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Year 3 Maths Patterns & Algebra

Number Patterns

Number patterns follow rules. At Year 3, we explore more complex patterns including those involving multiplication, larger numbers, and two-step rules.

Times Table Patterns

Multiplication tables are number patterns. The 3 times table:

3 6 9 12 15 18 21

Rule: add 3 each time (×3)

Patterns with Larger Numbers

Patterns can involve hundreds and thousands. Same rules, bigger numbers.

100, 200, 300, 400...

Rule: +100

1000, 900, 800, 700...

Rule: −100

Two-Step Rules

Some patterns have two operations in their rule.

1, 3, 7, 13, 21, ...

1 → 3: +2

3 → 7: +4

7 → 13: +6

13 → 21: +8

Rule: the amount added goes up by 2 each time

Function Machines

A function machine applies the same rule to each input number.

IN
3
5
8
→
× 4
→
OUT
12
20
32

Pattern Investigations

The 9s Pattern

9, 18, 27, 36, 45, 54, 63, 72, 81, 90

✓ The tens digit increases by 1 each time (0, 1, 2, 3, ...)

✓ The ones digit decreases by 1 each time (9, 8, 7, 6, ...)

✓ The digits always add to 9! (1+8=9, 2+7=9, 3+6=9...)

Odd and Even Patterns

Even numbers: +2

2, 4, 6, 8, 10, 12...

Always end in 0, 2, 4, 6, 8

Odd numbers: +2

1, 3, 5, 7, 9, 11...

Always end in 1, 3, 5, 7, 9

Key Vocabulary

pattern — a sequence of numbers that follow a rule
rule — the operation that transforms each number into the next
function machine — a model that applies the same rule to every input
term — each individual number in a pattern (first term, second term, etc.)

Knowledge Check

Question 1

What are the next two numbers in the pattern? 7, 14, 21, 28, ___, ___

Question 2

A function machine multiplies each input by 6. The input is 9. What is the output?

Question 3

What is the rule for this pattern? 500, 450, 400, 350, 300, ...

Question 4

Which of these is a true fact about the 9 times table pattern?

Lesson Summary