Math Matters in May!
Strategies to Build Conceptual Understanding of Multiplication
In this representation, the student is showing that he can decompose 48 into 6 groups of 8.
This third grader used a tape diagram (or bar model) to create 8 groups of 6. Then she skip counted by multiples of 6 to figure out the product.
Fact families are often used to show the relationship between multiplication and division. Here, this student also built an array showing 8 rows of 6. Once again, skip counting was used to determine the product.
Here's another tape diagram (also known as a bar model). This time, the student made 6 groups of 8 to find his product.
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This student understands the relationship between multiplication and division. He keeps dividing the whole by 2 until he's left with eight 6s.
The picture above shows 8 rows of 6, totaling 48.
This student decomposed 8 into 4 and 4. Then, he multiplied each factor of 4 by 6 (making partial products). To find his total product, he added his partial products together to get 48. If he had shown an array, he would have divided his 8 rows of 6 into 4 rows of 6 and 4 rows of 6. Each of the partial products in the array would total 24 and when added together, the total product would be 48.
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