/geometry/images/area/..%5C.%5C..%5C..%5C..%5C..%5CImages%5CSVG%5Cinkscape_pasted_image_20101001_094421.png (from https://www.mathsisfun.com/geometry/images/area/triangle-perim.svg)
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21:08:51 Error: "Not Found" (404) at link https://www.mathsisfun.com/geometry/GET (from https://www.mathsisfun.com/geometry/images/construct.js)
|
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21:08:53 Warning: Retry after error -5 (Unable to open local file) at link file:///C:/Images/SVG/pastedpic_10162008_083107.png (from https://www.mathsisfun.com/geometry/images/cylinder-pizza.svg)
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21:08:53 Error: "Not Found" (404) at link https://www.mathsisfun.com/numbers/images/nocdn/math-trainer.swf (from https://www.mathsisfun.com/numbers/math-trainer-flash.html)
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21:08:53 Error: "Not Found" (404) at link https://www.mathsisfun.com/numbers/images/nocdn/math-trainer.swf?m=Multiply (from https://www.mathsisfun.com/numbers/math-trainer-flash.html)
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21:08:54 Error: "Not Found" (404) at link https://www.mathsisfun.com/numbers/whole-numbers.html (from https://www.mathsisfun.com/numbers/digital-root.html)
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21:09:25 Error: "Not Found" (404) at link https://www.mathsisfun.com/money/images/nocdn/money-master-rand.swf (from https://www.mathsisfun.com/money/random-coins.html)
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21:09:33 Error: "Not Found" (404) at link https://www.mathsisfun.com/home/andy/9694_6555.png (from https://www.mathsisfun.com/puzzles/images/jeep.svg)
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21:09:42 Error: "Not Found" (404) at link https://www.mathsisfun.com/puzzles/images/lengthy-mystery.svg (from https://www.mathsisfun.com/puzzles/images/lengthy-relationship.svg)
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21:09:48 Warning: Retry after error -5 (Unable to open local file) at link file:///C:/Images/SVG/Banana.jpg (from https://www.mathsisfun.com/sets/images/function-sets.svg)
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21:09:48 Error: "Not Found" (404) at link https://www.mathsisfun.com/calculus/images/242.323 (from https://www.mathsisfun.com/calculus/images/integral-subs-3.svg)
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21:09:48 Error: "Not Found" (404) at link https://www.mathsisfun.com/calculus/images/535.323 (from https://www.mathsisfun.com/calculus/images/diff-eq-lin-d.svg)
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21:09:59 Error: "Not Found" (404) at link https://www.mathsisfun.com/measure/images/cubic-centimeter.svg (from https://www.mathsisfun.com/measure/images/cubic-cm.svg)
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21:09:59 Error: "Not Found" (404) at link https://www.mathsisfun.com/measure/images/-884.323 (from https://www.mathsisfun.com/measure/images/day-am-pm.svg)
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21:10:00 Error: "Not Found" (404) at link https://www.mathsisfun.com/measure/blizzard.jpg (from https://www.mathsisfun.com/measure/images/thermometer-inter.js)
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21:10:00 Error: "Not Found" (404) at link https://www.mathsisfun.com/measure/snow.jpg (from https://www.mathsisfun.com/measure/images/thermometer-inter.js)
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21:10:00 Error: "Not Found" (404) at link https://www.mathsisfun.com/measure/ice.jpg (from https://www.mathsisfun.com/measure/images/thermometer-inter.js)
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21:10:00 Error: "Not Found" (404) at link https://www.mathsisfun.com/measure/rainy.jpg (from https://www.mathsisfun.com/measure/images/thermometer-inter.js)
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21:10:00 Error: "Not Found" (404) at link https://www.mathsisfun.com/measure/sunny.jpg (from https://www.mathsisfun.com/measure/images/thermometer-inter.js)
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21:10:00 Error: "Not Found" (404) at link https://www.mathsisfun.com/measure/beach.jpg (from https://www.mathsisfun.com/measure/images/thermometer-inter.js)
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21:10:00 Error: "Not Found" (404) at link https://www.mathsisfun.com/measure/desert.jpg (from https://www.mathsisfun.com/measure/images/thermometer-inter.js)
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21:10:00 Error: "Not Found" (404) at link https://www.mathsisfun.com/measure/coffee.jpg (from https://www.mathsisfun.com/measure/images/thermometer-inter.js)
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21:10:00 Error: "Not Found" (404) at link https://www.mathsisfun.com/measure/boil.jpg (from https://www.mathsisfun.com/measure/images/thermometer-inter.js)
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21:10:00 Error: "Not Found" (404) at link https://www.mathsisfun.com/numbers/images/205.323 (from https://www.mathsisfun.com/numbers/images/pascals-triangle-squares.svg)
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21:10:00 Error: "Unable to open local file" (-5) after 2 retries at link file:///C:/Images/SVG/inkscape_pasted_image_20101001_094421.png (from https://www.mathsisfun.com/measure/images/square-m-vs-m-square.svg)
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21:10:01 Warning: Retry after error 500 (Internal Server Error) at link https://www.mathsisfun.com/worksheets/print.php?w=34175&ID=16155 (from https://www.mathsisfun.com/numbers/addition-column.html)
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21:10:01 Warning: Retry after error 500 (Internal Server Error) at link https://www.mathsisfun.com/worksheets/print.php?w=34170&ID=5450 (from https://www.mathsisfun.com/numbers/addition-column.html)
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21:10:01 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ruffle.js (from https://www.mathsisfun.com/images/ruffle/ruffle.js)
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21:10:01 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/e.url,document.location.href (from https://www.mathsisfun.com/images/ruffle/ruffle.js)
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21:10:01 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/memory/images/ (from https://www.mathsisfun.com/games/memory/memory.js)
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21:10:01 Error: "Not Found" (404) at link https://www.mathsisfun.com/home/jimmac/Desktop/wi-fi.png (from https://www.mathsisfun.com/images/inverse.svg)
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21:10:01 Error: "Not Found" (404) at link https://www.mathsisfun.com/home/Krug/Projekte/Icon-Sets/set2/png/7a.png (from https://www.mathsisfun.com/algebra/images/sentence-closed.svg)
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21:10:01 Error: "Not Found" (404) at link https://www.mathsisfun.com/algebra/images/218.323 (from https://www.mathsisfun.com/algebra/images/triangle-aas.svg)
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21:10:01 Error: "Not Found" (404) at link https://www.mathsisfun.com/geometry/THREE.LensFlare has been moved to /examples/js/objects/Lensflare.js (from https://www.mathsisfun.com/images/three.min.js)
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21:10:01 Error: "Not Found" (404) at link https://www.mathsisfun.com/geometry/THREE.SceneUtils has been moved to /examples/js/utils/SceneUtils.js (from https://www.mathsisfun.com/images/three.min.js)
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21:10:01 Warning: Retry after error -5 (Unable to open local file) at link file:///C:/Images/SVG/pastedpic_10162008_083107.png (from https://www.mathsisfun.com/geometry/images/cylinder-pizza.svg)
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21:10:01 Error: "Not Found" (404) at link https://www.mathsisfun.com/workermain.js (from https://www.mathsisfun.com/games/ninja/alpha/scripts/main.js)
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21:10:01 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/alpha/workermain.js (from https://www.mathsisfun.com/games/ninja/alpha/scripts/main.js)
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21:10:01 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/alpha/g,a (from https://www.mathsisfun.com/games/ninja/alpha/scripts/main.js)
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21:10:01 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/alpha/e,this.g_amk (from https://www.mathsisfun.com/games/ninja/alpha/scripts/main.js)
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21:10:01 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/alpha/dispatchworker.js (from https://www.mathsisfun.com/games/ninja/alpha/scripts/main.js)
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21:10:01 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/alpha/jobworker.js (from https://www.mathsisfun.com/games/ninja/alpha/scripts/main.js)
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21:10:02 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/arty/workermain.js (from https://www.mathsisfun.com/games/ninja/arty/scripts/main.js)
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21:10:02 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/arty/g,a (from https://www.mathsisfun.com/games/ninja/arty/scripts/main.js)
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21:10:02 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/arty/e,this.g_amk (from https://www.mathsisfun.com/games/ninja/arty/scripts/main.js)
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21:10:02 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/arty/dispatchworker.js (from https://www.mathsisfun.com/games/ninja/arty/scripts/main.js)
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21:10:02 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/arty/jobworker.js (from https://www.mathsisfun.com/games/ninja/arty/scripts/main.js)
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21:10:02 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/bottle/workermain.js (from https://www.mathsisfun.com/games/ninja/bottle/scripts/main.js)
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21:10:02 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/bottle/g,a (from https://www.mathsisfun.com/games/ninja/bottle/scripts/main.js)
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21:10:02 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/bottle/e,this.g_amk (from https://www.mathsisfun.com/games/ninja/bottle/scripts/main.js)
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21:10:02 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/bottle/dispatchworker.js (from https://www.mathsisfun.com/games/ninja/bottle/scripts/main.js)
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21:10:02 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/bottle/jobworker.js (from https://www.mathsisfun.com/games/ninja/bottle/scripts/main.js)
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21:10:04 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/lightybulb/workermain.js (from https://www.mathsisfun.com/games/ninja/lightybulb/scripts/main.js)
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21:10:04 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/lightybulb/g,a (from https://www.mathsisfun.com/games/ninja/lightybulb/scripts/main.js)
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21:10:04 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/lightybulb/e,this.g_amk (from https://www.mathsisfun.com/games/ninja/lightybulb/scripts/main.js)
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21:10:04 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/lightybulb/dispatchworker.js (from https://www.mathsisfun.com/games/ninja/lightybulb/scripts/main.js)
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21:10:04 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/lightybulb/jobworker.js (from https://www.mathsisfun.com/games/ninja/lightybulb/scripts/main.js)
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21:10:20 Error: "Not Found" (404) at link https://www.mathsisfun.com/puzzles/passiflora.jpg (from https://www.mathsisfun.com/puzzles/images/jigsaw.js)
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21:10:21 Warning: Retry after error -5 (Unable to open local file) at link file:///C:/Images/SVG/Banana.jpg (from https://www.mathsisfun.com/sets/images/function-sets.svg)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/a/tanks072/images/sprites/blueTank1.svg (from https://www.mathsisfun.com/games/a/tanks072/images/sprites/blueTank.svg)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/a/tanks072/images/sprites/redTank1.svg (from https://www.mathsisfun.com/games/a/tanks072/images/sprites/redTank.svg)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/a/tanks072/images/bg/tanks-basic.svg (from https://www.mathsisfun.com/games/a/tanks072/images/bg/basic.svg)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/a/tanks072/images/bg/tanks-snow.svg (from https://www.mathsisfun.com/games/a/tanks072/images/bg/snow.svg)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/a/tanks072/images/bg/tanks-moon.svg (from https://www.mathsisfun.com/games/a/tanks072/images/bg/moon.svg)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/balloon/workermain.js (from https://www.mathsisfun.com/games/ninja/balloon/scripts/main.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/balloon/g,a (from https://www.mathsisfun.com/games/ninja/balloon/scripts/main.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/balloon/e,this.g_amk (from https://www.mathsisfun.com/games/ninja/balloon/scripts/main.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/balloon/dispatchworker.js (from https://www.mathsisfun.com/games/ninja/balloon/scripts/main.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/balloon/jobworker.js (from https://www.mathsisfun.com/games/ninja/balloon/scripts/main.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/images/sounds/ (from https://www.mathsisfun.com/games/images/chessws.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/${my.imgHome}mancala-bank.svg (from https://www.mathsisfun.com/games/images/mancala.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/${my.imgHome}mancala-pit.svg (from https://www.mathsisfun.com/games/images/mancala.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/${my.imgHome}mancala-hilite.svg (from https://www.mathsisfun.com/games/images/mancala.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/node/images/sounds/ (from https://www.mathsisfun.com/games/images/tic-tac-toe-ws.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/home/yves/Bureau/openclipart/voilier_yves_guillou_01.png (from https://www.mathsisfun.com/measure/images/boat.svg)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/home/chris/public_html/w2.swantrust.org.uk/working_dir/tiling_rope.png (from https://www.mathsisfun.com/geometry/images/trefoil-knot.svg)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/worksheets/images/a/bw/ (from https://www.mathsisfun.com/worksheets/images/ws-kinder.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/worksheets/images/a/ (from https://www.mathsisfun.com/worksheets/images/ws-kinder.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/worksheets/images/fill/ (from https://www.mathsisfun.com/worksheets/images/ws-kinder.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/measure/my.img.src (from https://www.mathsisfun.com/measure/images/earth-simple.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/app.js (from https://www.mathsisfun.com/images/app.js)
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21:10:21 Error: "Internal Server Error" (500) after 2 retries at link https://www.mathsisfun.com/worksheets/print.php?w=34175&ID=16155 (from https://www.mathsisfun.com/numbers/addition-column.html)
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21:10:21 Error: "Internal Server Error" (500) after 2 retries at link https://www.mathsisfun.com/worksheets/print.php?w=34170&ID=5450 (from https://www.mathsisfun.com/numbers/addition-column.html)
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21:10:21 Error: "Unable to open local file" (-5) after 2 retries at link file:///C:/Images/SVG/pastedpic_10162008_083107.png (from https://www.mathsisfun.com/geometry/images/cylinder-pizza.svg)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/puzzles/images/-438.323 (from https://www.mathsisfun.com/puzzles/images/count-the-shapes-soln.svg)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/alpha/scripts/ (from https://www.mathsisfun.com/games/ninja/alpha/sw.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/alpha/scripts/a.request.url (from https://www.mathsisfun.com/games/ninja/alpha/sw.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/arty/scripts/ (from https://www.mathsisfun.com/games/ninja/arty/sw.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/arty/scripts/a.request.url (from https://www.mathsisfun.com/games/ninja/arty/sw.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/bottle/scripts/ (from https://www.mathsisfun.com/games/ninja/bottle/sw.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/bottle/scripts/a.request.url (from https://www.mathsisfun.com/games/ninja/bottle/sw.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/a/breaklock/l.default.URL,l.default.SOCIAL.MESSAGE,l.default.SOCIAL.TAGS (from https://www.mathsisfun.com/games/a/breaklock/app.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/lightybulb/scripts/ (from https://www.mathsisfun.com/games/ninja/lightybulb/sw.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/lightybulb/scripts/a.request.url (from https://www.mathsisfun.com/games/ninja/lightybulb/sw.js)
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21:10:21 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/a/mahjong/GET (from https://www.mathsisfun.com/games/a/mahjong/lib/l10n.js)
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21:10:24 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/a/astray/GET (from https://www.mathsisfun.com/games/a/astray/Three.js)
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21:10:24 Error: "Unable to open local file" (-5) after 2 retries at link file:///C:/Images/SVG/Banana.jpg (from https://www.mathsisfun.com/sets/images/function-sets.svg)
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21:10:24 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/balloon/scripts/ (from https://www.mathsisfun.com/games/ninja/balloon/sw.js)
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21:10:24 Error: "Not Found" (404) at link https://www.mathsisfun.com/games/ninja/balloon/scripts/a.request.url (from https://www.mathsisfun.com/games/ninja/balloon/sw.js)
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·
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www.mathsisfun.com/math-tools.html
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var Yc,Xc;_.Vc=function(a){return a?new _.Tc(_.Uc(a)):tb||(tb=new _.Tc)};_.Wc=function(a,b){return"string"===typeof b?a.getElementById(b):b};Yc=function(a,b){_.wc(b,function(c,d){c&&"object"==typeof c&&c.Eb&&(c=c.cb());"style"==d?a.style.cssText=c:"class"==d?a.className=c:"for"==d?a.htmlFor=c:Xc.hasOwnProperty(d)?a.setAttribute(Xc[d],c):0==d.lastIndexOf("aria-",0)||0==d.lastIndexOf("data-",0)?a.setAttribute(d,c):a[d]=c})};
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Xc={cellpadding:"cellPadding",cellspacing:"cellSpacing",colspan:"colSpan",frameborder:"frameBorder",height:"height",maxlength:"maxLength",nonce:"nonce",role:"role",rowspan:"rowSpan",type:"type",usemap:"useMap",valign:"vAlign",width:"width"};_.$c=function(a){a=a.document;a=_.Zc(a)?a.documentElement:a.body;return new _.Oc(a.clientWidth,a.clientHeight)};_.ad=function(a){return a?a.parentWindow||a.defaultView:window};
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_.dd=function(a,b){var c=b[1],d=_.bd(a,String(b[0]));c&&("string"===typeof c?d.className=c:Array.isArray(c)?d.className=c.join(" "):Yc(d,c));2<b.length&&_.cd(a,d,b,2);return d};
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_.cd=function(a,b,c,d){function e(h){h&&b.appendChild("string"===typeof h?a.createTextNode(h):h)}for(;d<c.length;d++){var f=c[d];if(!_.da(f)||_.ya(f)&&0<f.nodeType)e(f);else{a:{if(f&&"number"==typeof f.length){if(_.ya(f)){var g="function"==typeof f.item||"string"==typeof f.item;break a}if("function"===typeof f){g="function"==typeof f.item;break a}}g=!1}_.Nb(g?_.wa(f):f,e)}}};_.bd=function(a,b){b=String(b);"application/xhtml+xml"===a.contentType&&(b=b.toLowerCase());return a.createElement(b)};
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_.Zc=function(a){return"CSS1Compat"==a.compatMode};_.ed=function(a){for(var b;b=a.firstChild;)a.removeChild(b)};_.fd=function(a,b){if(!a||!b)return!1;if(a.contains&&1==b.nodeType)return a==b||a.contains(b);if("undefined"!=typeof a.compareDocumentPosition)return a==b||!!(a.compareDocumentPosition(b)&16);for(;b&&a!=b;)b=b.parentNode;return b==a};_.Uc=function(a){return 9==a.nodeType?a:a.ownerDocument||a.document};
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_.gd=function(a,b){if("textContent"in a)a.textContent=b;else if(3==a.nodeType)a.data=String(b);else if(a.firstChild&&3==a.firstChild.nodeType){for(;a.lastChild!=a.firstChild;)a.removeChild(a.lastChild);a.firstChild.data=String(b)}else _.ed(a),a.appendChild(_.Uc(a).createTextNode(String(b)))};_.Tc=function(a){this.T=a||_.r.document||document};_.Tc.prototype.A=function(a){return _.Wc(this.T,a)};_.Tc.prototype.S=function(a,b,c){return _.dd(this.T,arguments)};
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_.hd=function(a){a=a.T;return a.parentWindow||a.defaultView};_.Tc.prototype.appendChild=function(a,b){a.appendChild(b)};_.Tc.prototype.Yf=_.ed;_.Tc.prototype.g=_.fd;_.Tc.prototype.sc=_.gd;
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var id=function(){this.id="b"};id.prototype.toString=function(){return this.id};
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_.jd=function(a,b){this.type=a instanceof id?String(a):a;this.currentTarget=this.target=b;this.defaultPrevented=this.h=!1};_.jd.prototype.stopPropagation=function(){this.h=!0};_.jd.prototype.preventDefault=function(){this.defaultPrevented=!0};
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var kd=function(){if(!_.r.addEventListener||!Object.defineProperty)return!1;var a=!1,b=Object.defineProperty({},"passive",{get:function(){a=!0}});try{_.r.addEventListener("test",function(){},b),_.r.removeEventListener("test",function(){},b)}catch(c){}return a}();
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_.md=function(a,b){_.jd.call(this,a?a.type:"");this.relatedTarget=this.currentTarget=this.target=null;this.button=this.screenY=this.screenX=this.clientY=this.clientX=this.offsetY=this.offsetX=0;this.key="";this.charCode=this.keyCode=0;this.metaKey=this.shiftKey=this.altKey=this.ctrlKey=!1;this.state=null;this.j=!1;this.pointerId=0;this.pointerType="";this.g=null;if(a){var c=this.type=a.type,d=a.changedTouches&&a.changedTouches.length?a.changedTouches[0]:null;this.target=a.target||a.srcElement;this.currentTarget=
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b;(b=a.relatedTarget)?_.bc&&(_.Wb(b,"nodeName")||(b=null)):"mouseover"==c?b=a.fromElement:"mouseout"==c&&(b=a.toElement);this.relatedTarget=b;d?(this.clientX=void 0!==d.clientX?d.clientX:d.pageX,this.clientY=void 0!==d.clientY?d.clientY:d.pageY,this.screenX=d.screenX||0,this.screenY=d.screenY||0):(this.offsetX=_.cc||void 0!==a.offsetX?a.offsetX:a.layerX,this.offsetY=_.cc||void 0!==a.offsetY?a.offsetY:a.layerY,this.clientX=void 0!==a.clientX?a.clientX:a.pageX,this.clientY=void 0!==a.clientY?a.clientY:
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a.pageY,this.screenX=a.screenX||0,this.screenY=a.screenY||0);this.button=a.button;this.keyCode=a.keyCode||0;this.key=a.key||"";this.charCode=a.charCode||("keypress"==c?a.keyCode:0);this.ctrlKey=a.ctrlKey;this.altKey=a.altKey;this.shiftKey=a.shiftKey;this.metaKey=a.metaKey;this.j=_.ec?a.metaKey:a.ctrlKey;this.pointerId=a.pointerId||0;this.pointerType="string"===typeof a.pointerType?a.pointerType:ld[a.pointerType]||"";this.state=a.state;this.g=a;a.defaultPrevented&&_.md.P.preventDefault.call(this)}};
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_.z(_.md,_.jd);var ld={2:"touch",3:"pen",4:"mouse"};_.md.prototype.stopPropagation=function(){_.md.P.stopPropagation.call(this);this.g.stopPropagation?this.g.stopPropagation():this.g.cancelBubble=!0};_.md.prototype.preventDefault=function(){_.md.P.preventDefault.call(this);var a=this.g;a.preventDefault?a.preventDefault():a.returnValue=!1};
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var nd;nd="closure_listenable_"+(1E6*Math.random()|0);_.od=function(a){return!(!a||!a[nd])};
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var pd=0;
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var qd=function(a,b,c,d,e){this.listener=a;this.proxy=null;this.src=b;this.type=c;this.capture=!!d;this.re=e;this.key=++pd;this.Id=this.ae=!1},rd=function(a){a.Id=!0;a.listener=null;a.proxy=null;a.src=null;a.re=null};
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var sd=function(a){this.src=a;this.g={};this.h=0},ud;sd.prototype.add=function(a,b,c,d,e){var f=a.toString();a=this.g[f];a||(a=this.g[f]=[],this.h++);var g=td(a,b,d,e);-1<g?(b=a[g],c||(b.ae=!1)):(b=new qd(b,this.src,f,!!d,e),b.ae=c,a.push(b));return b};sd.prototype.remove=function(a,b,c,d){a=a.toString();if(!(a in this.g))return!1;var e=this.g[a];b=td(e,b,c,d);return-1<b?(rd(e[b]),Array.prototype.splice.call(e,b,1),0==e.length&&(delete this.g[a],this.h--),!0):!1};
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ud=function(a,b){var c=b.type;if(!(c in a.g))return!1;var d=_.va(a.g[c],b);d&&(rd(b),0==a.g[c].length&&(delete a.g[c],a.h--));return d};_.vd=function(a){var b=0,c;for(c in a.g){for(var d=a.g[c],e=0;e<d.length;e++)++b,rd(d[e]);delete a.g[c];a.h--}};sd.prototype.Bd=function(a,b,c,d){a=this.g[a.toString()];var e=-1;a&&(e=td(a,b,c,d));return-1<e?a[e]:null};
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sd.prototype.hasListener=function(a,b){var c=void 0!==a,d=c?a.toString():"",e=void 0!==b;return Ga(this.g,function(f){for(var g=0;g<f.length;++g)if(!(c&&f[g].type!=d||e&&f[g].capture!=b))return!0;return!1})};var td=function(a,b,c,d){for(var e=0;e<a.length;++e){var f=a[e];if(!f.Id&&f.listener==b&&f.capture==!!c&&f.re==d)return e}return-1};
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var wd,xd,yd,Bd,Dd,Ed,Fd,Id,Ad;wd="closure_lm_"+(1E6*Math.random()|0);xd={};yd=0;_.D=function(a,b,c,d,e){if(d&&d.once)return _.zd(a,b,c,d,e);if(Array.isArray(b)){for(var f=0;f<b.length;f++)_.D(a,b[f],c,d,e);return null}c=Ad(c);return _.od(a)?a.I(b,c,_.ya(d)?!!d.capture:!!d,e):Bd(a,b,c,!1,d,e)};
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Bd=function(a,b,c,d,e,f){if(!b)throw Error("B");var g=_.ya(e)?!!e.capture:!!e,h=_.Cd(a);h||(a[wd]=h=new sd(a));c=h.add(b,c,d,g,f);if(c.proxy)return c;d=Dd();c.proxy=d;d.src=a;d.listener=c;if(a.addEventListener)kd||(e=g),void 0===e&&(e=!1),a.addEventListener(b.toString(),d,e);else if(a.attachEvent)a.attachEvent(Ed(b.toString()),d);else if(a.addListener&&a.removeListener)a.addListener(d);else throw Error("C");yd++;return c};Dd=function(){var a=Fd,b=function(c){return a.call(b.src,b.listener,c)};return b};
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_.zd=function(a,b,c,d,e){if(Array.isArray(b)){for(var f=0;f<b.length;f++)_.zd(a,b[f],c,d,e);return null}c=Ad(c);return _.od(a)?a.pc(b,c,_.ya(d)?!!d.capture:!!d,e):Bd(a,b,c,!0,d,e)};_.Gd=function(a,b,c,d,e){if(Array.isArray(b))for(var f=0;f<b.length;f++)_.Gd(a,b[f],c,d,e);else d=_.ya(d)?!!d.capture:!!d,c=Ad(c),_.od(a)?a.Ab(b,c,d,e):a&&(a=_.Cd(a))&&(b=a.Bd(b,c,d,e))&&_.Hd(b)};
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_.Hd=function(a){if("number"===typeof a||!a||a.Id)return!1;var b=a.src;if(_.od(b))return ud(b.rb,a);var c=a.type,d=a.proxy;b.removeEventListener?b.removeEventListener(c,d,a.capture):b.detachEvent?b.detachEvent(Ed(c),d):b.addListener&&b.removeListener&&b.removeListener(d);yd--;(c=_.Cd(b))?(ud(c,a),0==c.h&&(c.src=null,b[wd]=null)):rd(a);return!0};Ed=function(a){return a in xd?xd[a]:xd[a]="on"+a};
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Fd=function(a,b){if(a.Id)a=!0;else{b=new _.md(b,this);var c=a.listener,d=a.re||a.src;a.ae&&_.Hd(a);a=c.call(d,b)}return a};_.Cd=function(a){a=a[wd];return a instanceof sd?a:null};Id="__closure_events_fn_"+(1E9*Math.random()>>>0);Ad=function(a){if("function"===typeof a)return a;a[Id]||(a[Id]=function(b){return a.handleEvent(b)});return a[Id]};
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_.E=function(){_.A.call(this);this.rb=new sd(this);this.Qi=this;this.Ge=null};_.z(_.E,_.A);_.E.prototype[nd]=!0;_.k=_.E.prototype;_.k.He=function(a){this.Ge=a};_.k.addEventListener=function(a,b,c,d){_.D(this,a,b,c,d)};_.k.removeEventListener=function(a,b,c,d){_.Gd(this,a,b,c,d)};
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_.k.dispatchEvent=function(a){var b,c=this.Ge;if(c)for(b=[];c;c=c.Ge)b.push(c);c=this.Qi;var d=a.type||a;if("string"===typeof a)a=new _.jd(a,c);else if(a instanceof _.jd)a.target=a.target||c;else{var e=a;a=new _.jd(d,c);Ja(a,e)}e=!0;if(b)for(var f=b.length-1;!a.h&&0<=f;f--){var g=a.currentTarget=b[f];e=Jd(g,d,!0,a)&&e}a.h||(g=a.currentTarget=c,e=Jd(g,d,!0,a)&&e,a.h||(e=Jd(g,d,!1,a)&&e));if(b)for(f=0;!a.h&&f<b.length;f++)g=a.currentTarget=b[f],e=Jd(g,d,!1,a)&&e;return e};
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_.k.K=function(){_.E.P.K.call(this);this.rb&&_.vd(this.rb);this.Ge=null};_.k.I=function(a,b,c,d){return this.rb.add(String(a),b,!1,c,d)};_.k.pc=function(a,b,c,d){return this.rb.add(String(a),b,!0,c,d)};_.k.Ab=function(a,b,c,d){return this.rb.remove(String(a),b,c,d)};var Jd=function(a,b,c,d){b=a.rb.g[String(b)];if(!b)return!0;b=b.concat();for(var e=!0,f=0;f<b.length;++f){var g=b[f];if(g&&!g.Id&&g.capture==c){var h=g.listener,l=g.re||g.src;g.ae&&ud(a.rb,g);e=!1!==h.call(l,d)&&e}}return e&&!d.defaultPrevented};
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_.E.prototype.Bd=function(a,b,c,d){return this.rb.Bd(String(a),b,c,d)};_.E.prototype.hasListener=function(a,b){return this.rb.hasListener(void 0!==a?String(a):void 0,b)};
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var Kd=function(a){_.E.call(this);this.g=a||window;this.h=_.D(this.g,"resize",this.l,!1,this);this.j=_.$c(this.g||window)};_.z(Kd,_.E);Kd.prototype.K=function(){Kd.P.K.call(this);this.h&&(_.Hd(this.h),this.h=null);this.j=this.g=null};Kd.prototype.l=function(){var a=_.$c(this.g||window);_.Pc(a,this.j)||(this.j=a,this.dispatchEvent("resize"))};
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var Ld=function(a){_.E.call(this);this.j=a?_.hd(a):window;this.o=1.5<=this.j.devicePixelRatio?2:1;this.h=(0,_.y)(this.s,this);this.l=null;(this.g=this.j.matchMedia?this.j.matchMedia("(min-resolution: 1.5dppx), (-webkit-min-device-pixel-ratio: 1.5)"):null)&&"function"!==typeof this.g.addListener&&"function"!==typeof this.g.addEventListener&&(this.g=null)};_.z(Ld,_.E);
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||||
Ld.prototype.start=function(){var a=this;this.g&&("function"===typeof this.g.addEventListener?(this.g.addEventListener("change",this.h),this.l=function(){a.g.removeEventListener("change",a.h)}):(this.g.addListener(this.h),this.l=function(){a.g.removeListener(a.h)}))};Ld.prototype.s=function(){var a=1.5<=this.j.devicePixelRatio?2:1;this.o!=a&&(this.o=a,this.dispatchEvent("a"))};Ld.prototype.K=function(){this.l&&this.l();Ld.P.K.call(this)};
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var Md=function(a,b){_.A.call(this);this.o=a;if(b){if(this.l)throw Error("D");this.l=b;this.g=_.Vc(b);this.h=new Kd(_.ad(b));this.h.He(this.o.h());this.j=new Ld(this.g);this.j.start()}};_.z(Md,_.A);Md.prototype.K=function(){this.g=this.l=null;this.h&&(this.h.O(),this.h=null);_.ca(this.j);this.j=null};ra(Mb,Md);
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||||
var Nd=function(a,b){this.l=a;this.j=b;this.h=0;this.g=null};Nd.prototype.get=function(){if(0<this.h){this.h--;var a=this.g;this.g=a.next;a.next=null}else a=this.l();return a};var Od=function(a,b){a.j(b);100>a.h&&(a.h++,b.next=a.g,a.g=b)};
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||||
var Pd,Qd=function(){var a=_.r.MessageChannel;"undefined"===typeof a&&"undefined"!==typeof window&&window.postMessage&&window.addEventListener&&!_.u("Presto")&&(a=function(){var e=_.bd(document,"IFRAME");e.style.display="none";document.documentElement.appendChild(e);var f=e.contentWindow;e=f.document;e.open();e.close();var g="callImmediate"+Math.random(),h="file:"==f.location.protocol?"*":f.location.protocol+"//"+f.location.host;e=(0,_.y)(function(l){if(("*"==h||l.origin==h)&&l.data==g)this.port1.onmessage()},
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this);f.addEventListener("message",e,!1);this.port1={};this.port2={postMessage:function(){f.postMessage(g,h)}}});if("undefined"!==typeof a&&!_.Ca()){var b=new a,c={},d=c;b.port1.onmessage=function(){if(void 0!==c.next){c=c.next;var e=c.Rg;c.Rg=null;e()}};return function(e){d.next={Rg:e};d=d.next;b.port2.postMessage(0)}}return function(e){_.r.setTimeout(e,0)}};
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||||
var Rd=function(){this.h=this.g=null};Rd.prototype.add=function(a,b){var c=Sd.get();c.set(a,b);this.h?this.h.next=c:this.g=c;this.h=c};Rd.prototype.remove=function(){var a=null;this.g&&(a=this.g,this.g=this.g.next,this.g||(this.h=null),a.next=null);return a};var Sd=new Nd(function(){return new Td},function(a){return a.reset()}),Td=function(){this.next=this.g=this.h=null};Td.prototype.set=function(a,b){this.h=a;this.g=b;this.next=null};Td.prototype.reset=function(){this.next=this.g=this.h=null};
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var Ud,Vd=!1,Wd=new Rd,Yd=function(a,b){Ud||Xd();Vd||(Ud(),Vd=!0);Wd.add(a,b)},Xd=function(){if(_.r.Promise&&_.r.Promise.resolve){var a=_.r.Promise.resolve(void 0);Ud=function(){a.then(Zd)}}else Ud=function(){var b=Zd;"function"!==typeof _.r.setImmediate||_.r.Window&&_.r.Window.prototype&&!_.u("Edge")&&_.r.Window.prototype.setImmediate==_.r.setImmediate?(Pd||(Pd=Qd()),Pd(b)):_.r.setImmediate(b)}},Zd=function(){for(var a;a=Wd.remove();){try{a.h.call(a.g)}catch(b){ba(b)}Od(Sd,a)}Vd=!1};
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var $d=function(a){if(!a)return!1;try{return!!a.$goog_Thenable}catch(b){return!1}};
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var ce,ne,le,je;_.be=function(a,b){this.g=0;this.B=void 0;this.l=this.h=this.j=null;this.o=this.s=!1;if(a!=_.ub)try{var c=this;a.call(b,function(d){_.ae(c,2,d)},function(d){_.ae(c,3,d)})}catch(d){_.ae(this,3,d)}};ce=function(){this.next=this.j=this.h=this.l=this.g=null;this.o=!1};ce.prototype.reset=function(){this.j=this.h=this.l=this.g=null;this.o=!1};var de=new Nd(function(){return new ce},function(a){a.reset()}),ee=function(a,b,c){var d=de.get();d.l=a;d.h=b;d.j=c;return d};
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_.be.prototype.then=function(a,b,c){return fe(this,"function"===typeof a?a:null,"function"===typeof b?b:null,c)};_.be.prototype.$goog_Thenable=!0;_.be.prototype.D=function(a,b){return fe(this,null,a,b)};_.be.prototype.catch=_.be.prototype.D;_.be.prototype.cancel=function(a){if(0==this.g){var b=new he(a);Yd(function(){ie(this,b)},this)}};
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var ie=function(a,b){if(0==a.g)if(a.j){var c=a.j;if(c.h){for(var d=0,e=null,f=null,g=c.h;g&&(g.o||(d++,g.g==a&&(e=g),!(e&&1<d)));g=g.next)e||(f=g);e&&(0==c.g&&1==d?ie(c,b):(f?(d=f,d.next==c.l&&(c.l=d),d.next=d.next.next):je(c),ke(c,e,3,b)))}a.j=null}else _.ae(a,3,b)},me=function(a,b){a.h||2!=a.g&&3!=a.g||le(a);a.l?a.l.next=b:a.h=b;a.l=b},fe=function(a,b,c,d){var e=ee(null,null,null);e.g=new _.be(function(f,g){e.l=b?function(h){try{var l=b.call(d,h);f(l)}catch(m){g(m)}}:f;e.h=c?function(h){try{var l=
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c.call(d,h);void 0===l&&h instanceof he?g(h):f(l)}catch(m){g(m)}}:g});e.g.j=a;me(a,e);return e.g};_.be.prototype.F=function(a){this.g=0;_.ae(this,2,a)};_.be.prototype.M=function(a){this.g=0;_.ae(this,3,a)};
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_.ae=function(a,b,c){if(0==a.g){a===c&&(b=3,c=new TypeError("E"));a.g=1;a:{var d=c,e=a.F,f=a.M;if(d instanceof _.be){me(d,ee(e||_.ub,f||null,a));var g=!0}else if($d(d))d.then(e,f,a),g=!0;else{if(_.ya(d))try{var h=d.then;if("function"===typeof h){ne(d,h,e,f,a);g=!0;break a}}catch(l){f.call(a,l);g=!0;break a}g=!1}}g||(a.B=c,a.g=b,a.j=null,le(a),3!=b||c instanceof he||oe(a,c))}};ne=function(a,b,c,d,e){var f=!1,g=function(l){f||(f=!0,c.call(e,l))},h=function(l){f||(f=!0,d.call(e,l))};try{b.call(a,g,h)}catch(l){h(l)}};
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||||
le=function(a){a.s||(a.s=!0,Yd(a.H,a))};je=function(a){var b=null;a.h&&(b=a.h,a.h=b.next,b.next=null);a.h||(a.l=null);return b};_.be.prototype.H=function(){for(var a;a=je(this);)ke(this,a,this.g,this.B);this.s=!1};
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||||
var ke=function(a,b,c,d){if(3==c&&b.h&&!b.o)for(;a&&a.o;a=a.j)a.o=!1;if(b.g)b.g.j=null,pe(b,c,d);else try{b.o?b.l.call(b.j):pe(b,c,d)}catch(e){qe.call(null,e)}Od(de,b)},pe=function(a,b,c){2==b?a.l.call(a.j,c):a.h&&a.h.call(a.j,c)},oe=function(a,b){a.o=!0;Yd(function(){a.o&&qe.call(null,b)})},qe=ba,he=function(a){_.aa.call(this,a)};_.z(he,_.aa);he.prototype.name="cancel";
|
||||
/*
|
||||
|
||||
Copyright 2005, 2007 Bob Ippolito. All Rights Reserved.
|
||||
Copyright The Closure Library Authors.
|
||||
SPDX-License-Identifier: MIT
|
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*/
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var re=function(a,b){this.s=[];this.J=a;this.ca=b||null;this.l=this.g=!1;this.j=void 0;this.F=this.N=this.D=!1;this.B=0;this.h=null;this.o=0};_.z(re,La);re.prototype.cancel=function(a){if(this.g)this.j instanceof re&&this.j.cancel();else{if(this.h){var b=this.h;delete this.h;a?b.cancel(a):(b.o--,0>=b.o&&b.cancel())}this.J?this.J.call(this.ca,this):this.F=!0;this.g||this.H(new se(this))}};re.prototype.M=function(a,b){this.D=!1;te(this,a,b)};
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var te=function(a,b,c){a.g=!0;a.j=c;a.l=!b;ue(a)},we=function(a){if(a.g){if(!a.F)throw new ve(a);a.F=!1}};re.prototype.callback=function(a){we(this);te(this,!0,a)};re.prototype.H=function(a){we(this);te(this,!1,a)};var ye=function(a,b,c){xe(a,b,null,c)},ze=function(a,b,c){xe(a,null,b,c)},xe=function(a,b,c,d){a.s.push([b,c,d]);a.g&&ue(a)};
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re.prototype.then=function(a,b,c){var d,e,f=new _.be(function(g,h){e=g;d=h});xe(this,e,function(g){g instanceof se?f.cancel():d(g);return Ae},this);return f.then(a,b,c)};re.prototype.$goog_Thenable=!0;var Be=function(a,b){b instanceof re?ye(a,(0,_.y)(b.qa,b)):ye(a,function(){return b})};re.prototype.qa=function(a){var b=new re;xe(this,b.callback,b.H,b);a&&(b.h=this,this.o++);return b};
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var Ce=function(a){return _.Qb(a.s,function(b){return"function"===typeof b[1]})},Ae={},ue=function(a){if(a.B&&a.g&&Ce(a)){var b=a.B,c=De[b];c&&(_.r.clearTimeout(c.g),delete De[b]);a.B=0}a.h&&(a.h.o--,delete a.h);b=a.j;for(var d=c=!1;a.s.length&&!a.D;){var e=a.s.shift(),f=e[0],g=e[1];e=e[2];if(f=a.l?g:f)try{var h=f.call(e||a.ca,b);h===Ae&&(h=void 0);void 0!==h&&(a.l=a.l&&(h==b||h instanceof Error),a.j=b=h);if($d(b)||"function"===typeof _.r.Promise&&b instanceof _.r.Promise)d=!0,a.D=!0}catch(l){b=l,
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a.l=!0,Ce(a)||(c=!0)}}a.j=b;d&&(h=(0,_.y)(a.M,a,!0),d=(0,_.y)(a.M,a,!1),b instanceof re?(xe(b,h,d),b.N=!0):b.then(h,d));c&&(b=new Ee(b),De[b.g]=b,a.B=b.g)},ve=function(){_.aa.call(this)};_.z(ve,_.aa);ve.prototype.message="Deferred has already fired";ve.prototype.name="AlreadyCalledError";var se=function(){_.aa.call(this)};_.z(se,_.aa);se.prototype.message="Deferred was canceled";se.prototype.name="CanceledError";var Ee=function(a){this.g=_.r.setTimeout((0,_.y)(this.j,this),0);this.h=a};
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Ee.prototype.j=function(){delete De[this.g];throw this.h;};var De={};
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var Fe=function(a,b){this.type=a;this.status=b};Fe.prototype.toString=function(){return Ge(this)+" ("+(void 0!=this.status?this.status:"?")+")"};var Ge=function(a){switch(a.type){case Fe.g.Lg:return"Unauthorized";case Fe.g.xg:return"Consecutive load failures";case Fe.g.TIMEOUT:return"Timed out";case Fe.g.Gg:return"Out of date module id";case Fe.g.Pe:return"Init error";default:return"Unknown failure type "+a.type}};ib.jb=Fe;ib.jb.g={Lg:0,xg:1,TIMEOUT:2,Gg:3,Pe:4};
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var He=function(){Lb.call(this);this.g={};this.j=[];this.l=[];this.ca=[];this.h=[];this.B=[];this.s={};this.N={};this.o=this.H=new Ib([],"");this.qa=null;this.M=new re;this.J=!1;this.F=0;this.Y=this.na=this.ma=!1};_.z(He,Lb);var Ie=function(a,b){_.aa.call(this,"Error loading "+a+": "+b)};_.z(Ie,_.aa);_.k=He.prototype;_.k.Xh=function(a){this.J=a};
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_.k.hg=function(a,b){if(!(this instanceof He))this.hg(a,b);else if("string"===typeof a){a=a.split("/");for(var c=[],d=0;d<a.length;d++){var e=a[d].split(":"),f=e[0];if(e[1]){e=e[1].split(",");for(var g=0;g<e.length;g++)e[g]=c[parseInt(e[g],36)]}else e=[];c.push(f);this.g[f]?(f=this.g[f].Tc(),f!=e&&f.splice.apply(f,[0,f.length].concat(e instanceof Array?e:_.Ua(_.v(e))))):this.g[f]=new Ib(e,f)}b&&b.length?(xa(this.j,b),this.qa=b[b.length-1]):this.M.g||this.M.callback();Je(this)}};
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_.k.Vh=function(a,b){if(this.s[a]){delete this.s[a][b];for(var c in this.s[a])return;delete this.s[a]}};_.k.ig=function(a){He.P.ig.call(this,a);Je(this)};_.k.isActive=function(){return 0<this.j.length};_.k.Bh=function(){return 0<this.B.length};
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var Le=function(a){var b=a.ma,c=a.isActive();c!=b&&(Ke(a,c?"active":"idle"),a.ma=c);b=a.Bh();b!=a.na&&(Ke(a,b?"userActive":"userIdle"),a.na=b)},Oe=function(a,b,c){var d=[];Aa(b,d);b=[];for(var e={},f=0;f<d.length;f++){var g=d[f],h=a.g[g];if(!h)throw Error("F`"+g);var l=new re;e[g]=l;h.g?l.callback(a.U):(Me(a,g,h,!!c,l),Ne(a,g)||b.push(g))}0<b.length&&(0===a.j.length?a.W(b):(a.h.push(b),Le(a)));return e},Me=function(a,b,c,d,e){c.j.push(new Hb(e.callback,e));Jb(c,function(f){e.H(new Ie(b,f))});Ne(a,
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b)?d&&(_.ta(a.B,b)||a.B.push(b),Le(a)):d&&(_.ta(a.B,b)||a.B.push(b))};
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He.prototype.W=function(a,b,c){var d=this;b||(this.F=0);var e=Pe(this,a);this.j=e;this.l=this.J?a:_.wa(e);Le(this);if(0!==e.length){this.ca.push.apply(this.ca,e);if(0<Object.keys(this.s).length&&!this.D.J)throw Error("G");a=(0,_.y)(this.D.F,this.D,_.wa(e),this.g,{dj:this.s,hj:!!c,Tf:function(f){var g=d.l;f=null!=f?f:void 0;d.F++;d.l=g;e.forEach(_.pb(_.va,d.ca),d);401==f?(Qe(d,new ib.jb(ib.jb.g.Lg,f)),d.h.length=0):410==f?(Re(d,new ib.jb(ib.jb.g.Gg,f)),Se(d)):3<=d.F?(Re(d,new ib.jb(ib.jb.g.xg,f)),
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Se(d)):d.W(d.l,!0,8001==f)},kk:(0,_.y)(this.ua,this)});(b=5E3*Math.pow(this.F,2))?_.r.setTimeout(a,b):a()}};
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var Pe=function(a,b){b=b.filter(function(e){return a.g[e].g?(_.r.setTimeout(function(){return Error("H`"+e)},0),!1):!0});for(var c=[],d=0;d<b.length;d++)c=c.concat(Te(a,b[d]));Aa(c);return!a.J&&1<c.length?(b=c.shift(),a.h=c.map(function(e){return[e]}).concat(a.h),[b]):c},Te=function(a,b){var c=Ka(a.ca),d=[];c[b]||d.push(b);b=[b];for(var e=0;e<b.length;e++)for(var f=a.g[b[e]].Tc(),g=f.length-1;0<=g;g--){var h=f[g];a.g[h].g||c[h]||(d.push(h),b.push(h))}d.reverse();Aa(d);return d},Je=function(a){a.o==
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a.H&&(a.o=null,a.H.onLoad((0,_.y)(a.gh,a))&&Qe(a,new ib.jb(ib.jb.g.Pe)),Le(a))},oa=function(a){if(a.o){var b=a.o.Wb(),c=[];if(a.s[b]){for(var d=_.v(Object.keys(a.s[b])),e=d.next();!e.done;e=d.next()){e=e.value;var f=a.g[e];f&&!f.g&&(a.Vh(b,e),c.push(e))}Oe(a,c)}a.qb()||(a.g[b].onLoad((0,_.y)(a.gh,a))&&Qe(a,new ib.jb(ib.jb.g.Pe)),_.va(a.B,b),_.va(a.j,b),0===a.j.length&&Se(a),a.qa&&b==a.qa&&(a.M.g||a.M.callback()),Le(a),a.o=null)}},Ne=function(a,b){if(_.ta(a.j,b))return!0;for(var c=0;c<a.h.length;c++)if(_.ta(a.h[c],
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b))return!0;return!1};He.prototype.load=function(a,b){return Oe(this,[a],b)[a]};var ma=function(a){var b=_.fa;b.o&&"synthetic_module_overhead"===b.o.Wb()&&(oa(b),delete b.g.synthetic_module_overhead);b.g[a]&&Ue(b,b.g[a].Tc()||[],function(c){c.g=new Gb;_.va(b.j,c.Wb())},function(c){return!c.g});b.o=b.g[a]};He.prototype.ua=function(){Re(this,new ib.jb(ib.jb.g.TIMEOUT));Se(this)};
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var Re=function(a,b){1<a.l.length?a.h=a.l.map(function(c){return[c]}).concat(a.h):Qe(a,b)},Qe=function(a,b){var c=a.l;a.j.length=0;for(var d=[],e=0;e<a.h.length;e++){var f=a.h[e].filter(function(l){var m=Te(this,l);return _.Qb(c,function(n){return _.ta(m,n)})},a);xa(d,f)}for(e=0;e<c.length;e++)_.ua(d,c[e]);for(e=0;e<d.length;e++){for(f=0;f<a.h.length;f++)_.va(a.h[f],d[e]);_.va(a.B,d[e])}var g=a.N.error;if(g)for(e=0;e<g.length;e++){var h=g[e];for(f=0;f<d.length;f++)h("error",d[f],b)}for(e=0;e<c.length;e++)a.g[c[e]]&&
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a.g[c[e]].Tf(b);a.l.length=0;Le(a)},Se=function(a){for(;a.h.length;){var b=a.h.shift().filter(function(c){return!this.g[c].g},a);if(0<b.length){a.W(b);return}}Le(a)},Ke=function(a,b){a=a.N[b];for(var c=0;a&&c<a.length;c++)a[c](b)},Ue=function(a,b,c,d,e){d=void 0===d?function(){return!0}:d;e=void 0===e?{}:e;b=_.v(b);for(var f=b.next();!f.done;f=b.next()){f=f.value;var g=a.g[f];!e[f]&&d(g)&&(e[f]=!0,Ue(a,g.Tc()||[],c,d,e),c(g))}};
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He.prototype.O=function(){ea(_.Ha(this.g),this.H);this.g={};this.j=[];this.l=[];this.B=[];this.h=[];this.N={};this.Y=!0};He.prototype.qb=function(){return this.Y};_.ia=function(){return new He};
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var Ve=function(a,b){this.g=a[_.r.Symbol.iterator]();this.h=b};Ve.prototype[Symbol.iterator]=function(){return this};Ve.prototype.next=function(){var a=this.g.next();return{value:a.done?void 0:this.h.call(void 0,a.value),done:a.done}};var We=function(a,b){return new Ve(a,b)};
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_.Xe=function(){};_.Xe.prototype.next=function(){return _.Ye};_.Ye={done:!0,value:void 0};_.Xe.prototype.ic=function(){return this};
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var bf=function(a){if(a instanceof Ze||a instanceof $e||a instanceof af)return a;if("function"==typeof a.next)return new Ze(function(){return a});if("function"==typeof a[Symbol.iterator])return new Ze(function(){return a[Symbol.iterator]()});if("function"==typeof a.ic)return new Ze(function(){return a.ic()});throw Error("I");},Ze=function(a){this.g=a};Ze.prototype.ic=function(){return new $e(this.g())};Ze.prototype[Symbol.iterator]=function(){return new af(this.g())};Ze.prototype.h=function(){return new af(this.g())};
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var $e=function(a){this.g=a};_.x($e,_.Xe);$e.prototype.next=function(){return this.g.next()};$e.prototype[Symbol.iterator]=function(){return new af(this.g)};$e.prototype.h=function(){return new af(this.g)};var af=function(a){Ze.call(this,function(){return a});this.j=a};_.x(af,Ze);af.prototype.next=function(){return this.j.next()};
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var cf=function(a,b){this.h={};this.g=[];this.j=this.size=0;var c=arguments.length;if(1<c){if(c%2)throw Error("y");for(var d=0;d<c;d+=2)this.set(arguments[d],arguments[d+1])}else if(a)if(a instanceof cf)for(c=a.Ec(),d=0;d<c.length;d++)this.set(c[d],a.get(c[d]));else for(d in a)this.set(d,a[d])};cf.prototype.sb=function(){df(this);for(var a=[],b=0;b<this.g.length;b++)a.push(this.h[this.g[b]]);return a};cf.prototype.Ec=function(){df(this);return this.g.concat()};_.ef=function(a,b){return a.has(b)};
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cf.prototype.has=function(a){return ff(this.h,a)};cf.prototype.bc=function(){return 0==this.size};cf.prototype.remove=function(a){ff(this.h,a)?(delete this.h[a],--this.size,this.j++,this.g.length>2*this.size&&df(this),a=!0):a=!1;return a};var df=function(a){if(a.size!=a.g.length){for(var b=0,c=0;b<a.g.length;){var d=a.g[b];ff(a.h,d)&&(a.g[c++]=d);b++}a.g.length=c}if(a.size!=a.g.length){var e={};for(c=b=0;b<a.g.length;)d=a.g[b],ff(e,d)||(a.g[c++]=d,e[d]=1),b++;a.g.length=c}};_.k=cf.prototype;
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_.k.get=function(a,b){return ff(this.h,a)?this.h[a]:b};_.k.set=function(a,b){ff(this.h,a)||(this.size+=1,this.g.push(a),this.j++);this.h[a]=b};_.k.forEach=function(a,b){for(var c=this.Ec(),d=0;d<c.length;d++){var e=c[d],f=this.get(e);a.call(b,f,e,this)}};_.k.keys=function(){return bf(this.ic(!0)).h()};_.k.values=function(){return bf(this.ic(!1)).h()};_.k.entries=function(){var a=this;return We(this.keys(),function(b){return[b,a.get(b)]})};
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_.k.ic=function(a){df(this);var b=0,c=this.j,d=this,e=new _.Xe;e.next=function(){if(c!=d.j)throw Error("J");if(b>=d.g.length)return _.Ye;var f=d.g[b++];return{value:a?f:d.h[f],done:!1}};return e};var ff=function(a,b){return Object.prototype.hasOwnProperty.call(a,b)};
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_.gf=function(){this.g=new cf;this.size=0};_.hf=function(a){var b=typeof a;return"object"==b&&a||"function"==b?"o"+_.za(a):b.charAt(0)+a};_.k=_.gf.prototype;_.k.add=function(a){this.g.set(_.hf(a),a);this.size=this.g.size};_.k.remove=function(a){a=this.g.remove(_.hf(a));this.size=this.g.size;return a};_.k.bc=function(){return 0===this.g.size};_.k.has=function(a){return _.ef(this.g,_.hf(a))};_.k.sb=function(){return this.g.sb()};_.k.values=function(){return this.g.values()};_.k.ic=function(){return this.g.ic(!1)};
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_.gf.prototype[Symbol.iterator]=function(){return this.values()};
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var jf=[],kf=function(a){function b(d){d&&Pb(d,function(e,f){e[f.id]=!0;return e},c.uk)}var c={uk:{},index:jf.length,fm:a};b(a.g);b(a.j);jf.push(c);a.g&&_.Nb(a.g,function(d){var e=d.id;e instanceof B&&d.module&&(e.fk=d.module)})};
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var lf=new B("MpJwZc","MpJwZc");
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var mf=new B("UUJqVe","UUJqVe");
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new B("Wt6vjf","Wt6vjf");
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new B("byfTOb","byfTOb");
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new B("LEikZe","LEikZe");
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new B("lsjVmc","lsjVmc");
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new B("pVbxBc");
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new B("tdUkaf");new B("fJuxOc");new B("ZtVrH");new B("WSziFf");new B("ZmXAm");new B("BWETze");new B("UBSgGf");new B("zZa4xc");new B("o1bZcd");new B("WwG67d");new B("z72MOc");new B("JccZRe");new B("amY3Td");new B("ABma3e");new B("GHAeAc","GHAeAc");new B("gSshPb");new B("klpyYe");new B("OPbIxb");new B("pg9hFd");new B("yu4DA");new B("vk3Wc");new B("IykvEf");new B("J5K1Ad");new B("IW8Usd");new B("IaqD3e");new B("jbDgG");new B("b8xKu");new B("d0RAGb");new B("AzG0ke");new B("J4QWB");new B("TuDsZ");new B("hdXIif");
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new B("mITR5c");new B("DFElXb");new B("NGntwf");new B("Bgf0ib");new B("Xpw1of");new B("v5BQle");new B("ofuapc");new B("FENZqe");new B("tLnxq");
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kf({g:[{id:Mb,jf:Md,multiple:!0}]});
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var nf={};
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var of=new id,pf=function(a,b){_.jd.call(this,a,b);this.node=b};_.x(pf,_.jd);
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_.qf=RegExp("^(ar|ckb|dv|he|iw|fa|nqo|ps|sd|ug|ur|yi|.*[-_](Adlm|Arab|Hebr|Nkoo|Rohg|Thaa))(?!.*[-_](Latn|Cyrl)($|-|_))($|-|_)","i");
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_.rf=RegExp("^(?:([^:/?#.]+):)?(?://(?:([^\\\\/?#]*)@)?([^\\\\/?#]*?)(?::([0-9]+))?(?=[\\\\/?#]|$))?([^?#]+)?(?:\\?([^#]*))?(?:#([\\s\\S]*))?$");_.sf=function(a){return a?decodeURI(a):a};_.tf=function(a,b){if(a){a=a.split("&");for(var c=0;c<a.length;c++){var d=a[c].indexOf("="),e=null;if(0<=d){var f=a[c].substring(0,d);e=a[c].substring(d+1)}else f=a[c];b(f,e?_.Rc(e):"")}}};
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_.uf=function(a,b,c){if(Array.isArray(b))for(var d=0;d<b.length;d++)_.uf(a,String(b[d]),c);else null!=b&&c.push(a+(""===b?"":"="+_.Qc(b)))};
|
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/*
|
||||
|
||||
SPDX-License-Identifier: Apache-2.0
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*/
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var vf;try{new URL("s://g"),vf=!0}catch(a){vf=!1}_.wf=vf;
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/*
|
||||
Copyright The Closure Library Authors.
|
||||
SPDX-License-Identifier: Apache-2.0
|
||||
*/
|
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_.xf=function(a,b){b||_.Vc();this.j=a||null};_.xf.prototype.Ba=function(a){a=a({},this.j?this.j.g():{});this.h(null,"function"==typeof _.yf&&a instanceof _.yf?a.Kb:null)};_.xf.prototype.h=function(){};
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var zf=function(a){this.h=a;this.j=this.h.g(mf)};zf.prototype.g=function(){this.h.qb()||(this.j=this.h.g(mf));return this.j?this.j.g():{}};var Af=function(a){var b=new zf(a);_.xf.call(this,b,a.get(Mb).g);this.l=new _.E;this.o=b};_.x(Af,_.xf);Af.prototype.g=function(){return this.o.g()};Af.prototype.h=function(a,b){_.xf.prototype.h.call(this,a,b);this.l.dispatchEvent(new pf(of,a,b))};ra(lf,Af);
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kf({g:[{id:lf,jf:Af,multiple:!0}]});
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var Bf=function(a,b){this.defaultValue=a;this.type=b;this.value=a};Bf.prototype.get=function(){return this.value};Bf.prototype.set=function(a){this.value=a};
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var Cf=function(a){Bf.call(this,a,"b")};_.x(Cf,Bf);Cf.prototype.get=function(){return this.value};
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var Df=function(){this.g={};this.j="";this.h={}};Df.prototype.toString=function(){var a=this.j+Ef(this);var b=this.h;var c=[],d;for(d in b)_.uf(d,b[d],c);b=c.join("&");c="";""!=b&&(c="?"+b);return a+c};
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var Ef=function(a){var b=[],c=(0,_.y)(function(d){void 0!==this.g[d]&&b.push(d+"="+this.g[d])},a);"1"==Ff(a,"md")?(c("md"),c("k"),c("ck"),c("am"),c("rs"),c("gssmodulesetproto")):(c("sdch"),c("k"),c("ck"),c("am"),c("rt"),"d"in a.g||Gf(a,"d","0"),c("d"),c("exm"),c("excm"),(a.g.excm||a.g.exm)&&b.push("ed=1"),c("im"),c("dg"),c("sm"),"1"==Ff(a,"br")&&c("br"),""!==Hf(a)&&c("wt"),c("gssmodulesetproto"),c("rs"),c("ee"),c("cb"),c("m"));return b.join("/")},Ff=function(a,b){return a.g[b]?a.g[b]:null},Gf=function(a,
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|
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|
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<title>Add Two Numbers and the Answer is Always 1089</title>
|
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<!-- #BeginEditable "Body" -->
|
||||
<h1 class="center">Always End With 1089</h1>
|
||||
<h3 class="center">Add two numbers together and always end with 1089.<br> <br>
|
||||
Here is How:</h3>
|
||||
<div class="center">
|
||||
<div style="display:inline-block; max-width:200px;"> Pick a three digit number.
|
||||
<b> The three digits used must be different</b>*. i.e. 123
|
||||
</div>
|
||||
<div style="display:inline-block; width:50px;">
|
||||
<img src="images/arrow.gif" alt="right arrow" height="30" width="30">
|
||||
</div>
|
||||
<div style="display:inline-block; max-width:200px;">Reverse that number. 123 becomes 321</div>
|
||||
</div>
|
||||
<p class="center"> <img src="images/arrow2.gif" alt="arrow new line" height="47" width="320"> </p>
|
||||
<div class="center">
|
||||
<div style="display:inline-block; max-width:200px;">Take the smallest three digit number from the largest.
|
||||
<br> 321 − 123 = 198
|
||||
</div>
|
||||
<div style="display:inline-block; width:50px;">
|
||||
<img src="images/arrow.gif" alt="right arrow" height="30" width="30">
|
||||
</div>
|
||||
<div style="display:inline-block; max-width:200px;">Take the answer and reverse that number. 198 becomes 891</div>
|
||||
</div>
|
||||
<p class="center"> <img src="images/arrow2.gif" alt="arrow new line" height="47" width="320"> </p>
|
||||
<div class="center">
|
||||
<div style="display:inline-block; max-width:200px;">Add that number to the
|
||||
answer of the subtraction.
|
||||
<br>891 + 198 = 1089
|
||||
</div>
|
||||
<div style="display:inline-block; width:50px;">
|
||||
<img src="images/arrow.gif" alt="right arrow" height="30" width="30">
|
||||
</div>
|
||||
<div style="display:inline-block; max-width:200px;">
|
||||
<h3>The answer will be 1089!</h3>
|
||||
</div>
|
||||
</div>
|
||||
<div class="center">
|
||||
<h4>So why does it do this? <br> <a href="1089algebra.html">Find out here</a></h4>
|
||||
</div>
|
||||
<div class="center">
|
||||
<br>
|
||||
</div>
|
||||
<br>
|
||||
<div class="center80">
|
||||
<h3>Footnotes</h3>
|
||||
<p>* But I ended with <b>198</b> not <b>1089</b> ... !</p>
|
||||
<p>This happens if you pick
|
||||
a number like 546. </p>
|
||||
<p>546 goes like this: 645−546=99, then 99+99=198. </p>
|
||||
<p>BUT if you assume that <b>099 is a 3 digit number</b>, you will get: <br>
|
||||
990−099=891, and 891+198=1089</p>
|
||||
<p><br></p>
|
||||
<p>* If you don't pick three different digits then this might happen: <br>
|
||||
343−343=0, 0+0=0</p>
|
||||
</div>
|
||||
<p> </p>
|
||||
<div class="related">
|
||||
<a href="algebra/index.html">Algebra Index</a>
|
||||
<a href="puzzles/index.html">Puzzles Index</a>
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@ -1,210 +0,0 @@
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<title>Why the Answer is Always 1089</title>
|
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|
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<article id="content" role="main">
|
||||
<!-- #BeginEditable "Body" -->
|
||||
|
||||
<h1 class="center">Why is it always 1089</h1>
|
||||
|
||||
<p><i><br>
|
||||
</i></p>
|
||||
<p><i>This is the reasoning behind <a href="1089.html">Always End With 1089</a>. </i></p>
|
||||
<p>We will need a little bit of <a href="algebra/index.html">algebra</a>, but stick with it, it is not difficult.</p>
|
||||
<p><br></p>
|
||||
<p class="center">Show the number as <b>ABC</b></p>
|
||||
<p class="center"><img src="images/arrow3.gif" alt="down arrow" height="30" width="30"></p>
|
||||
<p class="center">Reverse this to get <b>CBA</b></p>
|
||||
<p class="center"><img src="images/arrow3.gif" alt="down arrow" height="30" width="30"></p>
|
||||
<p class="center">Remember that A is Hundreds B
|
||||
is tens and C is units<br>
|
||||
Take <b>CBA</b> from <b>ABC</b> like this:</p>
|
||||
<p class="center"><img src="images/arrow3.gif" alt="down arrow" height="30" width="30"></p>
|
||||
<div class="simple">
|
||||
|
||||
|
||||
<table style="margin:auto;">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td style="text-align:center;"><br>
|
||||
</td>
|
||||
<td style="text-align:center; width:80px;"><b>Hundreds</b> </td>
|
||||
<td style="text-align:center; width:80px;"><b>Tens</b> </td>
|
||||
<td style="text-align:center; width:80px;"><b>Units</b> </td>
|
||||
</tr><tr>
|
||||
<td style="text-align:center;"><br>
|
||||
</td>
|
||||
<td style="text-align:center;">A </td>
|
||||
<td style="text-align:center;">B </td>
|
||||
<td style="text-align:center;">C </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td style="text-align:center;">Subtract:</td>
|
||||
<td style="text-align:center;">C </td>
|
||||
<td style="text-align:center;">B </td>
|
||||
<td style="text-align:center;">A </td>
|
||||
</tr><tr>
|
||||
<td style="text-align:center;"><br>
|
||||
</td>
|
||||
<td style="text-align:center;"><b>A−C </b></td>
|
||||
<td style="text-align:center;"><b>0 </b></td>
|
||||
<td style="text-align:center;"><b>C−A </b></td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
</div>
|
||||
<p class="center"><img src="images/arrow3.gif" alt="down arrow" height="30" width="30"></p>
|
||||
<p class="center">Now here is the trick:<br>
|
||||
Subtract 1 Hundred, and add 9 Tens and 10 Ones<br>
|
||||
(−100, +90, +10 = 0, so won't change answer):</p>
|
||||
<div class="simple">
|
||||
|
||||
|
||||
<table style="margin:auto;">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td style="text-align:center;"><br>
|
||||
</td>
|
||||
<td style="text-align:center; width:80px;"><b>Hundreds</b> </td>
|
||||
<td style="text-align:center; width:80px;"><b>Tens</b> </td>
|
||||
<td style="text-align:center; width:80px;"><b>Units</b> </td>
|
||||
</tr><tr>
|
||||
<td style="text-align:center;"><br>
|
||||
</td>
|
||||
<td style="text-align:center;">A<span class="hilite">−1</span></td>
|
||||
<td style="text-align:center;">B<span class="hilite">+9</span></td>
|
||||
<td style="text-align:center;">C<span class="hilite">+10</span></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td style="text-align:center;">Subtract:</td>
|
||||
<td style="text-align:center;">C </td>
|
||||
<td style="text-align:center;">B </td>
|
||||
<td style="text-align:center;">A </td>
|
||||
</tr><tr>
|
||||
<td style="text-align:center;"><br>
|
||||
</td>
|
||||
<td style="text-align:center;"><b>A−1−C </b></td>
|
||||
<td style="text-align:center;"><b>9 </b></td>
|
||||
<td style="text-align:center;"><b>10+C−A </b></td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
</div>
|
||||
<p class="center"><img src="images/arrow3.gif" alt="down arrow" height="30" width="30"></p>
|
||||
<p class="center">Last Step: Reverse the answer and<br>
|
||||
add the
|
||||
two numbers together.</p>
|
||||
<div class="simple">
|
||||
|
||||
|
||||
<table style="margin:auto;">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td style="text-align:center;"><br>
|
||||
</td>
|
||||
<td style="text-align:center; width:80px;"><b>Hundreds</b> </td>
|
||||
<td style="text-align:center; width:80px;"><b>Tens</b> </td>
|
||||
<td style="text-align:center; width:80px;"><b>Units</b> </td>
|
||||
</tr><tr>
|
||||
<td style="text-align:center;"><br>
|
||||
</td>
|
||||
<td style="text-align:center; width:80px;">A−1−C </td>
|
||||
<td style="text-align:center; width:80px;">9 </td>
|
||||
<td style="text-align:center; width:80px;">10+C−A </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td style="text-align:center;">Add:</td>
|
||||
<td style="text-align:center;">10+C−A </td>
|
||||
<td style="text-align:center;">9 </td>
|
||||
<td style="text-align:center;">A−1−C </td>
|
||||
</tr><tr>
|
||||
<td style="text-align:center;"><br>
|
||||
</td>
|
||||
<td style="text-align:center;">9 </td>
|
||||
<td style="text-align:center;">18 </td>
|
||||
<td style="text-align:center;">9 </td>
|
||||
</tr><tr>
|
||||
<td style="text-align:center;">Simplify:
|
||||
</td>
|
||||
<td style="text-align:center;">10 </td>
|
||||
<td style="text-align:center;">8 </td>
|
||||
<td style="text-align:center;">9 </td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
</div>
|
||||
<p class="center"><span class="large">As predicted the answer was 1089</span></p>
|
||||
<p class="center"> </p>
|
||||
|
||||
<div class="related">
|
||||
<a href="1089.html">Always End With 1089</a>
|
||||
<a href="puzzles/index.html">Puzzles Index</a>
|
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|
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@ -1,122 +0,0 @@
|
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<!DOCTYPE html>
|
||||
<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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<head>
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||||
<meta http-equiv="content-type" content="text/html; charset=utf-8">
|
||||
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||||
<!-- #BeginEditable "doctitle" -->
|
||||
<title>Does 0.999... equal 1?</title>
|
||||
<script>reSpell=[["math","maths"]];</script>
|
||||
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|
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<meta name="keywords" content="math, maths, mathematics, school, homework, education">
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<div class="bg">
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<script>document.write(getAdTop());</script>
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<!-- #BeginEditable "Body" -->
|
||||
|
||||
<h1 class="center">Is this really true?</h1>
|
||||
|
||||
<div class="center"><span class="large"><br></span></div>
|
||||
<div class="center"><span class="large">The idea is that 0.9 recurring<br>
|
||||
</span><span class="larger">(0.999...
|
||||
with the digits going on forever) </span><span class="large"><br>
|
||||
is actually equal to 1</span></div>
|
||||
<p><i>(Here we write 0.999...
|
||||
as notation for 0.9 recurring,
|
||||
some people put a little dot above the 9, or a line on top like this: 0.<span style="text-decoration: overline;">9</span>)</i></p>
|
||||
<h2>Does 0.999... = 1 ?</h2>
|
||||
<p>Let us start by having X = 0.999...</p>
|
||||
<p class="so">X = 0.999...</p>
|
||||
<p class="so">10X = 9.999...</p>
|
||||
<p><i>Subtract X from each side to give us:</i></p>
|
||||
<p class="so">9X = 9.999... − X</p>
|
||||
<p><i>but we know that X is 0.999..., so: </i></p>
|
||||
<p class="so">9X = 9.999... − 0.999...</p>
|
||||
<p class="so">9X = 9</p>
|
||||
<p><i>Divide both sides by 9:</i></p>
|
||||
<p class="so">X = 1</p>
|
||||
<p><i>But hang on a moment I thought we said
|
||||
X was equal to 0.999... ?<br>
|
||||
<br>
|
||||
Yes, it does, but from our calculations X is also equal to
|
||||
1, so:</i></p>
|
||||
<p class="so">X = 0.999... = 1</p>
|
||||
<p>And so:</p>
|
||||
<p class="so">0.999... = 1</p>
|
||||
<div align="left">
|
||||
<p> </p>
|
||||
<p><i>Does anyone disagree with this? Let me
|
||||
know on the <a href="https://www.mathisfunforum.com/index.php">Math is Fun Forum</a>.</i></p>
|
||||
</div>
|
||||
<p> </p>
|
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|
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<div class="related">
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<a href="numbers/index.html">Numbers Index</a>
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<a href="algebra/index.html">Algebra Index</a>
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@ -1,187 +0,0 @@
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<script>document.write(getAdTop());</script>
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|
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|
||||
</p>
|
||||
<br>
|
||||
<p class="larger">We can't find <i>"<span id="h1Name"></span>"</i></p>
|
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|
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|
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document.getElementById('h1Name').innerHTML = uri;
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document.getElementById('newName').value = uri;
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|
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function getQueryVariable(variable) {
|
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var query = window.location.search.substring(1);
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|
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for (var i = 0; i < vars.length; i++) {
|
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var pair = vars[i].split("=");
|
||||
if (pair[0] == variable) {
|
||||
return pair[1];
|
||||
}
|
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}
|
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return false;
|
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}
|
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|
||||
function URLGo() {
|
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var locn = document.URLForm.newName.value;
|
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this.location.href = "https://www.mathsisfun.com/" + locn;
|
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|
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|
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|
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stack.pop(); // remove current file name (or empty string)
|
||||
var url = stack.join("/"); // remove filename
|
||||
|
||||
var urlStt = "../"; // most urls are down one folder
|
||||
if (endsWith(url, "/mathsisfun")) urlStt = ""; // for urls at root
|
||||
if (endsWith(url, "mathsisfun.com")) urlStt = "";
|
||||
//console.log('url',endsWith(url, "/dlm"),url,urlStt)
|
||||
return urlStt
|
||||
}
|
||||
|
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|
||||
var reqPage = '/GET';
|
||||
var refPage = 'http://www.mathsisfun.com/images/player.js';
|
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|
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//console.log('reqPage',reqPage,refPage )
|
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logVisit(reqPage,refPage);
|
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//setTimeout(go404Sorry, 500);
|
||||
|
||||
function logVisit(reqPage,refPage) {
|
||||
var reqPageHex = toHex(reqPage);
|
||||
var refPageHex = toHex(refPage);
|
||||
add404(reqPageHex, refPageHex, "404", window.location.hostname);
|
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}
|
||||
|
||||
|
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function add404(pg, pgFrom, viewtype, hostname) {
|
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//console.log("add404", viewtype, hostname);
|
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var req;
|
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req = new XMLHttpRequest();
|
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|
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var params = "type=" + viewtype;
|
||||
params += "&site=mif";
|
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params += "&pg=" + encodeURIComponent(pg);
|
||||
params += "&pgfrom=" + encodeURIComponent(pgFrom);
|
||||
|
||||
req.open("POST", "https://mi2f.com/update.php", true); // NB: false=synchronous
|
||||
|
||||
req.setRequestHeader("Content-type", "application/x-www-form-urlencoded");
|
||||
req.send(params);
|
||||
}
|
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|
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function toHex(s) {
|
||||
var hex = '';
|
||||
for (var i = 0; i < s.length; i++) {
|
||||
hex += '' + s.charCodeAt(i).toString(16);
|
||||
}
|
||||
return hex;
|
||||
}
|
||||
|
||||
function go404Sorry() {
|
||||
|
||||
//var pg = reqPage;
|
||||
//var reloc = "https://" + window.location.hostname + "/handle-404-sorry.html?uri=" + encodeURIComponent(pg);
|
||||
//console.log('go404Sorry',reloc);
|
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//window.location.href = reloc;
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}
|
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|
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@ -1,187 +0,0 @@
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<!doctype html>
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<html lang="en">
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<meta charset="UTF-8">
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<meta name="keywords" content="math, maths, mathematics, school, homework, education">
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<script>document.write(getTrans());</script>
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<div id="adTop">
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<script>document.write(getAdTop());</script>
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|
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<img src="/images/art/sage-dig-bones.gif">
|
||||
</p>
|
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<br>
|
||||
<p class="larger">We can't find <i>"<span id="h1Name"></span>"</i></p>
|
||||
|
||||
<p class="larger">Try the search above ...<img src="/images/style/up.gif" width="46" height="46" align="absmiddle" /></p>
|
||||
|
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<p>... or try another name below:</p>
|
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|
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<div style="clear:both"></div>
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https://www.mathsisfun.com/
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<input type="text" id="newName" name="newName" style="font: 18px Arial; width:250px;" value='' />
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<input type="submit" name="Go" value="Go" style="font: 18px Arial;" onClick='URLGo(); return false;' />
|
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|
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|
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|
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<p> </p>
|
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|
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|
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<script>
|
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// var uri = getQueryVariable('uri');
|
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var uri = '/POST'
|
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|
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if (uri.charAt(0) == '/') uri = uri.substr(1);
|
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console.log("uri", uri);
|
||||
|
||||
document.getElementById('h1Name').innerHTML = uri;
|
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document.getElementById('newName').value = uri;
|
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|
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function getQueryVariable(variable) {
|
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var query = window.location.search.substring(1);
|
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var vars = query.split("&");
|
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for (var i = 0; i < vars.length; i++) {
|
||||
var pair = vars[i].split("=");
|
||||
if (pair[0] == variable) {
|
||||
return pair[1];
|
||||
}
|
||||
}
|
||||
return false;
|
||||
}
|
||||
|
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function URLGo() {
|
||||
var locn = document.URLForm.newName.value;
|
||||
this.location.href = "https://www.mathsisfun.com/" + locn;
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}
|
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function urlSttGet() {
|
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var stack = location.href.split("/");
|
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stack.pop(); // remove current file name (or empty string)
|
||||
var url = stack.join("/"); // remove filename
|
||||
|
||||
var urlStt = "../"; // most urls are down one folder
|
||||
if (endsWith(url, "/mathsisfun")) urlStt = ""; // for urls at root
|
||||
if (endsWith(url, "mathsisfun.com")) urlStt = "";
|
||||
//console.log('url',endsWith(url, "/dlm"),url,urlStt)
|
||||
return urlStt
|
||||
}
|
||||
|
||||
|
||||
var reqPage = '/POST';
|
||||
var refPage = 'http://www.mathsisfun.com/main4.js';
|
||||
|
||||
//console.log('reqPage',reqPage,refPage )
|
||||
logVisit(reqPage,refPage);
|
||||
//setTimeout(go404Sorry, 500);
|
||||
|
||||
function logVisit(reqPage,refPage) {
|
||||
var reqPageHex = toHex(reqPage);
|
||||
var refPageHex = toHex(refPage);
|
||||
add404(reqPageHex, refPageHex, "404", window.location.hostname);
|
||||
}
|
||||
|
||||
|
||||
function add404(pg, pgFrom, viewtype, hostname) {
|
||||
//console.log("add404", viewtype, hostname);
|
||||
var req;
|
||||
req = new XMLHttpRequest();
|
||||
|
||||
var params = "type=" + viewtype;
|
||||
params += "&site=mif";
|
||||
params += "&pg=" + encodeURIComponent(pg);
|
||||
params += "&pgfrom=" + encodeURIComponent(pgFrom);
|
||||
|
||||
req.open("POST", "https://mi2f.com/update.php", true); // NB: false=synchronous
|
||||
|
||||
req.setRequestHeader("Content-type", "application/x-www-form-urlencoded");
|
||||
req.send(params);
|
||||
}
|
||||
|
||||
function toHex(s) {
|
||||
var hex = '';
|
||||
for (var i = 0; i < s.length; i++) {
|
||||
hex += '' + s.charCodeAt(i).toString(16);
|
||||
}
|
||||
return hex;
|
||||
}
|
||||
|
||||
function go404Sorry() {
|
||||
|
||||
//var pg = reqPage;
|
||||
//var reloc = "https://" + window.location.hostname + "/handle-404-sorry.html?uri=" + encodeURIComponent(pg);
|
||||
//console.log('go404Sorry',reloc);
|
||||
//window.location.href = reloc;
|
||||
}
|
||||
|
||||
|
||||
</script>
|
||||
|
||||
<!-- #EndEditable -->
|
||||
|
||||
</article>
|
||||
<div id="adend" class="centerfull noprint">
|
||||
<script>document.write(getAdEnd());</script>
|
||||
</div>
|
||||
<footer id="footer" class="centerfull noprint">
|
||||
<script>document.write(getFooter());</script>
|
||||
</footer>
|
||||
<div id="copyrt">
|
||||
Copyright © 2020 MathsIsFun.com
|
||||
</div>
|
||||
<script>document.write(getBodyEnd());</script>
|
||||
</body>
|
||||
<!-- #EndTemplate -->
|
||||
</html>
|
||||
@ -1,151 +0,0 @@
|
||||
<!doctype html>
|
||||
<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
|
||||
|
||||
<!-- Mirrored from www.mathsisfun.com/Privacy.htm by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:59:11 GMT -->
|
||||
<head>
|
||||
<meta http-equiv="content-type" content="text/html; charset=utf-8">
|
||||
<!-- #BeginEditable "doctitle" -->
|
||||
<title>Maths is Fun - Privacy Statement</title>
|
||||
<!-- #EndEditable -->
|
||||
<meta name="keywords" content="math, maths, mathematics, school, homework, education">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
|
||||
<meta name="HandheldFriendly" content="true">
|
||||
<meta name="referrer" content="always">
|
||||
<link rel="stylesheet" type="text/css" href="style3.css">
|
||||
<script src="main3.js"></script>
|
||||
</head>
|
||||
|
||||
<body id="bodybg">
|
||||
<div class="bg">
|
||||
<div id="stt"></div>
|
||||
<div id="hdr"></div>
|
||||
<div id="logo"><a href="index.html"><img src="images/style/logo.svg" alt="Math is Fun"></a></div>
|
||||
<div id="gtran">
|
||||
<script>document.write(getTrans());</script>
|
||||
</div>
|
||||
<div id="adTopOuter" class="centerfull noprint">
|
||||
<div id="adTop">
|
||||
<script>document.write(getAdTop());</script>
|
||||
</div>
|
||||
</div>
|
||||
<div id="adHide">
|
||||
<div id="showAds1"><a href="javascript:showAds()">Show Ads</a></div>
|
||||
<div id="hideAds1"><a href="javascript:hideAds()">Hide Ads</a><br>
|
||||
<a href="about-ads.html">About Ads</a></div>
|
||||
</div>
|
||||
<div id="menuWide" class="menu">
|
||||
<script>document.write(getMenu(0));</script>
|
||||
</div>
|
||||
<div id="linkto">
|
||||
<div id="linktort">
|
||||
<script>document.write(getLinks());</script>
|
||||
</div>
|
||||
</div>
|
||||
<div id="search" role="search">
|
||||
<script>document.write(getSearch());</script>
|
||||
</div>
|
||||
<div id="menuSlim" class="menu">
|
||||
<script>document.write(getMenu(1));</script>
|
||||
</div>
|
||||
<div id="menuTiny" class="menu">
|
||||
<script>document.write(getMenu(2));</script>
|
||||
</div>
|
||||
<div id="extra"></div>
|
||||
</div>
|
||||
<div id="content" role="main"><!-- #BeginEditable "Body" -->
|
||||
|
||||
<h1 class="center">Privacy Statement for mathsisfun.com</h1>
|
||||
|
||||
<p align="center">Also Read: <a href="internet-safety.html">Internet Safety Guide</a></p>
|
||||
<div class="center80">
|
||||
<h3>Overview </h3>
|
||||
<p>Mathsisfun.com does not have memberships or subscriptions, and <b>does not keep any personally identifiable information</b> (except what you say when you <a href="contact.html">contact us</a>).</p>
|
||||
<p>We use "cookies" to store some settings such as when you click "Hide Ads". Advertisers may also use information about you that is out of our control. </p>
|
||||
</div>
|
||||
<p>Here are the details:</p>
|
||||
<p> </p>
|
||||
<p><i>This privacy statement discloses the privacy practices for mathsisfun.com, and advises you of what information may be collected
|
||||
via this website and what will happen to it.</i> </p>
|
||||
<ul>
|
||||
<li><i> What personally identifiable information of yours or third
|
||||
party personally identification is collected from you through the
|
||||
web site </i></li>
|
||||
<li><i> The organization collecting the information </i></li>
|
||||
<li><i>How the information is used </i></li>
|
||||
<li><i>With whom the information may be shared </i></li>
|
||||
<li><i>What choices are available to you regarding collection, use and
|
||||
distribution of the information </i></li>
|
||||
<li><i>The kind of security procedures that are in place to protect
|
||||
the loss, misuse or alteration of information under mathsisfun.com
|
||||
control </i></li>
|
||||
<li><i>How you can correct any inaccuracies in the information. </i> </li>
|
||||
</ul>
|
||||
<p align="center"> <br />
|
||||
<b><i>If you feel that we are not abiding by our privacy policy, please <a href="contact.html">contact us</a><br />
|
||||
<br />
|
||||
|
||||
</i></b></p>
|
||||
<h2>Information Collection and Use </h2>
|
||||
<p>Mathsisfun.com is the sole owner of the information collected on
|
||||
this site. We will not sell, share, or rent this information to
|
||||
others in ways different from what is disclosed in this statement.
|
||||
Mathsisfun.com collects only enough information to
|
||||
provide basic functionality and security. </p>
|
||||
<h2>Cookies </h2>
|
||||
<p>A cookie is a piece of data stored on the user's computer containing
|
||||
information about the user's visit. Usage of a cookie is in no way
|
||||
linked to any personally identifiable information while on our site.
|
||||
For instance, by setting a cookie on our site, the site can know if you pressed "hide ads". If a user rejects the cookie, they may still use our
|
||||
site. The only drawback to this is that the user will be limited
|
||||
in some areas of our site. </p>
|
||||
<h2>Advertisers</h2>
|
||||
<p>We use third-party advertising companies to serve ads when you visit our website. These companies may use information about your visits to this and other websites in order to provide advertisements about goods and services of interest to you. </p>
|
||||
<h2>Log Files</h2>
|
||||
<p>We use IP addresses to analyze
|
||||
trends, administer the site, track movement, and gather broad
|
||||
demographic information for aggregate use. IP addresses are not
|
||||
linked to personally identifiable information. We may
|
||||
share aggregated demographic information with our partners and advertisers.
|
||||
This is not linked to any personal information that can identify
|
||||
any individual person. </p>
|
||||
<h2> Links to Other Sites </h2>
|
||||
<p>This web site contains links to other sites. Please be aware that
|
||||
mathsisfun.com is not responsible for the privacy practices of such
|
||||
other sites. We encourage our users to be aware when they leave
|
||||
our site and to read the privacy statements of each and every web
|
||||
site that collects personally identifiable information. This privacy
|
||||
statement applies solely to information collected by this Web site.</p>
|
||||
<h2>Security </h2>
|
||||
<p>Mathsisfun.com is a free information-only service and sells
|
||||
no products directly. At no
|
||||
time will mathsisfun.com directly request address or payment details.
|
||||
However, some partner sites do sell direct. Please
|
||||
check as mathsisfun.com cannot be responsible for insecure transactions
|
||||
from other web sites. </p>
|
||||
<h2> Notification of Changes </h2>
|
||||
<p>If we decide to change our privacy policy, we will notify users
|
||||
on our Homepage so our users are always aware of what information
|
||||
we collect, how we use it, and under circumstances, if any, we disclose
|
||||
it. We will use information in accordance with the privacy policy
|
||||
under which the information was collected. </p>
|
||||
<p> </p>
|
||||
<p class="tiny">Last Updated: Tuesday 10 Mar 2019</p>
|
||||
<p>
|
||||
<center>
|
||||
</center>
|
||||
</p>
|
||||
<!-- #EndEditable --></div>
|
||||
<div id="adend" class="centerfull noprint">
|
||||
<script>document.write(getAdEnd());</script>
|
||||
</div>
|
||||
<div id="footer" class="centerfull noprint">
|
||||
<script>document.write(getFooter());</script>
|
||||
</div>
|
||||
<div id="copyrt">
|
||||
Copyright © 2019 MathsIsFun.com
|
||||
</div>
|
||||
<script>document.write(getBodyEnd());</script>
|
||||
</body>
|
||||
<!-- #EndTemplate -->
|
||||
<!-- Mirrored from www.mathsisfun.com/Privacy.htm by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:59:12 GMT -->
|
||||
</html>
|
||||
@ -1,112 +0,0 @@
|
||||
<!doctype html>
|
||||
<html lang="en">
|
||||
<!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
|
||||
<!-- Mirrored from www.mathsisfun.com/about-ads.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:35:35 GMT -->
|
||||
<head>
|
||||
<meta charset="UTF-8">
|
||||
<!-- #BeginEditable "doctitle" -->
|
||||
<title>About The Ads</title>
|
||||
<meta name="description" content="The site is free to use. No subscriptions or charges.">
|
||||
<!-- #EndEditable -->
|
||||
<meta name="keywords" content="math, maths, mathematics, school, homework, education">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
|
||||
<meta name="HandheldFriendly" content="true">
|
||||
<meta name="referrer" content="always">
|
||||
<link rel="preload" href="images/style/font-champ-bold.ttf" as="font" type="font/ttf" crossorigin>
|
||||
<link rel="preload" href="style4.css" as="style">
|
||||
<link rel="preload" href="main4.js" as="script">
|
||||
<link rel="stylesheet" href="style4.css">
|
||||
<script src="main4.js" defer></script>
|
||||
<!-- Global site tag (gtag.js) - Google Analytics -->
|
||||
<script async src="https://www.googletagmanager.com/gtag/js?id=UA-29771508-1"></script>
|
||||
<script>
|
||||
window.dataLayer = window.dataLayer || [];
|
||||
function gtag(){dataLayer.push(arguments);}
|
||||
gtag('js', new Date());
|
||||
gtag('config', 'UA-29771508-1');
|
||||
</script>
|
||||
</head>
|
||||
|
||||
<body id="bodybg">
|
||||
|
||||
<div id="stt"></div>
|
||||
<div id="adTop"></div>
|
||||
<header>
|
||||
<div id="hdr"></div>
|
||||
<div id="tran"></div>
|
||||
<div id="adHide"></div>
|
||||
<div id="cookOK"></div>
|
||||
</header>
|
||||
|
||||
<div class="mid">
|
||||
|
||||
<nav>
|
||||
<div id="menuWide" class="menu"></div>
|
||||
<div id="logo"><a href="index.html"><img src="images/style/logo.svg" alt="Math is Fun"></a></div>
|
||||
|
||||
<div id="search" role="search"></div>
|
||||
<div id="linkto"></div>
|
||||
|
||||
<div id="menuSlim" class="menu"></div>
|
||||
<div id="menuTiny" class="menu"></div>
|
||||
</nav>
|
||||
|
||||
<div id="extra"></div>
|
||||
|
||||
<article id="content" role="main">
|
||||
|
||||
<!-- #BeginEditable "Body" -->
|
||||
|
||||
|
||||
<h1 class="center">About The Ads</h1>
|
||||
|
||||
<p class="center larger">This website pays its bills with money from
|
||||
advertising.<br>
|
||||
The site is otherwise <b>free to use</b>. No subscriptions or charges.</p>
|
||||
|
||||
<h3>Ads use Cookies</h3>
|
||||
<p>We don't collect user data, but the ad publishers may do so, for ad personalization
|
||||
and measurement. <a href="https://policies.google.com/technologies/partner-sites">
|
||||
Read more about this, including how to turn it off</a>.</p>
|
||||
<p> </p>
|
||||
|
||||
<h3>Privacy</h3>
|
||||
<p>Your privacy is important to us. Read more at <a href="Privacy.html">Privacy</a>.</p>
|
||||
<p> </p>
|
||||
|
||||
<h3>Hiding Ads</h3>
|
||||
<p>Ads can sometimes be distracting, so you can <b>hide them for 36 hours</b>
|
||||
(yes they come back, but you can hide them again).</p>
|
||||
<p>Handy for classroom demonstrations!</p>
|
||||
<p>Click on the "Hide Ads" near the top right.</p>
|
||||
<p> </p>
|
||||
|
||||
<h3>Seen An Ad You Don't Like?</h3>
|
||||
<p>We do our best to ensure only good ads are shown, but sometimes a <b>bad ad</b>
|
||||
slips through.</p>
|
||||
<p>So <b>please</b> <a href="contact.html">let us know</a> of any ad you don't think
|
||||
should be there. Give as many details as possible (name and web address of
|
||||
advertiser, what page it appeared on, and a screenshot would be good) so it can be
|
||||
identified and blocked.</p>
|
||||
<p><br></p>
|
||||
<p>Thank You!</p>
|
||||
<p>Rod Pierce</p>
|
||||
<p> </p>
|
||||
|
||||
<div class="related">
|
||||
<a href="index-2.html">Home Page</a>
|
||||
</div>
|
||||
<!-- #EndEditable -->
|
||||
|
||||
</article>
|
||||
|
||||
<div id="adend" class="centerfull noprint"></div>
|
||||
<footer id="footer" class="centerfull noprint"></footer>
|
||||
<div id="copyrt">Copyright © 2021 MathsIsFun.com</div>
|
||||
|
||||
</div>
|
||||
</body>
|
||||
<!-- #EndTemplate -->
|
||||
|
||||
<!-- Mirrored from www.mathsisfun.com/about-ads.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:35:36 GMT -->
|
||||
</html>
|
||||
@ -1,119 +0,0 @@
|
||||
<!DOCTYPE html>
|
||||
<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
|
||||
|
||||
<!-- Mirrored from www.mathsisfun.com/aboutmathsisfun.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:59:34 GMT -->
|
||||
<head>
|
||||
<meta http-equiv="content-type" content="text/html; charset=utf-8">
|
||||
|
||||
|
||||
|
||||
<!-- #BeginEditable "doctitle" -->
|
||||
<title>About Math is Fun</title>
|
||||
<script>reSpell=[["math","maths"]];</script>
|
||||
|
||||
<meta name="description" content="We offer mathematics in an enjoyable and easy-to-learn manner, because we believe that mathematics is fun.">
|
||||
|
||||
<!-- #EndEditable -->
|
||||
<meta name="keywords" content="math, maths, mathematics, school, homework, education">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
|
||||
<meta name="HandheldFriendly" content="true">
|
||||
<meta name="referrer" content="always">
|
||||
<link rel="stylesheet" type="text/css" href="style3.css">
|
||||
<script src="main3.js"></script>
|
||||
</head>
|
||||
|
||||
<body id="bodybg">
|
||||
<div class="bg">
|
||||
<div id="stt"></div>
|
||||
<header>
|
||||
<div id="hdr"></div>
|
||||
<div id="logo"><a href="index.html"><img src="images/style/logo.svg" alt="Math is Fun"></a></div>
|
||||
<div id="gtran">
|
||||
<script>document.write(getTrans());</script>
|
||||
</div>
|
||||
<div id="adTopOuter" class="centerfull noprint">
|
||||
<div id="adTop">
|
||||
<script>document.write(getAdTop());</script>
|
||||
</div>
|
||||
</div>
|
||||
<div id="adHide">
|
||||
<div id="showAds1"><a href="javascript:showAds()">Show Ads</a></div>
|
||||
<div id="hideAds1"><a href="javascript:hideAds()">Hide Ads</a><br>
|
||||
<a href="about-ads.html">About Ads</a></div>
|
||||
</div>
|
||||
</header>
|
||||
<nav>
|
||||
<div id="menuWide" class="menu">
|
||||
<script>document.write(getMenu(0));</script>
|
||||
</div>
|
||||
<div id="linkto">
|
||||
<div id="linktort">
|
||||
<script>document.write(getLinks());</script>
|
||||
</div>
|
||||
</div>
|
||||
<div id="search" role="search">
|
||||
<script>document.write(getSearch());</script>
|
||||
</div>
|
||||
<div id="menuSlim" class="menu">
|
||||
<script>document.write(getMenu(1));</script>
|
||||
</div>
|
||||
<div id="menuTiny" class="menu">
|
||||
<script>document.write(getMenu(2));</script>
|
||||
</div>
|
||||
</nav>
|
||||
<div id="extra"></div>
|
||||
</div>
|
||||
<article id="content" role="main">
|
||||
<!-- #BeginEditable "Body" -->
|
||||
|
||||
<h1 class="center">About Math Is Fun</h1>
|
||||
|
||||
<h2>The Idea</h2>
|
||||
<p>We offer mathematics
|
||||
in an enjoyable and easy-to-learn manner, because we believe that mathematics is fun.</p>
|
||||
<h2>General</h2>
|
||||
<p>The site aims to cover the full Kindergarten to Year 12 <a href="links/index-curriculum.html">curriculum</a>.</p>
|
||||
<h2>Quality</h2>
|
||||
<p>Quality is important to us. Amongst our team are:</p>
|
||||
<ul>
|
||||
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<h1 align="center">Accuracy and Precision</h1>
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<p class="center"><i>They mean slightly different things!</i>
|
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</p>
|
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|
||||
<h2>Accuracy</h2>
|
||||
<p align="center">Accuracy is how close a measured value is to the <b>actual (true) value</b>.
|
||||
</p>
|
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<h2>Precision</h2>
|
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<p align="center">Precision is how close the measured values are <b>to each other</b>.
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<h2>Examples</h2>
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<h3>Here is an example of several values on the <a href="number-line.html">number line</a>:</h3>
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<p class="center"><img src="data/images/accuracy-precision.svg" alt="accuracy and precision" /></p>
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||||
<h3>And an example on a Target:</h3>
|
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<div class="simple">
|
||||
<table border="0" cellspacing="5" align="center">
|
||||
<tr align="center">
|
||||
<td><img src="images/hi-accuracy-low-precision.svg" alt="hi accuracy low precision" /></td>
|
||||
<td><img src="images/low-accuracy-hi-precision.svg" alt="low accuracy hi precision" /></td>
|
||||
<td><img src="images/hi-accuracy-hi-precision.svg" alt="hi accuracy hi precision" /></td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td><b>High Accuracy</b><br />
|
||||
Low Precision</td>
|
||||
<td>
|
||||
Low Accuracy<br />
|
||||
<b>High Precision
|
||||
|
||||
</b></td>
|
||||
<td><b>High Accuracy<br />
|
||||
High Precision
|
||||
</b></td>
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</tr>
|
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</table>
|
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</div>
|
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<div class="example">
|
||||
<h3>Example: Hitting the Post</h3>
|
||||
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/soccer-teams.jpg" width="209" height="86" alt="soccer goal"></p>
|
||||
<p>If you are playing football and you always hit the right goal post instead of scoring, then you are <b>not</b> accurate, but you <b>are</b> precise!</p>
|
||||
</div>
|
||||
|
||||
|
||||
<h2>How to Remember?</h2>
|
||||
<ul>
|
||||
<li>a<b>C</b>curate is <b>C</b>orrect (a bullseye).</li>
|
||||
<li>p<b>R</b>ecise is <b>R</b>epeating (hitting the same spot, but maybe not the correct spot)</li>
|
||||
</ul>
|
||||
<h2>Bias (don't let precision fool you!)</h2>
|
||||
<p>When we measure something several times and all values are close, they <b>may</b> all be wrong if there is a "<b>Bias</b>"</p>
|
||||
<p><b>Bias</b> is a systematic (built-in) error which makes all measurements wrong by a certain amount.</p>
|
||||
<h3>Examples of Bias</h3>
|
||||
<ul>
|
||||
<li>The scales read "1 kg" when there is nothing on them</li>
|
||||
<li>You always measure your height wearing shoes with thick soles.</li>
|
||||
<li>A stopwatch that takes half a second to stop when clicked</li>
|
||||
</ul>
|
||||
<p>In each case <b>all</b> measurements are wrong by the same amount. That is bias.</p>
|
||||
<h2>Degree of Accuracy</h2>
|
||||
<p>Degree of Accuracy depends on the instrument we are measuring with. But as a general rule:</p>
|
||||
<div class="def">
|
||||
<p>The Degree of Accuracy is <b>half a unit</b> each side of the unit of measure.</p>
|
||||
</div>
|
||||
|
||||
<h3>Examples:</h3>
|
||||
<div class="simple">
|
||||
<table border="0" align="center">
|
||||
|
||||
<tr align="center">
|
||||
<td>When an instrument measures in "1"s <br />
|
||||
any value between <b>6½</b> and <b>7½</b> is measured as <b>"7"</b></td>
|
||||
<td><img src="images/accuracy-1.svg" alt="7 plus minus 0.5" /></td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>When an instrument measures in "2"s <br />
|
||||
any value between <b>7</b> and <b>9</b> is measured as <b>"8"</b></td>
|
||||
<td><img src="images/accuracy-2.svg" alt="8 plus minus 1" /></td>
|
||||
</tr>
|
||||
</table>
|
||||
</div>
|
||||
|
||||
<p class="center"><i>(Notice that the arrow points to the same spot, but the measured values are different!<br />
|
||||
Read more at <a href="measure/error-measurement.html">Errors in Measurement</a>.
|
||||
)</i></p>
|
||||
<p> </p>
|
||||
<p>We should show final values that match the accuracy of our <b>least</b> accurate value used.</p>
|
||||
<div class="example">
|
||||
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/art/sage-looking-ear-down.gif" width="77" height="100" alt="dog"></p>
|
||||
<h3>Example: We are told the dog is about 2 feet high. </h3>
|
||||
<p>We can convert that to 609.6 mm, but that suggests we know the height to within 0.1 mm! </p>
|
||||
<p>So we should use <b>600 mm</b></p>
|
||||
</div>
|
||||
<p> </p>
|
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<div class="questions">
|
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<script type="text/javascript">getQ(5000, 1872, 1873, 1874, 1875, 3788, 3789, 3790, 3791, 5001);</script>
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</div>
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|
||||
|
||||
<div class="related"><a href="measure/error-measurement.html">Errors in Measurement
|
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</a> <a href="data/standard-deviation.html">Standard Deviation and Variance</a> <a href="length-conversion.html">How to Convert Lengths</a>
|
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<a href="area-conversion.html">How to Convert Areas</a>
|
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<a href="volume-conversion.html">How to Convert Volumes</a>
|
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<a href="temperature-conversion.html">Converting Temperatures (Celsius and Fahrenheit)</a> <a href="unit-conversion-tool.html">Unit Converter</a>
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Activity: Commutative, Associative and Distributive</h1>
|
||||
<p>Learn the difference between <a href="../associative-commutative-distributive.html">Commutative, Associative and Distributive Laws</a> by creating:</p>
|
||||
<p class="largest" align="center">Comic Book Super Heroes</p>
|
||||
<p class="center"><img src="images/comm-assoc-dist-1.jpg" alt="comm assoc dist 1" height="320" width="247"><br></p>
|
||||
<p>You will need:</p>
|
||||
<ul>
|
||||
<li>Coloring pencils</li>
|
||||
<li>Paper</li>
|
||||
<li>Imagination!</li>
|
||||
</ul>
|
||||
<p><br></p>
|
||||
<h2 align="left">Activity 1</h2>
|
||||
<p><b>Step 1:</b> The "Commutative Laws" say you can <b>swap numbers</b> over and still get the same answer ...</p>
|
||||
<p>... when you <b>add</b>:</p>
|
||||
<div class="center80">
|
||||
<p class="center large">a + b<b> = </b>b + a</p>
|
||||
</div>
|
||||
<h3 align="center">Example:</h3>
|
||||
<p class="center"><img src="../numbers/images/commutative-add.gif" alt="Commutative Law Addition" height="73" width="307"></p>
|
||||
<p> </p>
|
||||
<p>... or when you <b>multiply</b>:</p>
|
||||
<div class="center80">
|
||||
<p class="center large">a × b<b> = </b>b × a</p>
|
||||
</div>
|
||||
<h3 align="center">Example:</h3>
|
||||
<p class="center"><img src="../numbers/images/commutative-multiply.gif" alt="Commutative Law multiplication" height="102" width="186"></p>
|
||||
<p><br></p>
|
||||
<p><b>Step 2:</b> Does order of numbers matter when multiplying or adding?</p>
|
||||
<p><b>Step 3:</b> Using this information, try to draw a <span class="larger">super hero</span> whose super powers incorporates the fact that order doesn't matter.</p>
|
||||
<p>Your super hero could be a man, a woman, a dog, a robot, anything!</p>
|
||||
<p><b>Step 4:</b> Label your super hero <span class="larger">Commutative (Man/Woman/Dog/Whatever)</span></p>
|
||||
<p> </p>
|
||||
<p> </p>
|
||||
<h2 align="left">Activity 2:</h2>
|
||||
<p><b>Step 1:</b> The "Associative Laws" say that it doesn't matter how you group the numbers (i.e. which you calculate first) ...</p>
|
||||
<p>... when you <b>add</b>:</p>
|
||||
<div class="center80">
|
||||
<p class="center large">(a + b) + c<b> = </b>a + (b + c)</p>
|
||||
</div>
|
||||
<p class="center"><img src="../numbers/images/associative-add.gif" alt="Associative Law addition" height="76" width="415"></p>
|
||||
<p>... or when you <b>multiply</b>:</p>
|
||||
<div class="center80">
|
||||
<p class="center large">(a × b) × c<b> = </b>a × (b × c)</p>
|
||||
</div>
|
||||
<h3 align="center"><img src="../numbers/images/associative-multiply.gif" alt="Associative Law multiplication" height="114" width="278"></h3>
|
||||
<p><br></p>
|
||||
<p><b>Step 2:</b> Do the way we group numbers matter when multiplying or adding?</p>
|
||||
<p><b>Step 3:</b> Using this information, try to draw a super hero whose super powers incorporates the fact that the way we group numbers doesn't matter</p>
|
||||
<p><b>Step 4:</b> Label your super hero <span class="larger">Associative (Girl/Boy/Dog/Whatever)</span></p>
|
||||
<p> </p>
|
||||
<p><br></p>
|
||||
<h2 align="left">Activity 3</h2>
|
||||
<p><b>Step 1:</b> The "Distributive Law" says:</p>
|
||||
<div class="center80">
|
||||
<p class="center larger">a × (b + c) = a × b + a × c</p>
|
||||
</div>
|
||||
|
||||
<p>This is what it lets you do:</p>
|
||||
<p class="center"><img src="../numbers/images/distributive-law.gif" alt="Distributive Law" height="105" width="341"></p>
|
||||
<p class="center">3 lots of <b>(2+4)</b> is the same as <b>3 lots of 2</b> plus <b>3 lots of 4</b></p>
|
||||
<p> </p>
|
||||
<p><b>Step 2:</b> Though they kind of look the same, what's different between Associative and Distributive. Notice that one uses multiplication and addition, but the other uses either multiplication or addition. What else can you notice</p>
|
||||
<p><b>Step 3:</b> Using this information, try to draw a super hero whose super powers are distributive</p>
|
||||
<p><b>Step 4:</b> Label your super hero <span class="larger">Distributive (Woman/Man/Hamster/Whatever)</span></p>
|
||||
<p><br></p>
|
||||
<p class="center"><img src="images/comm-assoc-dist-2.jpg" alt="comm assoc dist 2" height="240" width="320"></p>
|
||||
<p class="center">Put your illustrations on the wall!</p>
|
||||
|
||||
<p> </p>
|
||||
<p align="right">Activity courtesy of <a href="hands-on-math.html">Hands On Math</a></p>
|
||||
<p> </p>
|
||||
<!-- #EndEditable -->
|
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|
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</article>
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|
||||
<h1 class="center">Activity: Averages Brain-Teaser</h1>
|
||||
|
||||
<p>Here is a little puzzle about <a href="../mean.html">averages</a>. Is it right?</p>
|
||||
<p> </p>
|
||||
|
||||
<div class="example">
|
||||
|
||||
<h3>Who is Better at Kicking Goals?</h3>
|
||||
<p style="float:right; margin: 0 0 5px 10px;"><img src="../images/soccer-teams.jpg" alt="soccer teams" height="86" width="209"></p>
|
||||
<p>At practice last week:</p>
|
||||
<ul>
|
||||
<li>You scored 2 of 10 shots at goal</li>
|
||||
<li>Sam scored 3 of 10 shots</li>
|
||||
</ul>
|
||||
<p>Sam is better!</p>
|
||||
<p> </p>
|
||||
<p>This week:</p>
|
||||
<ul>
|
||||
<li>You scored 53 of 100 shots</li>
|
||||
<li>Sam scored 6 of 10 shots</li>
|
||||
</ul>
|
||||
<p>Sam is still better.</p>
|
||||
<p> </p>
|
||||
<p>But let's <b>add up the scores for BOTH weeks</b>:</p>
|
||||
<ul>
|
||||
<li>You scored 55 of 110 shots: that is 50%</li>
|
||||
<li>Sam scored 9 of 20 shots: that is only 45%</li>
|
||||
</ul>
|
||||
|
||||
<p>Hang on! YOU are better!</p>
|
||||
<p> </p>
|
||||
<p>Sam was better last week and this week ... but you are better over both weeks?</p>
|
||||
</div>
|
||||
<p>Please explain.</p>
|
||||
<p> </p>
|
||||
<p>...</p>
|
||||
<p> </p>
|
||||
<p>Make a table with all the data and do the calculations yourself</p>
|
||||
|
||||
<table align="center" cellspacing="0" cellpadding="4" border="1">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td style="text-align:right;"> </td>
|
||||
<td align="center" width="200">Sam</td>
|
||||
<td align="center" width="200">You</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right" height="60">Last Week</td>
|
||||
<td> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right" height="60">This Week</td>
|
||||
<td> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right" height="60"><b>Both Weeks</b></td>
|
||||
<td> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p> </p>
|
||||
<p>....</p>
|
||||
<p> </p>
|
||||
<p> </p>
|
||||
<p><b>... read on after you have thought about it ...</b></p>
|
||||
<p> </p>
|
||||
<p> </p>
|
||||
<p>...</p>
|
||||
<p> </p>
|
||||
<p> </p>
|
||||
<p> </p>
|
||||
|
||||
<div class="example">
|
||||
|
||||
<h3>It is All True</h3>
|
||||
<p> </p>
|
||||
<p>Because you had SO MANY shots at goal this week, and did well at them, you lifted your two-week average above Sam's.</p>
|
||||
<p> </p>
|
||||
<p>At practice last week:</p>
|
||||
<ul>
|
||||
<li>You scored 2 of 10 (<b>20%</b>)</li>
|
||||
<li>Sam scored 3 of 10 (<b>30%</b>)</li>
|
||||
</ul>
|
||||
<p>This week:</p>
|
||||
<ul>
|
||||
<li><span class="hilite">You scored 53 of 100 (<b>53%</b>)</span></li>
|
||||
<li>Sam scored 6 of 10 (<b>60%</b>)</li>
|
||||
</ul>
|
||||
<p> </p>
|
||||
<p>For BOTH weeks:</p>
|
||||
<ul>
|
||||
<li>You scored 55 of 110 (<b>50%</b>)</li>
|
||||
<li>Sam scored 9 of 20 (<b>45%</b>)</li>
|
||||
</ul>
|
||||
<p> </p>
|
||||
</div>
|
||||
<p> </p>
|
||||
<p>To be fair, we should really compare the averages when your and Sam's attempts at goal is roughly the same.</p>
|
||||
<p>If Sam had attempted 100 shots this week, he may have scored 60 out of 100, and his two-week average would have been about <b>57%</b>, better than you.</p>
|
||||
<p>So be careful when comparing two sets of data with widely different counts.</p>
|
||||
<p class="info"> This is an example of "Simpson's paradox" if you want to find out more.</p>
|
||||
<p><i><br></i></p>
|
||||
<p><i>Note: only certain sets of data produce this "paradox", usually everything makes sense.</i></p>
|
||||
<p> </p>
|
||||
|
||||
<div class="related">
|
||||
<a href="../data/index.html">Data Index</a>
|
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</div>
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<h1 class="center">Activity: Buffon's Needle</h1>
|
||||
|
||||
<p class="center">How to estimate <a href="../numbers/pi.html">Pi</a> by dropping a match.</p>
|
||||
<div class="center80">
|
||||
|
||||
<p>A few hundred years ago people enjoyed betting on <a href="coin-grid.html">coins tossed on to the floor</a>: would the coin cross a line or not?</p>
|
||||
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/coin-1750.jpg" alt="coin 1750" height="133" width="240"></p>
|
||||
<p>A man (Georges-Louis Leclerc, the <i>Count of Buffon</i>) started thinking about this and worked out the <a href="../data/probability.html">probability</a>.</p>
|
||||
<p>It is called "Buffon's Needle" in his honor.</p>
|
||||
<p>Now it is your turn to have a go!</p>
|
||||
</div>
|
||||
<p>You will need:</p>
|
||||
<div class="simple">
|
||||
|
||||
<table style="border: 0; margin:auto;">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td style="text-align:center;"><img src="images/match-no-head.svg" alt="match no head" height="59" width="54"></td>
|
||||
<td>
|
||||
<p>A <b>match</b>, with the head cut off.<br>
|
||||
It must be less than 50 mm.</p>
|
||||
<p>(You can use a needle, but be careful!)</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td style="text-align:center;"><a href="images/buffons-needle-grid.gif"><img src="images/buffons-needle-grid.gif" alt="buffons needle grid" height="770" width="888"></a><br>
|
||||
</td>
|
||||
<td>
|
||||
<p>A sheet of paper with lines 50 mm apart.</p>
|
||||
<p><input onclick="printImg('images/buffons-needle-grid.gif')" value="Print this one" type="button"></p></td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
</div>
|
||||
|
||||
|
||||
<h2>Steps</h2>
|
||||
|
||||
<div class="bigul">
|
||||
<ul>
|
||||
<li>Measure the spacing of your lines (it may not print at exactly 50mm): ____ mm</li>
|
||||
<li>Measure the length of your match (must be less than the line spacing): ____ mm</li>
|
||||
<li>Make sure your sheet of paper is on a flat surface such as a table top or the floor.</li>
|
||||
<li>From a height of about 5cm, drop the match onto the paper and record whether it lands:
|
||||
|
||||
|
||||
<table style="border: 0;">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td>
|
||||
<p><span class="large">A:</span> Not touching a line</p>
|
||||
<p><span class="large">B:</span> Touching or crossing a line</p></td>
|
||||
<td><img src="images/buffons-needle-1.gif" alt="buffons needle A B" height="83" width="180"></td>
|
||||
</tr>
|
||||
</tbody></table></li>
|
||||
</ul>
|
||||
</div>
|
||||
<p>The exact height from which you drop the match is not important, but don't drop it so close to the paper that you are cheating!</p>
|
||||
<p>If the match rolls completely off the paper, then do not count that turn.</p>
|
||||
|
||||
|
||||
<h2>100 Times</h2>
|
||||
|
||||
<p>Now we will drop the match 100 times, but first ...</p>
|
||||
<div class="center80">
|
||||
<p class="center larger">... what percentage do you think will land A, or B?</p>
|
||||
</div>
|
||||
<p>Make a guess (estimate) before you begin the experiment:</p>
|
||||
|
||||
<table align="center" border="1">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td align="right" height="25">Your Guess for "A" (%):</td>
|
||||
<td style="width:80px;"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right" height="25">Your Guess for "B" (%):</td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p><b>OK let's begin</b>.</p>
|
||||
<p>Drop the match 100 times and record <span class="large">A</span> (does not touch a grid line) or <span class="large">B</span> (touches or crosses a grid line) using <a href="../data/tally-marks.html">Tally Marks</a>:</p>
|
||||
|
||||
<table width="100%" border="1">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td style="text-align:center;">match lands</td>
|
||||
<td width="50%">Tally</td>
|
||||
<td style="text-align:center;">Frequency</td>
|
||||
<td style="text-align:center;">Percentage</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td style="text-align:center;">
|
||||
<div class="large">A</div>(no touch)</td>
|
||||
<td height="70"> </td>
|
||||
<td style="text-align:center;"> </td>
|
||||
<td style="text-align:center;"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td style="text-align:center;">
|
||||
<div class="large">B</div>(crosses)</td>
|
||||
<td height="70"> </td>
|
||||
<td style="text-align:center;"> </td>
|
||||
<td style="text-align:center;"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td style="text-align:center;"> </td>
|
||||
<td style="text-align:right;">Totals:</td>
|
||||
<td style="text-align:center;">100</td>
|
||||
<td style="text-align:center;">100% </td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p>Now draw a <a href="../data/bar-graphs.html">Bar Graph</a> to illustrate your results. You can create one at <a href="../data/data-graph.html">Data Graphs (Bar, Line and Pie)</a>.</p>
|
||||
<ul>
|
||||
<li>Are the bars the same height?</li>
|
||||
<li>Did you expect them to be?</li>
|
||||
<li>How does the result compare with your guess?</li>
|
||||
</ul>
|
||||
|
||||
|
||||
<h2>Now Let's Estimate Pi</h2>
|
||||
|
||||
<p>Buffon used the results from his experiment with a needle to estimate the value of <span class="times">π</span> (<a href="../numbers/pi.html">Pi</a>). He worked out this formula:</p>
|
||||
<p class="center large"><span class="times">π</span> ≈ <span class="intbl"><em>2L</em><strong>xp</strong></span></p>
|
||||
<p>Where</p>
|
||||
<ul>
|
||||
<li>L is the length of the needle (or match in our case)</li>
|
||||
<li>x is the line spacing (50 mm for us)</li>
|
||||
<li>p is the proportion of needles crossing a line (case B)</li>
|
||||
</ul>
|
||||
<p>We can do it too!</p>
|
||||
|
||||
<div class="example">
|
||||
|
||||
<h3>Example: Sam had a match of length 31 mm, and a 40 mm line spacing and 49 of 100 drops crossed the line</h3>
|
||||
<p>So Sam had:</p>
|
||||
<ul>
|
||||
<li>L = 31</li>
|
||||
<li>x = 40</li>
|
||||
<li>p = 49/100 = 0.49</li>
|
||||
</ul>
|
||||
<p>Substituting these values into the formula, Sam got:</p>
|
||||
<p class="center large"><span class="times">π</span> ≈ <span class="intbl"><em>2 × 31</em><strong>40 × 0.49</strong></span> ≈ 3.16</p>
|
||||
</div>
|
||||
<p>Now it's your turn. Fill in the following table using <b>your own</b> results:</p>
|
||||
|
||||
<table align="center" border="1">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td align="right" height="25">Length of match "<b>L</b>" (mm):</td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right" height="25">Line Spacing "<b>x</b>" (mm):</td>
|
||||
<td style="width:80px;"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right" height="25"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right" height="25"><b>p</b> (the proportion of needles crossing a line):</td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p>And do the calculation:</p>
|
||||
<p class="center large"><span class="times">π</span> ≈ <span class="intbl">
|
||||
<em>2L</em>
|
||||
<strong>xp</strong>
|
||||
</span> ≈ <span class="intbl">
|
||||
<em>2 × _____</em>
|
||||
<strong>_____ × _____</strong>
|
||||
</span> ≈ _____</p>
|
||||
<p>Did you do any better?</p>
|
||||
<p>It won't be exact (because it is a random thing) but it may be close.</p>
|
||||
|
||||
|
||||
<h2>Changing The Subject</h2>
|
||||
|
||||
<p>The next part of this activity is to "<a href="../algebra/equation-formula.html">change the subject</a>" of the formula to work out the perfect value of "p" (the proportion of times the match crosses the line):</p>
|
||||
<div class="tbl">
|
||||
<div class="row"><span class="left">Start with:</span><span class="right"><span class="large"><span class="times">π</span> ≈ 2L/xp</span></span></div>
|
||||
<div class="row"><span class="left">multiply both sides by p:</span><span class="right"><span class="large"><span class="times">π</span>p</span> ≈ <span class="large">2L/x</span></span></div>
|
||||
<div class="row"><span class="left">divide both sides by <span class="times">π</span>:</span><span class="right"><span class="large">p </span>≈ <span class="large">2L/<span class="times">π</span>x</span></span></div>
|
||||
</div>
|
||||
<p>And we get:</p>
|
||||
<p class="center large">p ≈ <span class="intbl">
|
||||
<em>2L</em>
|
||||
<strong><span class="times">π</span>x</strong>
|
||||
</span></p>
|
||||
|
||||
<div class="example">
|
||||
|
||||
<h3>Example: Alex had a match of length 36 mm, and a 50 mm line spacing.</h3>
|
||||
|
||||
<p>So Alex had:</p>
|
||||
<ul>
|
||||
<li>L = 36</li>
|
||||
<li>x = 50</li>
|
||||
</ul>
|
||||
<p>Substituting these values into the formula, Alex got:</p>
|
||||
<p class="center large">p ≈ <span class="intbl">
|
||||
<em>2 × 36</em>
|
||||
<strong><span class="times">π</span> × 50</strong>
|
||||
</span> ≈ 0.46...</p>
|
||||
|
||||
<p>So Alex should expect the match to cross the line (case B) 46 times out of 100</p>
|
||||
</div>
|
||||
<p>Fill in the following table using <b>your own</b> results:</p>
|
||||
|
||||
<table align="center" border="1">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td align="right" height="25">Length of match "L" (mm):</td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right" height="25">Line Spacing "x" (mm):</td>
|
||||
<td style="width:80px;"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right" height="25"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right" height="25">Estimate for <b>p</b> (≈ 2L/<span class="times">π</span>x):</td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p>How close were you?</p>
|
||||
|
||||
|
||||
<h2>Different Size of Match</h2>
|
||||
|
||||
<p>Try repeating the experiment using a different sized match (but not larger then the line spacing!)</p>
|
||||
<ul>
|
||||
<li>Did you get better or worse results?</li>
|
||||
</ul>
|
||||
|
||||
|
||||
<h2>What You Have Done</h2>
|
||||
|
||||
<p>You have (hopefully) had fun running <b>an experiment</b>.</p>
|
||||
<p>You have had some experience with calculations.</p>
|
||||
<p>And you have seen the relationship between theory and reality.</p>
|
||||
<p> </p>
|
||||
|
||||
<div class="related">
|
||||
<a href="coin-grid.html">Activity: Dropping a Coin onto a Grid</a>
|
||||
<a href="pi-approximation.html">Activity: Find an Approximate Value For Pi</a>
|
||||
</div>
|
||||
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@ -1,346 +0,0 @@
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Activity:
|
||||
Clocks and Angles</h1>
|
||||
<p><i>This
|
||||
activity is about <a href="../time-clocks.html">Analog clocks</a> and the angles made by the
|
||||
hands of the clock. You can find out more about angles and how they're measured on the
|
||||
page <a href="../geometry/degrees.html">Degrees
|
||||
(Angles)</a>.</i></p>
|
||||
<p> </p>
|
||||
<h3> What is the angle between the hands of a clock at 1 o'clock?</h3>
|
||||
<p class="center"> <img style="width: 251px; height: 239px;" alt="clock1" src="images/clock1.jpg"></p>
|
||||
<p> At 1 o'clock the minute hand
|
||||
(red) points to the 12 and the
|
||||
hour hand (blue) points to the 1.
|
||||
So we need to find the angle between
|
||||
the 12
|
||||
and the 1.</p>
|
||||
<h3> How many of this angle are there in a complete turn?</h3>
|
||||
<p class="center"> <img style="width: 277px; height: 275px;" alt="clock2" src="images/clock2.jpg"></p>
|
||||
<p> There are 12 of them in a complete turn (360°), so each
|
||||
one
|
||||
must be
|
||||
<strong>360°
|
||||
÷ 12
|
||||
= 30°</strong>
|
||||
</p>
|
||||
<p> So the angle between
|
||||
the
|
||||
hands
|
||||
of a clock at 1 o'clock is
|
||||
<strong>30°</strong>
|
||||
.</p>
|
||||
<div class="center80">
|
||||
<p>
|
||||
<strong>Note:</strong>
|
||||
</p>
|
||||
<ul>
|
||||
<li>It doesn't
|
||||
matter whether we are talking about 1 am or 1
|
||||
pm, the answer is exactly the same for both.<br>
|
||||
<br>
|
||||
</li>
|
||||
<li>The angle between the hands at
|
||||
1 o'clock could also be given as the reflex angle 330°, but we will
|
||||
always give the smaller (acute or obtuse) angle.</li>
|
||||
</ul>
|
||||
</div>
|
||||
<h4> <br>
|
||||
</h4>
|
||||
<h3>What is the angle
|
||||
between the hands of a clock at 2:30? </h3>
|
||||
<p class="center"> <img style="width: 242px; height: 252px;" alt="clock3" src="images/clock3.jpg"></p>
|
||||
<div class="center80">At 2:30 the minute hand
|
||||
(red) points to the 6 and the hour hand
|
||||
(blue) points halfway between the 2 and the 3.</div>
|
||||
<h3> <br>
|
||||
So how many lots of 30° do we have this time?</h3>
|
||||
<p class="center"> <img style="width: 275px; height: 275px;" alt="clock4" src="images/clock4.jpg"></p>
|
||||
<ul>
|
||||
<li>The angle between the 5 and the 6 is
|
||||
<strong>30°</strong>
|
||||
</li>
|
||||
<li>The angle between the 4 and the
|
||||
5 is
|
||||
<strong>30°</strong>
|
||||
</li>
|
||||
<li>The angle between the 3 and the
|
||||
4 is
|
||||
<strong>30°</strong>
|
||||
</li>
|
||||
<li>The remaining angle is
|
||||
<strong>½ × 30° = 15°</strong>
|
||||
</li>
|
||||
</ul>
|
||||
<p> So the angle
|
||||
between the hands of a clock at
|
||||
<strong>2:30 = 30° + 30° + 30° + 15° = 105°</strong>
|
||||
</p>
|
||||
<p> </p>
|
||||
<h2>Your Turn</h2>
|
||||
<h3> Complete the following table (give the smaller angle in each case):<br>
|
||||
</h3>
|
||||
<table cellspacing="2" cellpadding="2" border="1">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td width="70"><strong>Time</strong></td>
|
||||
<td style="text-align: center;" width="70">1:00</td>
|
||||
<td style="text-align: center;" width="70">2:30</td>
|
||||
<td style="text-align: center;" width="70">7:00</td>
|
||||
<td style="text-align: center;" width="70">10:30</td>
|
||||
<td style="text-align: center;" width="70">11:20</td>
|
||||
<td style="text-align: center;" width="70">3:40</td>
|
||||
<td style="text-align: center;" width="70">5:15</td>
|
||||
<td style="text-align: center;" width="70">8:45</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40"><strong>Angle</strong></td>
|
||||
<td style="text-align: center;">30°</td>
|
||||
<td style="text-align: center;">105°</td>
|
||||
<td style="text-align: center;"><br></td>
|
||||
<td style="text-align: center;"><br></td>
|
||||
<td style="text-align: center;"><br></td>
|
||||
<td style="text-align: center;"><br></td>
|
||||
<td style="text-align: center;"><br></td>
|
||||
<td style="text-align: center;"><br></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
<p>Check your answers at the bottom of the page.</p>
|
||||
<p> </p>
|
||||
<h2>More Complicated Times </h2>
|
||||
<p>Finding the angle between the hands of a clock is easy as long
|
||||
as we don't use complicated times. </p>
|
||||
<p>For example finding the angle
|
||||
between the hands at 9:37 is much more difficult. You can try
|
||||
that one if you wish, but it's probably too hard.</p>
|
||||
<h3> <br>
|
||||
Example: At
|
||||
what times is the angle between the hands of a clock equal to
|
||||
30°?</h3>
|
||||
<p> Notice that the question asks for 'times'.
|
||||
There are many possible
|
||||
answers. Some of them are easy to find, others much more difficult.</p>
|
||||
<p>Here are two easy answers:</p>
|
||||
<table align="center" border="0">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><img alt="clock5" src="images/clock5a.jpg"></td>
|
||||
<td><img alt="clock5" src="images/clock5b.jpg"></td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td class="large">1 o'clock</td>
|
||||
<td class="large">11 o'clock</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td colspan="2"><strong>But what about
|
||||
this one?</strong></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td colspan="2" align="center"><img alt="clock6" src="images/clock6.jpg"></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td colspan="2" class="large" align="center">4:15 PM</td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p class="center"> </p>
|
||||
<p> At first glance, it looks like this might be a 30° angle also,
|
||||
but at 4:15, the hour hand has already moved
|
||||
a quarter of the way between the 4 and the 5. </p>
|
||||
<p>So the
|
||||
angle is
|
||||
<strong>30°
|
||||
+ ¼ × 30° = 30° + 7½° = 37½°</strong>
|
||||
.</p>
|
||||
<p> This might be a more accurate answer:</p>
|
||||
<p class="center"> <img style="width: 247px; height: 259px;" alt="clock7" src="images/clock7.jpg"></p>
|
||||
<p> Can you find more 30° angles like this one?</p>
|
||||
<p> </p>
|
||||
<h2>At what times of the day do the hands of a clock lie in a straight
|
||||
line?</h2>
|
||||
<p>
|
||||
<strong>In other words the angle between them is 180°?</strong>
|
||||
</p>
|
||||
<p> One obvious answer is 6 o'clock:</p>
|
||||
<p class="center"> <img style="width: 247px; height: 261px;" alt="clock8" src="images/clock8.jpg"></p>
|
||||
<h3> </h3>
|
||||
<h3>But what other answers could there be?</h3>
|
||||
<p> 9:15 is not correct for a similar reason that 4:15 didn't give us exactly a
|
||||
30° angle ... the hour hand has moved on beyond the 9.</p>
|
||||
<p> This seems to be a very difficult question to answer, but there is an
|
||||
easy way.</p>
|
||||
<h3> How many times between 6:00 am and 6:00 pm do the hands make a
|
||||
straight line?<br>
|
||||
</h3>
|
||||
<p> There must be at least one point time for each hour:</p>
|
||||
<ul>
|
||||
<li>one between 7:00 am and 8:00 am, </li>
|
||||
<li>one between 8:00 am and 9:00 am, </li>
|
||||
<li>one between
|
||||
9:00 am and 10:00 am, </li>
|
||||
<li>etc, up to ...</li>
|
||||
<li>one between 4:00 pm and 5:00 pm</li>
|
||||
</ul>
|
||||
<p> That makes 11 equal parts, and so:</p>
|
||||
<div class="so">12 Hours / 11 </div>
|
||||
<div class="so">= 1 + <sup>1</sup>/<sub>11</sub> hours</div>
|
||||
<div class="so">= 1 hour + <sup>60</sup>/<sub>11</sub> minutes</div>
|
||||
<div class="so">= 1 hour 5 <sup>5</sup>/<sub>11</sub> minutes </div>
|
||||
<div class="so">= 1 hour 5 ½ minutes (approximately)</div>
|
||||
<p>The next time after 6:00 am that the hands make a straight line is about
|
||||
<strong>7:05½ am</strong>
|
||||
:</p>
|
||||
<p class="center"> <img style="width: 247px; height: 261px;" alt="clock9" src="images/clock9.jpg"></p>
|
||||
<h2>Your Turn!</h2>
|
||||
<table cellspacing="2" cellpadding="2" border="1">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td width="70"><strong>Hours</strong></td>
|
||||
<td style="text-align: center;" width="70">7am - 8am</td>
|
||||
<td style="text-align: center;" width="70">8am - 9am</td>
|
||||
<td style="text-align: center;" width="70">9am - 10am</td>
|
||||
<td style="text-align: center;" width="70">10am - 11am</td>
|
||||
<td style="text-align: center;" width="70">11am - 12pm</td>
|
||||
<td style="text-align: center;" width="70">12pm - 1pm</td>
|
||||
<td style="text-align: center;" width="70">1pm - 2pm</td>
|
||||
<td style="text-align: center;" width="70">2pm - 3pm</td>
|
||||
<td style="text-align: center;" width="70">3pm - 4pm</td>
|
||||
<td style="text-align: center;" width="70">4pm - 5pm</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40"><strong>Time</strong></td>
|
||||
<td style="text-align: center;"><strong>7:05½ am</strong></td>
|
||||
<td style="text-align: center;"> </td>
|
||||
<td style="text-align: center;"><br></td>
|
||||
<td style="text-align: center;"><br></td>
|
||||
<td style="text-align: center;"><br></td>
|
||||
<td style="text-align: center;"><br></td>
|
||||
<td style="text-align: center;"><br></td>
|
||||
<td style="text-align: center;"><br></td>
|
||||
<td style="text-align: center;"><br></td>
|
||||
<td style="text-align: center;"><br></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
<p class="center"> You might
|
||||
like to check your answers on the page <a href="../time-clocks-analog-digital.html">Analog
|
||||
and Digital Clocks Animation</a></p>
|
||||
<h2> </h2>
|
||||
<h2>Can you work out the times of the day when the hands of a clock make a
|
||||
right angle?</h2>
|
||||
<p> (Hint: there are 22 of them)</p>
|
||||
<p> </p>
|
||||
<p> </p>
|
||||
<h3> Answer to the earlier exercise:</h3>
|
||||
<table cellspacing="2" cellpadding="2" border="1">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><strong>Time</strong></td>
|
||||
<td style="text-align: center;">1:00</td>
|
||||
<td style="text-align: center;">2:30</td>
|
||||
<td style="text-align: center;">7:00</td>
|
||||
<td style="text-align: center;">10:30</td>
|
||||
<td style="text-align: center;">11:20</td>
|
||||
<td style="text-align: center;">3:40</td>
|
||||
<td style="text-align: center;">5:15</td>
|
||||
<td style="text-align: center;">8:45</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><strong>Angle</strong></td>
|
||||
<td style="text-align: center;">30°</td>
|
||||
<td style="text-align: center;">105°</td>
|
||||
<td style="text-align: center;">150°</td>
|
||||
<td style="text-align: center;">135°</td>
|
||||
<td style="text-align: center;">140°</td>
|
||||
<td style="text-align: center;">130°</td>
|
||||
<td style="text-align: center;">67½°</td>
|
||||
<td style="text-align: center;">7½°</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
<p> </p>
|
||||
<div class="related">
|
||||
<a href="../time-clocks-analog-digital.html">Analog and Digital Clocks Animation</a>
|
||||
<a href="index.html">Activity Index</a>
|
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|
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<title>Activity: Dropping a Coin onto a Grid</title>
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<article id="content" role="main">
|
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<!-- #BeginEditable "Body" -->
|
||||
<h1 class="center">Activity: Dropping a Coin onto a Grid</h1>
|
||||
<div class="center80">
|
||||
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/coin-1750.jpg" alt="coin 1750" height="133" width="240"></p>
|
||||
<p>A few hundred years ago people enjoyed betting on coins tossed on to the floor ... would they cross a line or not?</p>
|
||||
<p>A man (Georges-Louis Leclerc, the <i>Count of Buffon</i>, see "<a href="buffons-needle.html">Buffon's Needle</a>") started thinking about this and worked out how to calculate the <a href="../data/probability.html">probability</a>.</p>
|
||||
<p>Now it is your turn to have a go!</p>
|
||||
</div>
|
||||
<p> </p>
|
||||
<p>You will need:</p>
|
||||
<div class="simple">
|
||||
<table align="center" border="0">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td align="center"><img src="../money/images/currency/us1.gif" style="vertical-align:middle;" alt="us 1 penny" height="47" width="48"><br>
|
||||
<img src="../money/images/currency/eu1.gif" style="vertical-align:middle;" alt="1 euro" height="45" width="44"> <img src="../money/images/currency/in5.gif" style="vertical-align:middle;" alt="india 5 rupee" height="55" width="55"></td>
|
||||
<td>
|
||||
<p>A <b>small round coin</b>,</p>
|
||||
<p>such as a US penny, a 1c Euro or 5 Rupee.</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="center"><a href="images/coin-grid.gif"><img src="images/coin-grid.gif" alt="grid" height="100" width="100" border="0"></a><br>
|
||||
</td>
|
||||
<td>
|
||||
<p>A sheet of paper with a grid of 30 mm squares.</p>
|
||||
<p><input onclick="printImg('images/coin-grid.gif')" value="Print this one" type="button"></p></td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
</div>
|
||||
<h2>Steps</h2>
|
||||
<div class="bigul">
|
||||
<ul>
|
||||
<li>Measure the diameter of your coin: ____ mm
|
||||
|
||||
<ul>
|
||||
<li>a US Penny is 19mm, a 1c Euro is 16.25mm, a Rs 5 is 23mm</li>
|
||||
</ul></li>
|
||||
<li>Also measure the spacing of your grid (it may not print at exactly 30mm): ____ mm</li>
|
||||
<li>Put your sheet of paper on a flat surface such as a table top or the floor.</li>
|
||||
<li>From a height of about 5cm, drop the coin onto the paper and record whether it lands:
|
||||
|
||||
<table border="0">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td>
|
||||
<p><span class="large">A:</span> Completely inside a square (not touching any grid lines)</p>
|
||||
<p><span class="large">B:</span> Crosses one or more lines</p></td>
|
||||
<td><img src="images/coin-grid-1.gif" alt="grid: coin A inside, and coin B on" height="103" width="188"></td>
|
||||
</tr>
|
||||
</tbody></table></li>
|
||||
</ul>
|
||||
</div>
|
||||
<p>The exact height from which you drop the coin is not important, but don't drop it so close to the paper that you are cheating!</p>
|
||||
<p>If the coin rolls completely off the paper, then do not count that turn.</p>
|
||||
<h2>100 Times</h2>
|
||||
<p>Now we will drop the coin 100 times, but first ...</p>
|
||||
<div class="center80">
|
||||
<p class="center larger">... what percentage do you think will land A, or B?</p>
|
||||
</div>
|
||||
<p>Make a guess (estimate) before you begin the experiment:</p>
|
||||
<table align="center" border="1">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td align="right" height="25">Your Guess for "A" (%):</td>
|
||||
<td width="80"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right" height="25">Your Guess for "B" (%):</td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p><b>OK let's begin</b>.</p>
|
||||
<p>Drop the coin 100 times and record <span class="large">A</span> (does not touch a line) or <span class="large">B</span> (touches a line) using <a href="../data/tally-marks.html">Tally Marks</a>:</p>
|
||||
<table width="100%" border="1">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td align="center">Coin lands</td>
|
||||
<td width="50%">Tally</td>
|
||||
<td align="center">Frequency</td>
|
||||
<td align="center">Percentage</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="center">
|
||||
<div class="large">A</div></td>
|
||||
<td height="70"> </td>
|
||||
<td align="center"> </td>
|
||||
<td align="center"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="center">
|
||||
<div class="large">B</div></td>
|
||||
<td height="70"> </td>
|
||||
<td align="center"> </td>
|
||||
<td align="center"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="center"> </td>
|
||||
<td align="right">Totals:</td>
|
||||
<td align="center">100</td>
|
||||
<td align="center">100% </td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p>Now draw a <a href="../data/bar-graphs.html">Bar Graph</a> to illustrate your results. You can create one at <a href="../data/data-graph.html">Data Graphs (Bar, Line and Pie)</a>.</p>
|
||||
<ul>
|
||||
<li>Are the bars the same height?</li>
|
||||
<li>Did you expect them to be?</li>
|
||||
<li>How does the result compare with your guess?</li>
|
||||
</ul>
|
||||
<h2>We Can Calculate What It Should Be ...</h2>
|
||||
<p>Here are some positions for the coin to land so it does <b>not quite touch</b> one of the lines:</p>
|
||||
<p class="center"><img src="images/coin-grid-2.gif" alt="coin grid inside different positions" height="101" width="404"></p>
|
||||
<div class="center80">
|
||||
<p>Place your coin on your grid (like above), and then put a mark on the paper where the center of the coin is (just a rough estimate will do).</p>
|
||||
</div>
|
||||
<table align="center" border="0">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><img src="images/coin-grid-3a.gif" alt="coin grid radius" height="133" width="162"></td>
|
||||
<td>
|
||||
<p>See how the coin's center is one radius <span class="large">r</span> away from a line.</p>
|
||||
<p>(Read about a Circle's <a href="../geometry/circle.html">Radius and Diameter</a>.)</p></td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<div class="center80">
|
||||
<p>Make lots of "center marks" then draw a box connecting them all like below:</p>
|
||||
</div>
|
||||
<p class="center"><img src="images/coin-grid-3.gif" alt="coin grid 30-d" height="133" width="254"><br>
|
||||
<span class="larger">d = Coin's diameter (2 × r)</span></p>
|
||||
<p class="center large">When a coin's <b>center</b> is within the yellow box it won't touch any line.</p>
|
||||
<p>The yellow box is smaller than the grid by <b>two radiuses</b> (= one diameter) of the coin.</p>
|
||||
<p>So what are the areas?</p>
|
||||
<ul>
|
||||
<li>The area of the grid square is 30 × 30 = 900 mm<sup>2</sup></li>
|
||||
<li>The area of the yellow box is (30-d) × (30-d) = (30-d)<sup>2</sup> mm<sup>2</sup></li>
|
||||
</ul>
|
||||
<p>The above calculation was for a 30 mm grid, but we can use <b>S</b> for grid size:</p>
|
||||
<ul>
|
||||
<li>The area of the grid square is S × S = S<sup>2</sup> mm<sup>2</sup></li>
|
||||
<li>The area of the yellow box is (S-d)<sup>2</sup> mm<sup>2</sup></li>
|
||||
</ul>
|
||||
<div class="example">
|
||||
<h3>Example: A 1c Euro (d=16.25 mm) on a 29mm grid (S=29 mm):</h3>
|
||||
<p>Grid Square = 29<sup>2</sup> = 841 mm<sup>2</sup></p>
|
||||
<p>Yellow Box = (29-16.25)<sup>2</sup> = 12.75<sup>2</sup> = 162 mm<sup>2</sup> (to the nearest mm<sup>2</sup>)</p>
|
||||
<p>So you should expect the coin to land <b>not</b> crossing a line of the grid approximately:</p>
|
||||
<p class="center larger">"A" = 162 / 841 = 19.3% of the time</p>
|
||||
<p>And "B" = 100% - 19.3% = 80.7%</p>
|
||||
</div>
|
||||
<p>Now do the calculations for <b>your own</b> grid size and coin size.</p>
|
||||
<table align="center" border="1">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td align="right" height="25">Grid Spacing <span class="large">S</span> (mm):</td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right" height="25">Diameter of Coin <span class="large">d</span> (mm):</td>
|
||||
<td width="80"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right" height="25">Area of Grid Square <span class="large">= S<sup>2</sup></span> (mm<sup>2</sup>):</td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right" height="25">Area of Yellow Box <span class="large">= (S-d)<sup>2</sup></span> (mm<sup>2</sup>):</td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right" height="25">"A" (%):</td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right" height="25">"B" (%):</td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<div class="center80">
|
||||
<p class="center larger">How do these theoretical results compare with your experimental results?</p>
|
||||
</div>
|
||||
<p>It won't be exact (because it is a random thing) but it may be close.</p>
|
||||
<h2>Different Sizes of Coin</h2>
|
||||
<p>Try repeating the experiment using a different sized coin.</p>
|
||||
<ul>
|
||||
<li>First calculate the theoretical value ... how does this affect the values for A and B?</li>
|
||||
<li>Then do the experiment to see how close it gets.</li>
|
||||
</ul>
|
||||
<h2>What You Have Done</h2>
|
||||
<p>You have (hopefully) had fun running <b>an experiment</b>.</p>
|
||||
<p>You have done some geometry, and had some experience calculating areas and probabilities.</p>
|
||||
<p>And you have seen the relationship between theory and reality.</p>
|
||||
<p> </p>
|
||||
<div class="related">
|
||||
<a href="buffons-needle.html">Activity: Buffon's Needle</a>
|
||||
<a href="index.html">Activity Index</a>
|
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
|
||||
<h1 class="center">Coloring (The Four Color
|
||||
Theorem)</h1>
|
||||
<p style="text-align: left;">This activity is about coloring, but don't
|
||||
think it's just kid's stuff. This investigation will lead to one of the
|
||||
most famous theorems of mathematics and some very interesting results.</p>
|
||||
<p style="text-align: left;">Have you ever colored in a pattern and
|
||||
wondered <b>how many colors</b> you need to use?</p>
|
||||
<p style="text-align: left;">There is only one rule</p>
|
||||
<div class="center80">
|
||||
<p class="center larger">Two sections that share a common edge cannot be colored the same!</p>
|
||||
</div>
|
||||
<p style="text-align: left;">Having a common corner is OK, just not an edge.</p>
|
||||
<p style="text-align: left;">Let's start with a simple pattern like a group
|
||||
of nine squares:</p>
|
||||
<p class="center"><img src="images/coloring-1.gif" width="198" height="198" alt="nine square grid" /><br>
|
||||
<input type="button" onClick="printImg('images/coloring-1.gif')" value="Print" /></p>
|
||||
<p style="text-align: left;">How many colors do you need to color the
|
||||
pattern of nine squares?</p>
|
||||
<p style="text-align: left;">You could use nine different colors, but
|
||||
could make do with as few as <b>two</b>:</p>
|
||||
<p class="center"><img src="images/coloring-2.gif" width="196" height="196" alt="nine square grid colored" /></p>
|
||||
<p style="text-align: left;"> </p>
|
||||
<h2 style="text-align: left;">A Little More Complicated</h2>
|
||||
<p style="text-align: left;">How about this one?</p>
|
||||
<p class="center"><img src="images/coloring-3.gif" width="212" height="210" alt="circle grid" />
|
||||
<br>
|
||||
<input type="button" onClick="printImg('images/coloring-3.gif')" value="Print" /></p>
|
||||
<p class="center">How many colors do you need this time?</p>
|
||||
<p class="center larger">Your turn ... try it ... then scroll down to see my answer</p>
|
||||
<p class="center">...</p>
|
||||
<p class="center">...</p>
|
||||
<p align="left">You could use four different colors, or you could make do with just
|
||||
<b>three</b>:</p>
|
||||
<p class="center"><img src="images/coloring-4.gif" width="209" height="210" alt="circle grid colored" /></p>
|
||||
<p>But you couldn't color this pattern with just two colors. Can you see
|
||||
why?</p>
|
||||
<h2>Even More Complicated</h2>
|
||||
<p>Let's try another:</p>
|
||||
<p class="center"><img src="images/coloring-5.gif" width="240" height="239" alt="fancy circle sections" />
|
||||
<br>
|
||||
<input type="button" onClick="printImg('images/coloring-5.gif')" value="Print" /></p>
|
||||
<p>How many colors do you need this time?</p>
|
||||
<p>Nine? Eight? Seven? Six? Five? Four?</p>
|
||||
<p class="center larger">Try it yourself before looking at my answer.</p>
|
||||
<p class="center">...</p>
|
||||
<p class="center">...</p>
|
||||
<table border="0" align="center">
|
||||
<tr>
|
||||
<td><p>I needed four colors to color this pattern.</p>
|
||||
<p>I can change the colors
|
||||
around a bit, but I still need four.</p>
|
||||
<p><span style="font-weight: bold;"> I
|
||||
can't color this pattern with fewer than four colors</span>.</p></td>
|
||||
<td><img src="images/coloring-6.gif" width="179" height="179" alt="fancy circle sections colored" /></td>
|
||||
</tr>
|
||||
</table>
|
||||
<h2>Maps</h2>
|
||||
<p>This could get a bit more interesting if we wanted to color a map.</p>
|
||||
<p><i>A map may not work when a country has two or more separate areas, such as Alaska (part of the US, but with Canada in-between) or Kaliningrad (part of Russia, but also not joined). But let's ignore that here.</i></p>
|
||||
<p>Here
|
||||
is a map of part of Europe, showing nine countries and how they border
|
||||
on each other:<span style="font-weight: bold;"> </span></p>
|
||||
<p class="center"><img src="images/coloring-europe-blank.svg" alt="europe blank" />
|
||||
<br>
|
||||
<input type="button" onClick="printImg('images/coloring-europe-blank.svg')" value="Print" /></p>
|
||||
<p class="center"><span class="larger">Try coloring in the map and see what is the fewest number of colors you
|
||||
need. </span></p>
|
||||
<p>Again, don't look at my answer until you have tried it yourself!</p>
|
||||
<p> </p>
|
||||
<p class="center">...</p>
|
||||
<p> </p>
|
||||
<p class="center">...</p>
|
||||
<p> </p>
|
||||
<p>Here is how I did it. I needed to use four
|
||||
colors:</p>
|
||||
<p class="center"><img src="images/coloring-europe-color.svg" alt="europe colored" /></p>
|
||||
<h2>Four Colors</h2>
|
||||
<p>It seems that any
|
||||
pattern or map can always be colored with <b>four colors</b>.</p>
|
||||
<p>In some cases,
|
||||
like the first example, we could use fewer than four. In many cases we could
|
||||
use a lot more colors if we wanted to, but a maximum of <b>four colors is
|
||||
enough</b>!</p>
|
||||
<p>This result has become one of the most famous theorems of mathematics
|
||||
and is known as <span style="font-weight: bold;">The Four Color
|
||||
Theorem.</span></p>
|
||||
<h3>So why is it important?</h3>
|
||||
<p>It is important because it was first stated in 1852, but was not proved
|
||||
until 1976. For over one hundred and twenty years some of the best
|
||||
mathematical brains in the world were unsuccessful in proving one of
|
||||
the simplest theorems in mathematics. There were many false proofs, and
|
||||
a whole new branch of mathematics - known as <span
|
||||
style="font-weight: bold;">Graph Theory</span> - was developed to try
|
||||
to solve the theorem. But nobody could prove it until in 1976 Appel and
|
||||
Haken proved the theorem with the aid of a computer.</p>
|
||||
<p>Some people think
|
||||
that, although their proof was correct, it was cheating to use a
|
||||
computer. What do you think?</p>
|
||||
<h2>A Map Can Be Changed!</h2>
|
||||
<p>Now look again at our previous two examples:</p>
|
||||
<p class="center"><img src="images/coloring-europe-reshape.svg" alt="europe colored vs circular sections" /></p>
|
||||
<p class="center large">Can you see the similarity between these two diagrams?</p>
|
||||
<p>Imagine the map of European countries was drawn on a piece of rubber
|
||||
that could be stretched. By stretching and skewing the piece of rubber
|
||||
in a certain way, you could end up with the circular diagram.</p>
|
||||
<p class="center larger">We say they are <span
|
||||
style="font-weight: bold;">homeomorphic. </span></p>
|
||||
<p>That's a big word, but a very simple idea: <b>one can become the other</b>.</p>
|
||||
<p>It also forms part
|
||||
of a huge branch of mathematics known as<span
|
||||
style="font-weight: bold;"> Topology. </span></p>
|
||||
<h2>One More: US States</h2>
|
||||
<p>Here is one for you to try on your own ... the "contiguous" (meaning all touching) United States (no Alaska or Hawaii).</p>
|
||||
<p>Can you color it using only 4 colors?</p>
|
||||
<p class="center"><img src="images/coloring-10.gif" width="714" height="425" alt="US contiguous blank" />
|
||||
<br>
|
||||
<input type="button" onClick="printImg('images/coloring-10.gif')" value="Print" /></p>
|
||||
<p> </p>
|
||||
<div class="related">
|
||||
<a href="index.html">Activity Index</a>
|
||||
<a href="../geometry/index.html">Geometry Index</a>
|
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@ -1,353 +0,0 @@
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Activity: Compare Lengths</h1>
|
||||
|
||||
<p>Let's ...</p>
|
||||
<div class="center80">
|
||||
<p class="center larger">Measure lengths in different ways.</p>
|
||||
</div>
|
||||
|
||||
|
||||
<h2 align="left">How Will We Measure?</h2>
|
||||
|
||||
<p>We will use these "measuring tools":</p>
|
||||
|
||||
<table style="border: 0; margin:auto;">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td style="text-align:center;"><img src="images/paperclips.jpg" alt="paperclips" height="92" width="200"></td>
|
||||
<td>Paperclips </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td style="text-align:center;"><img src="../measure/images/handspan.jpg" alt="handspan" height="124" width="200"></td>
|
||||
<td>Your hand</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td style="text-align:center;"><img src="images/string.jpg" alt="string" height="85" width="200"></td>
|
||||
<td>A small piece of string</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td style="text-align:center;"><img src="../measure/images/personal-measure-step.jpg" alt="personal measure step" height="106" width="200"></td>
|
||||
<td>Your steps </td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
|
||||
|
||||
<h2>Gather Items to Measure</h2>
|
||||
|
||||
<p>We want some things to measure! Gather up these items:</p>
|
||||
<ul>
|
||||
<li>A<b> small book</b></li>
|
||||
<li>A<b> large book</b></li>
|
||||
<li>A <b>pencil</b></li>
|
||||
<li>A <b>plate</b></li>
|
||||
<li>A <b>bag</b></li>
|
||||
</ul>
|
||||
<p>Put them all on a <b>Table</b>, which you can also measure!</p>
|
||||
|
||||
<table style="border: 0;">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><img src="images/compare-lengths-4.jpg" alt="back of chair" height="155" width="100"></td>
|
||||
<td>
|
||||
<p>Also measure the <b>height of a chair</b>.</p>
|
||||
<p>And the width and length of the <b>Room</b> you are in.</p></td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p> </p>
|
||||
|
||||
|
||||
<h2>How To Measure</h2>
|
||||
|
||||
<p class="center"><img src="images/compare-lengths-1.jpg" alt="paperclips across" height="148" width="300"><br>
|
||||
This book is 5 paperclips wide</p>
|
||||
<p> </p>
|
||||
<p class="center"><img src="images/compare-lengths-3.jpg" alt="compare lengths paperclips" height="103" width="296"><span style="page-break-before: always"><br>
|
||||
If you don't have enough paperclips, then pick up<br>
|
||||
the ones you started with and use them again</span></p>
|
||||
<p>You can put the chair on its side to measure it.</p>
|
||||
<p> </p>
|
||||
|
||||
<p style="float:right; margin: 10px;"><img src="images/paperclips.jpg" alt="paperclips" height="92" width="200"></p>
|
||||
|
||||
|
||||
<h2>Using Paperclips</h2>
|
||||
|
||||
<p>For each item:</p>
|
||||
<ul>
|
||||
<li>First guess how many Paperclips the length is</li>
|
||||
<li>Then measure it using the Paperclips</li>
|
||||
</ul>
|
||||
|
||||
<table align="center" border="1">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td class="large" width="200">Item</td>
|
||||
<td class="large" align="center" width="120"> Guess </td>
|
||||
<td class="large" align="center" width="120"> Actual </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><i>Example: Small Book</i></td>
|
||||
<td class="larger" align="center"> <i>3</i> </td>
|
||||
<td class="larger" align="center"> <i>4</i></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Small Book</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Large Book</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Plate</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Bag</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Chair (height)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Table (width)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Table (length)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p> </p>
|
||||
<p style="float:right; margin: 10px;"><img src="../measure/images/handspan.jpg" alt="handspan" height="124" width="200"></p>
|
||||
|
||||
|
||||
<h2 style="page-break-before: always">Using Your Hands:</h2>
|
||||
|
||||
<p style="page-break-before: always">First guess how many "hands" are needed, then do the actual measurement:</p>
|
||||
|
||||
<table align="center" border="1">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td class="large" width="200">Item</td>
|
||||
<td class="large" align="center" width="120"> Guess </td>
|
||||
<td class="large" align="center" width="120"> Actual </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Small Book</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Large Book</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Plate</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Bag</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Chair (height)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Table (width)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Table (length)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p> </p>
|
||||
<p style="float:right; margin: 10px;"><img src="images/string.jpg" alt="string" height="85" width="200"></p>
|
||||
|
||||
|
||||
<h2 style="page-break-before: always">Using String:</h2>
|
||||
|
||||
<p style="page-break-before: always">First guess how many lengths of your string are needed, then do the actual measurement:</p>
|
||||
|
||||
<table align="center" border="1">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td class="large" width="200">Item</td>
|
||||
<td class="large" align="center" width="120"> Guess </td>
|
||||
<td class="large" align="center" width="120"> Actual </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Chair (height)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Table (width)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Table (length)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Room (width)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Room (length)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p style="float:right; margin: 10px;"><img src="../measure/images/personal-measure-step.jpg" alt="personal measure step" height="106" width="200"></p>
|
||||
|
||||
|
||||
<h2 style="page-break-before: always">Using Your Steps:</h2>
|
||||
|
||||
<p style="page-break-before: always">Now step out these distances:</p>
|
||||
|
||||
<table align="center" border="1">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td class="large" width="200">Item</td>
|
||||
<td class="large" align="center" width="120"> Guess </td>
|
||||
<td class="large" align="center" width="120"> Actual </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Chair (height)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Table (width)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Table (length)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Room (width)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="40">Room (length)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
|
||||
|
||||
<h2>From Smallest to Largest</h2>
|
||||
|
||||
<p>Lastly, list all the items you measured, from the <b>smallest to largest</b> distance.</p>
|
||||
<p>Example: Small book, Plate, ...</p>
|
||||
|
||||
<table align="center" width="80%" border="1">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td height="180"> </td>
|
||||
</tr>
|
||||
</tbody></table>
|
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<p> </p>
|
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|
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<div class="related">
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<a href="index.html">Activity Index</a>
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Activity: Count to a Billion</h1>
|
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<p class="center"><i>How long does it take to count to a billion?</i></p>
|
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<table align="center" border="0">
|
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<tbody>
|
||||
<tr>
|
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<td><a href="../measure/stopwatches.html"><img src="images/timer-seconds.gif" alt="timer" height="81" width="254" border="0"></a></td>
|
||||
<td> </td>
|
||||
<td>To start, see how long it takes you to count from <b>1 to 100</b> <br>
|
||||
(you can time it using the <a href="../measure/stopwatches.html">Stopwatch</a>).</td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p>It took me 25 seconds to do the counting. <b>Use your own number of seconds in these estimates.</b></p>
|
||||
<p class="center larger">"I can count to 100 in 25 seconds" (put your own time here)</p>
|
||||
<p>So ... how long does it take to count to 1,000? Answer: 10 times 25 seconds, and then double that because it takes longer to say "one-hundred etc...", so that is about 10 minutes.</p>
|
||||
<p class="center"><span class="larger">"To count to <b>1,000</b> takes about 10 minutes"</span></p>
|
||||
<p>How long to 10,000? 10 times 10 minutes is 100 minutes. Plus extra for saying longer numbers and a little rest time is about 2 hours.</p>
|
||||
<p class="center"><span class="larger">"To count to <b>10,000</b> takes about 2 Hours"</span></p>
|
||||
<p>How long to 100,000? 10 times 2 Hours is 20 Hours. But the numbers take longer to say, and you need time to eat and sleep. So maybe 2 <i>very long</i> days.</p>
|
||||
<p class="center"><span class="larger">"To count to <b>100,000</b> is 2 Hard Day's work"</span></p>
|
||||
<p class="center"><i>MrBeast on YouTube counted to 100,000 in 40 hours straight. <br>
|
||||
He later continued on to 200,000 taking 55 hours</i>.</p>
|
||||
<p>How long to 1 Million? 10 times 2 Days is 20 Days. Longer numbers and longer breaks will make that at least 1 month.</p>
|
||||
<p class="center"><span class="larger">"To count to <b>1,000,000</b> is at least 1 month's work"</span></p>
|
||||
<p class="center"> </p>
|
||||
<p><b>Wow! Over a month to count to a Million! But it only took 25 seconds to count to 100.</b></p>
|
||||
<p> </p>
|
||||
<p><i>Back in 2007 Jeremy Harper counted to a million in 89 days at 16 hours a day for charity. He wasn't in a hurry and may have been able to count faster I think!</i></p>
|
||||
<p><i>Note: if you could count at the same speed as you did to 100 it would still take nearly 70 hours.</i></p>
|
||||
<h2>Now Onwards to a Billion</h2>
|
||||
<p>Assuming your voice could hold out and you get really good at saying numbers:</p>
|
||||
<p>How long to 10 Million? 10 times 1 month is 10 months, so about one year. </p>
|
||||
<p class="center"><span class="larger">"To count to <b>10 Million</b> is about 1 Year's work"</span></p>
|
||||
<p>How long to 100 Million? 10 times 1 year is 10 Years (at least).</p>
|
||||
<p class="center"><span class="larger">"To count to <b>100 Million</b> is at least 10 Year's work"</span></p>
|
||||
<p>And now ... how long to 1 Billion? 10 times 10 years is ... 100 years or more!</p>
|
||||
<p class="center"><span class="large">"To count to <b>1 Billion</b> will take over 100 years"</span></p>
|
||||
<p class="center"> </p>
|
||||
<p><i>What?</i> 25 seconds to count to 100, but <b>100 Years</b> to count to a Billion. Amazing.</p>
|
||||
<p>(Now don't get me started on a Trillion!)</p>
|
||||
<p> </p>
|
||||
<p><b>How long would it take you?</b></p>
|
||||
<p> </p>
|
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|
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<div class="related">
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<a href="../numbers/index.html">Numbers Index</a>
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<title>Activity: Counting Cars</title>
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<h1 class="center">Activity: Counting Cars</h1>
|
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|
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<table style="border: 0;">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><img src="images/cars.jpg" alt="cars" height="115" width="200"></td>
|
||||
<td> </td>
|
||||
<td>
|
||||
<p class="larger">Count how many cars pass by on the road.</p>
|
||||
<p>Make sure you do the counting from a safe place!</p></td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p>Choose a time, say from 11:00 to 11:10 in the morning</p>
|
||||
<ul>
|
||||
<li>If you count for 10 minutes, then you can multiply by 6 to find how many cars per hour</li>
|
||||
<li>If you count for 15 minutes, then you can multiply by 4 to find how many cars per hour</li>
|
||||
</ul>
|
||||
|
||||
<table style="border: 0; margin:auto;">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><img src="../data/images/tally-12.svg" alt="tally 12" height="38" width="118"></td>
|
||||
<td>Use <a href="../data/tally-marks.html">Tally Marks</a> to help you keep count</td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p>You can use this form. Write down the time you start, and when you finish.</p>
|
||||
|
||||
<table align="center" width="80%" border="1">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td align="center" width="100"><span class="larger">Start Time</span></td>
|
||||
<td align="center" width="100"><span class="larger">End Time</span></td>
|
||||
<td>
|
||||
<p class="larger">Tally Marks</p></td>
|
||||
<td align="center" width="80"><span class="larger">Total</span></td>
|
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</tr>
|
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<tr>
|
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<td align="center" valign="top">
|
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<p class="larger">__ : __</p></td>
|
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<td align="center" valign="top">
|
||||
<p class="larger">__ : __</p></td>
|
||||
<td height="120"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p class="center larger">Cars Per Hour = ________</p>
|
||||
<p>OK, off you go!</p>
|
||||
<p>Note: If you are in a class, then each of you could choose a different time, and the teacher could put all the results together in a nice <a href="../data/data-graph.html">Line Graph</a>.</p>
|
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<p> </p>
|
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<a href="../data/index.html">Data Index</a>
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|
||||
|
||||
<!-- #BeginEditable "Body" -->
|
||||
|
||||
|
||||
<h1 class="center">Activity: Counting Coins</h1>
|
||||
|
||||
<p class="center">Collecting and counting money!</p>
|
||||
<div style="float: left; margin: 5px;"><img src="../money/images/coin-stack-add.jpg" alt="coin stack add" height="140" width="106"></div>
|
||||
<p><span style="color: #660033; font: 400 17px/27px Verdana, Georgia, helvetica, serif; ">Step 1: </span>Collect all the coins in the house! (I am sure your family won't mind when you say you are learning mathematics.)</p>
|
||||
<p><span style="color: #ff3300; font: 400 17px/27px Verdana, Georgia, helvetica, serif; ">Step 2:</span> Sort them into groups (<b>5c</b> in one group, <b>10c</b> in another, etc)</p>
|
||||
<p><span style="color: #990099; font: 400 17px/27px Verdana, Georgia, helvetica, serif; ">Step 3:</span> Count how many in each group, then calculate the group value.</p>
|
||||
|
||||
<div class="example">
|
||||
<p>Example: You count your <b>5c</b> coins, and find you have <b>15</b> of them.</p>
|
||||
<p class="center larger">5c × 15 = <b>75c</b></p>
|
||||
</div>
|
||||
<p>You can use this form:</p>
|
||||
|
||||
<table align="center" width="50%" border="1">
|
||||
<tbody>
|
||||
<tr style="text-align:center;">
|
||||
<td class="larger">Coin</td>
|
||||
<td class="larger">How Many</td>
|
||||
<td class="larger">Value</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td class="larger"> </td>
|
||||
<td class="larger"> </td>
|
||||
<td class="larger"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td class="larger"> </td>
|
||||
<td class="larger"> </td>
|
||||
<td class="larger"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td class="larger"> </td>
|
||||
<td class="larger"> </td>
|
||||
<td class="larger"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td class="larger"> </td>
|
||||
<td class="larger"> </td>
|
||||
<td class="larger"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td class="larger"> </td>
|
||||
<td class="larger"> </td>
|
||||
<td class="larger"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td class="larger"> </td>
|
||||
<td class="larger"> </td>
|
||||
<td class="larger"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td class="larger"> </td>
|
||||
<td class="larger"> </td>
|
||||
<td class="larger"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td colspan="2" align="right">
|
||||
<p class="larger">Total Value:</p></td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p><span style="color: #006600; font: 400 17px/27px Verdana, Georgia, helvetica, serif; ">Step 4</span>: Add up all the group totals so you know how much money you have!</p>
|
||||
|
||||
<table style="border: 0; margin:auto;">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td style="text-align:center;">
|
||||
<p class="larger">Tell everyone what a good job you did ...</p>
|
||||
<p class="larger">... and ask if you can keep the money!</p></td>
|
||||
<td><img src="../money/images/coin-stack.jpg" alt="coin stack" height="100" width="75"></td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p> </p>
|
||||
<p>Tip: If you make stacks of coins <b>exactly 10 high</b> it is easier to calculate the totals.</p>
|
||||
<p> </p>
|
||||
|
||||
<div class="related">
|
||||
<a href="../money/index.html">Money Index</a>
|
||||
</div>
|
||||
<!-- #EndEditable -->
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|
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<div id="copyrt">Copyright © 2022 Rod Pierce</div>
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@ -1,310 +0,0 @@
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<head>
|
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<!-- #BeginEditable "doctitle" -->
|
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<title>Activity: Currency Conversion</title>
|
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</div>
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<div id="content" role="main"><!-- #BeginEditable "Body" -->
|
||||
<h1 align="center">Activity: Currency Conversion</h1>
|
||||
<p> In this activity, you will learn how to convert money between different currencies using an exchange rate table and a calculator.</p>
|
||||
<p>You will need </p>
|
||||
<ul>
|
||||
<li>a calculator (or use <a href="../scientific-calculator.html">this calculator</a>)</li>
|
||||
<li>A current list of exchange rates (look up on the internet)</li>
|
||||
</ul>
|
||||
<h2>Vacation!</h2>
|
||||
<p>The Brown family are going to visit many different countries on their vacation. </p>
|
||||
<p>From their home in <b>New York</b> they travel to <b>Toronto</b> (Canada), <b>London</b> (England), <b>Rome</b> (Italy), <b>New Delhi</b> (India), <b>Tokyo</b> (Japan) and <b>Sydney</b> (Australia), before returning home across the Pacific. </p>
|
||||
<p>The route is shown on the following map:</p>
|
||||
<p align="center"><img src="images/currencies.gif" width="710" height="370" alt="currencies journey" /></p>
|
||||
|
||||
<p>Mr. Brown uses his credit card to change money from USD ($US) to the local currency in each of the locations they visit.</p>
|
||||
<p>Because currencies change all the time, the amount of money Mr. Brown receives in each local currency will change from day to day. But the following table (old data) will give you an idea of how currencies are converted:</p>
|
||||
<table border="1" align="center" cellpadding="2"
|
||||
cellspacing="2">
|
||||
<tbody>
|
||||
<tr>
|
||||
|
||||
<td>Currency</td>
|
||||
<td style="text-align: center;">Code</td>
|
||||
<td style="text-align: center;">USD/1 unit</td>
|
||||
<td style="text-align: center;">Units/ 1 USD</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Australian Dollar</td>
|
||||
|
||||
<td style="text-align: center;">AUD</td>
|
||||
<td style="text-align: center;">0.9612</td>
|
||||
<td style="text-align: center;">1.0405</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Canadian Dollar</td>
|
||||
<td style="text-align: center;">CAD</td>
|
||||
|
||||
<td style="text-align: center;">0.9788</td>
|
||||
<td style="text-align: center;">1.0219</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Euro</td>
|
||||
<td style="text-align: center;">EUR</td>
|
||||
<td style="text-align: center;">1.3065</td>
|
||||
|
||||
<td style="text-align: center;">0.7655</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>British Pound</td>
|
||||
<td style="text-align: center;">GBP</td>
|
||||
<td style="text-align: center;">1.5553</td>
|
||||
<td style="text-align: center;">0.6431</td>
|
||||
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Indian Rupee</td>
|
||||
<td style="text-align: center;">INR</td>
|
||||
<td style="text-align: center;">0.02174</td>
|
||||
<td style="text-align: center;">46.1225</td>
|
||||
</tr>
|
||||
|
||||
<tr>
|
||||
<td>Japanese Yen</td>
|
||||
<td style="text-align: center;">JPY</td>
|
||||
<td style="text-align: center;">0.011916</td>
|
||||
<td style="text-align: center;">83.9337</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
|
||||
</table>
|
||||
<p>You will notice that there are two sets of figures for each country – the USD/ 1 unit and the Units/ 1 USD. This is because you get one rate for changing from $US to the foreign currency and a different rate for changing back from the foreign currency to the $US. This is how the banks make their money.</p>
|
||||
<p>Note The banks also make a commission on every transaction, so they make even more money out of us! But to keep things simple we will ignore that.</p>
|
||||
<p>So which figure should you use?</p>
|
||||
<p>The USD/ 1 unit figure tells us how to convert one unit of the foreign currency to the US currency. The Units/ 1 USD figure tells us how to convert one unit of the US currency to the foreign currency.</p>
|
||||
<h2>Your Turn</h2>
|
||||
<p>Find today's current exchange rates! Use the internet to find them and fill them in:</p>
|
||||
<table border="1" align="center" cellpadding="2"
|
||||
cellspacing="2">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td>Currency</td>
|
||||
<td style="text-align: center;">Code</td>
|
||||
<td style="text-align: center;">USD/1 unit</td>
|
||||
<td style="text-align: center;">Units/ 1 USD</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Australian Dollar</td>
|
||||
<td style="text-align: center;">AUD</td>
|
||||
<td style="text-align: center;"> </td>
|
||||
<td style="text-align: center;"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Canadian Dollar</td>
|
||||
<td style="text-align: center;">CAD</td>
|
||||
<td style="text-align: center;"> </td>
|
||||
<td style="text-align: center;"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Euro</td>
|
||||
<td style="text-align: center;">EUR</td>
|
||||
<td style="text-align: center;"> </td>
|
||||
<td style="text-align: center;"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>British Pound</td>
|
||||
<td style="text-align: center;">GBP</td>
|
||||
<td style="text-align: center;"> </td>
|
||||
<td style="text-align: center;"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Indian Rupee</td>
|
||||
<td style="text-align: center;">INR</td>
|
||||
<td style="text-align: center;"> </td>
|
||||
<td style="text-align: center;"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Japanese Yen</td>
|
||||
<td style="text-align: center;">JPY</td>
|
||||
<td style="text-align: center;"> </td>
|
||||
<td style="text-align: center;"> </td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
<h2>Let's look at an example </h2>
|
||||
<p>Mr. Brown converts USD500 to Canadian dollars. How much does he receive?</p>
|
||||
<p>We are converting to Canadian dollars, so we use the second row of the table We are converting from the US currency to the Canadian currency, so we should use the Units/ 1 USD column:</p>
|
||||
<table border="1" align="center" cellpadding="2"
|
||||
cellspacing="2">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td>Currency</td>
|
||||
<td style="text-align: center;">Code</td>
|
||||
<td style="text-align: center;">USD/1 unit</td>
|
||||
<td style="text-align: center;">Units/ 1 USD</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Australian Dollar</td>
|
||||
<td style="text-align: center;">AUD</td>
|
||||
<td style="text-align: center;">0.9612</td>
|
||||
<td style="text-align: center;">1.0405</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Canadian Dollar</td>
|
||||
<td style="text-align: center;">CAD</td>
|
||||
<td style="text-align: center;">0.9788</td>
|
||||
<td class="hi" style="text-align: center;">1.0219</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Euro</td>
|
||||
<td style="text-align: center;">EUR</td>
|
||||
<td style="text-align: center;">1.3065</td>
|
||||
<td style="text-align: center;">0.7655</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>British Pound</td>
|
||||
<td style="text-align: center;">GBP</td>
|
||||
<td style="text-align: center;">1.5553</td>
|
||||
<td style="text-align: center;">0.6431</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Indian Rupee</td>
|
||||
<td style="text-align: center;">INR</td>
|
||||
<td style="text-align: center;">0.02174</td>
|
||||
<td style="text-align: center;">46.1225</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Japanese Yen</td>
|
||||
<td style="text-align: center;">JPY</td>
|
||||
<td style="text-align: center;">0.011916</td>
|
||||
<td style="text-align: center;">83.9337</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
<p>So he receives USD500 × 1.0219 = CAD510.95</p>
|
||||
<h2>Your Turn</h2>
|
||||
<p>How much will Mr. Brown receive if he changes </p>
|
||||
<ul>
|
||||
<li>USD1000 to British pounds? </li>
|
||||
<li>USD650 to Euro?</li>
|
||||
<li>USD400 to Indian Rupees? </li>
|
||||
</ul>
|
||||
<h2>Another example</h2>
|
||||
<p>When the Brown family arrives back in the US from Australia, Mr. Brown finds that he has AUD220 left over and wants to change it back into USD. How much does he receive?</p>
|
||||
<p>We are converting from Australian dollars, so we use the first row of the table We are converting from the Australian currency to the US currency, so we should use the USD/ 1 unit column:</p>
|
||||
<table border="1" align="center" cellpadding="2"
|
||||
cellspacing="2">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td>Currency</td>
|
||||
<td style="text-align: center;">Code</td>
|
||||
<td style="text-align: center;">USD/1 unit</td>
|
||||
<td style="text-align: center;">Units/ 1 USD</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Australian Dollar</td>
|
||||
<td style="text-align: center;">AUD</td>
|
||||
<td class="hi" style="text-align: center;">0.9612</td>
|
||||
<td style="text-align: center;">1.0405</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Canadian Dollar</td>
|
||||
<td style="text-align: center;">CAD</td>
|
||||
<td style="text-align: center;">0.9788</td>
|
||||
<td style="text-align: center;">1.0219</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Euro</td>
|
||||
<td style="text-align: center;">EUR</td>
|
||||
<td style="text-align: center;">1.3065</td>
|
||||
<td style="text-align: center;">0.7655</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>British Pound</td>
|
||||
<td style="text-align: center;">GBP</td>
|
||||
<td style="text-align: center;">1.5553</td>
|
||||
<td style="text-align: center;">0.6431</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Indian Rupee</td>
|
||||
<td style="text-align: center;">INR</td>
|
||||
<td style="text-align: center;">0.02174</td>
|
||||
<td style="text-align: center;">46.1225</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Japanese Yen</td>
|
||||
<td style="text-align: center;">JPY</td>
|
||||
<td style="text-align: center;">0.011916</td>
|
||||
<td style="text-align: center;">83.9337</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
|
||||
<p>So he receives AUD220 × 0.9612 = USD211.46</p>
|
||||
<h2>Your Turn</h2>
|
||||
<p>Mr. Brown also has some other money left over. How much will he receive in USD for: </p>
|
||||
<ul>
|
||||
<li>2,000 Yen? </li>
|
||||
<li>3,500 Indian Rupees? </li>
|
||||
<li>70 Euro? </li>
|
||||
</ul>
|
||||
<p> </p>
|
||||
<div class="related">
|
||||
<a href="../money/money-master.html">Money Master</a> <a href="../money/currency.html">Currencies</a> <a href="index.html">Activities Index</a>
|
||||
</div>
|
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
|
||||
<h1 class="center">Activity: Day of the Week Born</h1>
|
||||
<p> </p>
|
||||
<p>Conduct a Survey to find if there is any truth behind this Rhyme:</p>
|
||||
<div class="indent50px"><i>Monday's child is fair of face,<br />
|
||||
Tuesday's child is full of grace,<br />
|
||||
Wednesday's child is full of woe,<br />
|
||||
Thursday's child has far to go.<br />
|
||||
Friday's child is loving and giving,<br />
|
||||
Saturday's child works hard for a living,<br />
|
||||
But the child born on the Sabbath Day,<br />
|
||||
Is fair and wise and good in every way.</i></div>
|
||||
<p>Use the <a href="../games/dayofweek.html">Day of the Week</a> application to find which day of the week each person was born.</p>
|
||||
<p> </p>
|
||||
<p>Go through each step of<a href="../data/survey-conducting.html"> Conducting a Survey</a>: </p>
|
||||
<ul>
|
||||
<li>Step one: create the questions</li>
|
||||
<li>Step two: ask the questions</li>
|
||||
<li>Step three: tally the results</li>
|
||||
<li>Step four: present the results</li>
|
||||
</ul>
|
||||
<p>It should be very interesting asking the questions ... have fun!</p>
|
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<p> </p>
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<a href="index.html">Activity Index</a>
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<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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<meta http-equiv="content-type" content="text/html; charset=UTF-8">
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<!-- #BeginEditable "doctitle" -->
|
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<title>Activity: Design a Deck</title>
|
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<meta name="Description" content="Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.">
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<!-- #BeginEditable "Body" -->
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||||
<h1 class="center">Activity: Design a Deck</h1>
|
||||
|
||||
<p>Alex wants to build a deck for the house.</p>
|
||||
<p>It should be shaped about like this:</p>
|
||||
<p class="center"><img src="images/deck-1.gif" alt="deck 4m x 2m" height="152" width="291"></p>
|
||||
<p>(Choose a different size if you want, maybe to fit a place outside your home?)</p>
|
||||
<p>Alex can buy some beautiful hardwood, but it is only available in the following sizes:</p>
|
||||
<ul>
|
||||
<li>Width: 90 mm</li>
|
||||
<li>Lengths: 3.0 m, 3.6 m, 4.2 m, 4.8 m, 6.0 m</li>
|
||||
</ul>
|
||||
<p>Please tell Alex how many of each length he will need.</p>
|
||||
<p class="large">Note: Be Practical! Think about actually using real boards to make this deck.</p>
|
||||
<ul>
|
||||
<li>Alex can cut the boards into smaller lengths, but <b>not into smaller widths</b>.</li>
|
||||
<li>Tell Alex if the shape he wants should be changed to fit the boards (but not by too much or it won't fit the house!)</li>
|
||||
<li>You should order extra boards in case some are bad quality, or Alex makes a mistake when cutting.</li></ul>
|
||||
<p>Fill out how many of each length are needed:</p>
|
||||
<ul>
|
||||
<li>3.0 m:</li>
|
||||
<li>3.6 m:</li>
|
||||
<li>4.2 m:</li>
|
||||
<li>4.8 m:</li>
|
||||
<li>6.0 m:</li></ul>
|
||||
<ul>
|
||||
</ul>
|
||||
|
||||
|
||||
<h2>Extension</h2>
|
||||
|
||||
<p>Another practical thing: you don't want cuts to line up, so having two boards of 3.0m exactly next to each other is bad.</p>
|
||||
<p>Also try for a different size of deck ... maybe a new and interesting shape?</p>
|
||||
<p> </p>
|
||||
|
||||
<div class="related">
|
||||
<a href="../geometry/index.html">Geometry Index</a>
|
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<a href="index.html">Activities Index</a>
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<div id="copyrt">Copyright © 2022 Rod Pierce</div>
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@ -1,289 +0,0 @@
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<!-- Mirrored from www.mathsisfun.com/activity/dice-experiment-1.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:42:02 GMT -->
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<!-- #BeginEditable "doctitle" -->
|
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<title>Activity: An Experiment with a Die</title>
|
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<meta name="Description" content="Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.">
|
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<!-- #BeginEditable "Body" -->
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|
||||
|
||||
<h1 class="center">Activity: An Experiment with a Die</h1>
|
||||
|
||||
<table style="border: 0; margin:auto;">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td>
|
||||
<p>You will need:</p>
|
||||
<ul>
|
||||
<li>A single <a href="../geometry/fair-dice.html">die</a></li>
|
||||
</ul></td>
|
||||
<td> </td>
|
||||
<td><img src="../geometry/images/single-die.svg" alt="single die" height="104" width="113"></td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<div class="words">
|
||||
|
||||
<h3>Interesting point</h3>
|
||||
<p>Many people think that one of these cubes is called "a dice". But no!</p>
|
||||
<p>The <b>plural is dice</b>, but the singular is <b>die</b>. (i.e. 1 die, 2 dice.)</p>
|
||||
</div>
|
||||
<p>The common die has six faces:</p>
|
||||
<p class="center"><img src="images/dice2.gif" alt="dice faces 1 to 6" height="61" width="297"></p>
|
||||
<p class="center">We usually call the faces 1, 2, 3, 4, 5 and 6.</p>
|
||||
|
||||
|
||||
<h2>High, Low, and Most Likely</h2>
|
||||
|
||||
|
||||
<p><b>Question: If you roll a die:</b></p>
|
||||
<ul>
|
||||
<li>1. What is the <b>least</b> possible score?</li>
|
||||
<li>2. What is the <b>greatest</b> possible score?</li>
|
||||
<li>3. What do you think is the <b>most likely</b> score?</li>
|
||||
</ul>
|
||||
<div class="center80">
|
||||
<p>The first two questions are quite easy to answer:</p>
|
||||
<ul>
|
||||
<li>1. The <b>least</b> possible score must be <b>1</b></li>
|
||||
<li>2. The <b>greatest</b> possible score must be <b>6</b></li>
|
||||
<li>3. The <b>most likely</b> score is ... ???</li>
|
||||
</ul>
|
||||
<p>Are they all just as likely? Or will some happen more often?</p>
|
||||
</div>
|
||||
<p>Let us see which is most likely ...</p>
|
||||
|
||||
|
||||
<h2>The Experiment</h2>
|
||||
|
||||
<div class="center80">
|
||||
<p class="center larger"><b>Throw</b> a die 60 times,<br>
|
||||
<b>record</b> the scores in a tally table.</p>
|
||||
</div>
|
||||
<p>You can record the results in this table using <a href="../data/tally-marks.html">tally marks</a>:</p>
|
||||
|
||||
<table align="center" cellpadding="5" border="1">
|
||||
<tbody>
|
||||
<tr style="text-align:center;">
|
||||
<td class="larger"> Score</td>
|
||||
<td class="larger" width="300">Tally</td>
|
||||
<td class="larger">Frequency</td>
|
||||
</tr>
|
||||
<tr style="text-align:center;">
|
||||
<td class="larger">1</td>
|
||||
<td> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr style="text-align:center;">
|
||||
<td class="larger">2</td>
|
||||
<td style="width:300px;"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr style="text-align:center;">
|
||||
<td class="larger">3</td>
|
||||
<td style="width:300px;"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr style="text-align:center;">
|
||||
<td class="larger">4</td>
|
||||
<td style="width:300px;"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr style="text-align:center;">
|
||||
<td class="larger">5</td>
|
||||
<td style="width:300px;"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr style="text-align:center;">
|
||||
<td class="larger">6</td>
|
||||
<td style="width:300px;"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr style="text-align:center;">
|
||||
<td> </td>
|
||||
<td align="right" width="300">Total Frequency = </td>
|
||||
<td class="larger">60</td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p class="largest">OK, Go!</p>
|
||||
<p class="center">... ...</p>
|
||||
<p class="center">... ...</p>
|
||||
<p class="center">... ...</p>
|
||||
<p style="float:left; margin: 0 10px 5px 0;"><img src="images/die-results-empty.gif" alt="die results empty" height="208" width="300"></p>
|
||||
<p><b>Finished ...?</b></p>
|
||||
<p>Now draw a bar graph to illustrate your results.</p>
|
||||
<p>You can make your own.</p>
|
||||
<p>Or you can use <a href="../data/data-graph.html">Data Graphs (Bar, Line and Pie)</a> then print it out.</p>
|
||||
<div style="clear:both"></div>
|
||||
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/die-results.gif" alt="die results" height="152" width="220"></p>
|
||||
<p>You may get something like this:</p>
|
||||
<div style="clear:both"></div>
|
||||
<div class="center80">
|
||||
<ul>
|
||||
<li>Are the bars all the same height?</li>
|
||||
<li>If not ... why not?</li>
|
||||
</ul>
|
||||
</div>
|
||||
|
||||
|
||||
<h2>60 Throws</h2>
|
||||
|
||||
<p>OK, why did I ask you to make <b>60</b> throws? Well, 6 throws is not enough for good results. 600 will give good results but is a lot of work. So 60 seems OK, and is also <b>10 lots of 6</b>.</p>
|
||||
<p>So we should <b>expect</b> <b>10</b> of each number, like this:</p>
|
||||
<p class="center"><img src="images/die-results-theory.gif" alt="die results theory" height="207" width="300"><br>
|
||||
<br>
|
||||
Those are the <b>theoretical</b> values,<br>
|
||||
as opposed to the <b>experimental</b> ones you got from your <b>experiment</b>!<br>
|
||||
</p>
|
||||
<div class="center80">
|
||||
<p class="center larger">How do those theoretical results compare with your experimental results?</p>
|
||||
</div>
|
||||
<p>This graph and your graph should be <b>similar</b>, but they are not likely to be exactly the same, as your experiment relied on <b>chance</b>, and the number of times you did it was fairly small.</p>
|
||||
<p>If you did the experiment a very large number of times, you would get results much closer to the theoretical ones.</p>
|
||||
|
||||
|
||||
<h2>Questions</h2>
|
||||
|
||||
<ul>
|
||||
<div class="bigul">
|
||||
<li>Which face came up most often? ____</li>
|
||||
<li>Which face came up least often? ____</li>
|
||||
<li>Do you think you would get the same results if you did this again? Yes / No</li>
|
||||
</div>
|
||||
</ul>
|
||||
<div class="center80">
|
||||
<p class="larger">An experiment gives results.</p>
|
||||
<p class="larger">When done again it may give <b>different</b> results!</p>
|
||||
<p class="larger">So it is important to know when results are <b>good quality</b>, or just <b>random</b>.</p>
|
||||
</div>
|
||||
|
||||
|
||||
<h2>Probability</h2>
|
||||
|
||||
<p>On the page <a href="../data/probability.html">Probability</a> you will find a formula:</p>
|
||||
<p class="center">Probability of an event happening = <span class="intbl"><em>Number of ways it can happen</em><strong>Total number of outcomes</strong></span></p>
|
||||
|
||||
<div class="example">
|
||||
|
||||
<h3>Example: Probability of a 2</h3>
|
||||
<p>We know there are 6 possible outcomes.</p>
|
||||
<p>And there is only 1 way to get a 2.</p>
|
||||
<p>So the probability of getting 2 is:</p>
|
||||
<p class="center larger">Probability of a 2 = <span class="intbl"><em>1</em><strong>6</strong></span></p>
|
||||
</div>
|
||||
<p>Doing that for each score gets us:</p>
|
||||
|
||||
<table style="border: 0; margin:auto;">
|
||||
<tbody>
|
||||
<tr style="text-align:center;">
|
||||
<td style="width:100px;"> Score</td>
|
||||
<td style="width:100px;">Probability</td>
|
||||
</tr>
|
||||
<tr style="text-align:center;">
|
||||
<td>1</td>
|
||||
<td>1/6</td>
|
||||
</tr>
|
||||
<tr style="text-align:center;">
|
||||
<td>2</td>
|
||||
<td>1/6</td>
|
||||
</tr>
|
||||
<tr style="text-align:center;">
|
||||
<td>3</td>
|
||||
<td>1/6</td>
|
||||
</tr>
|
||||
<tr style="text-align:center;">
|
||||
<td>4</td>
|
||||
<td>1/6</td>
|
||||
</tr>
|
||||
<tr style="text-align:center;">
|
||||
<td>5</td>
|
||||
<td>1/6</td>
|
||||
</tr>
|
||||
<tr style="text-align:center;">
|
||||
<td>6</td>
|
||||
<td>1/6</td>
|
||||
</tr>
|
||||
<tr style="text-align:center;">
|
||||
<td> </td>
|
||||
<td class="larger">Total = 1</td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p class="center larger">The sum of all the probabilities is <b>1</b></p>
|
||||
<div class="center80">
|
||||
<p class="center">For any experiment:</p>
|
||||
<p class="center">The sum of the probabilities of <b>all</b> possible outcomes is always equal to <b>1</b></p>
|
||||
</div>
|
||||
<p> </p>
|
||||
|
||||
<div class="related">
|
||||
<a href="dice-experiment-2.html">An Experiment with 2 Dice</a>
|
||||
<a href="../data/index.html">Data Index</a>
|
||||
<a href="../geometry/fair-dice.html">Fair Dice</a>
|
||||
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|
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<div id="copyrt">Copyright © 2022 Rod Pierce</div>
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<!-- #BeginEditable "Body" -->
|
||||
<h1 class="center">Activity: An Experiment with Dice</h1>
|
||||
|
||||
<p>Let's throw two dice and add the scores ...</p>
|
||||
<table align="center" border="0">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td>
|
||||
<p>You will need:</p>
|
||||
<ul>
|
||||
<li>Two <a href="../geometry/fair-dice.html">dice</a></li>
|
||||
</ul></td>
|
||||
<td width="50"> </td>
|
||||
<td><img src="../geometry/images/pair-dice2.svg" alt="pair dice"></td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<div class="words">
|
||||
<h3>Interesting point</h3>
|
||||
<p>Many people think that one of these cubes is called "a dice". But no!</p>
|
||||
<p>The <b>plural is dice</b>, but the singular is <b>die</b>: i.e. 1 die, 2 dice.</p>
|
||||
</div>
|
||||
<p>The common die has six faces:</p>
|
||||
<p class="center"><img src="images/dice2.gif" alt="dice faces 1 to 6" height="61" width="297"></p>
|
||||
<p class="center">We usually call the faces 1, 2, 3, 4, 5 and 6.</p>
|
||||
|
||||
<h2>Throwing Two Dice and Adding the Scores ...</h2>
|
||||
<div class="example">
|
||||
<p>Example: when one die shows 2 and the other shows 6 the total score is 2 + 6 = 8</p>
|
||||
<p class="center"><img src="images/dice3.gif" alt="dice 2 + 6 = 8" height="59" width="216"></p>
|
||||
</div>
|
||||
<p class="large">Question: Can you get a total of <b>8</b> any other way?</p>
|
||||
<div class="dotpoint">
|
||||
<p>What about <b>6 + 2 = 8</b> (the other way around), is that a different way?</p>
|
||||
<p>Yes! Because the two dice are different.</p>
|
||||
<div class="example">
|
||||
<p>Example: imagine one die is colored red and the other is colored blue.</p>
|
||||
<p>There are two possibilities:</p>
|
||||
<p class="center"><img src="images/dice4.gif" alt="2 blue + 6 red = 8 and 2 red + 6 blue = 8 " style="max-width:100%" height="81" width="383"></p>
|
||||
|
||||
<p>So 2 + 6 and 6 + 2 are different.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="dotpoint">
|
||||
<p>And you can get <b>8</b> with other numbers, such as <b>3 + 5 = 8</b> and <b>4 + 4 = 8</b></p>
|
||||
</div>
|
||||
<h2>High, Low, and Most Likely</h2>
|
||||
<p>Before we start, let's think about what might happen.</p>
|
||||
<p><b>Question: If you throw 2 dice together and add the two scores: </b></p>
|
||||
<ul>
|
||||
<li>1. What is the <b>least</b> possible total score?</li>
|
||||
<li>2. What is the <b>greatest</b> possible total score?</li>
|
||||
<li>3. What do you think is the <b>most likely</b> total score?</li>
|
||||
</ul>
|
||||
<div class="center80">
|
||||
<p>The first two questions are quite easy to answer:</p>
|
||||
<ul>
|
||||
<li>1. The <b>least</b> possible total score must be 1 + 1 = <b>2 </b></li>
|
||||
<li>2. The <b>greatest</b> possible total score must be 6 + 6 = <b>12</b></li>
|
||||
<li>3. The <b>most likely</b> total score is ... ???</li>
|
||||
</ul>
|
||||
<p>Are they all just as likely? Or will some happen more often?</p>
|
||||
</div>
|
||||
<p>To help answer the third question let us try an experiment.</p>
|
||||
<h2>The Experiment</h2>
|
||||
<div class="center80">
|
||||
<p class="center larger"><b>Throw</b> two dice together 108 times, <br>
|
||||
<b>add</b> the scores together each time, <br>
|
||||
<b>record</b> the scores in a tally table.</p>
|
||||
</div>
|
||||
<p>Why 108? That seems a strange number to choose. I will explain later.</p>
|
||||
<p>You can record the results in this table using <a href="../data/tally-marks.html">tally marks</a>:</p>
|
||||
<table align="center" cellpadding="5" border="1">
|
||||
<tbody>
|
||||
<tr align="center">
|
||||
<td class="larger">Added<br>
|
||||
Scores</td>
|
||||
<td class="larger" width="300">Tally</td>
|
||||
<td class="larger">Frequency</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td class="larger">2</td>
|
||||
<td width="300"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td class="larger">3</td>
|
||||
<td width="300"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td class="larger">4</td>
|
||||
<td width="300"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td class="larger">5</td>
|
||||
<td width="300"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td class="larger">6</td>
|
||||
<td width="300"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td class="larger">7</td>
|
||||
<td width="300"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td class="larger">8</td>
|
||||
<td width="300"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td class="larger">9</td>
|
||||
<td width="300"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td class="larger">10</td>
|
||||
<td width="300"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td class="larger">11</td>
|
||||
<td width="300"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td class="larger">12</td>
|
||||
<td width="300"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td> </td>
|
||||
<td align="right" width="300">Total Frequency = </td>
|
||||
<td class="larger">108</td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p class="largest">OK, Go!</p>
|
||||
<p class="center">... ...</p>
|
||||
<p class="center">... ...</p>
|
||||
<p class="center"> </p>
|
||||
<p style="float:left; margin: 0 10px 5px 0;"><img src="images/die-results-empty.gif" alt="die results empty" height="208" width="300"></p>
|
||||
<p><b>Finished ...? </b></p>
|
||||
<p>Now draw a bar graph to illustrate your results.</p>
|
||||
<p>You can make your own.</p>
|
||||
<p>Or you can use <a href="../data/data-graph.html">Data Graphs (Bar, Line and Pie)</a> then print it out.</p>
|
||||
<div style="clear:both"></div>
|
||||
<p style="float:right; margin: 0 0 5px 10px;"><img src="images/dice-results-thumb.gif" alt="dice results thumb" height="137" width="200"></p>
|
||||
<p>You may get something like this:</p>
|
||||
<div style="clear:both"></div>
|
||||
<div class="center80">
|
||||
<ul>
|
||||
<li>Are the bars all about the same height?</li>
|
||||
<li>If not ... why not?</li>
|
||||
</ul>
|
||||
</div>
|
||||
<h2>So Why Did We Get That Shape?</h2>
|
||||
<p>The explanation is simple:</p>
|
||||
<ul>
|
||||
<div class="bigul">
|
||||
<li>There is only <b>one</b> way to get a total of <b>2</b> (1 + 1),</li>
|
||||
<li>but there are <b>six</b> ways of getting a total of <b>7</b> (1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2 and 6 + 1)</li>
|
||||
</div>
|
||||
</ul>
|
||||
<p>Here is a table of all possibile outcomes, and the totals. I have also shown what adds to 7 in <b>bold</b>.</p>
|
||||
<table align="center" border="0">
|
||||
<tbody>
|
||||
<tr align="center">
|
||||
<td> </td>
|
||||
<td> </td>
|
||||
<td colspan="6"><b>Score on One Die</b></td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td width="50"> </td>
|
||||
<td width="50"> </td>
|
||||
<td class="large" width="50">1</td>
|
||||
<td class="large" width="50">2</td>
|
||||
<td class="large" width="50">3</td>
|
||||
<td class="large" width="50">4</td>
|
||||
<td class="large" width="50">5</td>
|
||||
<td class="large" width="50">6</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td rowspan="6"><b>Score<br>
|
||||
on the<br>
|
||||
Other<br>
|
||||
Die</b></td>
|
||||
<td class="large">1</td>
|
||||
<td bgcolor="#99CCFF">2</td>
|
||||
<td bgcolor="#FFCCCC">3</td>
|
||||
<td bgcolor="#CCCC99">4</td>
|
||||
<td bgcolor="#9966FF">5</td>
|
||||
<td bgcolor="#00CC99">6</td>
|
||||
<td bgcolor="#9999FF"><b>7</b></td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td class="large">2</td>
|
||||
<td bgcolor="#FFCCCC">3</td>
|
||||
<td bgcolor="#CCCC99">4</td>
|
||||
<td bgcolor="#9966FF">5</td>
|
||||
<td bgcolor="#00CC99">6</td>
|
||||
<td bgcolor="#9999FF"><b>7</b></td>
|
||||
<td bgcolor="#FFFFCC">8</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td class="large">3</td>
|
||||
<td bgcolor="#CCCC99">4</td>
|
||||
<td bgcolor="#9966FF">5</td>
|
||||
<td bgcolor="#00CC99">6</td>
|
||||
<td bgcolor="#9999FF"><b>7</b></td>
|
||||
<td bgcolor="#FFFFCC">8</td>
|
||||
<td bgcolor="#99CCCC">9</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td class="large">4</td>
|
||||
<td bgcolor="#9966FF">5</td>
|
||||
<td bgcolor="#00CC99">6</td>
|
||||
<td bgcolor="#9999FF"><b>7</b></td>
|
||||
<td bgcolor="#FFFFCC">8</td>
|
||||
<td bgcolor="#99CCCC">9</td>
|
||||
<td bgcolor="#FFFF66">10</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td class="large">5</td>
|
||||
<td bgcolor="#00CC99">6</td>
|
||||
<td bgcolor="#9999FF"><b>7</b></td>
|
||||
<td bgcolor="#FFFFCC">8</td>
|
||||
<td bgcolor="#99CCCC">9</td>
|
||||
<td bgcolor="#FFFF66">10</td>
|
||||
<td bgcolor="#999900">11</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td class="large">6</td>
|
||||
<td bgcolor="#9999FF"><b>7</b></td>
|
||||
<td bgcolor="#FFFFCC">8</td>
|
||||
<td bgcolor="#99CCCC">9</td>
|
||||
<td bgcolor="#FFFF66">10</td>
|
||||
<td bgcolor="#999900">11</td>
|
||||
<td bgcolor="#9933FF">12</td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p class="center">You can see there is only 1 way to get 2, there are 2 ways to get 3, and so on.</p>
|
||||
<p>Let us count the ways of getting each total and put them in a table:</p>
|
||||
<table align="center" border="0">
|
||||
<tbody>
|
||||
<tr align="center">
|
||||
<td width="100">Total<br>
|
||||
Score</td>
|
||||
<td width="100">Number of <br>
|
||||
Ways to Get <br>
|
||||
Score</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>2</td>
|
||||
<td><b>1</b></td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>3</td>
|
||||
<td><b>2</b></td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>4</td>
|
||||
<td><b>3</b></td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>5</td>
|
||||
<td><b>4</b></td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>6</td>
|
||||
<td><b>5</b></td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>7</td>
|
||||
<td><b>6</b></td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>8</td>
|
||||
<td><b>5</b></td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>9</td>
|
||||
<td><b>4</b></td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>10</td>
|
||||
<td><b>3</b></td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>11</td>
|
||||
<td><b>2</b></td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>12</td>
|
||||
<td><b>1</b></td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td> </td>
|
||||
<td>Total = 36</td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p>Can you see the <a href="../geometry/symmetry-reflection.html">Symmetry</a> in this table?</p>
|
||||
<ul>
|
||||
<li>2 and 12 have the same number of ways = 1 each</li>
|
||||
<li>3 and 11 have the same number of ways = 2 each</li>
|
||||
<li>4 and 10 have the same number of ways = 3 each</li>
|
||||
<li>5 and 9 have the same number of ways = 4 each</li>
|
||||
<li>6 and 8 have the same number of ways = 5 each</li>
|
||||
</ul>
|
||||
<h2>108 Throws</h2>
|
||||
<p>OK, why 108 throws? Well, 36 throws isn't enough for good results, 360 throws is great but takes a long time. So 108 (which is <b>3 lots of 36)</b> seems about right.</p>
|
||||
<p>So let's multiply all these numbers by 3 to match our total of 108:</p>
|
||||
<table align="center" border="0">
|
||||
<tbody>
|
||||
<tr align="center">
|
||||
<td width="100">Total<br>
|
||||
Score</td>
|
||||
<td width="100">Number of <br>
|
||||
Ways to Get <br>
|
||||
Score</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>2</td>
|
||||
<td>3</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>3</td>
|
||||
<td>6</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>4</td>
|
||||
<td>9</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>5</td>
|
||||
<td>12</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>6</td>
|
||||
<td>15</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>7</td>
|
||||
<td>18</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>8</td>
|
||||
<td>15</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>9</td>
|
||||
<td>12</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>10</td>
|
||||
<td>9</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>11</td>
|
||||
<td>6</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>12</td>
|
||||
<td>3</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td> </td>
|
||||
<td>Total = 108</td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p>Those are the <b>theoretical</b> values, as opposed to the <b>experimental</b> ones you got from your experiment.</p>
|
||||
<p>The <b>theoretical</b> values look like this in a bar graph:</p>
|
||||
<p class="center"><img src="images/dice5.jpg" alt="dice results" height="243" width="350"></p>
|
||||
<div class="center80">
|
||||
<p class="center larger">How do these theoretical results compare with your experimental results?</p>
|
||||
</div>
|
||||
<p>This graph and your graph should be quite similar, but they are not likely to be exactly the same, as your experiment relied on <b>chance</b>, and the number of times you did it was fairly small.</p>
|
||||
<p>If you did the experiment a very large number of times, you should get results much closer to the theoretical ones.</p>
|
||||
<p>And, by the way, we've now answered the question from near the beginning of the experiment:</p>
|
||||
<div class="center80">
|
||||
<p class="larger">What is the most likely total score?</p>
|
||||
<ul>
|
||||
<li><b>7</b> has the highest bar, so 7 is the most likely total score.</li>
|
||||
</ul>
|
||||
<p>Hey, is that why people talk about <b>Lucky 7</b> ... ?</p>
|
||||
</div>
|
||||
<h2>Probability</h2>
|
||||
<p>On the page <a href="../data/probability.html">Probability</a> you will find a formula:</p>
|
||||
<p class="center">Probability of an event happening = <span class="intbl">
|
||||
<em>Number of ways it can happen</em>
|
||||
<strong>Total number of outcomes</strong>
|
||||
</span></p>
|
||||
<div class="example">
|
||||
<h3>Example: Probability of a total of 2</h3>
|
||||
<p>We know there are 36 possible outcomes.</p>
|
||||
<p>And there is only 1 way to get a total score of 2.</p>
|
||||
<p>So the probability of getting 2 is:</p>
|
||||
<p class="center larger">Probability of a 2 = <span class="intbl">
|
||||
<em>1</em>
|
||||
<strong>36</strong>
|
||||
</span></p>
|
||||
|
||||
</div>
|
||||
<p>Doing that for each score gets us:</p>
|
||||
<table align="center" border="0">
|
||||
<tbody>
|
||||
<tr align="center">
|
||||
<td width="100">Total<br>
|
||||
Score</td>
|
||||
<td width="100">Probability</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>2</td>
|
||||
<td>1/36</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>3</td>
|
||||
<td>2/36</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>4</td>
|
||||
<td>3/36</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>5</td>
|
||||
<td>4/36</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>6</td>
|
||||
<td>5/36</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>7</td>
|
||||
<td>6/36</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>8</td>
|
||||
<td>5/36</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>9</td>
|
||||
<td>4/36</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>10</td>
|
||||
<td>3/36</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>11</td>
|
||||
<td>2/36</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td>12</td>
|
||||
<td>1/36</td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td> </td>
|
||||
<td class="larger">Total = 1</td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<div><i>(Note: I didn't simplify the fractions)
|
||||
</i></div>
|
||||
<p class="center larger">The sum of all the probabilities is <b>1</b></p>
|
||||
<div class="center80">
|
||||
<p class="center">For any experiment:</p>
|
||||
<p class="center">The sum of the probabilities of <b>all </b>possible outcomes is always equal to <b>1</b></p>
|
||||
</div>
|
||||
<p class="center"> </p>
|
||||
<div class="related">
|
||||
<a href="dice-experiment-1.html">An Experiment with 1 Die</a>
|
||||
<a href="../data/index.html">Data Index</a>
|
||||
<a href="../geometry/fair-dice.html">Fair Dice</a>
|
||||
</div>
|
||||
<!-- #EndEditable -->
|
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|
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<meta http-equiv="content-type" content="text/html; charset=utf-8">
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
|
||||
<h1 class="center">Activity: Discover Capacity (Volumes)</h1>
|
||||
<p>It is interesting to find how much things can hold, so today we will ...</p>
|
||||
<div class="center80">
|
||||
<p class="center larger">Measure Capacity!</p>
|
||||
</div>
|
||||
<p>You will need:</p>
|
||||
<ul>
|
||||
<li>Measuring Cup (for larger items)</li>
|
||||
<li>Measuring Spoons (for smaller items)</li>
|
||||
<li>Pen and paper</li>
|
||||
</ul>
|
||||
<h2>Relative Sizes</h2>
|
||||
<p class="center"><img src="../measure/images/cups-various.jpg" width="300" height="170" alt="cups various" /><br>
|
||||
Find Cups around the house ... <br>
|
||||
...
|
||||
include at least one<b> small </b>one.</p>
|
||||
<p class="center"><img src="../measure/images/pour-glass-cup.jpg" width="200" height="193" alt="pour glass cup" /><br>
|
||||
Now, use the small one to fill each of the other ones in turn.</p>
|
||||
<p><b>Record your results here:</b><b></b></p>
|
||||
<table border="1" align="center">
|
||||
<tr>
|
||||
<td class="large"> </td>
|
||||
<td colspan="2" align="center" class="large">How Many</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td class="large">Description of Cup or Glass</td>
|
||||
<td width="120" align="center" class="large"> Guess </td>
|
||||
<td width="120" align="center" class="large"> Actual </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Smallest</td>
|
||||
<td height="30" align="center">1</td>
|
||||
<td align="center">1</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</table>
|
||||
<h2>Measured Sizes</h2>
|
||||
<p>Use a <a href="../measure/measuring-cups.html">Measuring Cup</a> to measure how many milliliters (ml) or fluid ounces (fl oz) fit into each of your cups or glasses.</p>
|
||||
<p class="center"><img src="../measure/images/150ml.jpg" width="138" height="216" alt="150ml" /><br>
|
||||
A measuring cup showing 150ml</p>
|
||||
<p class="center"><img src="../measure/images/cup-pouring.jpg" width="300" height="195" alt="cup pouring" /><br>
|
||||
Pouring a cup into a measuring cup.</p>
|
||||
<h3>What if the cup is larger then the measuring cup?</h3>
|
||||
<p>Fill the measuring cup to the top mark, empty it and start again. Add up the total.</p>
|
||||
<table border="1" align="center">
|
||||
<tr>
|
||||
<td class="large"> </td>
|
||||
<td colspan="2" align="center" class="large">Capacity (ml or fl oz)</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td class="large">Description of Cup or Glass</td>
|
||||
<td width="120" align="center" class="large"> Guess </td>
|
||||
<td width="120" align="center" class="large"> Actual </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30" align="center"> </td>
|
||||
<td align="center"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</table>
|
||||
<h2>Spoons</h2>
|
||||
<p>We can also measure capacity using measuring spoons.</p>
|
||||
<p class="center"><img src="../measure/images/measuring-spoons-2.jpg" width="300" height="201" alt="measuring spoons" /><br>
|
||||
Measuring Spoons (Tbs means Tablespoon, Tsp means Teaspoon)</p>
|
||||
<p class="center"><img src="../measure/images/pouring-tbs-cup.jpg" width="300" height="257" alt="pouring 1 tbs cup" /><br>
|
||||
Pouring a tablespoon of water into a cup</p>
|
||||
<p>This time we will count how many <b>tablespoons</b> (tbs) you need to fill a cup. A tablespoon holds about 15ml.</p>
|
||||
<table border="1" align="center">
|
||||
<tr>
|
||||
<td class="large"> </td>
|
||||
<td colspan="2" align="center" class="large"> Tablespoons</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td class="large">Description of Cup or Glass</td>
|
||||
<td width="120" align="center" class="large"> Guess </td>
|
||||
<td width="120" align="center" class="large"> Actual </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30" align="center"> </td>
|
||||
<td align="center"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</table>
|
||||
<h2>From Smallest to Largest</h2>
|
||||
<p>Lastly, list all the items you measured, from the <b>smallest to largest</b> capacity.</p>
|
||||
<p>Example: Tiny clear glass, small white cup, ...</p>
|
||||
<table width="80%" border="1" align="center">
|
||||
<tr>
|
||||
<td height="180"> </td>
|
||||
</tr>
|
||||
</table>
|
||||
<div class="related">
|
||||
<a href="../measure/metric-volume.html">Metric Volume</a>
|
||||
<a href="personal-measures.html">Personal Measures Activity</a>
|
||||
<a href="index.html">Activity Index</a>
|
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Activity: Discover Lengths</h1>
|
||||
<p>This is a simple but very useful activity:</p>
|
||||
<div class="center80">
|
||||
<p class="center larger">Measure the length, width and height of everyday items</p>
|
||||
</div>
|
||||
<p>You will need:</p>
|
||||
<ul>
|
||||
<li>A ruler (for smaller items)</li>
|
||||
<li>A tape measure (for larger items)</li>
|
||||
<li>Pen and paper</li>
|
||||
</ul>
|
||||
<p>Measure using millimeters (mm) or inches (in). Try to do both if you can.</p>
|
||||
<h2 align="left">Length</h2>
|
||||
<div class="center80">
|
||||
<p class="center larger"><b>Length</b> is the distance from end to end.</p>
|
||||
</div><p style="float:right; margin: 0 0 5px 10px;"><img src="../geometry/images/cuboid-lwh.svg" width="206" alt="cuboid" /></p>
|
||||
<p>But "Length" can <b>also</b> mean the longer distance across:</p>
|
||||
<ul>
|
||||
<li><b>Length</b>: Longer distance across</li>
|
||||
<li><b>Width</b>: Smaller distance across</li>
|
||||
<li><b>Height</b>: vertical distance</li>
|
||||
</ul>
|
||||
<p>But here we are interested in any distance (length, width or height).</p>
|
||||
<div class="words">
|
||||
<p>Spelling: Leng<b>th</b> and Wid<b>th</b> end in "th", but Heigh<b>t</b> ends in a "t"</p>
|
||||
</div>
|
||||
<h2>Using A Ruler</h2>
|
||||
<p>Make sure one end of the object is at the "0" mark and read the number at the other end. You can also count the little marks between the numbers for a more accurate answer.</p>
|
||||
<p class="center"><img src="images/lengths-4.jpg" width="300" height="114" alt="length fork" /><br>
|
||||
Measuring the length of a fork (8 inches or 200 mm long)</p>
|
||||
<h2>Using a Tape Measure</h2>
|
||||
<p>A tape measure has a little right-angled "hook" at the start ... you can use this to hold on to one edge while you pull the tape measure to the other edge.</p>
|
||||
<p>Make sure you measure straight across (or straight up and down) or your answer will be wrong.</p>
|
||||
<p class="center"><img src="images/lengths-1.jpg" width="200" height="146" alt="length across door" /><br>
|
||||
Measuring the width of a door (820 mm wide).</p>
|
||||
<p class="center"><img src="images/lengths-2.jpg" width="250" height="128" alt="length across table" /><br>
|
||||
Measuring the width of a table.</p>
|
||||
<p class="center"><img src="images/lengths-3.jpg" width="120" height="220" alt="length back of chair" /><br>
|
||||
Measuring the height of a chair.</p>
|
||||
|
||||
<h2>Fill In This Table</h2>
|
||||
<p style="page-break-before: always">Measure the following items (including three others that you find):</p>
|
||||
<table border="1" align="center">
|
||||
<tr>
|
||||
<td width="200" class="large">Item</td>
|
||||
<td width="120" align="center" class="large"> Guess </td>
|
||||
<td width="120" align="center" class="large"> Actual </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Paperclip (width)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Teaspoon (length)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Fork (length)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Pencil (length)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Chair seat (height)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Chair back (height)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Table (width)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Table (length)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Table (height)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Door (width)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Door (height)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Car (width)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Car (length)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Car (height)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Hallway (width)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Hallway (length)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Hallway (height)</td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</table>
|
||||
<h2>From Smallest to Largest</h2>
|
||||
<p>Now, list the items above, from the <b>smallest to largest</b> distance:</p>
|
||||
<p>Example: Paperclip (width), Teaspoon (length), Pencil (length), ...</p>
|
||||
<table width="80%" border="1" align="center">
|
||||
<tr>
|
||||
<td height="180"> </td>
|
||||
</tr>
|
||||
</table>
|
||||
<p> </p>
|
||||
<div class="related">
|
||||
<a href="../measure/metric-length.html">Metric Length</a>
|
||||
<a href="index.html">Activity Index</a>
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@ -1,221 +0,0 @@
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<!-- #BeginEditable "Body" -->
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|
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<h1 class="center">Activity: Discover Mass (Weight)</h1>
|
||||
|
||||
<p>Mass is how much matter is in something. We can measure this by weighing. So today we will be ...</p>
|
||||
<div class="center80">
|
||||
<p class="center larger">Weighing!</p>
|
||||
</div>
|
||||
<p>You will need:</p>
|
||||
<ul>
|
||||
<li>Kitchen Scales (for smaller items)</li>
|
||||
<li>Bathroom Scales (for larger items)</li>
|
||||
<li>Pen and paper</li>
|
||||
</ul>
|
||||
<p>You can measure using grams (g), kilograms (kg), ounces (oz) or lbs (lb).</p>
|
||||
|
||||
<table style="border: 0; margin:auto;">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><img src="../measure/images/scales-digital-0kg.jpg" alt="scales digital 0kg" height="229" width="200"></td>
|
||||
<td><img src="../measure/images/weighing-dog.jpg" alt="weighing dog" height="229" width="137"></td>
|
||||
</tr>
|
||||
<tr style="text-align:center;">
|
||||
<td>Weigh a child</td>
|
||||
<td>Weigh your dog</td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
|
||||
|
||||
<h2>Examples</h2>
|
||||
|
||||
<p class="center"><img src="../measure/images/measuring-1kg-2.jpg" alt="measuring 1kg " height="240" width="200"><br>
|
||||
Using Kitchen Scales to measure 1 kg (2.2 lb) of sugar</p>
|
||||
<p class="center"><img src="../measure/images/weighing-2-5kg-digital.jpg" alt="weighing 2.5kg digital" height="184" width="200"><br>
|
||||
Using Bathroom Scales to measure a 2.5 kg weight</p>
|
||||
<p style="float:left; margin: 0 10px 5px 0;"><img src="../measure/images/weighing-knife.jpg" alt="weighing knife" height="286" width="200"></p>
|
||||
<p>This knife weighs about 75 g (nearly 3 oz)</p>
|
||||
<p><b>How did I measure that?</b></p>
|
||||
<p>Between <b>0</b> and <b>4oz</b> there are 4 spaces, so each mark means 1oz. The pointer is nearly up to the 3rd mark, which means nearly 3oz.</p>
|
||||
<p>Likewise between <b>0</b> and <b>100g</b> there are 4 spaces, so each mark means 25g.<br>
|
||||
The pointer is on the 3rd mark, which means 75g.</p>
|
||||
<div style="clear:both"></div>
|
||||
<p><b>Some ideas of things to measure:</b></p>
|
||||
<ul>
|
||||
<li>Jars of food</li>
|
||||
<li>Bottles (empty or full)</li>
|
||||
<li>Spoons</li>
|
||||
<li>Cups (with and without water)</li>
|
||||
<li>Books</li>
|
||||
<li>Toys</li>
|
||||
<li>People</li>
|
||||
<li>Bags</li>
|
||||
</ul>
|
||||
|
||||
|
||||
<h2>Fill In This Table</h2>
|
||||
|
||||
<p style="page-break-before: always">Write down your Guess just before you measure the Actual weight. As you measure more things, your guesses can get better.</p>
|
||||
|
||||
<table align="center" border="1">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td class="large" width="200">Item</td>
|
||||
<td class="large" align="center" width="120"> Guess </td>
|
||||
<td class="large" align="center" width="120"> Actual </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="30"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
|
||||
|
||||
<h2>From Smallest to Largest</h2>
|
||||
|
||||
<p>Lastly, list all the items you measured, from the <b>smallest to largest</b> mass.</p>
|
||||
<p>Example: Small bottle (empty), spoon, ...</p>
|
||||
|
||||
<table align="center" width="80%" border="1">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td height="180"> </td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p> </p>
|
||||
<p> </p>
|
||||
|
||||
<div class="related">
|
||||
<a href="../measure/metric-mass.html">Metric Mass</a>
|
||||
<a href="index.html">Activity Index</a>
|
||||
</div>
|
||||
<!-- #EndEditable -->
|
||||
|
||||
</article>
|
||||
|
||||
<div id="adend" class="centerfull noprint"></div>
|
||||
<footer id="footer" class="centerfull noprint"></footer>
|
||||
<div id="copyrt">Copyright © 2022 Rod Pierce</div>
|
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|
||||
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|
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|
||||
|
||||
|
||||
</body><!-- #EndTemplate -->
|
||||
<!-- Mirrored from www.mathsisfun.com/activity/discover-mass.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:57:28 GMT -->
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||||
</html>
|
||||
@ -1,131 +0,0 @@
|
||||
<!DOCTYPE html>
|
||||
<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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<!-- Mirrored from www.mathsisfun.com/activity/division-around-you.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:57:50 GMT -->
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|
||||
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
|
||||
|
||||
<!-- #BeginEditable "doctitle" -->
|
||||
<title>Division In the World Around You</title>
|
||||
<meta name="description" content="Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.">
|
||||
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<link rel="preload" href="../style4.css" as="style">
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<link rel="preload" href="../main4.js" as="script">
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<link rel="stylesheet" href="../style4.css">
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gtag('js', new Date());
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gtag('config', 'UA-29771508-1');
|
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</script>
|
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</head>
|
||||
|
||||
<body id="bodybg">
|
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|
||||
<div id="stt"></div>
|
||||
<div id="adTop"></div>
|
||||
<header>
|
||||
<div id="hdr"></div>
|
||||
<div id="tran"></div>
|
||||
<div id="adHide"></div>
|
||||
<div id="cookOK"></div>
|
||||
</header>
|
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|
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<div class="mid">
|
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<nav>
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<div id="menuWide" class="menu"></div>
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<div id="logo"><a href="../index.html"><img src="../images/style/logo.svg" alt="Math is Fun"></a></div>
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<div id="menuTiny" class="menu"></div>
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<div id="extra"></div>
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<article id="content" role="main">
|
||||
|
||||
<!-- #BeginEditable "Body" -->
|
||||
|
||||
|
||||
<h1 class="center">Division Examples In the World Around You</h1>
|
||||
|
||||
<p>Look for <b>examples of division</b> in the world around you.</p>
|
||||
|
||||
<div class="example">
|
||||
|
||||
<h3>Example: A Box of 12 Eggs </h3>
|
||||
<p class="center"><img src="images/divide-eggs.svg" alt="divide eggs by 2 or 6" height="102" width="323"></p>
|
||||
<p>There are 12 eggs in 2 rows of 6:</p>
|
||||
<ul>
|
||||
<li>so 12 divided by 2 is <b>6</b></li>
|
||||
<li>and 12 divided by 6 is <b>2</b></li>
|
||||
</ul>
|
||||
</div>
|
||||
<p>Sketch the division you find, and show <b>both division facts</b>.</p>
|
||||
<p>Look for things like ice cubes in a tray, chocolates in a box, tiles on a wall, paving stones, etc.</p>
|
||||
|
||||
<table align="center" cellpadding="10" border="2">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td class="large" width="150">Your Example</td>
|
||||
<td class="large" width="300">Your Sketch</td>
|
||||
<td class="large">The Division Facts</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="200"> </td>
|
||||
<td>
|
||||
<p class="largest">__ ÷ __ = ___</p>
|
||||
<p> </p>
|
||||
<p class="largest">__ ÷ __ = ___</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="200"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="200"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td height="200"> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p> </p>
|
||||
|
||||
<p> </p>
|
||||
|
||||
<div class="related">
|
||||
<a href="index.html">Activity Index</a>
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<div id="adend" class="centerfull noprint"></div>
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<footer id="footer" class="centerfull noprint"></footer>
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<div id="copyrt">Copyright © 2022 Rod Pierce</div>
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</body><!-- #EndTemplate -->
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<!-- Mirrored from www.mathsisfun.com/activity/division-around-you.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:57:50 GMT -->
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</html>
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@ -1,450 +0,0 @@
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<!DOCTYPE html>
|
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<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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|
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<!-- Mirrored from www.mathsisfun.com/activity/drawing-squares.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:58:08 GMT -->
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<head>
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||||
<meta http-equiv="content-type" content="text/html; charset=UTF-8">
|
||||
|
||||
<!-- #BeginEditable "doctitle" -->
|
||||
<title>Activity: Drawing Squares</title>
|
||||
<meta name="description" content="Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.">
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<!-- #BeginEditable "Body" -->
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||||
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||||
|
||||
<h1 class="center">Activity: Drawing Squares</h1>
|
||||
|
||||
<p>For this activity all you need is a grid of dots, a pencil and your
|
||||
brain.</p>
|
||||
|
||||
<h3>Let us discover how many squares you can make on different grids:</h3>
|
||||
<p class="center"><img src="images/drawing-squares-grids.svg" alt="grids 1x1, 2x2, 3x3, etc" style="max-width:100%" height="144" width="455"></p>
|
||||
<p class="center"><strong>Note:</strong> "1 by 1" means how many <b>sides</b> (not how many dots).</p>
|
||||
|
||||
<h3><br>
|
||||
So, let's try drawing in
|
||||
some squares and count how many:</h3>
|
||||
|
||||
<h3>1 by 1</h3>
|
||||
|
||||
<table style="border: 0;">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td>Well,
|
||||
that's easy, there's just one: </td>
|
||||
<td> </td>
|
||||
<td><img src="images/squares3.gif" alt="squares3" height="35" width="38"></td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
|
||||
<h3>2 by
|
||||
2</h3>
|
||||
|
||||
<table style="border: 0;">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td>That seems to be easy too. There are four of them, aren't there?</td>
|
||||
<td> </td>
|
||||
<td><img src="images/squares4.gif" alt="squares4" height="60" width="62"></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td style="text-align:right;">But
|
||||
wait, that's not the complete answer.<br>
|
||||
There's also this bigger
|
||||
one:</td>
|
||||
<td style="text-align:right;"> </td>
|
||||
<td><img src="images/squares5.gif" alt="squares5" height="60" width="65"></td>
|
||||
</tr>
|
||||
</tbody></table>
|
||||
<p>That makes
|
||||
five squares altogether - four
|
||||
1 by 1 squares and one
|
||||
2 by 2 square</p>
|
||||
|
||||
|
||||
<h2>Your Turn !</h2>
|
||||
|
||||
<h3>3 by 3</h3>
|
||||
|
||||
|
||||
<table border="0">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td>
|
||||
<p>Over to you now.</p>
|
||||
<p class="right">Here's the grid:</p></td>
|
||||
<td> </td>
|
||||
<td><img src="images/squares6.gif" alt="squares6" height="88" width="88"></td>
|
||||
|
||||
</tr>
|
||||
</tbody></table> <div class="center80">
|
||||
<p><strong>Hint:</strong> For
|
||||
the 3 by 3 case, you will expect to get 1 by 1 squares, 2 by 2 squares
|
||||
and 3 by 3 squares. How many of each?</p>
|
||||
</div><p><br></p>
|
||||
<p><input onclick="printImg('images/squares-grid.gif')" value="You could also print this bigger grid" type="button"><br><img src="images/squares-grid.gif" alt="squares grid" height="325" width="326">
|
||||
</p>
|
||||
|
||||
<p><br></p>
|
||||
|
||||
<p> </p>
|
||||
<p><strong>Now you can start to fill in a table:</strong></p>
|
||||
<div style="overflow:auto;">
|
||||
|
||||
<table cellspacing="2" cellpadding="2" border="1">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td style="width:100px;"> </td>
|
||||
<td align="center" width="100"> How Many<br>
|
||||
1 by 1 squares</td>
|
||||
<td align="center" width="100"> How Many<br>
|
||||
2 by 2 squares</td>
|
||||
<td align="center" width="100"> How Many<br>
|
||||
3 by 3 squares</td>
|
||||
<td align="center" width="100"> How Many<br>
|
||||
4 by 4 squares</td>
|
||||
<td align="center" width="100"> How Many<br>
|
||||
5 by 5 squares</td>
|
||||
<td align="center" width="100"><strong>Total</strong></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="center" height="25">1 by
|
||||
1 Grid:</td>
|
||||
<td style="text-align:center;">1</td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td style="text-align:center;">1</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="center" height="25">2 by
|
||||
2 Grid:</td>
|
||||
<td style="text-align:center;">4</td>
|
||||
<td style="text-align:center;">1</td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td style="text-align:center;">5</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="center" height="25">3 by
|
||||
3 Grid:</td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="center" height="25">4 by
|
||||
4 Grid:</td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="center" height="25">5 by
|
||||
5 Grid:</td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
</div>
|
||||
<p> </p>
|
||||
|
||||
|
||||
<h2>Did you notice anything about the numbers in the table?</h2>
|
||||
|
||||
<p>They are all <a href="../numberpatterns.html">square
|
||||
numbers</a>:</p>
|
||||
<ul>
|
||||
<li>1<sup>2</sup> = <b>1</b>,</li>
|
||||
<li>2<sup>2</sup> = <b>4</b>,</li>
|
||||
<li>3<sup>2</sup> = <b>9</b>,</li>
|
||||
<li>etc ...</li>
|
||||
</ul>
|
||||
<p>and the totals are found
|
||||
by adding together square numbers.</p>
|
||||
|
||||
<h3>Formula to The Rescue ... !</h3>
|
||||
<p>There is actually a <a href="../definitions/formula.html">formula</a> for adding the first <strong>n</strong> square numbers:</p>
|
||||
<p class="center larger">S<sub>n</sub> = n(n+1)(2n+1) / 6</p>
|
||||
|
||||
<div class="example">
|
||||
|
||||
<h3>Example: The number of squares in the <strong>5 by 5</strong> case</h3>
|
||||
<p>Try <a href="../algebra/substitution.html">substituting</a> <strong>n = 5</strong> into the formula:</p>
|
||||
|
||||
<div class="so"> S<sub>n</sub> = n(n+1)(2n+1) / 6 </div>
|
||||
<div class="so"> S<sub>5</sub> = 5 × (5+1) × (2×5+1) / 6 </div>
|
||||
<div class="so"> S<sub>5</sub> = 5 × 6 × 11 / 6 </div>
|
||||
<div class="so"> S<sub>5</sub> = 55 </div>
|
||||
|
||||
</div>
|
||||
|
||||
<h3> </h3>
|
||||
|
||||
|
||||
<h2>So, we seem to have solved the question. Yipee!</h2>
|
||||
|
||||
<h3>But wait ... there's more!</h3>
|
||||
<p>I said you would need to use your brains. Let's go back to the 2 by 2 case:</p>
|
||||
|
||||
<h3>2 by
|
||||
2</h3>
|
||||
<p>There is another square too, this one:</p>
|
||||
<blockquote> <img src="images/squares7.gif" alt="squares9" height="61" width="65"></blockquote>
|
||||
<div class="center80">
|
||||
<p><strong>Why is it a <a href="../quadrilaterals.html">square</a>? </strong>It has four equal sides and four right angles, so that's a square.</p>
|
||||
</div>
|
||||
<p>So, that makes
|
||||
six squares altogether.</p>
|
||||
<p>Four
|
||||
1 by 1 squares, one
|
||||
2 by 2 square and one
|
||||
<b>x by x</b> square.</p>
|
||||
<div class="center80">
|
||||
<p>What is the value of <b>x</b>? We can use <a href="../pythagoras.html">Pythagoras'
|
||||
Theorem</a> to find it:</p>
|
||||
<div class="so"> x<sup>2</sup> = 1<sup>2</sup> + 1<sup>2</sup> = 1 + 1 = 2 </div>
|
||||
<div class="so"> So x = √2 </div>
|
||||
</div>
|
||||
<p>So, we have <strong>four
|
||||
1 by 1 squares</strong>, <strong>one
|
||||
2 by 2 square</strong> and <strong>one √2
|
||||
by √2 square</strong>.</p>
|
||||
|
||||
|
||||
<h2>Your Turn !</h2>
|
||||
|
||||
<h3>3 by 3</h3>
|
||||
<ul>
|
||||
<li>Are there any more squares?</li>
|
||||
</ul>
|
||||
<p><strong>YES</strong>! Can you find them?</p>
|
||||
|
||||
<h3>4 by 4 and 5 by 5</h3>
|
||||
<p>Also try the 4 by 4 grid, and the 5 by 5 grid</p>
|
||||
<p>As you proceed, you will find squares like these:</p>
|
||||
<p class="center"><img src="images/squares8.svg" alt="tilted squares" style="max-width:100%" height="274" width="512"></p>
|
||||
<p> </p>
|
||||
|
||||
|
||||
<h2>What are the lengths of the sides of these squares?</h2>
|
||||
|
||||
<p>You can use <a href="../pythagoras.html">Pythagoras'
|
||||
Theorem</a> to work that out yourself</p>
|
||||
|
||||
<h3>In each case, how many do you get of each one?</h3>
|
||||
<p>Here is a table to help you:</p>
|
||||
<div class="simple">
|
||||
|
||||
<table border="1">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td> </td>
|
||||
<td style="text-align:center;">How Many<br>
|
||||
1 by 1 </td>
|
||||
<td style="text-align:center;">How Many<br>
|
||||
2 by 2 </td>
|
||||
<td style="text-align:center;">How Many<br>
|
||||
3 by 3 </td>
|
||||
<td style="text-align:center;">How Many<br>
|
||||
4 by 4 </td>
|
||||
<td style="text-align:center;">How Many<br>
|
||||
5 by 5 </td>
|
||||
<td style="text-align:center;">How Many<br>
|
||||
√2 by<br>
|
||||
√2 </td>
|
||||
<td style="text-align:center;">How Many<br>
|
||||
√5 by √5 </td>
|
||||
<td style="text-align:center;">How Many<br>
|
||||
√8 by √8 </td>
|
||||
<td style="text-align:center;">How Many<br>
|
||||
√10 by √10</td>
|
||||
<td style="text-align:center;">How Many<br>
|
||||
√13 by √13 </td>
|
||||
<td style="text-align:center;">How Many<br>
|
||||
√17 by √17</td>
|
||||
<td style="text-align:center;"><strong>Total</strong></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="30">1 by 1 Grid:</td>
|
||||
<td style="text-align:center;">1</td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td style="text-align:center;">1</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="30">2 by
|
||||
2 Grid:</td>
|
||||
<td style="text-align:center;">4</td>
|
||||
<td style="text-align:center;">1</td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td style="text-align:center;">1</td>
|
||||
<td style="text-align:center;"> </td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td style="text-align:center;">6</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="30">3 by
|
||||
3 Grid:</td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="30">4 by
|
||||
4 Grid:</td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td height="30">5 by
|
||||
5 Grid:</td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
<td><br></td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
</div>
|
||||
<p> </p>
|
||||
|
||||
|
||||
<h2>Advanced</h2>
|
||||
|
||||
<p>Can you find a formula to calculate the number of squares that have
|
||||
lengths that are square roots?</p>
|
||||
<p>Can you then find a formula for the total number of squares in
|
||||
each case?</p>
|
||||
<p>Are there any more squares lurking in there that we've missed?</p>
|
||||
|
||||
|
||||
<h2>Conclusion</h2>
|
||||
|
||||
<p>What started off as seeming to be a simple exercise turned out to
|
||||
be quite complex. You really <b>do</b> need to use your brains to think this
|
||||
one through, but it's a challenging and rewarding exercise.</p>
|
||||
<p> </p>
|
||||
|
||||
<div class="related">
|
||||
<a href="index.html">Activity Index</a>
|
||||
</div>
|
||||
|
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<!-- #BeginEditable "Body" -->
|
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<h1 class="center">Activity: Estimation</h1>
|
||||
<p>This
|
||||
activity is about <a
|
||||
href="../numbers/estimation.html">estimation</a> and doing a <a href="../definitions/survey.html">survey</a>.</p>
|
||||
<h2>How
|
||||
many red marbles?</h2>
|
||||
<p style="float:left; margin: 0 10px 5px 0;"><img src="images/marbles-asstd.gif" width="99" height="114" alt="marbles assorted" /></p>
|
||||
<p>For this experiment you will need a bag of marbles of various
|
||||
colors - red, blue, green, yellow etc. The total number of marbles is
|
||||
not really important, but you will find it easier to work with a number
|
||||
like 50. What is important is that you do not know how many of each
|
||||
color there are. So you will have to ask a friend or relative to choose
|
||||
the marbles for you.</p>
|
||||
<p>You will <a
|
||||
href="../numbers/estimation.html">estimate</a> how many red marbles there are in the bag.</p>
|
||||
<h3>So why don't you just count them?</h3>
|
||||
<p>Of course you could, but this experiment will teach you how to make an
|
||||
estimate.</p>
|
||||
<p>Scientists and statisticians use this method all the time to
|
||||
make estimates in
|
||||
real world situations where they can't just simply count.</p>
|
||||
<div class="example">
|
||||
<h3>Example: Blood Types</h3>
|
||||
<p>There are four different human blood types, called A, B, AB and O.</p>
|
||||
<p><b>To test everyone, as you can imagine, would be very hard!</b></p>
|
||||
<p>So to find out
|
||||
how many people in the world have each blood type, scientists take a
|
||||
sample of (say) 1,000 people and test their blood type.</p>
|
||||
<p>From the sample
|
||||
they can estimate how many of each type there are in the world. </p>
|
||||
</div>
|
||||
<h2>Now you're ready to begin the experiment. It's very simple.</h2>
|
||||
<ul>
|
||||
<li>Shake
|
||||
the marbles in the bag.</li>
|
||||
<li>Take
|
||||
one marble without looking and record its color.</li>
|
||||
<li>Return
|
||||
the marble to the bag.</li>
|
||||
<li>Repeat
|
||||
this process 100 times.</li>
|
||||
</ul>
|
||||
<h2>Why do you return the marble to the bag?<br></h2>
|
||||
<p>So that the conditions for choosing the second
|
||||
marble are exactly the same as the conditions for choosing the first
|
||||
marble.</p>
|
||||
<p>If the first marble you choose is red and you don't replace
|
||||
it, then for your second
|
||||
choice there is one less red marble in the bag, which makes the chance of choosing another red marble
|
||||
less.</p>
|
||||
<h2>How do you record the color?</h2>
|
||||
<p><strong>You can use a <a href="../data/tally-marks.html">tally/frequency</a> table like this:</strong></p>
|
||||
<table border="1" align="center" cellpadding="2"
|
||||
cellspacing="2">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><strong>Color</strong></td>
|
||||
<td><strong>Tally</strong></td>
|
||||
<td><strong>Frequency</strong></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Red</td>
|
||||
<td></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Blue</td>
|
||||
<td></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Green</td>
|
||||
<td></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Yellow</td>
|
||||
<td></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Purple</td>
|
||||
<td></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td></td>
|
||||
<td></td>
|
||||
<td>Total = 100</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
<br>
|
||||
<br>
|
||||
<div class="center80">
|
||||
<p>I have included five colors in my table, but yours could be different.</p>
|
||||
<p>Once you've completed choosing 100 times, you can work out the <a
|
||||
href="../data/relative-frequency.html">relative
|
||||
frequency</a> of red by dividing the number of red marbles by 100.</p>
|
||||
<p> </p>
|
||||
<p>For example, if you record
|
||||
<strong>22 red marbles</strong> in your table, then the
|
||||
relative frequency of <strong>red</strong>
|
||||
is
|
||||
<strong>22/100 = 0.22</strong></p>
|
||||
</div>
|
||||
<h2>How does this help you estimate the
|
||||
number of red marbles in the bag?</h2>
|
||||
<p>That's easy. If there are <strong>50</strong> marbles in the bag and <strong>red</strong> occurred <strong>22</strong> times out of <strong>100</strong>, then it should occur <strong>11</strong> times out of <strong>50</strong>.</p>
|
||||
<p>In other words, the fractions <strong>22/100</strong> and <strong>11/50</strong> are <a
|
||||
href="../equivalent_fractions.html">equivalent
|
||||
fractions</a>.<br>
|
||||
An easier way is just to multiply <strong>0.22 by 50</strong>: <strong>0.22 × 50 = 11</strong></p>
|
||||
<p>When you've finished the calculations, you can check how many red
|
||||
marbles there really are in the bag.</p>
|
||||
<ul>
|
||||
<li><strong>How good was your estimate?</strong></li>
|
||||
<li><strong>How can you get a better estimate?</strong></li>
|
||||
</ul>
|
||||
<p>To get a better estimate, don't count straight away.<br>
|
||||
Instead, repeat the
|
||||
experiment several times and calculate the <a
|
||||
href="../mean.html">mean</a> number of red
|
||||
marbles.</p>
|
||||
<p>Then you can compare your mean number with the actual number in the
|
||||
bag.<br>
|
||||
You should get a much better estimate, and may even get it exactly
|
||||
right.</p>
|
||||
<div class="center80">
|
||||
<p>As a variation on this experiment, you could use Smarties or M and M's.
|
||||
But you may be tempted
|
||||
to eat some and ruin the results of your experiment!</p>
|
||||
</div>
|
||||
<h2>How many A's?</h2>
|
||||
<p>Another variation on
|
||||
the above experiment can be done using the letters from the game of
|
||||
Scrabble. In the game of Scrabble there are 100 tiles. 98 of the tiles
|
||||
are inscribed with letters of the alphabet, the other two are blank. Remove the blank ones, so you will have 98 tiles.</p>
|
||||
<div class="center80">
|
||||
<p>If you don't have the game of Scrabble, then you could make your own
|
||||
tiles. You<strong> will need 98 square pieces of cardboard, all the same size:
|
||||
2 cm by 2 cm will do. </strong></p>
|
||||
<p>Write letters on the tiles as follows:</p>
|
||||
<table border="0" align="center">
|
||||
<tr>
|
||||
<td width="200"><ul>
|
||||
<li>9 A's</li>
|
||||
<li>2 B's</li>
|
||||
<li>2 C's,</li>
|
||||
<li>4 D's,</li>
|
||||
<li>12
|
||||
E's,</li>
|
||||
<li>2 F's,</li>
|
||||
<li>3 G's,</li>
|
||||
<li>2 H's,</li>
|
||||
<li>9 I's,</li>
|
||||
<li>1 J,</li>
|
||||
<li>1 K,</li>
|
||||
<li>4 L's,</li>
|
||||
<li>2 M's,</li>
|
||||
</ul></td>
|
||||
<td width="200"><ul>
|
||||
<li>6 N's,</li>
|
||||
<li>8 O's,</li>
|
||||
<li>2 P's,</li>
|
||||
<li>1 Q,</li>
|
||||
<li>6 R's,</li>
|
||||
<li>4 S's,</li>
|
||||
<li>6 T's,</li>
|
||||
<li>4 U's,</li>
|
||||
<li>2 V's,</li>
|
||||
<li>2 W's,</li>
|
||||
<li>1 X,</li>
|
||||
<li>2 Y's</li>
|
||||
<li>1
|
||||
Z</li>
|
||||
</ul></td>
|
||||
</tr>
|
||||
</table>
|
||||
</div>
|
||||
<p>Pretend that you don't know
|
||||
how many A's there are.
|
||||
Now do the experiment in the same way that you did the marbles
|
||||
experiment.</p>
|
||||
<p><br>
|
||||
<strong>Record your results in a table as before:</strong></p>
|
||||
<table border="1" align="center" cellpadding="2"
|
||||
cellspacing="2">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><strong>Letter</strong></td>
|
||||
<td><strong>Tally</strong></td>
|
||||
<td><strong>Frequency</strong></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>A</td>
|
||||
<td></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>B</td>
|
||||
<td></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>C</td>
|
||||
<td></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>D</td>
|
||||
<td></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>E</td>
|
||||
<td></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>etc ...</td>
|
||||
<td></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td></td>
|
||||
<td></td>
|
||||
<td>Total = 100</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
<div class="center80">
|
||||
<p>The only
|
||||
difference is that you will need a much longer table going all the way
|
||||
to Z.</p>
|
||||
<p>When you've
|
||||
finished, calculate the <a
|
||||
href="../data/relative-frequency.html">relative
|
||||
frequency</a> of the letter <strong>A</strong> and
|
||||
estimate the number of A's in the bag by multiplying the relative
|
||||
frequency by <strong>98</strong>.</p>
|
||||
<p>Do this several times and calculate the <a
|
||||
href="../mean.html">mean</a>.</p>
|
||||
<br>
|
||||
</div>
|
||||
<h3>What result did you get?</h3>
|
||||
<h2>How many people have blood type O?</h2>
|
||||
<p>Now you've learned how to make an estimate from a sample,
|
||||
you are ready to do a real-life experiment.<br>
|
||||
Before you begin you should
|
||||
read the pages <a
|
||||
href="../data/survey-conducting.html">How to Do
|
||||
a Survey</a> and <a href="../data/survey-questionnaire.html">Survey
|
||||
Questions</a>.</p>
|
||||
<h2><br>
|
||||
How many people in the world have
|
||||
blood type O?</h2>
|
||||
<p>There
|
||||
are four different human blood types, called <strong>A</strong>, <strong>B</strong>, <strong>AB</strong> and <strong>O</strong>
|
||||
. It is
|
||||
obviously impractical to test everybody in the world; so, to find out
|
||||
how many people in the world have each blood type, you get
|
||||
a
|
||||
sample of 100 people and find out their blood type. From the
|
||||
sample you can estimate how many people in the world have
|
||||
blood type O.</p>
|
||||
<p>But this could be a difficult experiment as many people don't even
|
||||
know their own blood type!</p>
|
||||
<p>And, since you can't test them for blood
|
||||
type, you will have to just count the ones who do know. So to get 100 who <b>do</b> know their blood type means a sample size much greater than 100.</p>
|
||||
<div class="center80">
|
||||
<p><strong>Note:</strong> Depending on where you live in the world, you could use a
|
||||
different physical characteristic such as hair color or eye color. But,
|
||||
if you live in some countries, you may not have a good variation of
|
||||
different colors. That's why I chose blood type.</p>
|
||||
</div>
|
||||
<h2>Which sample?</h2>
|
||||
<p>If you are still at school, then you could use your school population
|
||||
do do your survey. Ask permission first, then go around different
|
||||
classrooms.</p>
|
||||
<p>But you might get a better result doing your survey in a
|
||||
local shopping center or mall. When you stop people, tell them that you
|
||||
are doing a survey and politely ask them if they would mind telling you
|
||||
their blood type.</p>
|
||||
<h3>Ignore the ones who refuse to answer or who don't know.</h3>
|
||||
<p><strong>Keep going
|
||||
until you have 100 positive answers.</strong><br>
|
||||
Record your results in a table, as follows:</p>
|
||||
<table border="1" align="center" cellpadding="2"
|
||||
cellspacing="2">
|
||||
<tbody>
|
||||
<tr>
|
||||
<td><strong>Blood type</strong></td>
|
||||
<td><strong>Tally</strong></td>
|
||||
<td><strong>Frequency</strong></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>A</td>
|
||||
<td></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>B</td>
|
||||
<td></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>AB</td>
|
||||
<td></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>O</td>
|
||||
<td></td>
|
||||
<td></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td></td>
|
||||
<td></td>
|
||||
<td>Total = 100</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
<br>
|
||||
When you have
|
||||
finished, you can work out the relative frequency of blood type <strong>O</strong> from
|
||||
your sample.<br>
|
||||
Divide the number with blood type <strong>O </strong>by <strong>100</strong>.
|
||||
<p>You can expect to get a better result if you use a bigger sample, or if
|
||||
you take several samples and calculate the mean.</p>
|
||||
<p>Now all you need to know is how many people there are in the world. A quick search on the internet should answer this for you.</p>
|
||||
<h2>Can you now estimate how many people in the world have blood type O?</h2>
|
||||
<p> </p>
|
||||
<p> </p>
|
||||
<div class="related">
|
||||
<a href="index.html">Activity Index</a>
|
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|
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<article id="content" role="main"><!-- #BeginEditable "Body" -->
|
||||
|
||||
<h1 class="center">The Fishing Rod</h1>
|
||||
<p>Sam finished making this very beautiful fishing rod, <b>1.4 m</b> long:</p>
|
||||
<p class="center"><img src="images/fishing-rod.svg" alt="fishing rod"></p>
|
||||
<p>On the weekend Sam takes the new fishing rod to the train station on the way to a great fishing spot.</p>
|
||||
<p> </p>
|
||||
<h3>Not Allowed</h3>
|
||||
<p>But the Station Master says "Sorry Sam, but it is <b>longer than 1 m</b>. No one is allowed to take things on the train that are more than 1 m long. New rules you know."</p>
|
||||
<p>Sam thinks for a bit, then asks "when is the next train?"</p>
|
||||
<p>"In half an hour" says the Station Master.</p>
|
||||
<p>Half an hour later Sam is back again, with the same fishing rod. It is not altered at all, not cut or shrunk or pulled apart or anything. But the Station Master measures it and says "OK Sam you can get on the train with that."</p>
|
||||
<p>What did Sam do?</p>
|
||||
<p> </p>
|
||||
<p style="width:100px; margin:auto; border-top:3px solid blue;"></p>
|
||||
<p> </p>
|
||||
<p style="text-align:center; color:blue;">Don't go any further until you have a solution!</p>
|
||||
<p> </p>
|
||||
<p style="width:100px; margin:auto; border-top:3px solid blue;"></p>
|
||||
<p> </p>
|
||||
<h3>Sam's Solution</h3>
|
||||
<p>Sam cut a piece of cardboard into a <b>1 m square</b> and placed the fishing rod along the diagonal and covered it all in wrapping paper.</p>
|
||||
<p class="center"><img src="images/fishing-rod-square.svg" alt="fishing rod in a square"></p>
|
||||
<div class="fun"><p style="float:right; margin: 0 0 5px 10px;"><img src="../images/unit-square-diagonal.gif" alt="Unit Square Diagonal" width="128" height="141" /></p>
|
||||
<p>In fact the diagonal of a 1 m square is slightly longer:</p>
|
||||
<p class="center">it is actually <b>√2 = 1.4142...</b></p>
|
||||
<p>Read <a href="../pythagoras.html">Pythagoras Theorem</a> to learn more.</p>
|
||||
</div>
|
||||
<div style="clear:both"></div>
|
||||
<p>The Station Master measured its length and width and found them both "not more than 1 m" and so all was satisfactory.</p>
|
||||
<p> </p>
|
||||
<p>Such are the ways of the world.</p>
|
||||
<p> </p>
|
||||
<h3>Daydreaming at the River</h3>
|
||||
<p>Sam enjoyed a lovely day at the river, and daydreamed about a new fishing rod, but this one will be longer!</p>
|
||||
<p>In fact it will be <b>1.7m</b> long.</p>
|
||||
<p>Is there any way Sam could get such a fishing rod past the friendly (but stubborn) Station Master?</p>
|
||||
<p> </p>
|
||||
<p> </p>
|
||||
|
||||
<div class="related"><a href="../pythagoras.html">Pythagoras Theorem</a> <a href="index.html">Activity Index</a></div>
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</nav>
|
||||
<div id="extra"></div>
|
||||
</div>
|
||||
<article id="content" role="main">
|
||||
<!-- #BeginEditable "Body" -->
|
||||
<h1 class="center">Activity: Garden Area</h1>
|
||||
<p style="float:left; margin: 0 10px 5px 0;"><img src="images/garden.jpg" width="220" height="133" alt="garden" /></p>
|
||||
<p class="center larger"><i>Have you ever wondered what the area of your garden is?</i></p>
|
||||
<p class="center larger">Let us try and find out!</p>
|
||||
<div style="clear:both"></div>
|
||||
<div class="center80">
|
||||
<p class="center larger">You will need a garden, a tape measure, pen and paper ... and your brains.</p>
|
||||
</div>
|
||||
<h2>I don't have a garden, so what can I do?</h2>
|
||||
<p>If you don't have a garden, maybe a friend has one, or your relatives have one, so use theirs.</p>
|
||||
<p style="float:left; margin: 0 10px 5px 0;"><img src="../measure/images/tape-measure.jpg" width="95" height="133" alt="tape measure" /></p>
|
||||
<h2>How accurate should my measurements be?</h2>
|
||||
<p>Try to measure to the nearest centimeter (or half-inch), so the error will be as small as possible.</p>
|
||||
<p>You should get a good estimate, as long as you are careful with your measuring.</p>
|
||||
|
||||
<h2>Is there a simple way to find the area of my garden?</h2>
|
||||
<p>If your garden is a rectangle, then you have a simple calculation. You just have to measure its width and length and multiply them together:</p>
|
||||
<table border="0" align="center">
|
||||
<tr>
|
||||
<td><img src="images/area-rectangle.gif" width="101" height="68" alt="area rectangle" /></td>
|
||||
<td> </td>
|
||||
<td><p class="larger">Rectangle:
|
||||
Area = W × L</p>
|
||||
<ul>
|
||||
<li>W = width</li>
|
||||
<li>L = length</li>
|
||||
</ul></td>
|
||||
</tr>
|
||||
</table>
|
||||
<p class="center"><b>But that makes this activity just too easy ... <br>
|
||||
... so go find another garden with a more interesting shape!</b></p>
|
||||
<h2>My garden is a difficult shape, so how can I find its area?</h2>
|
||||
<p>Good! This activity just got <i><b>interesting</b></i> ...</p>
|
||||
<p>It may be one of the shapes on the page <a href="../area.html">Area of Plane Shapes</a>, then you just have to decide which shape, make the measurements, and use the formula.</p>
|
||||
<div class="center80">
|
||||
<p class="center">But you could also break up your difficult shape into <a href="../triangle.html">triangles</a>:<br>
|
||||
<img src="../geometry/images/area-3-triangles.gif" width="176" height="126" alt="area 3 triangles" /><br>
|
||||
<br>
|
||||
Then measure the base (<b>b</b>) and height (<b>h</b>) of each triangle: <br>
|
||||
<img src="../geometry/images/area-3-triangles-b.gif" width="306" height="148" alt="area 3 triangles separated" /></p>
|
||||
<p class="center">Write down each measurement carefully so you know which triangle it belongs to.</p>
|
||||
<p class="center">Now go inside and calculate each area
|
||||
(using <span class="larger">Area = ½b × h</span>) and add them all up.</p>
|
||||
</div>
|
||||
<h2>But my garden is different ...</h2>
|
||||
<p class="larger">... in fact it's not any shape at all ... it has some straight edges and some curved parts. What should I do?</p>
|
||||
<p>Maybe it looks something like this:</p>
|
||||
<p class="center"><img src="images/garden-area.gif" width="215" height="180" alt="garden area" /><br></p>
|
||||
<p>You could try covering your garden with a grid of squares – these could be 1 meter squares or 1 foot squares, something like this:</p>
|
||||
<p class="center"><img src="images/garden-area-grid.gif" width="350" height="207" alt="garden area grid" /><br></p>
|
||||
<h3>How do I make a grid?</h3>
|
||||
<p>Try using pegs in the ground and join them up with string. Make sure they are the right distance apart and all angles are right angles.</p>
|
||||
<h3>How does this help? The grid and the outline of the garden don't match. There are lots of corners and curved parts.</h3>
|
||||
<p>Count the squares!</p>
|
||||
<p>There are special methods talked about on the <a href="../geometry/area.html">Area</a> page. The simplest method is:</p>
|
||||
<ul>
|
||||
<li>more than half a square counts as 1</li>
|
||||
<li>less than half a square counts as 0</li>
|
||||
</ul>
|
||||
<p class="center"><br>
|
||||
<img src="images/garden-area-grid-count.gif" width="358" height="206" alt="garden area grid count" /><br>
|
||||
An estimate for this area is <b>41 m<sup>2</sup></b>. <br>
|
||||
(This is just an example.
|
||||
Your garden is different of course.)</p>
|
||||
<p>If your grid is 1 foot by 1 foot, then the area will be in square feet. </p>
|
||||
<h2>Why should I want to know the area of my garden?</h2>
|
||||
<p>There might be lots of reasons:</p>
|
||||
<ul>
|
||||
<li>You want to re-turf the garden. How much grass should you order? How much will it cost?</li>
|
||||
<li>You want to plant the garden with tomato plants. These have to be planted a certain distance apart. How many plants could you plant? What will be your expected yield of tomatoes?</li>
|
||||
<li>You want to hold a barbeque party. How many people could comfortably fit into your garden?</li>
|
||||
</ul>
|
||||
<p align="center" class="center80">You can now do <a href="garden-grass.html">Activity: Grass for the Garden</a></p>
|
||||
<h2>I am finished ... what have I learned?</h2>
|
||||
<p>You have learned about measuring, recording data, drawing, and calculating area, well done!</p>
|
||||
<p> </p>
|
||||
<div class="related">
|
||||
<a href="../geometry/area.html">Area</a>
|
||||
<a href="../area.html">Area of Plane Shapes</a>
|
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</div>
|
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Activity: Grass for the Garden</h1>
|
||||
<table border="0">
|
||||
<tr>
|
||||
<td><span class="larger"><i><img src="images/garden.jpg" width="220" height="133" alt="garden" /></i></span></td>
|
||||
<td><p class="center larger"><i>You want to re-turf the garden</i></p>
|
||||
<p class="center larger">Let us try and find out what it will cost!</p></td>
|
||||
</tr>
|
||||
</table>
|
||||
<p>Your first step is to find the area. The <a href="garden-area.html">Garden Area Activity</a> shows you how.</p>
|
||||
<table width="50%" border="1" align="center">
|
||||
<tr>
|
||||
<td><p class="larger">Area of Garden m<sup>2</sup> (or ft<sup>2</sup>):</p></td>
|
||||
</tr>
|
||||
</table>
|
||||
<p>Now, you have two choices:</p>
|
||||
<ul>
|
||||
<li>buy <b>seed</b> (and enjoy watching the grass grow), or</li>
|
||||
<li>buy <b>turf</b> (and get instant weed-free results)?</li>
|
||||
</ul>
|
||||
<p class="larger">Let us work out the cost of each.</p>
|
||||
<p><i>Note: I include sample values, but you should use your own garden area, and also find out the cost of seed and turf where you live.</i></p>
|
||||
<p> </p>
|
||||
<img src="images/grass-seed.jpg" width="118" height="167" style="float:left; margin: 20px; " alt="grass seed" />
|
||||
<h2>Seed<br></h2>
|
||||
<p>How much grass seed should I order? <br></p>
|
||||
<p>You've already calculated the area of your garden, so now you will have to find out how much seed will cover each square meter, or each square foot.</p>
|
||||
<p>This might also depend on which kind of grass seed you want to use, so you will have to decide that first.<br></p>
|
||||
<p>You could visit your local garden center or farm supply store and read the instructions on the seed packet, or ask the store keeper for advice. Write down your choice here:</p>
|
||||
<table width="50%" border="1" align="center">
|
||||
<tr>
|
||||
<td><p class="larger">Type of Grass Seed:</p></td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td><p class="larger">How Much Seed per m<sup>2</sup> (or ft<sup>2</sup>):</p></td>
|
||||
</tr>
|
||||
</table>
|
||||
<p>While you are at the store, collect some prices.</p>
|
||||
<table width="50%" border="1" align="center">
|
||||
<tr>
|
||||
<td align="right"><p class="larger">Packet Size:</p></td>
|
||||
<td width="70"> </td>
|
||||
<td width="70"> </td>
|
||||
<td width="70"> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right"><p class="larger">Cost:</p></td>
|
||||
<td> </td>
|
||||
<td> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</table>
|
||||
<p><br>
|
||||
Now you've got all the information, what kind of calculation will you need to do? <br></p>
|
||||
<div class="example">
|
||||
<h3>Example:
|
||||
The area of my garden is 41m<sup>2</sup><br></h3>
|
||||
<p>I found out from the local garden center that I will need 55g of seed for each m<sup>2</sup>.</p>
|
||||
<p>So the total amount of seed I will need is:</p>
|
||||
<p class="center">41 × 55g = 2,255g</p>
|
||||
<p>But the area calculation was only a rough estimate, so maybe I need to buy, say, 5% extra.<br></p>
|
||||
<p class="center">That makes 2,255g × 105% = 2,368g</p>
|
||||
<p>Or about <b>2.4 kg</b><br></p>
|
||||
</div>
|
||||
<div class="center80">
|
||||
<p class="center larger">Tip: Always order a little more than you need!</p>
|
||||
<p class="center">Just in case your estimate is wrong, or some gets wasted.</p>
|
||||
</div>
|
||||
<p>Suppose the garden center only sells seed in 500g or 1kg packets. How many packets do I need to buy, and which is the most economical?<br></p>
|
||||
<p>I could buy:</p>
|
||||
<ul>
|
||||
<li>Five 500g packets</li>
|
||||
<li>Three 500g packets and one 1kg packet</li>
|
||||
<li>One 500g packet and two 1kg packets</li>
|
||||
</ul>
|
||||
<p>Which do you think is the cheapest way of doing it?<br></p>
|
||||
<p>Maybe the third choice is the cheapest. It's usually more economical to buy larger quantities.</p>
|
||||
<p>But watch out! Sometimes they might sell the smaller quantity at a special rate as a special promotion. Also check out the prices of different brands to get the best bargain.<br></p>
|
||||
<h3>Too Much?</h3>
|
||||
<p>But won't that be too much seed? <br></p>
|
||||
<p>Yes, of course you will have some seed left over (unless you are very lucky), but you can keep some in case you need to reseed part of your lawn another time, or in case the birds ate some of the seed!</p>
|
||||
<h3><br>
|
||||
How much will it cost?<br></h3>
|
||||
<p>Once you know how many packets of seed you need, and what sizes, you can calculate the cost of the seed. That's easy. <br></p>
|
||||
<div class="example">
|
||||
<h3>Example: A 500g packet of seed costs $20 and a 1kg packet costs $35.</h3>
|
||||
<p><br></p>
|
||||
<div class="tbl">
|
||||
<div class="row"><span class="left">I need one 500g packet, so 1 × $20 =</span><span class="right">$20</span></div>
|
||||
<div class="row"><span class="left">I need two 1kg packets, so 2 × $35 =</span><span class="right">$70</span></div>
|
||||
<div class="row"><span class="left">The total cost is:</span><span class="right"><b>$90</b></span></div>
|
||||
</div>
|
||||
<p> </p>
|
||||
</div>
|
||||
<p>Your Turn:</p>
|
||||
<table border="1" align="center" cellpadding="5">
|
||||
<tr align="center">
|
||||
<td class="larger">Packet Size</td>
|
||||
<td class="larger">Quantity</td>
|
||||
<td class="larger">Cost Per<br>
|
||||
Packet</td>
|
||||
<td class="larger">Total Cost</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right"> </td>
|
||||
<td align="right"> </td>
|
||||
<td> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right"> </td>
|
||||
<td align="right"> </td>
|
||||
<td> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="right"> </td>
|
||||
<td align="right"> </td>
|
||||
<td> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td colspan="3" align="right"><b>Grand Total:</b></td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</table>
|
||||
<p>Note: you might have to do the calculations using square feet, and find out the costs of different sizes of packet in 1lb packets and 2lb packets. But the idea's the same.</p>
|
||||
<p> </p>
|
||||
|
||||
<img src="images/turf.jpg" width="200" height="141" style="float:left; margin: 20px;" alt="turf" /><h2>Turf</h2>
|
||||
|
||||
<p>Some people prefer to use turf instead of seed. It may be easier and quicker to lay, but will it cost more?</p>
|
||||
<p>The calculation should be fairly simple. First of all, decide which kind of turf you need.<br></p>
|
||||
<p>Then all you need to know is the cost of 1m<sup>2</sup> of turf (or 1ft<sup>2</sup> of turf). Again, you should be able to find out this information from your local garden center or farm supply store.</p>
|
||||
<div class="example">
|
||||
<p>Example: I found out from the local garden center that turf costs $4.20 per m<sup>2</sup></p>
|
||||
<p>I have an area of 41m<sup>2</sup>, but this was only a rough estimate, and I may lose some when cutting it to shape, say 10% extra.</p>
|
||||
<p class="center">That's 41m<sup>2</sup> × 110% = 45m<sup>2</sup></p>
|
||||
<p>Then the cost of turfing my garden is 45 × $4.20 = <b>$189.00</b></p>
|
||||
</div>
|
||||
<p>For me it costs about twice as much as seeding, but this is just an example. Try it for your own garden.</p>
|
||||
<table width="50%" border="1" align="center">
|
||||
<tr align="center">
|
||||
<td width="33%"><p class="larger">Turf
|
||||
Area</p></td>
|
||||
<td width="33%"><p class="larger">Cost per Area</p></td>
|
||||
<td width="33%"><p class="larger">Total Cost</p></td>
|
||||
</tr>
|
||||
<tr align="center">
|
||||
<td height="50"> </td>
|
||||
<td> </td>
|
||||
<td> </td>
|
||||
</tr>
|
||||
</table>
|
||||
<p>Note: you might have to do the calculations using square feet, and find out the cost per 1ft<sup>2</sup> of turf.</p>
|
||||
<p> </p>
|
||||
<p>Now you know the cost of both choices, which do you chose?</p>
|
||||
<table width="50%" border="1" align="center">
|
||||
<tr align="center">
|
||||
<td align="left"><p class="larger">Your Choice:</p></td>
|
||||
</tr>
|
||||
</table>
|
||||
<p> </p>
|
||||
<p> </p>
|
||||
<div class="related">
|
||||
<a href="index.html">Activities Index</a>
|
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<a href="../money/index.html">Money Index</a>
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<h1 class="center">Activity: Tomatoes for the Garden</h1>
|
||||
<p><span class="larger">How many tomato plants can fit into your garden?</span><br></p>
|
||||
<p>And, if all the conditions for growth are right, what is your expected yield?</p>
|
||||
|
||||
<div class="center80">
|
||||
<p><strong>This depends on:</strong></p>
|
||||
<ul>
|
||||
<li>The size of your garden</li>
|
||||
<li>How close together you plant the tomato plants</li>
|
||||
</ul>
|
||||
</div>
|
||||
|
||||
<p>Plant them too close and they won't grow well, so you will need to spread them out.</p>
|
||||
<p>You could find
|
||||
out the best distance between plants from a gardening book, or the internet.</p>
|
||||
<p><i>And it may depend on the variety of tomato, so make sure you do your research first.</i></p>
|
||||
|
||||
<h2>Your first step is to find the shape of your garden and plot it on a sheet of paper.</h2>
|
||||
<p>You can do the <a href="garden-area.html">Garden Area</a> activity first if you want</p>
|
||||
|
||||
|
||||
<div class="example">
|
||||
<p>As an example, suppose they must be planted 50cm apart,</p>
|
||||
<p>How could they best
|
||||
fit into the example garden below?</p>
|
||||
</div>
|
||||
<p class="center"><img src="images/garden-tomato-1.gif" width="223" height="190" alt="garden tomato 1" /></p>
|
||||
|
||||
<h3>If you plant one tomato plant at random in the garden, say at point X, then where do you plant the next one?</h3>
|
||||
<p>It has to be at least 50cm away, so it could be anywhere on the <b>circumference
|
||||
of the circle</b> of radius 5ocm, like this:</p>
|
||||
<p class="center"><img src="images/garden-tomato-2.gif" width="266" height="175" alt="garden tomato 50cm" /></p>
|
||||
|
||||
<h3>Choose any spot on the circle, then draw another circle ... like this:</h3>
|
||||
<p class="center"><img src="images/garden-tomato-3.gif" width="224" height="188" alt="garden tomato 2" /></p>
|
||||
|
||||
<p>Continue on like that ...</p>
|
||||
<p class="center"><img src="images/garden-tomato-4.gif" width="222" height="188" alt="garden tomato 2 rows" /></p>
|
||||
<p>Just make sure each plant is no closer than 50cm to any other one.</p>
|
||||
<p><b>That was just one way</b> ... not even a good one, as there is wasted space along the edge of the garden.</p>
|
||||
<p>So hopefully you can do better.<br></p>
|
||||
<h2>Here are some ideas:<strong></strong></h2>
|
||||
<ul>
|
||||
<li>Pick a good starting position (in other words, where do you place point X?)</li>
|
||||
<li>Is it better to start measuring from one edge of the garden? But then, not all edges are straight, so which edge should I choose?</li>
|
||||
<li>Maybe a grid will help, like this one:</li>
|
||||
</ul>
|
||||
|
||||
<p class="center"><img src="images/garden-tomato-5.gif" width="229" height="185" alt="garden on grid" /></p>
|
||||
|
||||
<p>Keep each of your attempts, it is interesting to see how you can improve on your plan.</p>
|
||||
<p>Good Luck!</p>
|
||||
|
||||
<h2>What is your expected yield?</h2>
|
||||
<p>Once you've decided on how many plants you can fit into your garden,
|
||||
then you can work out the expected yield of tomatoes from your garden.
|
||||
That's a simple multiplication.</p>
|
||||
|
||||
<div class="example">
|
||||
<p>For example, I estimate that I can plant 200 tomato plants in my garden and the expected yield per plant is 5 kg.</p>
|
||||
<p>So I expect the total yield to be about
|
||||
<strong>200 × 5kg = 1,000kg</strong> or <strong>1 tonne</strong>!</p>
|
||||
</div>
|
||||
|
||||
<p>And, if I sell my tomatoes for $2 a kilogram, then I'm on to a winner.
|
||||
Perhaps this is a better choice than having a lawn in my back garden!</p>
|
||||
|
||||
<h2>But what about the cost of fertiliser and insecticides and all the time
|
||||
it takes to nurture those tomatoes?</h2>
|
||||
<p>Well, that's another story ... you can work all that out!</p>
|
||||
<p> </p>
|
||||
|
||||
<h2>Follow Up</h2>
|
||||
|
||||
<p>Instead of planting tomatoes, what about having a
|
||||
barbecue party for your friends?</p>
|
||||
<p>But how many friends could you invite
|
||||
to your party without the garden being overcrowded?</p>
|
||||
<p><b>Just use the same method!</b></p>
|
||||
<p>Except the plants are replaced by people, and maybe they should be
|
||||
two meters apart instead of 50 centimeters. But the idea is the
|
||||
same.</p>
|
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<p> </p>
|
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<a href="index.html">Activity Index</a>
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<meta name="description" content="Activity to go and find functions in nature, and photograph them!" />
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Finding Graphs of Functions in Nature</h1>
|
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<p class="large">Go find functions in nature, and photograph them!</p>
|
||||
<p>Studying <a href="../sets/functions-common.html">Graphs of Functions</a>?</p>
|
||||
<p>Well, some graphs of functions appear a lot, so knowing their shapes gives you a much better shot at graphing them correctly and catching common errors.</p>
|
||||
<h2>What do you need?</h2>
|
||||
<ul>
|
||||
<li>Either a graphing calculator, or a printout of the <a href="../sets/functions-common.html">graphs of functions</a></li>
|
||||
<li>A park or nature trail with plenty of trees or backyard</li>
|
||||
<li>A camera</li>
|
||||
<li>A keen eye for natural (not human made) shapes</li>
|
||||
</ul>
|
||||
<p>Here are a few examples:</p>
|
||||
<div class="simple">
|
||||
<table border="0" align="center">
|
||||
<tr>
|
||||
<td align="center">
|
||||
<p class="center"> </p>
|
||||
<p><img src="../algebra/images/y-mxpb-graph.svg" alt="y=mx+b graph" /></p>
|
||||
<p><span class="larger">f(x) = mx + b</span></p>
|
||||
</td>
|
||||
<td align="center">
|
||||
<p class="center"><img src="../sets/images/function-reciprocal.svg" alt="Reciprocal function" /></p>
|
||||
<p class="center"><span class="larger">f(x) = 1/x</span></p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="center">
|
||||
<p class="center"><img src="../sets/images/function-square.svg" alt="Square function" /></p>
|
||||
<p class="center"><span class="larger"> f(x) = x<sup>2</sup></span></p>
|
||||
</td>
|
||||
<td align="center">
|
||||
<p class="center"><img src="../sets/images/function-square-root.gif" alt="Square root function" width="308" height="160" /></p>
|
||||
<p class="center"><span class="larger">f(x) = √x</span></p>
|
||||
</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td align="center">
|
||||
<p class="center"><img src="../sets/images/function-absolute.svg" alt="Absolute Value function" /></p>
|
||||
<p class="center"><span class="larger">f(x) = |x|</span></p>
|
||||
</td>
|
||||
<td align="center"><img src="../sets/images/function-exponential-e.gif" alt="natural exponential function" width="344" height="199" />
|
||||
<br> <span class="larger">f(x) = e<sup>x</sup></span></td>
|
||||
</tr>
|
||||
</table>
|
||||
</div>
|
||||
<p>And here are some example photos we took to give you an idea:
|
||||
<br></p>
|
||||
<h2>Graph of f(x) = mx + b</h2>
|
||||
<p>The graph of f(x) = mx+b is a straight line, thus you are looking for something in nature that resembles a straight line. For example:</p>
|
||||
<p class="center"><img src="images/graphs-functions-nature-1.jpg" width="191" height="329" alt="stick straight line" />
|
||||
<br> TAKE A PIC!</p>
|
||||
<h2><br>
|
||||
Graph of f(x) = x<sup>2</sup> or -x<sup>2</sup></h2>
|
||||
<p>The graph of f(x) = x<sup>2</sup> looks like a U, and -x<sup>2</sup> is like a ∩, thus you are looking for something that resembles a U or ∩. For example:</p>
|
||||
<p class="center"><img src="images/graphs-functions-nature-2.jpg" width="159" height="183" alt="stick x squared" />
|
||||
<br> TAKE A PIC!</p>
|
||||
<h2><br>
|
||||
Graph of Square Root: f(x) = √x <br></h2>
|
||||
<p>The graph of f(x) = √x looks something like the lower case letter r, for example:</p>
|
||||
<p class="center"><img src="images/graphs-functions-nature-3.jpg" width="194" height="315" alt="stick square root" />
|
||||
<br> TAKE A PIC!</p>
|
||||
<h2><br>
|
||||
Graph of Absolute Value: f(x) = |x|<br></h2>
|
||||
<p>The graph of f(x) = |x| looks some thing like the letter V, for example:</p>
|
||||
<p class="center"><img src="images/graphs-functions-nature-4.jpg" width="196" height="311" alt="stick absolute function" />
|
||||
<br> TAKE A PIC!</p>
|
||||
<p><br> See what other graphs you can find...</p>
|
||||
<p><br> When done, compare your pics of nature to the graphs of functions and put together a presentation.</p>
|
||||
<p> </p>
|
||||
<p align="right">Activity courtesy of <a href="hands-on-math.html">Hands On Math</a></p>
|
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<div class="related">
|
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<a href="../sets/functions-common.html">Common Functions</a>
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<h1 class="center">Hands On Math Website</h1>
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<p> </p>
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<p><span class="larger">Hands on Math</span> is a free blog by Jeremiah Dyke that offers innovative hands on strategies for teaching math concepts to primary and secondary teachers.
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<img src="images/hands-on-math.jpg" style="float:right; margin: 10px;" alt="hands on math" height="266" width="400"></p>
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|
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<p>All materials, downloads are maintained for free.</p>
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<p> </p>
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<p class="center"><a href="http://handsonmath.blogspot.com/" class="larger">Visit Hands on Math</a></p>
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Activity: How High?</h1>
|
||||
<p>For this activity you will need:</p>
|
||||
<ul>
|
||||
<li>A piece of cardboard or thin sheet of wood, about the size
|
||||
of a sheet of paper.</li>
|
||||
<li>A piece of string about 30cm or 1 foot long:</li>
|
||||
</ul>
|
||||
<img alt="string" src="images/howhigh1.jpg">
|
||||
<ul>
|
||||
<li>A drawing pin (thumbtack) or a small nail:</li>
|
||||
</ul>
|
||||
<img alt="pin" src="images/howhigh2.jpg">
|
||||
<ul>
|
||||
<li>A small rock (one you can tie the string to):</li>
|
||||
</ul>
|
||||
<img alt="howhigh3" src="images/howhigh3.jpg">
|
||||
<ul>
|
||||
<li>A tape measure:</li>
|
||||
</ul>
|
||||
<img alt="tape measures" src="images/howhigh4.jpg">
|
||||
<ul>
|
||||
<li>scissors</li>
|
||||
<li>glue</li>
|
||||
</ul>
|
||||
|
||||
<h2>Aim</h2>
|
||||
The aim of this activity is to measure the height of a tall building or
|
||||
tree.<br>
|
||||
I will illustrate this with a tree, but the method is just the
|
||||
same for a building.<br>
|
||||
<br>
|
||||
<p class="center"><img alt="tree" src="images/howhigh5.jpg"></p>
|
||||
<h3> </h3>
|
||||
<h3>Suppose you want to measure the height.</h3>
|
||||
<p><strong>Can I just measure it with
|
||||
a tape measure?</strong><br>
|
||||
That won't be easy. You may have to climb the tree to do that. Dangerous!</p>
|
||||
<p>But there is another, easier, way!</p>
|
||||
<div class="center80">
|
||||
<p>Measure a length <b>along the ground</b> and measure the <b>angle θ</b> to the top of the tree:</p>
|
||||
<p class="center"><img alt="tree with angle" src="images/howhigh6.jpg"></p>
|
||||
<p><i>Surveyors and engineers use special equipment to measure these
|
||||
distances and angles accurately. The instrument they use to measure the
|
||||
angle is called a theodolite.
|
||||
In this activity you will make a simple theodolite. You won't get
|
||||
accurate answers, but it will help you to understand how surveyors do
|
||||
their work.</i></p>
|
||||
</div>
|
||||
<p><strong>There are three parts to this activity:</strong></p>
|
||||
<ul>
|
||||
<li>Making a simple theodolite.</li>
|
||||
<li>Measuring the angle and the distance along the ground.</li>
|
||||
<li>Using the measurements to find the height of the tree.</li>
|
||||
</ul>
|
||||
<h2>Making a Simple Theodolite</h2>
|
||||
<p><strong>Step 1:</strong> Print
|
||||
out this <a href="images/howhigh7.jpg">image</a> of a protractor onto A4 paper.<br>
|
||||
You will need to change the page
|
||||
orientation to landscape. </p>
|
||||
<p><strong>Step 2:</strong> You do not need to cut
|
||||
out the picture of the protractor, but you will need to cut as near as
|
||||
you can to the top edge - just leave a small space, enough for you to
|
||||
attach the drawing pin or nail.</p>
|
||||
<p><strong>Step3:</strong> Glue your picture of the
|
||||
protractor with its straight-edge lying along the<br>
|
||||
top edge of your
|
||||
cardboard or timber:</p>
|
||||
<p class="center"><img alt="protractor on wood" src="images/howhigh8.svg"></p>
|
||||
<p><strong>Step 4:</strong> Tie the small rock to
|
||||
one end of the piece of string:</p>
|
||||
<p class="center"><img alt="rock on string" src="images/howhigh9.jpg"></p>
|
||||
<p><strong>Step 5:</strong> Attach the other end of
|
||||
the string to the top middle point of the <br>
|
||||
protractor using the drawing
|
||||
pin or
|
||||
nail:</p>
|
||||
<p class="center"><img alt="protractor on wood with rock on string" src="images/howhigh10.jpg"></p>
|
||||
<p>When you allow the rock to pull the string downwards, gravity will make
|
||||
it hang vertically. Even if you tilt the piece of cardboard or timber
|
||||
at an angle, the string will still hang vertically:</p>
|
||||
<p class="center"><img alt="protractor string at 90" src="images/howhigh11a.svg"> <img alt="protractor string at 60" src="images/howhigh11b.svg"></p>
|
||||
<p><strong>Can you see how the angle of 30°
|
||||
is related to the angle shown by the string on the protractor?</strong></p>
|
||||
<h2><br>
|
||||
Measuring the Angle
|
||||
and the Distance Along the Ground</h2>
|
||||
<p>First of all, find a good place to stand about <strong>100 feet or 30m
|
||||
away from the tree</strong>. Make sure that you are standing on level ground and
|
||||
in a safe place. Mark the place with a stick. Now you are ready to
|
||||
measure.</p>
|
||||
<p>To measure the angle, you just point your 'theodolite'' towards the top
|
||||
of the tree. Put your eye as close as possible to one edge of the
|
||||
protractor; then, looking along the straight edge, point it directly at
|
||||
the top of the tree:</p>
|
||||
<p class="center"><img alt="howhigh12" src="images/howhigh12.jpg"></p>
|
||||
<p>Hold the string and weight in position before you lower the theodolite.
|
||||
Then read the angle from the theodolite as the angle the vertical
|
||||
weight on
|
||||
the string makes with the protractor. Adjust your answer to find
|
||||
the <a href="../algebra/trig-finding-angle-right-triangle.html">angle
|
||||
of elevation</a>, <strong>θ</strong>, from
|
||||
your eye to the top of the tree.</p>
|
||||
<p>To find the distance, <strong>d</strong>, use your tape measure to measure from the
|
||||
stick to the base of the tree, or more exactly to the midpoint of the
|
||||
base of the tree - <strong>can you see how to make allowance for that?</strong></p>
|
||||
<h2>Using the
|
||||
Measurements to Find the Height of the Tree</h2>
|
||||
<p>You can calculate the height of the tree using a scale diagram on a
|
||||
piece of paper,<br>
|
||||
following these steps:</p>
|
||||
<ul>
|
||||
<li>Draw a horizontal line:</li>
|
||||
</ul>
|
||||
<img alt="howhigh13" src="images/howhigh13.jpg">
|
||||
<ul start="2">
|
||||
<li>At a point, <strong>C</strong>, near the right end of the line, measure an angle
|
||||
equal to the angle, <strong>θ</strong>, from your experiment:</li>
|
||||
</ul>
|
||||
<img alt="howhigh14" src="images/howhigh14.jpg">
|
||||
<ul start="3">
|
||||
<li>Choosing a suitable scale, measure the distance x equivalent to
|
||||
the distance <strong>d</strong> you measured in your experiment. Mark a point <strong>B</strong>:</li>
|
||||
</ul>
|
||||
<img alt="howhigh15" src="images/howhigh15.jpg">
|
||||
<ul start="4">
|
||||
<li>Draw the perpendicular at <strong>B</strong> to meet the sloping line at <strong>A</strong>:</li>
|
||||
</ul>
|
||||
<img alt="howhigh16" src="images/howhigh16.jpg">
|
||||
<ul start="5">
|
||||
<li>Measure the height, <strong>y</strong>, of <strong>A</strong> above <strong>B</strong>:</li>
|
||||
</ul>
|
||||
<img alt="howhigh17" src="images/howhigh17.jpg">
|
||||
<ul start="6">
|
||||
<li>Using the scale from step 3, convert <strong>y</strong> back to find the height, <strong>h</strong>, of the tree.</li>
|
||||
</ul>
|
||||
<h2>Wait!</h2>
|
||||
<ul class="bigul">
|
||||
<li>Did you notice anything wrong?</li>
|
||||
<li>Where was your eye when you measured the angle θ?</li>
|
||||
<li>Can you think of a way to compensate for that error?</li>
|
||||
</ul>
|
||||
<h2>Another Way</h2>
|
||||
<p>There is an alternative way to calculate the height of the tree using <a href="../sine-cosine-tangent.html">trigonometry</a>.<br>
|
||||
If you know how to do this, then go ahead.</p>
|
||||
<ul>
|
||||
<li>How accurate will your answer be?</li>
|
||||
</ul>
|
||||
<h3>Can you list below some things about this experiment that tell you that
|
||||
your answer is not very accurate?</h3>
|
||||
<ol>
|
||||
<li> </li>
|
||||
<li> </li>
|
||||
<li> </li>
|
||||
<li> </li>
|
||||
<li> </li>
|
||||
</ol>
|
||||
<h3>Any more?</h3>
|
||||
|
||||
<p><strong>Try to find out how</strong><strong> a real theodolite is made and why it gives much
|
||||
more accurate measurements.</strong></p>
|
||||
<p> </p>
|
||||
<div class="related">
|
||||
<a href="index.html">Activities Index</a>
|
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</div>
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