3rd Grade · Number & Operations - Fractions
3.NF.A.3: Find equal fractions, like 1/2 = 2/4, and compare fractions by size
3.NF.A.3 is a 3rd 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
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1, recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram. d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
In plain words
Find equal fractions, like 1/2 = 2/4, and compare fractions by size.
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 6
A pizza is cut into 6 equal slices. Which fraction names the whole pizza?
- 1/6
- 6/1
- 6/6
Where students can get stuck
Find equal fractions, like 1/2 = 2/4.
- Adding 1 to both the numerator and denominator (the top and bottom numbers), so 1/2 becomes 2/3, which is a different amount.
- Placing 1/2 and 2/4 at different spots on a number line from 0 to 1, as if they were different numbers.
- Thinking 6/6 is bigger than 1 because 6 is a big number, when six sixths make exactly one whole.
Compare fractions by size.
- Deciding 3/8 is greater than 3/4 because 8 is larger than 4, forgetting that eighths are smaller pieces.
- Overusing the idea that bigger numbers can mean smaller pieces, and deciding 2/6 is more than 5/6.
- Mixing up the > and < signs, writing 2/3 < 1/3 even after saying out loud that 2/3 is more.
Effective teaching strategies
- Fold two same-size paper strips into halves and fourths side by side, so students see that 1/2 and 2/4 cover the same length.
- Ask students to compare fractions with the same numerator, such as 3/8 and 3/4, by thinking about the size of each piece.
- Pose the question “the same whole?” before each comparison, so students check that both wholes are the same size.
Units that teach this standard
Find where 3.NF.A.3 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
Eureka Math²
Everyday Mathematics
i-Ready Classroom Mathematics
Illustrative Mathematics
Into Math
Math Expressions
Reveal Math
Zearn Math
Don’t see your curriculum? Contact Bobby and we’ll see if we can help!
Share it with families
Each skill has its own guide for families, with a plain-language look at the skill, 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.