Generate Numerical Patterns from a Given Rule

Students generate a sequence of numbers by repeatedly applying a given rule (e.g., add 3, multiply by 2) starting from a given number. They recognize how the rule determines each successive term in the pattern.

Try three of them

Real questions from this skill, graded here. No account, and nothing is saved.

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

0 of 20

20 rungs. A star at the top.

13, 28, 43,

How it is taught

0:00 of 3:11

A numerical pattern is a list that follows one rule again and again.

Each term comes from applying that rule to the term before it.

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.

14, 30, 46, ___ — 62. Each term is 16 more than the one before it, so the fourth is 62.

Start at 2, rule: add 3

A number pattern is a list of numbers that follow a rule. Let's build one together!

Here's our plan: start at two, and the rule is add three. We'll keep using that rule again and again.

Our first term is the starting number — two.

Now we apply the rule: add three.

Two plus three is five. So our second term is five.

Apply the rule again — add three.

Five plus three is eight. The third term is eight.

One more time — add three.

Eight plus three is eleven. The fourth term is eleven.

And once more — add three.

Eleven plus three is fourteen. The fifth term is fourteen.

Grade 5 · Building a sequence by following a rule

Our pattern is two, five, eight, eleven, fourteen — each term is three more than the last.

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.

More of the library

Every skill has a page

Practise this skill free

14 days of every skill, practice packets, Fluency sheets and up to four students. No card.

Start free