Number patterns that follow a rule
In 4th grade, children learn to build number and shape patterns from a rule, like "start at 3 and add 6," and to notice and explain features the rule does not state.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 4th 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
A pattern starts at 1, and the rule is multiply by 3. Which of these numbers will be in the pattern?
- 21
- 81
- 13
Why this matters
Spotting what stays the same in a pattern, and asking why, is where your child's algebraic thinking begins. Next year they compare two patterns side by side and plot them on a graph. In middle school, a rule like "start at 3 and add 6" is written with a letter, and patterns become the functions and graphs at the heart of algebra.
Where kids can get stuck
- Adding the wrong amount partway through, writing 3, 9, 15, 20 instead of checking each step against the rule.
- Noticing a feature, like "the numbers are all odd," but explaining it with a guess that does not connect to the rule.
- Confusing the starting number with the rule, so "start at 4, add 5" becomes 5, 9, 13 instead of 4, 9, 14.
How you can help
- Count steps on a walk using a rule, such as starting at 2 and adding 4 at each lamppost. Then ask your child whether the numbers will ever be odd, and why they think so.
- Build a growing pattern with blocks or coins: 1, then 3, then 5. Ask your child to make the next one and to predict how many would be in the 10th without building it.
- Make up rules for each other in the car. One person says "start at 5, add 10" and the other lists numbers, then both look for something surprising, like every number ending in 5.
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 patterns this way?
Following a rule practices addition or multiplication, but noticing what the rule did not say builds reasoning. When your child spots that "add 6 starting from 3" always gives odd numbers, and explains why, they are doing the kind of thinking used throughout later math. Teachers ask for explanations because the explanation, not the list of numbers, shows real understanding.
What kinds of features might my child notice in a pattern?
Common ones include whether the numbers are all odd or all even, whether they alternate, what the ones digits do, and how fast the numbers grow. For example, with "start at 5, add 5," the ones digit goes 5, 0, 5, 0. In a shape pattern, your child might notice that every third shape is a circle. Any true observation with a reason counts.
How do patterns connect to algebra later on?
Patterns are an early form of a function: a rule that turns one number into another. In 5th grade, your child compares two patterns, such as add 3 and add 6, and sees that one is always double the other. In middle school, rules are written with letters, like y = 6x + 3, and graphed. Spotting and explaining features now builds the habits that make that step feel familiar.
Make learning math fun
Bobby's Math Club turns 4th grade math practice into something fun to do together.
- Unlimited free practice
- A few minutes a day, at just the right level
- 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.
Ready to watch your child’s confidence grow?
Your 4th grade child can start today with free, unlimited practice that grows with them.
Join the clubNote for teachers: This skill is covered by Common Core math standard 4.OA.C.5: “Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.” Learn how Bobby's Math Club can help your students grow. (Common Core 4.OA.5)