5th Grade · Operations & Algebraic Thinking
5.OA.B.3: Make two number patterns from two rules, and compare them
5.OA.B.3 is a 5th 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
Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule "Add 3" and the starting number 0, and given the rule "Add 6" and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
In plain words
Make two number patterns from two rules, and compare them.
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
Ana and Luis both start with $0. Each week, Ana saves $5 and Luis saves $10. When Ana has $15, how much does Luis have?
- $25
- $40
- $30
Where students can get stuck
- Comparing numbers within one list, so they notice "it goes up by 3" but miss that each second-list number is double its partner.
- Swapping the order in an ordered pair, so they plot (6, 3) instead of (3, 6).
- Starting the second pattern at the wrong number, so the two lists no longer line up term by term.
Effective teaching strategies
- Build two lists with students from the rules “start at 0, add 3” and “start at 0, add 6,” then write the matching terms side by side as pairs.
- Ask students to look across each pair instead of down each list, and say how the second number compares with the first, such as twice as large.
- Show students how to write each matching pair as an ordered pair, then have them plot (3, 6) and point to the number that tells how far to go across.
Units that teach this standard
Find where 5.OA.B.3 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.
Bridges in Mathematics
enVision Mathematics
i-Ready Classroom Mathematics
Illustrative Mathematics
Math Expressions
Don’t see your curriculum? Contact Bobby and we’ll see if we can help!
Share it with families
Families can read Comparing two number patterns on a grid 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.