Maryland Math 4.NOS.E.13.a
The Standard
- 4.NOS.E.13
- Apply and extend previous understandings of multiplication to multiply a fraction by a whole number (b × c/d).
Estimate products by reasoning about benchmark numbers and assess reasonableness of answers (e.g., 4 × 1/2 will be less than 4 because I have 4 groups of something less than 1).
Maryland College and Career Ready Standards for Mathematics (2025) · BUILD FRACTIONS FROM UNIT FRACTIONS BY APPLYING AND EXTENDING PREVIOUS UNDERSTANDINGS OF OPERATIONS ON WHOLE NUMBERS.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use familiar fractions, such as 1/2 and 1, to estimate a whole number times a fraction. They check whether an answer fits the size of the fraction.
What Mastery Looks Like
- A student says 6 × 7/8 is close to 6, but less than 6, because 7/8 is close to 1. They reject 7 as an answer because six groups of less than 1 cannot total more than 6.
Common Misconceptions
- Some students think multiplication always makes a number larger, so they accept 4 × 1/2 = 8. Others multiply both parts of the fraction and write 4 × 1/2 = 4/8.
How to Assess It
- Exit ticket: Without finding the exact product, estimate 6 × 7/8. Is 7 a reasonable answer? Explain using 1 as a benchmark.
Lesson moves
Ways to Teach It
Have pairs predict 4 × 3/4 using 1/2 and 1 as benchmarks, then lay out four 3/4 fraction strips to check.
Ask students to write: Is 8 × 7/8 closer to 4 or 8? Explain using the size of 7/8.
Sort cards showing 6 × 1/4, 6 × 1/2, and 6 × 7/8 under 'below 3,' 'equal to 3,' or 'near 6.'
A recipe needs 3/4 cup of oats per batch; estimate the oats for five batches and explain why the total is under five cups.
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