Illustrative Mathematics Grade 4, Unit 2: Fraction Equivalence and Comparison
In this unit, your child uses tape diagrams and number lines to see why fractions like 3/4 and 6/8 are equal, and to compare fractions with different denominators. They use the factors and multiples from the last unit to find common denominators. Next, they add, subtract, and multiply fractions.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
What is my child learning in Unit 2?
- Partitioning tape diagrams and number lines into smaller parts to show that fractions like 1/3 and 4/12 are equivalent. Learn more: Why fractions like 3/4 and 6/8 are equal
- Comparing fractions by reasoning about the size of the parts, a common denominator, or how close each is to 1/2 or 1. Learn more: Comparing fractions like 2/3 and 5/6
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
What is the missing number? 4/5 = ?/10
- 4
- 9
- 8
How you can help
- Fold a paper strip into thirds, then fold each third into fourths. Ask how many twelfths match one third, and why the amount didn't change.
- Ask your child which is closer to a whole, 7/8 or 5/6, by thinking about the piece that's missing from each.
- Compare two partly eaten pizzas of the same size: 3/4 left on one and 5/8 on the other. Ask which has more left and how your child knows.
Where kids can get stuck
- Adding 2 to the numerator and denominator, so 1/3 seems equal to 3/5.
- Comparing fractions of two wholes without noticing that the wholes are different sizes.
- Thinking 5/12 is greater than 3/4 because 5 and 12 are bigger numbers.
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
- numerator
- The top number of a fraction, telling how many equal parts are counted.
- denominator
- The bottom number of a fraction, telling how many equal parts make one whole.
- equivalent fractions
- Fractions that name the same amount, like 3/4 and 6/8.
- tape diagram
- A drawing of bars that shows how the amounts in a story problem compare.
- number line
- A line with numbers at equal distances, used to show and compare amounts.
- common denominator
- The same denominator shared by two fractions, which makes them easy to compare or add.
- benchmark fraction
- A familiar fraction, like 1/2 or 1, used to compare other fractions.
Ready to build your child’s confidence with fraction comparison?
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 4 Unit 2 cover?
Illustrative Mathematics Grade 4 Unit 2 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.