用面积模型理解分数加法

几何画板及绘图内容加载中，请稍等……

2016-03-21 02:27

所属专题 Fraction Book Fraction Book

① 本范例通过面积模型直观展示两个分数相加的过程，将抽象的分数运算转化为可视化的图形拼接。② 核心数学概念是分数的意义、同分母与异分母分数加法，以及通分（利用最小公倍数）的几何表示。③ 作图要点：使用GeoGebra的Point、Circle、Segment、Polygon等命令构造矩形或正方形区域，通过Sequence生成点阵（DotsBottom、DotsTop等）表示分子，利用GCD计算公分母，并用Mirror、OrthogonalLine等辅助线划分区域，最终通过多个多边形（poly1、poly2、poly3）和虚线（DashedLines）展示分数部分的组合。④ 适合小学高年级至初中阶段的学生学习分数运算，也可用于教师课堂演示，帮助学生建立分数加法的直观理解。

GeoGebra 命令及参数

Point(c) → A
Circle(A, squaresize) → d
OrthogonalLine(A, c) → e
Intersect(d, e, 2) → B_1
Intersect(d, c, 2) → C
Segment(B_1, C) → f
Mirror(A, f) → A'
Sequence((x(A) + (i * squareside / denominator2), y(A)), i, 1, denominator2) → DotsBottom
Sequence((x(B_1) + (i * squareside / denominator2), y(B_1)), i, 1, denominator2) → DotsTop
Polygon(A, (x(A) + (numerator2 * squaresize / denominator2), y(A)), (x(B_1) + (numerator2 * squaresize / denominator2), y(B_1)), B_1) → poly1, a, h, i, j
Sequence(Segment[(x(A) + (i * squaresize / denominator2), y(A)), (x(B_1) + (i * squaresize / denominator2), y(B_1))], i, 1, denominator2) → DashedLines1
Polygon(A, C, A', B_1) → poly2, a_1, c_1, a', b_1
Point(c) → B
Circle(B, squaresize) → g
OrthogonalLine(B, c) → b
Intersect(g, b, 2) → E
Intersect(g, c, 2) → F
OrthogonalLine(E, b) → k
OrthogonalLine(F, c) → l
Intersect(k, l) → G
Sequence((x(B), y(B) + (i * squaresize / denominator1)), i, 1, denominator1) → DotsLeft
Sequence((x(F), y(F) + (i * squaresize / denominator1)), i, 1, denominator1) → DotsRight
Sequence(Segment[(x(B), y(B) + (i * squaresize / denominator1)), (x(F), y(F) + (i * squaresize / denominator1))], i, 1, denominator1) → DashedLines2
Polygon(B, F, (x(F), y(F) + (numerator1 * squaresize / denominator1)), (x(B), y(B) + (numerator1 * squaresize / denominator1))) → poly3, d_1, f_1, m, n
Polygon(B, F, G, E) → poly4, d_2, f_2, g_1, e_1
GCD(MixedNum, commondenom) → ReduceBy
Random(2, 10) → seeddenominator1
Random(2, 10) → seeddenominator2