In previous lessons, students have found products of whole numbers, decimals, and fractions. The goal of this lesson is for students to examine the size of the product compared to the sizes of its factors. For example, students know that if they find a product of two whole numbers greater than 1, such as , then the value of the product is greater than the value of either factor. They also know that the value of a product of fractions, such as , is less than the value of either factor. In this lesson, students study the situation in which one of the factors is a fraction and the other is a whole number. They make the comparison, using any strategy that makes sense to them. This might include calculating the value of the product, thinking about the meaning of the fractions, or using a diagram.
Action and Expression
None
Learning Goals
Explain (orally and in writing) strategies for comparing with its factor , when is a fraction and is a whole number.
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Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.
Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.