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Ideas Inspired by Teaching Student-Centered Mathematics

Distributive Property - (3-5, pg. 66) Supply students with several sheets of centimeter grid paper. (BLM 7-13 16-19 Links to an external site.) Assign each pair of students a product such as 6 x 8. (Products can vary across the class or all be the same.) The task is to find all of the different ways to make a single slice through the rectangle. For each slice students write an equation. For slice of one row of 8, students would write 6 x 8 = 5 x 8 + 1 x 8. The individual products can be written in array form.

Making Connections

Commutative Property - when two numbers are multiplied together, the product is the same regardless of the order. (1 x 2 is the same as 2 x 1) A deep understanding of this property will assist them in the future when solving algebraic equations. In the classroom, students could work in pairs to build rectangles on grid paper or with tiles or cubes. Students should first describe each representation with a multiplication sentence. (Multiply number of rows by number of columns, then turn the figure 90 degrees and describe it with another number sentence.)

Discuss how these are two different problems that yield the same solution.

Associative Property - when three or more numbers are multiplied, the product is the same regardless how the numbers are grouped. When teaching this concept, you will need to explain to the students that the parenthesis communicates to complete that part of the problem first, and then multiply the rest of the numbers from left to right.
(3 x 4) x 5 = 3 x (4 x 5) To solve the left side of the equation, first multiply 3x4 to get twelve and then multiply 12 times 5
to get 60. To solve the other side of the equation, first multiply 4 times 5 to get 20, then multiply 20 by 3
to get 60.

Graphic organizer:
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(pictured) with any of the properties of multiplication.