Maryland Math 5.NOS.D.13.a
The Standard
- 5.NOS.D.13
- Apply and extend previous understandings of multiplication to multiply a fraction by a fraction, with one or both factors greater than 1.
Estimate products by reasoning about benchmark numbers and assess reasonableness of answers.
Maryland College and Career Ready Standards for Mathematics (2025) · APPLY AND EXTEND PREVIOUS UNDERSTANDINGS OF MULTIPLICATION AND DIVISION TO MULTIPLY AND DIVIDE FRACTIONS.
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use familiar numbers like 0, 1/2, and 1 to estimate fraction products. They use the estimate to check whether a calculated answer makes sense.
What Mastery Looks Like
- A student estimates 3 7/8 × 1/2 as about 2. They can explain why 7 3/4 cannot be the product: taking half should make 3 7/8 smaller.
Common Misconceptions
- Some students expect multiplication to always make a number larger. Others treat an estimate as the exact answer or round 1/2 up to 1 before multiplying.
How to Assess It
- Exit ticket: Estimate 3 7/8 × 1/2. Which answer is reasonable, 1 15/16 or 7 3/4? Explain using a benchmark.
Lesson moves
Ways to Teach It
Give pairs fraction strips to build 3 7/8, then have them find half and compare it with 2 whole strips.
Ask students to write why 7/8 × 4 should be close to, but less than, 4.
Give pairs cards showing 3/8 × 8, 7/8 × 4, and 1/2 × 9; have them match each to a benchmark estimate.
Show a recipe calling for 3 7/8 cups of oats and ask students to estimate the amount needed for half a batch.
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