Illustrative Mathematics Grade 5, Unit 3: Multiplying and Dividing Fractions
In this unit, your child extends fraction multiplication to areas of rectangles with fraction side lengths and learns to divide a whole number by a unit fraction and a unit fraction by a whole number. Questions like how many 1/3-hour practice sessions fit in 2 hours make the meaning concrete. It builds on fractions as quotients and comes before wrapping up adding and subtracting fractions.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
What is my child learning in Unit 3?
- Finding the area of rectangles with fraction side lengths, like 2/3 by 1/2 foot = 1/3 square foot, by tiling and multiplying. Learn more: Multiplying fractions, like 2/3 × 4/5
- Dividing a whole number by a unit fraction, like 2 ÷ 1/3 = 6, and a unit fraction by a whole number, like 1/5 ÷ 2 = 1/10. Learn more: Dividing with fractions, like 1/2 ÷ 4
Sample questions to try together
These are real questions from our 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
The blue part of the rectangle shows 1/3 × 2/5, and the whole rectangle is 1. What is 1/3 × 2/5?
- 2/15
- 2/13
- 3/8
How you can help
- Ask how many 1/3-hour practice times fit into 2 hours. Let your child draw a timeline, then check that 2 ÷ 1/3 is 6.
- Draw a square on graph paper and shade 2/3 of its width and 1/2 of its height. Ask your child what part of the whole square the overlap covers, 1/3.
- Share 1/5 of a sheet cake between 2 people. Ask your child what fraction of the whole cake each person gets, 1/10, and to draw it.
Where kids can get stuck
- Adding the side lengths of a 2/3 by 1/2 rectangle and calling 7/6 its area.
- Multiplying instead of dividing, so 2 ÷ 1/3 becomes 2/3 instead of 6.
- Mixing up sharing with grouping, answering “how many 1/4-cup scoops in 2 cups” with 1/2 instead of 8.
Practice makes perfect
Bobby's Math Club has practice problems that adapt to your child’s level, each with a detailed explanation and an easy-to-follow video, so your child can build confidence in these skills one step at a time.
Words your child will hear
- area
- How much surface a flat shape covers, like a tabletop.
- side length
- How long one side of a shape is.
- square unit
- A square with 1-unit sides, used to measure area.
- unit fraction
- A fraction with 1 as its numerator, like 1/3 or 1/8.
- dividend
- The number being divided, like 32 in 32 ÷ 4.
- divisor
- The number that tells how many groups, or how big each group is, in division.
- quotient
- The answer to a division problem, like 8 in 32 ÷ 4 = 8.
- product
- The answer to a multiplication problem, like 24 in 6 × 4 = 24.
Want to help your child master fractions in area and division?
In Bobby's Math Club, your child practices these skills 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.
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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.
Which math standards does Illustrative Mathematics Grade 5 Unit 3 cover?
Illustrative Mathematics Grade 5 Unit 3 covers these math standards. Each one links to what it means, sample questions, and teaching strategies.
For teachers: Unit names and order vary between editions and districts, so your school’s own materials have the exact sequence. Learn how Bobby's Math Club can help your students grow.