Generate and Compare Two Numerical Patterns

Students generate two numerical patterns using two different rules and the same starting value. They record corresponding terms in a table and identify relationships such as one sequence being consistently double or half the other.

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Grade 5 · Algebraic Thinking: Numerical Patterns and Relationships · question 1 of 3

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20 rungs. A star at the top.

A: 3, 6, 9, 12 · B: 12, 24, 36, 48 → B ÷ A =

How it is taught

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Two patterns can start at the same number.

Each pattern grows by its own rule.

Matching terms can keep a ratio.

Read it: Read the table both ways

A counts by 4: 4, 8, 12, 16. B counts by 16: 16, 32, 48, 64. Line them up, and every B is 4 times the A above it.

Put the terms in a table, one column for each place in the pattern.
Read along a row to find the step from one term to the next.
Read down a column to see how the top row and the bottom row are related.

A adds 4 each time and B adds 16, which is 4 groups of 4, so B grows 4 times as fast.

Each B is 4 times its A, all the way along: 24 × 4 = 96 at the end of the table.

A single pattern works the same way: put each term under its position, and read along for the step.

Read along a row for each pattern's step, and down a column for how the two patterns are related.

Adding 4 to A instead of multiplying, and saying the B under 16 is 16 + 4 = 20.

B is 4 times A, so the B under 16 is 16 × 4 = 64.

A: 8, 16, 24 · B is 3 times A. What is B's third term? — 72. Every B is 3 times its A, so the third is 24 times 3: 72.

Rule A: +3, Rule B: +6, both start at 0

Today we'll make two number patterns from the same start, then look for how they connect.

Here are our rules. Rule A says add three. Rule B says add six. Both patterns begin at zero.

We'll record each step in a table so we can compare the two patterns side by side.

Step zero: both patterns start at zero.

Step one for Rule A: zero plus three is three.

Step one for Rule B: zero plus six is six.

Step two: three plus three is six, and six plus six is twelve.

Step three: six plus three is nine, and twelve plus six is eighteen.

Step four: nine plus three is twelve, and eighteen plus six is twenty-four.

Look closely — every Rule B term is exactly double the matching Rule A term.

Adding six instead of three makes the pattern grow twice as fast. Rule B is always two times Rule A!

Grade 5 · Two rules, same start — spot the relationship

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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