CCSS.Math.Content.5.NF.B.5
The standard
Interpret multiplication as scaling (resizing), by:
Common Core State Standards for Mathematics
What this standard means
Students need to see multiplication as resizing, not just repeated addition. They compare a factor to 1 and predict whether the product will be larger, smaller, or the same as the other factor. They also explain why multiplying by a fraction less than 1 makes a quantity smaller, while multiplying by a number greater than 1 makes it larger.
Mastery looks like students reasoning before calculating. They can say, “Two-thirds of 30 must be less than 30,” or “5 times 3/2 is more than 5.” Students often get stuck thinking multiplication always makes numbers bigger, especially with fractions less than 1.
Ways to teach it
- Have students use grid paper to shade a rectangle, then resize it by 1/2, 3/2, and 2 and compare the areas.
- Ask students to explain: Without multiplying, is 4/5 × 60 greater than, less than, or equal to 60?
- Show five expressions like 7 × 2/3 and 7 × 5/4, and have students sort them as bigger, smaller, or same.
- Connect to recipes by asking whether multiplying a batch by 1/2, 1, or 3 will make fewer, same, or more cookies.
Plan a lesson for CCSS.Math.Content.5.NF.B.5
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Related standards
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- CCSS.Math.Content.5.NF.B.5a
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.