Maryland Math 5.NOS.D.14
The Standard
Interpret multiplication as scaling (sizing) in context. Compare the size of a product to the size of one factor based on the size of the other factor, without performing the indicated multiplication. Explain why multiplying a given number by a fraction greater than a 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explain why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relate the principle of fraction equivalence a/b = (n × a)/(n × b) to the Identity Property of Multiplication.
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 predict whether multiplying a positive number by a fraction makes it larger, smaller, or unchanged, without calculating. They explain their prediction by comparing the fraction with 1. They show why multiplying the numerator and denominator by the same number does not change a fraction's value.
What Mastery Looks Like
- Given 12 × 3/4 and 12 × 5/4, students say the first product is less than 12 and the second is greater, without calculating. They explain that 2/3 equals 6/9 because multiplying by 3/3 means multiplying by 1.
Common Misconceptions
- Students may think multiplying always makes a number bigger, even when the multiplier is 3/4. Some think doubling both parts of a fraction doubles its value, rather than leaving it unchanged.
How to Assess It
- Exit ticket: Without multiplying, compare 10 × 4/5 and 10 × 6/5 with 10. Then explain why 3/4 equals 9/12 using 3/3.
Lesson moves
Ways to Teach It
Give pairs two 12-inch paper strips; mark fourths, build 3/4 and 5/4 of one strip, then compare both lengths with 12 inches.
Ask students to write why 8 × 2/3 must be less than 8, even without finding the product.
Play Greater or Smaller: show 9 × 7/8, 9 × 8/8, and 9 × 9/8; students sort them by comparison with 9.
Use a recipe with 4 cups of broth; students predict how much broth 3/4 or 5/4 of the recipe needs.
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Related Standards
- 4.NOS.E.13.b
Use understanding of multiplication as equal groups to multiply a unit fraction by whole number (e.g., interpret b × 1/d as b groups of 1/d).
- 4.NOS.E.13.c
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Represent and explain the computation by connecting concrete models, drawings, and/or equations to the meaning of multiplication and division.
- 4.AT.A.1
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