Number & Algebra

Patterns: Repeating and Growing

Year 1 · Year 2

✓Recognise and identify repeating patterns with objects, drawings, and numbers.
✓Describe the 'core' or 'rule' of a repeating pattern.
✓Continue and create repeating patterns using various elements.
✓Recognise and identify growing patterns with objects, drawings, and numbers.
✓Describe the 'rule' of a growing pattern.
✓Continue and create growing patterns using various elements.

Key concepts

Pattern

A pattern is a sequence of things that follow a rule. It can be made with shapes, colours, numbers, sounds, or actions.

Repeating Pattern

A repeating pattern is a pattern where a group of items or actions, called the 'core', repeats over and over again.

Core (or Unit of Repeat)

The 'core' is the part of a repeating pattern that repeats. For example, in 'red, blue, red, blue', the core is 'red, blue'.

Growing Pattern

A growing pattern is a pattern where each step changes by adding or subtracting the same amount, or by following another consistent rule, making the pattern get bigger or smaller in a predictable way.

Rule

The 'rule' is the instruction that tells you how a pattern works or how it changes from one step to the next.

Key facts to remember

1A pattern is a sequence of things that follows a rule.
2Repeating patterns have a 'core' (or unit of repeat) that repeats over and over.
3Growing patterns change by adding or subtracting the same amount each time, or by following another consistent rule.
4The 'rule' tells us how a pattern works or changes.
5Patterns can be found in shapes, colours, numbers, sounds, and movements.
6Understanding patterns helps us predict what comes next.

Worked examples

Example 1

What comes next in this pattern? Circle, Square, Circle, Square, Circle, ___, ___

I1. Look carefully at the pattern: Circle, Square, Circle, Square, Circle.

II2. Identify the part that repeats. The sequence 'Circle, Square' repeats.

III3. This repeating part is the 'core' of the pattern.

IV4. Continue the pattern by adding the next items from the core.

Answer

Square, Circle

Saying the pattern out loud can help you hear the repeating part.

Example 2

Describe the core of this pattern: Red block, Blue block, Yellow block, Red block, Blue block, Yellow block. Then draw the next two blocks.

I1. Look at the sequence of coloured blocks.

II2. Find the group of blocks that repeats. The sequence 'Red block, Blue block, Yellow block' is seen twice.

III3. This sequence is the 'core' of the pattern.

IV4. To draw the next two blocks, use the first two blocks from the core.

Answer

Core: Red block, Blue block, Yellow block. Next two blocks: Red block, Blue block.

The core must be the smallest part that repeats.

Example 3

What is the rule for this number pattern? 2, 4, 6, 8, ___, ___

I1. Look at the numbers and how they change from one to the next.

II2. From 2 to 4, we add 2 (2 + 2 = 4).

III3. From 4 to 6, we add 2 (4 + 2 = 6).

IV4. From 6 to 8, we add 2 (6 + 2 = 8).

V5. The rule is 'add 2' each time. This is a growing pattern.

VI6. Continue the pattern by adding 2 to the last number: 8 + 2 = 10, then 10 + 2 = 12.

Answer

Rule: Add 2. Next numbers: 10, 12.

Check the rule for at least two steps to make sure it's consistent.

Example 4

Draw the next two steps in this pattern: Step 1: 1 triangle. Step 2: 2 triangles. Step 3: 3 triangles.

I1. Observe how the number of triangles changes in each step.

II2. From Step 1 to Step 2, 1 triangle is added (1 + 1 = 2).

III3. From Step 2 to Step 3, 1 triangle is added (2 + 1 = 3).

IV4. The rule is 'add 1 triangle to the previous step'. This is a growing pattern.

V5. To find Step 4, add 1 triangle to Step 3 (3 + 1 = 4 triangles).

VI6. To find Step 5, add 1 triangle to Step 4 (4 + 1 = 5 triangles).

Answer

Step 4: 4 triangles. Step 5: 5 triangles.

Growing patterns can increase or decrease.

Common mistakes

✗Not identifying the full 'core' of a repeating pattern (e.g., saying 'red' is the core of 'red, blue, red, blue, yellow').
✗Confusing repeating patterns with growing patterns.
✗Incorrectly identifying the 'rule' for a growing pattern (e.g., saying 'add 1' for a pattern that adds 2).
✗Only looking at the first two items and not checking if the rule works for the whole pattern.

Exam tips

★Always look carefully at the beginning of the pattern to find the rule or the core.
★Say the pattern out loud to help you hear or see the repeat or the change.
★Use drawing, counting, or objects to help you continue patterns.
★Check your answer by applying the rule to make sure it makes sense for the whole pattern.

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