Multiplication as equal groups
In 3rd grade, children learn that multiplication means equal groups, so 5 x 7 is the total number of things in 5 groups of 7.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 3rd 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
Hana has 3 plates with 5 strawberries on each plate. She writes 3 × 5. What does 3 × 5 tell her?
- How many strawberries there are in all
- How many strawberries are on each plate
- How many plates she has
Why this matters
Seeing multiplication as equal groups gives your child a picture to hold on to behind every times table they learn. It makes division make sense later this year, and picturing 5 x 7 as five bags of 7 gives your child a way back to a fact they forget. The same picture carries into finding the area of a rectangle, multiplying numbers like 6 x 24 in 4th grade, and multiplying fractions in 5th grade.
Where kids can get stuck
- Drawing 5 groups with a different number of things in each, not seeing that every group must be the same size.
- Adding the two numbers instead of multiplying, so 5 x 7 becomes 12.
- Swapping the number of groups and the size of each group, so a story for 3 x 6 turns into 6 bags of 3.
How you can help
- Set the table together and ask how many forks are needed if 4 people each get 2, then say it as a times sentence: 4 groups of 2 is 4 x 2.
- Point out equal groups at the grocery store, such as egg cartons with 2 rows of 6 or packs of 4 yogurts, and ask your child to name the multiplication fact.
- Lay out toy cars or crackers in 3 piles of 5 and ask your child to tell you the times sentence, then change it to 5 piles of 3.
If it’s helpful, you can sign up for free, adaptive practice in Bobby's Math Club.
Questions parents ask
Why is my child learning multiplication as equal groups instead of memorizing times tables first?
Knowing what 6 x 4 means gives your child a way back to the answer when memory fails. They can picture 6 groups of 4 and count up by fours. Children who only memorize often guess when a fact slips. Memorizing still matters, and it comes later in 3rd grade, but it holds better when it sits on top of a clear picture of equal groups.
Is 3 x 4 the same as 4 x 3?
They give the same total, 12, but they describe different pictures. 3 x 4 is 3 groups of 4, while 4 x 3 is 4 groups of 3. In 3rd grade, teachers usually read the first number as the number of groups. Your child will soon learn that switching the order never changes the total, which cuts the number of facts to learn almost in half.
How do I know my child understands multiplication and is not only reciting facts?
Ask your child to tell or draw a story for a fact, such as 4 x 6. If they can describe 4 boxes with 6 crayons each and explain why the total is 24, they understand it. If they can say 24 but cannot show what it means, spend a little time drawing groups together before pushing for speed.
Make learning math fun
Bobby's Math Club turns 3rd grade math practice into something fun to do together.
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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.
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Join the clubNote for teachers: This skill is covered by Common Core math standard 3.OA.A.1: “Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7.” Learn how Bobby's Math Club can help your students grow. (Common Core 3.OA.1)