Visualizing the Commutative Law of Multiplication

Loading the math board and drawing, please wait…

2020-10-27 22:25

This example visually demonstrates the commutative law of multiplication (a×b=b×a) through dynamic geometry. It involves core mathematical concepts such as multiplication, 2D surfaces, function graphs, area, natural numbers, and limits. The construction utilizes GeoGebra commands like If, Sequence, and Polygon, along with objects like a, b, c, Ax, Ay, da, db, A, dis, over, Bx, By, B, A2, A3, A4, B2, B3, B4, list1, list2, list3, list4, poly1, a_1, a2, a3, a4, poly2, b_1, b2, b3, b4, text1, equalPt, text2, text3, text4, text5, text6. It is suitable for middle school students and above to understand the geometric meaning of the commutative law of multiplication.

GeoGebra Commands & Parameters

If(a < 4, 2, If[a < 7, 1.5, 1]) → Ax
If(b < 4, 2, If[b < 7, 1.5, 1]) → Ay
If(a < 4, 2, If[a < 7, 3.5, 5]) → da
If(b < 4, 2, If[b < 7, 3.5, 5]) → db
If(da / a < db / b, da / a, db / b) → dis
If(a < 4, 2, If[a < 7, 1.5, 1]) → By
Sequence(Segment[A + (j * (A2 - A) / a), A4 + (j * (A2 - A) / a)], j, 0, a) → list1
Sequence(Segment[A + (j * (A4 - A) / b), A2 + (j * (A4 - A) / b)], j, 0, b) → list2
Sequence(Segment[B + (j * (B2 - B) / b), B4 + (j * (B2 - B) / b)], j, 0, b) → list3
Sequence(Segment[B + (j * (B4 - B) / a), B2 + (j * (B4 - B) / a)], j, 0, a) → list4
Polygon(A, A2, A3, A4) → poly1, a_1, a2, a3, a4
Polygon(B, B2, B3, B4) → poly2, b_1, b2, b3, b4

AI Drawing Prompt Reference

Draw two adjacent rectangular grids. The left rectangle is divided into a by b small squares, and the right rectangle into b by a small squares, demonstrating that a×b equals b×a. Each rectangle has grid lines drawn inside, and the areas are equal. Add text labels showing the multiplication equality. Sliders control the values of a and b, adjusting grid density and rectangle size while keeping areas equal.

The prompt above was compiled from the original drawing commands and is for reference only.