Comparing two number patterns on a grid
In 5th grade, children learn to build two number patterns from two rules, to compare them side by side and explain why they are linked, and to plot the matching pairs on a grid.
By Robert “Bobby” BarnettMath teacher, parent, and founder of Bobby’s Math Club
Try these with your child
These are real questions from our 5th 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
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
Why this matters
Spotting how two patterns move together is your child's first real glimpse of how one quantity depends on another. Noticing that one list is always double another grows into the tables, graphs, and equations of 6th and 7th grade, and later into the straight-line graphs of science class, where distance grows with time or cost grows with the number of items bought.
Where kids 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.
How you can help
- Compare two savings plans at the kitchen table: one person saves $2 a week, the other $4. Write five weeks of totals for each and ask your child what they notice about the two columns.
- Build two towers of blocks or coins, adding 2 to one and 4 to the other each turn. After five turns, ask your child why the second tower is always twice as tall, and listen for "adding 4 is adding 2 twice."
- Make up rules for each other during a car ride, like "start at 0, add 5" and "start at 0, add 10." Say the lists aloud together and ask how the matching numbers compare.
Bobby's Math Club offers free practice that grows with your child.
Questions parents ask
Why is my child learning number patterns this way?
Building two patterns side by side trains your child to look for relationships, not only for the next number. Spotting that one list is always double the other is a real mathematical observation, and graphing the pairs turns it into a picture. Teachers use simple rules like "add 3" and "add 6" so the arithmetic stays easy and the thinking about relationships gets the attention.
What is an ordered pair in 5th grade math?
An ordered pair is two numbers written in parentheses, like (3, 6), that mark one point on a grid. The first number tells how far to go across, and the second tells how far to go up. In this skill, each pair comes from matching terms in the two patterns. The order matters, because (3, 6) and (6, 3) are different points.
How does this connect to what my child learns next?
In 6th grade, your child will use tables and simple equations to describe how one quantity changes with another, such as cost and number of items. Later, those relationships appear as straight-line graphs. Noticing that "the second number is always twice the first" is an early version of writing y = 2x, which comes a few years from now.
Make learning math fun
Bobby's Math Club turns 5th grade math practice into something fun to do together.
- Unlimited practice, completely free
- 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.
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Join the clubNote for teachers: This skill is covered by Common Core math standard 5.OA.B.3: “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.” Learn how Bobby's Math Club can help your students grow. (Common Core 5.OA.3)