小学四年级假分数可视化演示
2017-08-22 14:03
本GeoGebra范例用于小学四年级数学教学，通过矩形面积模型直观演示假分数的概念。用户可通过交互按钮调节分子与分母的数值，观察分数对应的整数部分与真分数部分的图形表示。范例利用多边形序列绘制等分矩形，结合取模运算与条件判断，动态展示假分数如何拆分为整数与真分数之和，帮助学生理解假分数与带分数之间的转换关系。
GeoGebra 画板及绘图内容加载中，请稍等……
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<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<command name="If">
<input a0="ShowChi" a1=""顯示下圖代表的數值 (帶分數形式，未約簡)"" a2=""Show the value represented by the following figure (in mixed numbers, not simplified)""/>
<output a0="Text42"/>
</command>
<element type="text" label="Text42">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="239" b="213" alpha="255"/>
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<element type="numeric" label="BaseX2">
<value val="-5.9"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
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<labelMode val="1"/>
<slider min="-10" max="5" absoluteScreenLocation="true" width="200" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="BaseY2">
<value val="-10.3"/>
<show object="false" label="true"/>
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<labelMode val="1"/>
<slider min="-15" max="5" absoluteScreenLocation="true" width="200" fixed="true" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
</element>
<command name="Mod">
<input a0="n2" a1="Denom2"/>
<output a0="FracNum2"/>
</command>
<element type="numeric" label="FracNum2">
<value val="3"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="RectNum2" exp="ceil(n2 / Denom2)" />
<element type="numeric" label="RectNum2">
<value val="3"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="Whole2" exp="floor(n2 / Denom2)" />
<element type="numeric" label="Whole2">
<value val="2"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
</element>
<expression label="A" exp="(-7.62507, 3.4)" type="point"/>
<element type="point" label="A">
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<objColor r="0" g="0" b="255" alpha="0"/>
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<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
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<pointSize val="5"/>
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<expression label="B" exp="(22.32838, 3.4)" type="point"/>
<element type="point" label="B">
<show object="false" label="false"/>
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<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="22.32838" y="3.4" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
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<command name="Segment">
<input a0="A" a1="B"/>
<output a0="SegSeperation"/>
</command>
<element type="segment" label="SegSeperation">
<show object="true" label="false"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<coords x="0" y="29.95345" z="-101.84172999999998"/>
<lineStyle thickness="2" type="15" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
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<command name="Sequence">
<input a0="Segment[(BaseX2 + (s * RectNum2), BaseY2 + (h / Denom2 * l)), (BaseX2 + (s * RectNum2) + width, BaseY2 + (h / Denom2 * l))]" a1="l" a2="1" a3="Denom2 - 1"/>
<output a0="LastBoxSegments2"/>
</command>
<element type="list" label="LastBoxSegments2">
<show object="true" label="true" ev="4"/>
<condition showObject="Mod[n2, Denom2] ≠ 0"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<expression label="TextAns2" exp=""\frac{" + (LaTeX[n]) + "}{" + (LaTeX[Denom]) + "}"" />
<element type="text" label="TextAns2">
<show object="false" label="false" ev="8"/>
<condition showObject="ShowNum"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="191" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2" size="18" style="0"/>
<startPoint x="-5.858079352154633" y="11.44985371592267" z="1"/>
</element>
<expression label="TextAns22" exp=""\frac{" + (LaTeX[n2]) + "}{" + (LaTeX[Denom2]) + "}"" />
<element type="text" label="TextAns22">
<show object="true" label="false" ev="8"/>
<condition showObject="ShowNum2"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="208" g="240" b="192" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2" size="18" style="0"/>
<startPoint x="-6.409916113732915" y="-3.2505261808976806" z="1"/>
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<command name="Sequence">
<input a0="Polygon[(BaseX + (s * RectNum), BaseY + (h / Denom * (l - 1))), (BaseX + (s * RectNum), BaseY + (h / Denom * l)), (BaseX + (s * RectNum) + width, BaseY + (h / Denom * l)), (BaseX + (s * RectNum) + width, BaseY + (h / Denom * (l - 1)))]" a1="l" a2="1" a3="If[Mod[n, Denom] ≟ 0, Denom, Mod[n, Denom]]"/>
<output a0="NumPartFraction"/>
</command>
<element type="list" label="NumPartFraction">
<show object="true" label="true" ev="4"/>
<objColor r="128" g="0" b="128" alpha="0.1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<command name="Sequence">
<input a0="Sequence[Polygon[(BaseX + (s * j), BaseY + (h / Denom * (l - 1))), (BaseX + (s * j), BaseY + (h / Denom * l)), (BaseX + (s * j) + width, BaseY + (h / Denom * l)), (BaseX + (s * j) + width, BaseY + (h / Denom * (l - 1)))], l, 1, Denom]" a1="j" a2="1" a3="RectNum - 1"/>
<output a0="NumPartWhole"/>
</command>
<element type="list" label="NumPartWhole">
<show object="true" label="true" ev="4"/>
<objColor r="128" g="0" b="128" alpha="0.1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<command name="Sequence">
<input a0="Polygon[(BaseX2 + (s * RectNum2), BaseY2 + (h / Denom2 * (l - 1))), (BaseX2 + (s * RectNum2), BaseY2 + (h / Denom2 * l)), (BaseX2 + (s * RectNum2) + width, BaseY2 + (h / Denom2 * l)), (BaseX2 + (s * RectNum2) + width, BaseY2 + (h / Denom2 * (l - 1)))]" a1="l" a2="1" a3="If[Mod[n2, Denom2] ≟ 0, Denom2, Mod[n2, Denom2]]"/>
<output a0="NumPartFraction2"/>
</command>
<element type="list" label="NumPartFraction2">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
<angleStyle val="0"/>
</element>
<command name="Sequence">
<input a0="Sequence[Polygon[(BaseX2 + (s * j), BaseY2 + (h / Denom2 * (l - 1))), (BaseX2 + (s * j), BaseY2 + (h / Denom2 * l)), (BaseX2 + (s * j) + width, BaseY2 + (h / Denom2 * l)), (BaseX2 + (s * j) + width, BaseY2 + (h / Denom2 * (l - 1)))], l, 1, Denom2]" a1="j" a2="1" a3="RectNum2 - 1"/>
<output a0="NumPartWhole2"/>
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<element type="list" label="NumPartWhole2">
<show object="true" label="true"/>
<objColor r="0" g="100" b="0" alpha="0.15"/>
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<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
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</element>
<command name="Segment">
<input a0="(BaseX2 + (s * RectNum2), BaseY2 + 0)" a1="(BaseX2 + (s * RectNum2), BaseY2 + h)"/>
<output a0="LastBoxSide12"/>
</command>
<element type="segment" label="LastBoxSide12">
<show object="true" label="false"/>
<objColor r="0" g="100" b="0" alpha="0"/>
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<labelMode val="0"/>
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<lineStyle thickness="2" type="0" typeHidden="1"/>
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<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="(BaseX2 + (s * RectNum2), BaseY2 + h)" a1="(BaseX2 + (s * RectNum2) + width, BaseY2 + h)"/>
<output a0="LastBoxSide22"/>
</command>
<element type="segment" label="LastBoxSide22">
<show object="true" label="false"/>
<objColor r="0" g="100" b="0" alpha="0"/>
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<labelMode val="0"/>
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<lineStyle thickness="2" type="0" typeHidden="1"/>
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<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="(BaseX2 + (s * RectNum2) + width, BaseY2 + h)" a1="(BaseX2 + (s * RectNum2) + width, BaseY2 + 0)"/>
<output a0="LastBoxSide32"/>
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<element type="segment" label="LastBoxSide32">
<show object="true" label="false"/>
<objColor r="0" g="100" b="0" alpha="0"/>
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<command name="Segment">
<input a0="(BaseX2 + (s * RectNum2) + width, BaseY2 + 0)" a1="(BaseX2 + (s * RectNum2), BaseY2 + 0)"/>
<output a0="LastBoxSide42"/>
</command>
<element type="segment" label="LastBoxSide42">
<show object="true" label="false"/>
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</construction>
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