使用部分积法计算多位数与一位数的乘法
几何画板及绘图内容加载中,请稍等……
本范例演示了如何使用部分积法计算多位数与一位数的乘法,通过分拆多位数并逐步计算每部分的积,最后将结果相加得到最终答案。涉及的核心数学概念包括乘法分配律、部分积法以及面积模型。作图要点使用了GeoGebra的Shuffle, Element, TextToUnicode, SelectedIndex, If, Intersect, Point, Polygon, Sequence, Zip, Translate等命令和对象。适合小学中高年级学生学习多位数乘法,帮助理解乘法运算的原理和步骤。
GeoGebra 命令及参数
Shuffle(Sequence[t, t, 1, 3]) → allCases, {2, 3, 1}Element(allCases, Mod[countQuestion, Length[allCases]] + 1) → caseNumShuffle(Sequence[t, t, 1, 9]) → allD4, {8, 1, 9, 7, 5, 6, 3, 4, 2}Element(allD4, Mod[countQuestion, Length[allD4]] + 1) → d4Shuffle(Sequence[t, t, 1, 9]) → allD2, {9, 5, 3, 7, 6, 2, 4, 8, 1}Element(allD2, Mod[countQuestion, Length[allD2]] + 1) → d2Shuffle(Sequence[t, t, 1, 9]) → allD3, {8, 9, 1, 5, 6, 2, 3, 4, 7}Element(allD3, Mod[countQuestion, Length[allD3]] + 1) → d3Shuffle(Sequence[t, t, 2, 9]) → allMult, {7, 8, 9, 6, 2, 5, 3, 4}Element(allMult, Mod[countQuestion, Length[allMult]] + 1) → multShuffle(Sequence[t, t, 0, 9]) → allD1, {6, 2, 0, 8, 5, 4, 9, 7, 1, 3}Element(allD1, Mod[countQuestion, Length[allD1]] + 1) → d1TextToUnicode(("" * currentProd)) → uniResultSelectedIndex(ddMenu) → isIf(caseNum ≟ 1, 217 + 74, caseNum ≟ 2, 255 + 73, 292 + 65) → obj5PosYIntersect(xAxis, yAxis) → APoint(xAxis) → BIf(caseNum ≠ 3, A + (0, -1.5), If[caseNum ≟ 3 ∧ currentProd ≥ 10000, A + (-1, -1.5), A + (0, -1.5)]) → recapTextPosPolygon({A, D, DH, AH}) → rett31Polygon({D, C, CH, DH}) → rett32Polygon({C, E, EH, CH}) → rett33Polygon({E, B, BH, EH}) → rett34Polygon({A, C, CH, AH}) → rett11Polygon({C, B, BH, CH}) → rett12Polygon({A, F, FH, AH}) → rett21Polygon({F, G, GH, FH}) → rett22Polygon({G, B, BH, GH}) → rett23Sequence((k, 7), k, If[caseNum ≟ 1, 3, caseNum ≟ 2, 2, 1], x(B) - x(A), If[caseNum ≟ 1, (0.5 * (x(B) - x(A))), caseNum ≟ 2, (1 / 3 * (x(B) - x(A))), (1 / 4 * (x(B) - x(A)))]) → anchorsUpZip(Text[("" * A), B, false, true, 1, 0], A, If[caseNum ≟ 1, allValues1Up, caseNum ≟ 2, allValues2Up, allValues3Up], B, anchorsUp + (-0.15, -0.5)) → allTextsUpSequence((k, 3), k, If[caseNum ≟ 1, 3, caseNum ≟ 2, 2, 1], x(B) - x(A), If[caseNum ≟ 1, (0.5 * (x(B) - x(A))), caseNum ≟ 2, (1 / 3 * (x(B) - x(A))), (1 / 4 * (x(B) - x(A)))]) → anchorsInSequence((-14, k), k, If[caseNum ≟ 1, 0, caseNum ≟ 2, -3, -5], 4, If[caseNum ≟ 1, 2, caseNum ≟ 2, 2, 3]) → rightAnchorsVert1Polygon({A, C, CH, AH}) → rett11FramePolygon({C, B, BH, CH}) → rett12FramePolygon({A, F, FH, AH}) → rett21FramePolygon({F, G, GH, FH}) → rett22FramePolygon({G, B, BH, GH}) → rett23FramePolygon({A, D, DH, AH}) → rett31FramePolygon({D, C, CH, DH}) → rett32FramePolygon({C, E, EH, CH}) → rett33FramePolygon({E, B, BH, EH}) → rett34FramePolygon(C, B, BH, CH) → pulsingObject1, f, g, i, jPolygon(G, B, BH, GH) → pulsingObject2, k, l, m, nPolygon(E, B, BH, EH) → pulsingObject3, p, q, r, sIf(caseNum ≟ 1, 260, caseNum ≟ 2, 302, caseNum ≟ 3, 345) → separatBottYPolygon({R1, R2, R3, R4}) → hlRett11Translate(R1, Vector[(0, 0), (0, -1)]) → R1'Translate(R2, Vector[(0, 0), (0, -1)]) → R2'Translate(R3, Vector[(0, 0), (0, -1)]) → R3'Translate(R4, Vector[(0, 0), (0, -1)]) → R4'Polygon({R1 + (0, -1.85), R2 + (0, -1.85), R3 + (0, -1.85), R4 + (0, -1.85)}) → hlRett12Translate(hlRett11, Vector[(0, 0), (0, -3.65)]) → hlRett23Translate(hlRett23, Vector[(0, 0), (0, -1.65)]) → hlRett32
AI 绘图提示语参考
绘制一个乘法分解图,展示一个多位数乘以一位数的过程。首先,画出一个矩形,代表乘法的乘积。然后,将矩形分解成多个小矩形,每个小矩形代表乘法的中间结果。例如,如果多位数是217,一位数是74,那么矩形会被分解成两个部分,分别代表200乘以74和17乘以74的结果。最后,用文字标注每个小矩形的尺寸和乘积。
以上提示语为根据原始绘图命令整理而来,仅供参考。