Spotting patterns in times tables
In 3rd grade, children learn to find patterns in addition and multiplication tables, such as every multiple of 4 being even, and to explain why each pattern happens.
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
Look at this pattern: When the input is 1, the output is 3. When the input is 2, the output is 4. When the input is 3, the output is 5. What is the output when the input is 4?
- 6
- 7
- 8
Why this matters
Each pattern your child explains is proof to them that math makes sense and follows rules they can understand. It helps in practical ways too: knowing that an even number times any number is even tells your child that an odd answer to 6 x 7 must be wrong. This habit of asking why a pattern works grows into the reasoning used in algebra and the rest of later math.
Where kids can get stuck
- Trusting a pattern after a few examples, such as deciding every multiple of 3 is odd after seeing 3, 9, and 15.
- Describing a pattern only by how the numbers look, saying "it goes up by 5" without explaining why.
- Losing their place in the grid or reading a row as a column, then describing a pattern that is not there.
How you can help
- Count house numbers on a walk and notice that one side of the street is often all even and the other all odd, then ask your child why adding 2 keeps that true.
- Skip count by 5s together while climbing stairs and ask your child what they notice about the last digit, then ask them to explain why it only ends in 5 or 0.
- Ask your child to predict whether a product will be even or odd before working it out, such as 7 x 8, and then check together whether they were right.
Want a little more? Try Bobby's Math Club for free practice that adapts to your child.
Questions parents ask
Why is my child being asked to explain number patterns, not only find them?
Explaining a pattern shows your child understands why it happens, which means they can trust it and use it. A child who knows why multiples of 10 end in zero can use that to multiply quickly. Explaining also builds the habit of asking whether a rule always works, which becomes important in later math and science.
What patterns in the multiplication table should my child notice?
Common ones include: the 2s, 4s, 6s, 8s, and 10s are always even; the 5s end in 0 or 5; the 9s have digits that add to 9 up to 90; and the table mirrors itself across the diagonal because 4 x 6 and 6 x 4 are equal. Noticing these can make the table feel much smaller to learn.
How can I tell if my child understands a pattern or is repeating it?
Ask why it works and whether it will keep working with bigger numbers. If your child says multiples of 4 are always even because each one can be split into two equal groups, they understand it. If they only say "because they are," try exploring the pattern with objects, such as rows of buttons, to show where it comes from.
Make learning math fun
Bobby's Math Club turns 3rd grade math practice into something fun to do together.
- Unlimited practice, completely free
- Practice that starts where your child is and grows with them
- Hints when they are stuck, and a celebration when it clicks
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.D.9: “Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.” Learn how Bobby's Math Club can help your students grow. (Common Core 3.OA.9)