Shortcuts that make times tables easier
In 3rd grade, children learn to make harder facts easier by rearranging or breaking apart numbers, such as finding 4 x 7 as 4 x 5 plus 4 x 2.
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
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
Why this matters
With these shortcuts in hand, your child no longer faces 100 separate facts to memorize one by one. Breaking 4 x 7 into 4 x 5 and 4 x 2 turns one hard fact into two easy ones. The same move returns in 4th grade, where 6 x 23 becomes 6 x 20 plus 6 x 3, and again in middle school algebra, so it is one of the most useful ideas your child will meet.
Where kids 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.
How you can help
- Arrange 6 rows of 7 pennies, then slide a ruler between the fifth and sixth columns so your child sees 6 x 5 and 6 x 2 together make 6 x 7.
- Ask your child to explain how they could work out a fact they find hard, like 8 x 6, using one they know well, such as 8 x 5.
- Count wheels on 3 tricycles at the park, then ask whether 3 x 3 gives the same total as 3 x 3 counted the other way around, and why.
Want a little more? Try Bobby's Math Club for free practice that adapts to your child.
Questions parents ask
Why is my child breaking numbers apart instead of memorizing times tables?
Breaking numbers apart helps your child figure out facts they have not memorized yet, using the ones they have. If 7 x 8 slips their mind, they can do 7 x 5 = 35 and 7 x 3 = 21, then add to get 56. Memorizing is still expected by the end of 3rd grade, and these strategies are often what make the facts stick.
Does my child need to know words like commutative and distributive?
Not usually. Some teachers mention the names, but what matters in 3rd grade is that your child can use the ideas: switching the order, grouping numbers differently, and breaking a number into parts. If your child can explain why 4 x 7 equals 4 x 5 plus 4 x 2, they understand the property even without its formal name.
How will breaking numbers apart help my child later?
In 4th grade, children multiply numbers like 7 x 46 by splitting 46 into 40 and 6, then multiplying each part by 7 and adding. That is the same idea they are using now with 4 x 7. It also shows up in middle school algebra. Learning it now with small numbers makes it familiar when the numbers grow.
Make learning math fun
Bobby's Math Club turns 3rd grade math practice into something fun to do together.
- Free, unlimited practice for every child in your family
- Questions matched to your child’s level, a few minutes a day
- You see their progress and what to work on next
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.B.5: “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.)” Learn how Bobby's Math Club can help your students grow. (Common Core 3.OA.5)