4.OA.5: Generate and Analyze Patterns
Also written as 4.OA.C.5 and CCSS.MATH.CONTENT.4.OA.C.5 · Cluster: Generate and analyze patterns.
The Official Wording
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.
Common Core State Standards, Grade 4, Operations & Algebraic Thinking · Read it at the source · Checked October 14, 2026
What 4.OA.5 Means in Plain English
Fourth graders take a rule and a starting point and build the pattern, with numbers or with shapes. The rule “start at 2, add 5” gives 2, 7, 12, 17, 22. Then they hunt for what the rule never mentioned: the ones digits take turns, 2 and 7.
The heart of it is saying why: two jumps of 5 make 10, so the ones digit keeps coming back. In 5th grade students run two rules side by side, compare the terms, and graph the pairs on a coordinate plane (5.OA.3).
4.OA.5 I Can Statements
- I can make a number or shape pattern that follows a rule.
- I can find a feature of a pattern the rule didn’t mention.
- I can explain why that feature keeps happening.
4.OA.5 Worked Example
One rule, eight terms, and a pattern inside the pattern that students can predict and explain.
Start at 2 and follow the rule “add 5.” Write the first eight terms. What do you notice that the rule doesn’t say, and why does it keep happening?
- Apply the rule again and again, building each new term from the one before.2, 7, 12, 17, 22, 27, 32, 37
- Look only at the ones digits. They take turns.2, 7, 2, 7, 2, 7, 2, 7
- Why? Two jumps of 5 add 10, and adding 10 changes the tens digit but never the ones.2 → 12 → 22 → 32
- The terms also switch between even and odd, because adding an odd number flips even to odd and odd to even.even, odd, even, odd
Check it: Predict before computing: the 10th term should end in 7 and be odd. Keep going, 42, 47. It does.
Common Mistakes with 4.OA.5
Leaving out the starting number
“Start at 2, add 5” written as 7, 12, 17, 22
Try this: Write the starting number first and label it term 1. The rule only makes the terms that come after it.
Describing the rule instead of a feature
“I notice the numbers go up by 5”
Try this: Cover the rule and ask what else is true. Point students to the ones digits, to odd and even, and to every other term.
Explaining a feature with the feature
“It goes odd, even, odd, even because that’s the pattern”
Try this: Ask for the reason inside the rule: adding 5, an odd number, always turns odd into even and even into odd.
Where 4.OA.5 Fits
Practice 4.OA.5
Quick Check
- Start at 4 and add 6. Write the first five terms. Will any term be odd?
- Start at 1 and multiply by 3. Write the first five terms. What do you notice?
- A shape pattern repeats square, circle, triangle. What is the 20th shape?