Maryland Math 5.NOS.D.12.a
The Standard
- 5.NOS.D.12
- Apply and extend previous understandings of multiplication to multiply a fraction by a fraction.
Estimate products by reasoning about benchmark numbers and assess reasonableness of answers (e.g., 1/2 × 3/4 will be less than 3/4 because I will have one half of 3/4).
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 benchmarks such as 0, 1/2, and 1 to estimate products of fractions. They check whether an answer makes sense by thinking about how much of one fraction they are taking.
What Mastery Looks Like
- For 1/2 × 3/4, a student places the answer between 1/4 and 1/2. They reject 6/4 because taking half of 3/4 cannot give more than 3/4.
Common Misconceptions
- Some students add the fractions instead of multiplying them. Others think multiplication always makes a number larger, so they accept a product greater than both fractions.
How to Assess It
- Exit ticket: Estimate 2/3 × 3/4 using benchmarks. Could 5/4 be the product? Explain why or why not.
Lesson moves
Ways to Teach It
Shade 3/4 of a paper rectangle, fold it in half, and compare the overlapping area with 1/4 and 1/2.
Ask, "Can 5/6 × 2/3 be greater than 2/3? Explain without multiplying."
Give pairs cards showing 1/2 × 3/4, 2/3 × 3/4, and 3/4 × 3/4; have them sort estimates from least to greatest.
A recipe uses 3/4 cup of oats; ask students to estimate the oats needed for half a batch before measuring.
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