3rd Grade · Operations & Algebraic Thinking
3.OA.D.9: Spot and explain number patterns, like 3, 6, 9, 12
3.OA.D.9 is a 3rd grade Common Core math standard in Operations & Algebraic Thinking. Here’s what it really covers, and how you can help your students learn it.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
The standard
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.
In plain words
Spot and explain number patterns, like 3, 6, 9, 12.
Sample questions from student practice
These questions from Bobby's Math Club are the kinds of questions your students will see. You can try answering them to see what a student might see.
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
Where students 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.
Effective teaching strategies
- Color the multiples of 3 or 4 on a hundreds chart or multiplication table, and ask students what they notice before telling them.
- Ask students to explain a pattern with a property of operations, such as why every product in the 6s row is double the product in the 3s row.
- Test a pattern claim with more examples before accepting it, such as checking whether every multiple of 3 is odd by listing 3, 6, 9, and 12.
Units that teach this standard
Find where 3.OA.D.9 lands in the program you teach. Each unit has a guide written for families. Unit names and order vary between editions and districts, so your school’s own materials have the exact sequence.
enVision Mathematics
Eureka Math²
Everyday Mathematics
i-Ready Classroom Mathematics
Illustrative Mathematics
Math Expressions
Reveal Math
Don’t see your curriculum? Contact Bobby and we’ll see if we can help!
Share it with families
Families can read Spotting patterns in times tables for a plain-language look at this skill, with three questions to try together and ideas for helping at home.
Help every student practice problem solving at home
In Bobby's Math Club, students practice at just the right level, with a hint when they need one, a clear explanation after every question, and kid-friendly videos. Unlimited practice is free for every family.
See how it works for teachers
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.