5th Grade · Number & Operations - Fractions
5.NF.B.5: See how multiplying by a fraction can make a number bigger or smaller
5.NF.B.5 is a 5th grade Common Core math standard in Number & Operations - Fractions. Here’s what it really covers, and how you can help your students learn it.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
The standard
Interpret multiplication as scaling (resizing), by: a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. b. 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.
In plain words
See how multiplying by a fraction can make a number bigger or smaller.
Sample questions from student practice
These questions from Bobby's Math Club are the kinds of questions your students will see. You can try answering them to see what a student might see.
Question 1 of 3
Omar usually practices the violin for 15 minutes. Today he practiced 1 1/3 times as long. Did he practice more or less than 15 minutes?
- Exactly 15 minutes
- More than 15 minutes
- Less than 15 minutes
Where students can get stuck
- Believing multiplication always makes a number bigger, so 1/2 × 8 = 4 looks like an arithmetic mistake.
- Assuming any fraction makes a number smaller, so they expect 7/6 × 12 to be less than 12.
- Missing that multiplying by 3/3 or 5/5 keeps a number the same, so 2/3 = 10/15 feels like a trick.
Effective teaching strategies
- Ask students to predict whether 2 × 8, 1/2 × 8, and 7/6 × 8 are greater or less than 8 before computing, then sort the expressions by their predictions.
- Show on a number line that 1/2 × 8 is half of 8 and 3/2 × 8 is one and a half groups of 8, so each factor resizes the 8.
- Rename 2/3 as 10/15 by multiplying by 5/5, and ask students why multiplying by 5/5 leaves the value unchanged.
Units that teach this standard
Find where 5.NF.B.5 lands in the program you teach. Each unit has a guide written for families. Unit names and order vary between editions and districts, so your school’s own materials have the exact sequence.
Bridges in Mathematics
enVision Mathematics
i-Ready Classroom Mathematics
Illustrative Mathematics
Math Expressions
Reveal Math
Don’t see your curriculum? Contact Bobby and we’ll see if we can help!
Share it with families
Families can read When multiplying makes a number smaller for a plain-language look at this skill, with three questions to try together and ideas for helping at home.
Help every student practice fractions at home
In Bobby's Math Club, students practice at just the right level, with a hint when they need one, a clear explanation after every question, and kid-friendly videos. Unlimited practice is free for every family.
See how it works for teachers
Written by Robert “Bobby” Barnett
Bobby is an award-winning math teacher, the author of Meet Every Learner’s Needs, and the father of two elementary-school math learners. He uses Bobby’s Math Club with his own kids a few times every week. Learn more or contact Bobby.