有向数的加减法（2）
2015-01-21 04:29
本范例演示有向数（带符号整数）的加减法运算。通过交互式按钮，用户可生成随机题目并查看计算过程。利用向量和序列等GeoGebra命令，直观展示正负数加减时的数值变化规律，帮助学生理解有向数运算的代数意义与几何直观。
GeoGebra 画板及绘图内容加载中，请稍等……
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.288.0" id="a35c451c-2034-4d5f-af79-0bc8ae41b1f9" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="960" height="660" />
<perspectives>
</perspectives>
<labelingStyle val="3"/>
<font size="18"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="958" height="658"/>
<coordSystem xZero="883.6471336181064" yZero="329.64586005043753" scale="25.958425502496837" yscale="25.955870539356752"/>
<evSettings axes="true" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="3" grid="10"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true" tickDistance="1" tickExpression=""/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true" tickDistance="1" tickExpression=""/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<expression label ="list3" exp="{"$+$", "$-$"}"/>
<element type="list" label="list3">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="244" y="23"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<comboBox val="true"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
<font serif="true" sizeM="1.4" size="8" style="0"/>
<caption val="Choose:"/>
</element>
<expression label ="MaxNum" exp="15"/>
<element type="numeric" label="MaxNum">
<value val="15"/>
<show object="false" label="false"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<command name="Sequence">
<input a0="If[i > 0, "$+", "$"] + (Text[i]) + "$"" a1="i" a2="(-MaxNum)" a3="MaxNum"/>
<output a0="list1"/>
</command>
<element type="list" label="list1">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="13" y="23"/>
<labelMode val="3"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<selectedIndex val="7"/>
<comboBox val="true"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
<font serif="true" sizeM="1.4" size="8" style="0"/>
<caption val="Choose:"/>
</element>
<expression label="a" exp="SelectedIndex[list1] - MaxNum - 1" />
<element type="numeric" label="a">
<value val="-8"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<selectionAllowed val="false"/>
</element>
<command name="Sequence">
<input a0="If[i > 0, "$+", "$"] + (Text[i]) + "$"" a1="i" a2="(-MaxNum)" a3="MaxNum"/>
<output a0="list2"/>
</command>
<element type="list" label="list2">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="449" y="23"/>
<labelMode val="3"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<selectedIndex val="17"/>
<comboBox val="true"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
<font serif="true" sizeM="1.4" size="8" style="0"/>
<caption val="Choose:"/>
</element>
<expression label="b" exp="SelectedIndex[list2] - MaxNum - 1" />
<element type="numeric" label="b">
<value val="2"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<selectionAllowed val="false"/>
</element>
<element type="button" label="button1">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelOffset x="313" y="148"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetVisibleInView[text1,1,lang==1] SetVisibleInView[text1eng,1,lang!=1] SetVisibleInView[u,1,true] SetVisibleInView[button2,1,true] SetVisibleInView[pic1,1,true] SetVisibleInView[pic2,1,true] SetVisibleInView[pic3,1,true] SetVisibleInView[pic4,1,true]"/>
<font serif="false" sizeM="2" size="18" style="0"/>
<caption val="Step 1"/>
</element>
<element type="button" label="button2">
<show object="true" label="true" ev="1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelOffset x="313" y="252"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetVisibleInView[text2,1,lang==1] SetVisibleInView[text2eng,1,lang!=1] SetVisibleInView[v,1,true] SetVisibleInView[button3,1,true] SetVisibleInView[textQ2,1,true] "/>
<font serif="false" sizeM="2" size="18" style="0"/>
<caption val="Step 2"/>
</element>
<element type="button" label="button3">
<show object="true" label="true" ev="1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelOffset x="313" y="356"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetVisibleInView[text3,1,lang==1] SetVisibleInView[text3eng,1,lang!=1] SetVisibleInView[button4,1,true] SetVisibleInView[Q,1,true] SetVisibleInView[textQ3,1,true]"/>
<font serif="false" sizeM="2" size="18" style="0"/>
<caption val="Result"/>
</element>
<command name="Vector">
<input a0="(0.5, 0)" a1="(0.5, a)"/>
<output a0="u"/>
</command>
<element type="vector" label="u">
<show object="true" label="false" ev="1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<coords x="0" y="-8" z="0"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<coordStyle style="cartesian"/>
<startPoint x="0.5" y="0" z="1"/>
</element>
<element type="button" label="button4">
<show object="true" label="true" ev="1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelOffset x="313" y="459"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetVisibleInView[pic1,1,false] SetVisibleInView[pic2,1,false] SetVisibleInView[pic3,1,false] SetVisibleInView[pic4,1,false] SetVisibleInView[text1,1,false] SetVisibleInView[text2,1,false] SetVisibleInView[text3,1,false] SetVisibleInView[text1eng,1,false] SetVisibleInView[text2eng,1,false] SetVisibleInView[text3eng,1,false] SetVisibleInView[u,1,false] SetVisibleInView[v,1,false] SetVisibleInView[Q,1,false] SetVisibleInView[button2,1,false] SetVisibleInView[button3,1,false] SetVisibleInView[button4,1,false] SetVisibleInView[textQ2,1,false] SetVisibleInView[textQ3,1,false]"/>
<font serif="false" sizeM="2" size="18" style="0"/>
<caption val="Start over"/>
</element>
<element type="point" label="P">
<show object="true" label="true"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="-67" y="16"/>
<labelMode val="3"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<auxiliary val="true"/>
<coords x="0" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="1"/>
<caption val="Start"/>
</element>
<command name="If">
<input a0="SelectedIndex[list3] ≟ 1" a1="a + b" a2="a - b"/>
<output a0="answer"/>
</command>
<element type="numeric" label="answer">
<value val="-6"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<selectionAllowed val="false"/>
</element>
<command name="Vector">
<input a0="(1, a)" a1="(1, answer)"/>
<output a0="v"/>
</command>
<element type="vector" label="v">
<show object="true" label="false" ev="1"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0" y="2" z="0"/>
<lineStyle thickness="7" type="0" typeHidden="1"/>
<coordStyle style="cartesian"/>
<startPoint x="1" y="-8" z="1"/>
</element>
<expression label="Q" exp="(0, answer)" type="point" />
<element type="point" label="Q">
<show object="true" label="true" ev="5"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="31" y="15"/>
<labelMode val="3"/>
<coords x="0" y="-6" z="1"/>
<pointSize val="5"/>
<pointStyle val="1"/>
<caption val="Destination"/>
</element>
<expression label="text3" exp=""終點是 " + answer + """ />
<element type="text" label="text3">
<show object="true" label="false" ev="9"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<absoluteScreenLocation x="427" y="377"/>
</element>
<element type="image" label="pic3">
<file name="be3baa76f13161411b0b8a955d92a7e6\images2.jpg"/>
<inBackground val="false"/>
<absoluteScreenLocation x="503" y="208"/> <show object="true" label="false" ev="1"/>
<condition showObject="a < 0"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
</element>
<element type="image" label="pic1">
<file name="f6d332056483e301db46ccfa1e64ad0c\images1.jpg"/>
<inBackground val="false"/>
<absoluteScreenLocation x="504" y="208"/> <show object="true" label="false" ev="1"/>
<condition showObject="a ≥ 0"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
</element>
<element type="image" label="pic2">
<file name="f6d332056483e301db46ccfa1e64ad0c\images1.jpg"/>
<inBackground val="false"/>
<absoluteScreenLocation x="690" y="207"/> <show object="true" label="false" ev="1"/>
<condition showObject="b ≥ 0"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<selectionAllowed val="false"/>
</element>
<element type="image" label="pic4">
<file name="be3baa76f13161411b0b8a955d92a7e6\images2.jpg"/>
<inBackground val="false"/>
<absoluteScreenLocation x="689" y="207"/> <show object="true" label="false" ev="1"/>
<condition showObject="b < 0"/>
<objColor r="0" g="0" b="0" alpha="1"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<selectionAllowed val="false"/>
</element>
<element type="button" label="buttonRan">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="191" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelOffset x="705" y="25"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[list1,Random[1,2*MaxNum+1]] SetValue[list2,Random[1,2*MaxNum+1]] SetValue[list3,Random[1,2]] RunClickScript[button4]"/>
<font serif="false" sizeM="2" size="18" style="0"/>
<caption val="Random"/>
</element>
<expression label="textQ3" exp=""= " + (LaTeX[answer]) + """ />
<element type="text" label="textQ3">
<show object="true" label="false" ev="9"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2" size="18" style="0"/>
<absoluteScreenLocation x="16" y="346"/>
</element>
<command name="If">
<input a0="SelectedIndex[list3] ≟ 1" a1="If[b ≥ 0, "+", "-"]" a2="If[b < 0, "+", "-"]"/>
<output a0="signMiddle"/>
</command>
<element type="text" label="signMiddle">
<show object="false" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<absoluteScreenLocation x="834" y="279"/>
</element>
<expression label="text2" exp=""" + (If[a ≥ 0, "由零開始，先上升" + (abs(a)) + "層，", "由零開始，先下跌" + (abs(a)) + "層，"] + (If[signMiddle ≟ "+", "然後上升" + (abs(b)) + "層", "然後下跌" + (abs(b)) + "層"])) + """ />
<element type="text" label="text2">
<show object="true" label="false" ev="9"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<absoluteScreenLocation x="427" y="274"/>
</element>
<expression label="textQ1" exp=""(" + (LaTeX[If[a > 0, "+", ""]]) + "" + (LaTeX[a]) + ")" + (LaTeX[If[SelectedIndex[list3] ≟ 1, "+", "-"]]) + "(" + (LaTeX[If[b > 0, "+", ""]]) + "" + (LaTeX[b]) + ")"" />
<element type="text" label="textQ1">
<show object="true" label="false" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2" size="18" style="0"/>
<absoluteScreenLocation x="16" y="139"/>
</element>
<expression label="textQ2" exp=""=" + (LaTeX[If[a > 0, "+", ""]]) + " " + (LaTeX[a]) + "" + (LaTeX[signMiddle]) + "" + (LaTeX[Text[abs(b)]]) + """ />
<element type="text" label="textQ2">
<show object="true" label="false" ev="9"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="2" size="18" style="0"/>
<absoluteScreenLocation x="16" y="244"/>
</element>
<element type="button" label="button0">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelOffset x="728" y="459"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[lang,If[lang==1,2,1]] RunClickScript[buttonLang] RunClickScript[button4]"/>
<font serif="false" sizeM="1.4" size="8" style="0"/>
<caption val="中文"/>
</element>
<element type="button" label="buttonLang">
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelOffset x="924" y="502"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetCaption[button0,If[lang==1,"ENG","中文"]] SetCaption[list1,If[lang==1,"選擇：","Choose: "]] SetCaption[list2,If[lang==1,"選擇：","Choose: "]] SetCaption[list3,If[lang==1,"選擇：","Choose: "]] SetCaption[button1,If[lang==1,"第一步","Step 1"]] SetCaption[button2,If[lang==1,"第二步","Step 2"]] SetCaption[button3,If[lang==1,"結果","Result"]] SetCaption[button4,If[lang==1,"重新開始","Start over"]] SetCaption[buttonRan,If[lang==1,"隨機","Random"]] SetCaption[P,If[lang==1,"起點","Start"]] SetCaption[Q,If[lang==1,"終點","Destination"]]"/>
<font serif="false" sizeM="2" size="18" style="0"/>
</element>
<element type="numeric" label="lang">
<value val="2"/>
<symbolic val="true" />
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="3"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<expression label="text3eng" exp=""The destination is " + answer + "."" />
<element type="text" label="text3eng">
<show object="true" label="false" ev="9"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<absoluteScreenLocation x="434" y="378"/>
</element>
<expression label="text2eng" exp=""Start at 0. Move " + (If[a ≥ 0, "up for " + (abs(a)) + " unit", "down for " + (abs(a)) + " unit"]) + "" + (If[abs(a) ≟ 1, "", "s"]) + ". Then move " + (If[signMiddle ≟ "+", "up for " + (abs(b)) + " unit", "down for " + (abs(b)) + " unit"]) + "" + (If[abs(b) ≟ 1, "", "s"]) + "."" />
<element type="text" label="text2eng">
<show object="true" label="false" ev="9"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<absoluteScreenLocation x="434" y="274"/>
</element>
<expression label="text1" exp=""加上" + (abs(a)) + "個 ，" + (If[SelectedIndex[list3] ≟ 1, "加上" + (abs(b)) + "個", "拿走" + (abs(b)) + "個"]) + """ />
<element type="text" label="text1">
<show object="true" label="true" ev="9"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<absoluteScreenLocation x="426" y="172"/>
</element>
<expression label="text1eng" exp=""add " + (abs(a)) + " , " + (If[SelectedIndex[list3] ≟ 1, "add " + (abs(b)), "take away " + (abs(b))]) + """ />
<element type="text" label="text1eng">
<show object="true" label="false" ev="9"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="3"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<absoluteScreenLocation x="435" y="177"/>
</element>
</construction>
</geogebra>