When multiplying makes a number smaller
In 5th grade, children learn to see multiplication as resizing, and to tell without calculating whether multiplying by a fraction makes a number bigger or smaller.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 5th grade practice. Tap the speaker to hear one read aloud, or the light bulb for a hint, and talk about the answer together.
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
Why this matters
Many children grow up sure that multiplying always makes numbers bigger, and freeing your child from that belief now saves real trouble with fractions and decimals later. Seeing multiplication as stretching or shrinking lets them predict an answer before working it out, a strong way to catch mistakes. It also leads into scale drawings, maps, percentages, and the proportional thinking of 6th and 7th grade.
Where kids 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.
How you can help
- Talk through recipe changes while cooking: if you make 1 1/2 batches, will you need more or less flour than the recipe says? What about half a batch? Have your child predict before measuring.
- Look at a map together and talk about how a small distance on paper stands for a much larger distance in real life. Ask your child whether the map scales the real world up or down.
- Pose quick car-ride questions: is 2/3 of 30 more or less than 30? Is 4/3 of 30 more or less than 30? Ask your child to explain without calculating the exact numbers.
Bobby's Math Club offers free practice that grows with your child.
Questions parents ask
Why is my child learning that multiplication can make numbers smaller?
With whole numbers, multiplying almost always made a number bigger, so many children assume that is a rule. Fractions break it. Multiplying by 1/2 takes half of a number, which is smaller. Seeing multiplication as resizing helps your child make sense of fraction and decimal multiplication and spot answers that are clearly wrong.
How can my child tell if an answer will be bigger or smaller without calculating?
Have your child compare the fraction to 1. If the fraction is less than 1, like 3/4, the result is smaller than the starting number. If it is more than 1, like 5/4, the result is bigger. If it equals 1, like 6/6, the result stays the same. This quick check works for decimals too.
Where does this idea of scaling show up later?
Scaling is central to middle school math. Your child will use it with scale drawings and maps, percentages such as 80% of a price, and proportional relationships in 7th grade. In science, it appears in resizing measurements. A child who understands why 3/4 × 10 is less than 10 has a strong foundation for all of these.
Make learning math fun
Bobby's Math Club turns 5th grade math practice into something fun to do together.
- Free, unlimited practice for every child in your family
- Practice that starts where your child is and grows with them
- Level-ups, badges, and a cheer for every win
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.
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Join the clubNote for teachers: This skill is covered by Common Core math standard 5.NF.B.5: “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.” Learn how Bobby's Math Club can help your students grow. (Common Core 5.NF.5)