5.OA.3: Generate Patterns and Graph Ordered Pairs
Also written as 5.OA.B.3 and CCSS.MATH.CONTENT.5.OA.B.3 · Cluster: Analyze patterns and relationships.
The Official Wording
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.
Common Core State Standards, Grade 5, Operations & Algebraic Thinking · Read it at the source · Checked October 14, 2026
What 5.OA.3 Means in Plain English
Fifth graders run two rules at once. Start both at 0, add 2 to one and 8 to the other: 0, 2, 4, 6 and 0, 8, 16, 24. Each term in the second list is four times its partner because each step adds four times as much.
Then the pairs become points: (0, 0), (2, 8), (4, 16), (6, 24) on a coordinate grid (5.G.1), and they line up. That straight line is a first look at a proportional relationship, which 6th graders study as ratio tables and graphs in 6.RP.3.
5.OA.3 I Can Statements
- I can generate a number pattern from a rule and a starting number.
- I can explain how the terms of two patterns are related.
- I can form ordered pairs from two patterns and graph them.
5.OA.3 Worked Example
Two rules, two lists, one relationship, and the points that make it visible.
Rule A: start at 0, add 2. Rule B: start at 0, add 6. Generate five terms of each, compare the matching terms, and graph the ordered pairs.
- Generate Rule A. Start at 0 and keep adding 2.A: 0, 2, 4, 6, 8
- Generate Rule B underneath it, term by term. Start at 0 and keep adding 6.B: 0, 6, 12, 18, 24
- Compare partners. 6 is three 2s, 12 is three 4s, 18 is three 6s. Every B term is three times its A term, because each step adds 6, which is three times the 2 that A adds.B = 3 × A: 3 × 2 = 6, 3 × 4 = 12, 3 × 6 = 18
- Make ordered pairs with the A term first and the B term second.(0, 0), (2, 6), (4, 12), (6, 18), (8, 24)
- Plot them: across by the A term, up by the B term. The points fall on one straight line through the origin.Across 2 and up 6, across 4 and up 12, and so on
Check it: Predict the next pair before computing it: A is 10, so B should be 30. Adding 6 to 24 gives 30. The rule and the relationship agree.
Common Mistakes with 5.OA.3
Comparing within a list instead of across
“B goes up by 6” given as the relationship between the two patterns
Try this: Write the lists one above the other in a table and draw a vertical arrow between each pair, so the comparison runs down, not along.
Swapping the coordinates
(6, 2) plotted for the pair with A = 2 and B = 6
Try this: Label the table columns x and y before pairing, and read every pair the same way: across first, then up.
Describing the relationship with addition
“B is always 4 more than A” after seeing 2 and 6, which fails at 4 and 12
Try this: Test any claim against two different pairs. “4 more” works for (2, 6) but not (4, 12), while “three times” works for both.
Where 5.OA.3 Fits
Practice 5.OA.3
Quick Check
- Rule A: start at 0, add 4. Rule B: start at 0, add 12. Write the first four terms of each.
- How are the terms of Rule B related to the terms of Rule A?
- Write the ordered pairs for those four terms, A first.