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Comparing Two Number Patterns

A 50-minute Grade 5 lesson on generating two sequences from two rules and finding the relationship between corresponding terms — the first step towards graphing a function.

Comparing Two Number Patterns is a free 50-minute Grade 5 maths lesson plan for Common Core standard 5.OA.B.3 — make and compare two number patterns. It is timed across 5 sections, gives the exact wording to use where the wording carries the mathematics, names 3 misconceptions with the teaching move that addresses each, and ends with an exit ticket and a printable worksheet with its answer key.

Grade:
Grade 5
Length:
50 minutes
Standard:
5.OA.B.3

Grade 5 · Operations & Algebraic Thinking

5.OA.B.3

Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms.

Objective

Students will be able to generate two patterns from two rules and describe the relationship between corresponding terms.

Students are successful when they can

  • Generates both sequences in a table with matching positions.
  • States the relationship between corresponding terms.
  • Predicts a corresponding term without generating every term.

What you need

  • Two-column tables with a position column
  • Squared paper for plotting pairs
  • Rule cards in pairs
  • The printable practice sheet linked at the end of this plan

The lesson

Warm-up — two rules, side by side

6 min
  1. Rule A: start at 0, add 3. Rule B: start at 0, add 6. Generate six terms of each in a table.
  2. 0, 3, 6, 9, 12, 15 and 0, 6, 12, 18, 24, 30. No comment yet.

Teach — line them up and look across

15 min
  1. Number the positions 1 to 6 and put the two sequences in columns beside them.
  2. Ask what is true of every row. Each B term is double the corresponding A term.
  3. Ask why. B adds twice as much each step and both started at zero, so it stays twice as far along.
  4. Now change B to start at 2 and add 6. The doubling breaks. Ask what happens and why.
  5. Say the caution: the relationship depends on the starting values as well as the steps.
  6. Plot the pairs as points on squared paper. They lie on a straight line, and that is worth seeing once.
“Generate both, put them in a table, and look across the rows rather than down the columns. The relationship is between the pairs, not inside one sequence.”

Guided practice — find the relationship

14 min
  1. Pairs take two rule cards, generate eight terms of each in a table, and state the relationship.
  2. They test the relationship on a term further along before claiming it.
  3. Then they plot the pairs and describe the shape.

Independent practice

12 min
  1. Students complete a two patterns page.
  2. Relationships stated from the first two rows only are the error — a claim tested on two cases is a guess.

Close

3 min
  1. Give two rules and ask only whether the relationship will be a doubling, without generating anything.
  2. Predicting from the rules is where this leads.

What goes wrong, and why

Each of these is a reasoning error rather than carelessness. The fix addresses the reasoning.

Says B is triple A because it holds for the first pair.

Why: One case has been generalised. With both sequences starting at small numbers, coincidences are common.

Fix: Require the relationship to be tested on at least three widely separated rows before it is written down.

Compares the sequences by their step sizes only and ignores the starting values.

Why: The rules are the most visible input, and the starting number looks like a detail.

Fix: Run the same two step sizes with different starting values. The relationship changes, and the starting number stops being a detail.

Misaligns the two sequences by one position.

Why: The two lists have been written separately and matched by eye rather than by position.

Fix: Always use a table with a numbered position column. The alignment is structural rather than visual.

If they are not there yet

  • Use two adding rules that both start at zero, where the relationship is a clean multiple.
  • Provide the table with the position column already filled in.

If they finish early

  • Find two rules whose corresponding terms differ by a constant rather than a factor.
  • Given one sequence and the relationship, generate the other.
  • Plot both sequences against position and compare the two lines.

Exit ticket

Rule A: start at 0, add 4. Rule B: start at 0, add 12. Write four terms of each and describe the relationship.

What to look for: 0, 4, 8, 12 and 0, 12, 24, 36, with B being three times A. A relationship claimed from the first pair alone is worth querying even when it is right.

Printable practice for 5.OA.B.3

Free to print and copy, answer key included. Each sheet can generate a fresh set of problems for a retake.

Questions about Comparing Two Number Patterns

How long does the Comparing Two Number Patterns lesson take?

50 minutes, split across 5 timed sections: warm-up 6 min, teach 15 min, guided practice 14 min, independent practice 12 min, close 3 min. The minutes are stated per section and add up to the stated length, so the plan can be cut or extended at a section boundary rather than abandoned halfway.

Which standard does Comparing Two Number Patterns teach?

CCSS.MATH.CONTENT.5.OA.B.3 — 5.OA.B.3, Operations & Algebraic Thinking for Grade 5: “Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms.” In plain terms, make and compare two number patterns.

What do I need to teach this lesson?

Two-column tables with a position column, squared paper for plotting pairs, rule cards in pairs and the printable practice sheet linked at the end of this plan. Everything listed is either ordinary classroom equipment or a free printable from this site — there is nothing to buy and nothing to prepare beyond photocopying.

What mistakes should I expect in this lesson?

Three, each a reasoning error rather than carelessness: says B is triple A because it holds for the first pair; compares the sequences by their step sizes only and ignores the starting values and misaligns the two sequences by one position. The plan gives the thinking behind each one and the teaching move that addresses the thinking rather than the symptom.

How do I know whether the lesson worked?

The exit ticket asks: “Rule A: start at 0, add 4. Rule B: start at 0, add 12. Write four terms of each and describe the relationship.” 0, 4, 8, 12 and 0, 12, 24, 36, with B being three times A. A relationship claimed from the first pair alone is worth querying even when it is right. That tells you whether the class needs a reteach or a thirty-second conversation before you plan tomorrow.

Is there a worksheet to go with Comparing Two Number Patterns?

Yes — 2 printable 5.OA.B.3 worksheets, linked at the end of the plan and free like the rest of the site. Each one comes with an answer key and 25 versions, so the practice after the lesson can be a different paper on every desk.

Is Comparing Two Number Patterns free to use?

Yes. The plan, its printables and their answer keys are free to read, print and photocopy for your own class, with no account and no email capture. It was last reviewed on 5 September 2026. Please do not resell it or republish it as your own.

Last reviewed 2026-09-05. Aligned to 5.OA.B.3 of the Common Core State Standards for mathematics.