3rd Grade · Operations & Algebraic Thinking
3.OA.B.5: Break numbers apart to multiply, like 4 × 7 = (4 × 5) + (4 × 2)
3.OA.B.5 is a 3rd grade Common Core math standard in Operations & Algebraic Thinking. 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
Apply properties of operations as strategies to multiply and divide. Examples: If 6 x 4 = 24 is known, then 4 x 6 = 24 is also known. (Commutative property of multiplication.) 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30. (Associative property of multiplication.) Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 5) + (8 x 2) = 40 + 16 = 56. (Distributive property.)
In plain words
Break numbers apart to multiply, like 4 × 7 = (4 × 5) + (4 × 2).
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
Diego has 9 plates with 2 strawberries on each plate. Amara has 2 plates with 9 strawberries on each plate. Who has more strawberries, or do they have the same number?
- Amara has more
- Diego has more
- They have the same number
Where students can get stuck
- Breaking a number apart but multiplying only one piece, so 4 x 7 becomes 4 x 5 + 2 = 22 instead of 28.
- Expecting the order trick to work for division too, so 12 ÷ 3 and 3 ÷ 12 seem equal.
- Splitting a number into awkward pieces, such as 7 into 3 and 4, which leaves facts no easier than before.
Effective teaching strategies
- Show 4 × 7 as an array and cut it into a 4 × 5 piece and a 4 × 2 piece, so students see both pieces must be multiplied and then added.
- Have students turn a fact they know into one they do not, such as using 5 × 8 to find 6 × 8 by adding one more group of 8.
- Ask students to show with an array that 3 × 12 equals 12 × 3, then find 3 × 12 by breaking the 12 into 10 and 2.
Units that teach this standard
Find where 3.OA.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
Eureka Math
Eureka Math²
Everyday Mathematics
i-Ready Classroom Mathematics
Illustrative Mathematics
Don’t see your curriculum? Contact Bobby and we’ll see if we can help!
Share it with families
Families can read Shortcuts that make times tables easier for a plain-language look at this skill, with three questions to try together and ideas for helping at home.
Help every student practice problem solving 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.