Magic Candy Bar: Geometric Demo of Fractions and Probability
2019-02-22 13:50
This GeoGebra example uses a candy bar geometric model to demonstrate fractions, random experiments, and probability concepts. Constructed with polygons, rays, and points, it illustrates conditional probability, confidence intervals, and geometric mean calculations for interactive learning.
In collections
百變糖果棒
Loading the GeoGebra board and drawing, please wait…
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.525.0" app="classic" platform="w" id="3e4b18a5-a52e-40f2-96db-6d3e7685ef2f" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="900" height="600" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.27666666666666667" orientation="0" />
</panes>
<views>
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="false" inframe="false" stylebar="false" location="1,1,1" size="500" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="true" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="true" location="2" size="545" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="3" size="200" window="56,111,250,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="4097" visible="false" inframe="false" stylebar="true" location="0" size="166" window="1673,432,700,550" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
</views>
<toolbar show="true" items="0 | 73 | 41 42 40 | 6 | 100002 | 100003 | 100004 | 100005 | 100012 | 100013 | 100014 | 100015 | 100016 | 100006 | 100007 | 100008 | 100021 100020 100019 100018 100017 100009 | 100010 | 100011 | 100001" position="1" help="false" />
<input show="false" cmd="true" top="false" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="2"/>
<font size="16"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="898" height="545"/>
<coordSystem xZero="37.72727272727273" yZero="421.45454545454544" scale="1.722610722610724" yscale="26.534070000000007"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="2" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="250" b="205"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<grid distX="1" distY="1" distTheta="0.5235987755982988"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="1" spreadsheet="1"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="point" label="A">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="25" y="12" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<expression label="B" exp="A + (30, 0)" type="point" />
<element type="point" label="B">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="55" y="12" z="1"/>
<pointSize val="2"/>
<pointStyle val="0"/>
</element>
<expression label="C" exp="B + (0, 2)" type="point" />
<element type="point" label="C">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="55" y="14" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<expression label="D" exp="A + (0, 2)" type="point" />
<element type="point" label="D">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="25" y="14" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Polygon">
<input a0="A" a1="B" a2="C" a3="D"/>
<output a0="poly1" a1="a" a2="b" a3="c" a4="d"/>
</command>
<element type="polygon" label="poly1">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="false" label="false" ev="4"/>
<objColor r="192" g="192" b="192" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<element type="segment" label="a">
<show object="false" label="false" ev="4"/>
<objColor r="160" g="160" b="160" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0" y="30" z="-360"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="b">
<show object="false" label="false" ev="4"/>
<objColor r="160" g="160" b="160" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="-2" y="0" z="110"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="c">
<show object="false" label="false" ev="4"/>
<objColor r="160" g="160" b="160" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="0" y="-30" z="420"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="d">
<show object="false" label="false" ev="4"/>
<objColor r="160" g="160" b="160" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="false"/>
<coords x="2" y="0" z="-50"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Text">
<input a0=""\frac{1}{12}"" a1="Centroid[poly1] + (-8, 0.75)" a2="true" a3="true"/>
<output a0="text1"/>
</command>
<element type="text" label="text1">
<show object="false" label="false" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1" size="0" style="0"/>
<startPoint x="32" y="13.75" z="1"/>
</element>
<element type="button" label="重設">
<show object="true" label="true"/>
<objColor r="255" g="255" b="255" alpha="1"/>
<bgColor r="102" g="0" b="153" alpha="255"/>
<layer val="0"/>
<labelOffset x="15" y="16"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<javascript val="ggbApplet.reset()"/>
</element>
<element type="point" label="E">
<show object="false" label="false"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="7" y="10" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="point" label="F">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="1" playing="false"/>
<coords x="0" y="10" z="1"/>
<pointSize val="1"/>
<pointStyle val="2"/>
</element>
<command name="whole">
<input a0="F"/>
<output a0="G" a1="f" a2="g" a3="h" a4="i" a5="q1"/>
</command>
<element type="point" label="G">
<show object="false" label="false"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="360" y="10" z="1"/>
<pointSize val="2"/>
<pointStyle val="0"/>
</element>
<element type="segment" label="f">
<show object="true" label="false"/>
<objColor r="160" g="160" b="160" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="2" y="0" z="0"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="g">
<show object="true" label="false"/>
<objColor r="160" g="160" b="160" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="-360" z="4320"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="h">
<show object="true" label="false"/>
<objColor r="160" g="160" b="160" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-2" y="0" z="720"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="segment" label="i">
<show object="true" label="false"/>
<objColor r="160" g="160" b="160" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0" y="360" z="-3600"/>
<lineStyle thickness="3" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="polygon" label="q1">
<lineStyle thickness="2" type="0" typeHidden="1"/>
<show object="true" label="false" ev="4"/>
<objColor r="255" g="255" b="0" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
</element>
<expression label="text2" exp=""1 (原味)""/>
<element type="text" label="text2">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="false" sizeM="1.4" size="7" style="0"/>
<startPoint x="181.0040595399194" y="11.05349304429432" z="1"/>
</element>
<element type="point" label="base1">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="59" y="6" z="1"/>
<pointSize val="1"/>
<pointStyle val="2"/>
</element>
<element type="image" label="pic1">
<file name="03e23b20535bbeb8523180aba8864f13/screenshot.png"/>
<inBackground val="false"/>
<startPoint number="0" exp="base1"/>
<startPoint number="1" exp="base2"/>
<startPoint number="2" exp="top"/>
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="1"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="point" label="top">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="59" y="8" z="1"/>
<pointSize val="1"/>
<pointStyle val="2"/>
</element>
<expression label="text3" exp=""幾分之幾?""/>
<element type="text" label="text3">
<show object="true" label="false" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<font serif="false" sizeM="1.4" size="7" style="0"/>
<startPoint exp="K"/>
<labelOffset x="-46" y="-20"/>
</element>
<expression label="H" exp="base1 + (1, 0)" type="point" />
<element type="point" label="H">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<coords x="60" y="6" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
<command name="Ray">
<input a0="base1" a1="H"/>
<output a0="j"/>
</command>
<element type="ray" label="j">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<coords x="0" y="1" z="-6"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="j"/>
<output a0="base2"/>
</command>
<element type="point" label="base2">
<show object="true" label="false" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="335" y="6" z="1"/>
<pointSize val="5"/>
<pointStyle val="2"/>
</element>
<expression label="K" exp="(base1 + base2) / 2" type="point" />
<element type="point" label="K">
<show object="false" label="false" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="2"/>
<labelMode val="0"/>
<coords x="197" y="6" z="1"/>
<pointSize val="3"/>
<pointStyle val="0"/>
</element>
</construction>
</geogebra>