CCSS.Math.Content.5.NF.B.5b
The standard
Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.
Common Core State Standards for Mathematics
What this standard means
Students need to explain how the size of a factor affects the size of a product. They should see that multiplying by a number greater than 1 makes the result larger, multiplying by a number between 0 and 1 makes it smaller, and multiplying by 1 keeps it the same.
Mastery looks like students predicting product size before calculating and justifying with a model, number line, or words. They often get stuck thinking multiplication always makes bigger. They may also miss that forms like 2/2, 3/3, and 10/10 are all just 1.
Ways to teach it
- Use fraction strips to model 6 times 1/2, 6 times 3/2, and 6 times 2/2, then compare each product to 6.
- Ask students to explain in writing: How can multiplying make a number smaller without doing subtraction?
- Give four problems, such as 8 times 3/4 and 8 times 5/4, and have students circle larger, smaller, or same before solving.
- Use recipe scaling: compare making half a batch, one batch, and one and a half batches of 12 muffins.
Plan a lesson for CCSS.Math.Content.5.NF.B.5b
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Related standards
- CCSS.Math.Content.5.NF.B.4
Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
- CCSS.Math.Content.4.NF.A.1
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts d...
- CCSS.Math.Content.4.NF.B.4b
Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.
- CCSS.Math.Content.4.NF.B.4
Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.