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Commutative Law of Multiplication

Commutative Law of Multiplication
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2015-11-07 09:04
Coordinate GeometrySolid Geometry
This example demonstrates the commutative law of multiplication, i.e., ab=ba, through a 2-dimensional perspective. It uses the volume of a cuboid to intuitively explain the properties of multiplication. By adjusting the dimensions of the cuboid, the product remains unchanged. The core mathematical concepts involved include multiplication, cuboid volume, and geometric construction. It utilizes GeoGebra commands such as If, Sequence, and Polygon. Suitable for students from upper elementary to middle school to learn about the properties of multiplication and geometric concepts.

GeoGebra Commands & Parameters

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

AI Drawing Prompt Reference

Draw a cuboid to demonstrate the commutative law of multiplication, showing that length times width equals width times length. The volume remains constant as dimensions are adjusted, using line segments and quadrilaterals to visually explain the properties of multiplication, suitable for elementary and middle school students learning multiplication and geometric concepts.
The prompt above was compiled from the original drawing commands and is for reference only.