GeoGebra 探究3与9的整除性：因数-倍数关系的图形化练习

几何画板及绘图内容加载中，请稍等……

2024-05-16 13:29

所属专题 Teilbarkeitsregeln

这个范例通过交互式几何/文字标注与随机列表，展示数是否能被3或9整除的规律在不同输入下的表现。核心数学概念包括：因数与倍数、可整除性规则、把关于整除的判断转化为可验证条件，并用于说明或反驳一般性说法。作图要点是将“题目/状态文本”和若干计算结果对象组织起来：利用多边形对象（Polygon）作为界面/布局或示意元素，使用随机列表（RandomList3、RandomList9）生成待检数据；用中点（Midpoint）与文本框（Textfield）、元素集合（Element）承载与更新显示；通过元素操作（Append、Remove）、条件判断（If、IsInRegion）与拼接（Join）实现交互逻辑；同时包含文本对象（如多组 ColorText*）用于提示与结论呈现，最终让学生在练习中观察并验证整除规则。适合5–6年级用于“数感与因数倍数”主题的课堂探究、练习与形成性评价。

GeoGebra 命令及参数

Polygon(Q1E1, Q1E2, 4) → Q1, q1_1, q1_2, q1_3, q1_4, Q1E3, Q1E4
Polygon(Q2E1, Q2E2, 4) → Q2, q2_1, q2_2, q2_3, q2_4, Q2E3, Q2E4
Polygon(Q3E1, Q3E2, 4) → Q3, q3_4, q3_1, q3_2, q3_3, Q3E3, Q3E4
Shuffle(Sequence[Element[Shuffle[Sequence[(k * 3), k, 1, 333]], i], i, 1, 5]) → RandomList3, {117, 591, 651, 807, 303}
Shuffle(Sequence[Element[Shuffle[Sequence[(k * 9), k, 1, 111]], i], i, 1, 5]) → RandomList9, {189, 423, 270, 909, 180}
Shuffle(Sequence[Element[Shuffle[Sequence[k, k, 100, 1000] \ Sequence[(k * 3), k, 1, 333]], i], i, 1, 5]) → RandomListNot39, {371, 625, 583, 232, 316}
Shuffle(Unique[Join[{RandomList3, RandomList9, RandomListNot39}]]) → RandomListNum, {232, 651, 180, 909, 316, 591, 270, 303, 117, 371, 625, 807, 583, 189, 423}
Midpoint(Corner[NumText7, 1], Corner[NumText7, 3]) → Pos7
Midpoint(Corner[NumText10, 1], Corner[NumText10, 3]) → Pos10
Midpoint(Corner[T1830, 1], Corner[T1830, 3]) → Pos1830
Midpoint(Corner[NumText6, 1], Corner[NumText6, 3]) → Pos6
Midpoint(Corner[NumText3, 1], Corner[NumText3, 3]) → Pos3
Midpoint(Corner[T1826, 1], Corner[T1826, 3]) → Pos1826
Midpoint(Corner[NumText5, 1], Corner[NumText5, 3]) → Pos5
Midpoint(Corner[NumText9, 1], Corner[NumText9, 3]) → Pos9
Midpoint(Corner[T2628, 1], Corner[T2628, 3]) → Pos2628
Midpoint(Corner[NumText8, 1], Corner[NumText8, 3]) → Pos8
Midpoint(Corner[NumText4, 1], Corner[NumText4, 3]) → Pos4
Midpoint(Corner[NumText2, 1], Corner[NumText2, 3]) → Pos2
Midpoint(Corner[NumText1, 1], Corner[NumText1, 3]) → Pos1
Textfield(aInput) → InputBox1
Textfield(bInput) → InputBox2
Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, ptopleftcornerfeedback, ptoprightcornerfeedback, pbottomrightcornerfeedback, pbottomleftcornerfeedback
Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForX, {7, 10, 3, 6, 10, 10, 6, 1, 5, 9, 3, 6, 5, 10, 4, 10, 1, 3, 9, 2, 1, 1, 0, 2, 1, 4, 2, 8, 7, 9, 9, 5, 8, 9, 1, 5, 8, 6, 1, 7, 2, 10, 1, 2, 4, 1, 3, 2, 3, 1, 7, 8, 2, 2, 7, 2, 6, 9, 4, 7, 10, 8, 6, 4, 2, 9, 10, 8, 0, 5, 10, 5, 7, 3, 5, 0, 7, 9, 8, 9, 7, 2, 3, 9, 3, 5, 2, 0, 7, 3, 2, 2, 0, 1, 8, 9, 1, 4, 5, 10}
Element(randomNosForX, Mod[questionCount, 100] + 1) → numX
Shuffle(Sequence[Random[0, 10], i, 1, 100]) → randomNosForY, {5, 5, 1, 6, 1, 7, 1, 10, 10, 0, 8, 6, 8, 4, 1, 5, 1, 3, 5, 4, 3, 5, 8, 8, 1, 3, 2, 9, 7, 4, 2, 2, 2, 9, 10, 7, 6, 3, 1, 4, 3, 5, 7, 8, 5, 0, 2, 10, 6, 2, 6, 9, 4, 7, 9, 7, 9, 8, 10, 10, 10, 6, 4, 10, 0, 2, 9, 6, 9, 1, 0, 5, 5, 5, 7, 5, 1, 10, 10, 8, 3, 9, 3, 9, 2, 1, 7, 0, 3, 3, 8, 6, 2, 0, 5, 7, 4, 5, 4, 6}
Element(randomNosForY, Mod[questionCount, 100] + 1) → numY
Append(true, Sequence[If[randomNosForX(i) ≟ randomNosForX(i - 1), false, true], i, 2, 100]) → stayX
Append(true, Sequence[If[randomNosForY(i) ≟ randomNosForY(i - 1), false, true], i, 2, 100]) → stayY
Remove(Sequence[If[stayX(i), randomNosForX(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
Remove(Sequence[If[stayY(i), randomNosForY(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
If(Mod[num1, 9] ≟ 0, 2, Mod[num1, 3] ≠ 0, 3, 1) → num1meta
If(Mod[num2, 9] ≟ 0, 2, Mod[num2, 3] ≠ 0, 3, 1) → num2meta
If(Mod[num3, 9] ≟ 0, 2, Mod[num3, 3] ≠ 0, 3, 1) → num3meta
If(Mod[num4, 9] ≟ 0, 2, Mod[num4, 3] ≠ 0, 3, 1) → num4meta
If(Mod[num5, 9] ≟ 0, 2, Mod[num5, 3] ≠ 0, 3, 1) → num5meta
If(Mod[num6, 9] ≟ 0, 2, Mod[num6, 3] ≠ 0, 3, 1) → num6meta
If(Mod[num7, 9] ≟ 0, 2, Mod[num7, 3] ≠ 0, 3, 1) → num7meta
If(Mod[num8, 9] ≟ 0, 2, Mod[num8, 3] ≠ 0, 3, 1) → num8meta
If(Mod[num9, 9] ≟ 0, 2, Mod[num9, 3] ≠ 0, 3, 1) → num9meta
If(Mod[num10, 9] ≟ 0, 2, Mod[num10, 3] ≠ 0, 3, 1) → num10meta
IsInRegion(Pos1, If[num1meta ≟ 1, Q1, num1meta ≟ 2, Q2, Q3]) → correct1
IsInRegion(Pos2, If[num2meta ≟ 1, Q1, num2meta ≟ 2, Q2, Q3]) → correct2
IsInRegion(Pos3, If[num3meta ≟ 1, Q1, num3meta ≟ 2, Q2, Q3]) → correct3
IsInRegion(Pos4, If[num4meta ≟ 1, Q1, num4meta ≟ 2, Q2, Q3]) → correct4
IsInRegion(Pos5, If[num5meta ≟ 1, Q1, num5meta ≟ 2, Q2, Q3]) → correct5
IsInRegion(Pos6, If[num6meta ≟ 1, Q1, num6meta ≟ 2, Q2, Q3]) → correct6
IsInRegion(Pos7, If[num7meta ≟ 1, Q1, num7meta ≟ 2, Q2, Q3]) → correct7
IsInRegion(Pos8, If[num8meta ≟ 1, Q1, num8meta ≟ 2, Q2, Q3]) → correct8
IsInRegion(Pos9, If[num9meta ≟ 1, Q1, num9meta ≟ 2, Q2, Q3]) → correct9
IsInRegion(Pos10, If[num10meta ≟ 1, Q1, num10meta ≟ 2, Q2, Q3]) → correct10
Join(Sequence[Element[Sequence[Sequence[Q1E1 + ((i * dfx), ((-k) * dfy)), i, 0, 2], k, 0, 3], j], j, 1, 4]) → PunkteMenge1
Join(Sequence[Element[Sequence[Sequence[Q2E1 + ((i * dfx), ((-k) * dfy)), i, 0, 2], k, 0, 3], j], j, 1, 4]) → PunkteMenge2
Join(Sequence[Element[Sequence[Sequence[Q3E1 + ((i * dfx), ((-k) * dfy)), i, 0, 2], k, 0, 3], j], j, 1, 4]) → PunkteMenge3
Text(CorrHelper, A, false, true, 0, 0) → Text11

AI 绘图提示语参考

这是一个交互式数学探索图形，包含多个四边形（Q1、Q2、Q3）代表数字区域，以及一系列中点标记（Pos1到Pos10）用于定位。图形中设有输入框（InputBox1、InputBox2）和文本区域（NumText1到NumText10），用于显示和输入数字。随机生成的数字列表（RandomList3、RandomList9等）被映射到四边形中，通过If和IsInRegion判断每个数字是否落在对应区域，并显示正确或错误提示。整体布局采用Polygon和Midpoint等几何工具构建，体现数字与区域的可视化关系，适合用于教学数字的整除性判断。

以上提示语为根据原始绘图命令整理而来，仅供参考。