Patterns

Repeating Patterns and Shape PatternsColour Patterns and Number PatternsCompleting Patterns and Creating Own Patterns

Repeating Patterns and Shape Patterns

What are repeating patterns?

A repeating pattern is a sequence that repeats the same block over and over again. The block that repeats is called the pattern core or unit of repeat. Think of it like a song chorus that keeps coming back!

What are shape patterns?

Shape patterns use different shapes like circles, squares, triangles, and stars to create a repeating design. You can find shape patterns on wallpaper, clothes, and carpets!

How to identify repeating patterns:

  • Step 1: Look for a group that keeps appearing
  • Step 2: Check if the same sequence happens again and again
  • Step 3: Predict what comes next by looking at the core

Examples of repeating patterns:

PatternCore UnitNext in Sequence
🔴🔵🔴🔵🔴🔵🔴🔵🔴
△□○△□○△□○△□○△
1,2,3,1,2,3,1,21,2,33
ABABABABA
Figure — Repeating Patterns and Shape Patterns
Patterns Colour: Red, Blue, Red, Blue… Shape: ? ← What comes next? Number: 246 810 __ ← skip count by 2!
1
Worked Example

What comes next in this pattern? △ □ ○ △ □ ○ △ □ ___

Solution
  • Look at the pattern: △ □ ○ then △ □ ○ then △ □
  • The core is [△ □ ○]
  • After △ □ comes ○
  • So the next shape is ○

Answer: ○

2
Worked Example

Draw the next three shapes in this repeating pattern: ★ ◆ ★ ◆ ★ ◆ __ __ __

Solution
  • The pattern core is [★ ◆]
  • It repeats: ★ ◆ then ★ ◆ then ★ ◆
  • Next three shapes follow the core:

- 1st next: ★

- 2nd next: ◆

- 3rd next: ★

  • So the next three are: ★, ◆, ★

Answer: ★ ◆ ★

3
Worked Example

A pattern is made using shapes: ● ■ ▲ ● ■ ▲ ● ■ ▲. If this pattern continues, what will be the 15th shape? What is the core length?

Solution
  • First, identify the core: [● ■ ▲] (3 shapes long)
  • The pattern repeats every 3 shapes
  • To find the 15th shape, divide 15 by 3: 15 ÷ 3 = 5 exactly
  • When it divides exactly, the shape is the LAST one in the core
  • Last shape in core is ▲
  • Core length = 3 shapes

Answer: The 15th shape is ▲, core length = 3

Key Points

  • Repeating patterns have a core that repeats over and over
  • Shape patterns use different shapes to form the pattern
  • The pattern core is the smallest part that repeats
  • Common patterns: ABAB, AABB, ABC, ABB, AAB
  • To find what comes next, look at the core
  • Repeating patterns are everywhere in nature and daily life!

Colour Patterns and Number Patterns

What are colour patterns?

Colour patterns use different colours in a repeating sequence. You can find colour patterns in rainbow stripes, beaded bracelets, floor tiles, and festive decorations!

What are number patterns?

Number patterns follow a special rule. Instead of colours or shapes, we use numbers. Each number changes by adding, subtracting, or following a rule.

Types of number patterns:

Pattern TypeRuleExampleNext Number
Add constantAdd same number2,4,6,8,10+2 = 12
Subtract constantSubtract same number20,18,16,14-2 = 12
Count by 2sAdd 25,7,9,11,13+2 = 15
Count by 5sAdd 55,10,15,20+5 = 25
Count by 10sAdd 1010,20,30,40+10 = 50

How to find a number pattern:

  • Step 1: Find the difference between two numbers next to each other
  • Step 2: Check if the same difference works for all pairs
  • Step 3: Apply the rule to find the next number
Figure — Colour Patterns and Number Patterns
Patterns Colour: Red, Blue, Red, Blue… Shape: ? ← What comes next? Number: 246 810 __ ← skip count by 2!
1
Worked Example

Identify the colour pattern and state the core: 🔴 🟡 🔴 🟡 🔴 🟡 🔴

Solution
  • Look at the colours: 🔴 then 🟡 then 🔴 then 🟡
  • The pattern alternates between red and yellow
  • The smallest repeating block is [🔴 🟡]
  • Core = 🔴 🟡 (2 colours)
  • Next colour would be 🟡

Answer: Core is [🔴 🟡]

2
Worked Example

Find the rule and the next two numbers: 5, 10, 15, 20, __, __

Solution
  • Find the difference between numbers:

- 10 - 5 = 5

- 15 - 10 = 5

- 20 - 15 = 5

  • The rule is: Add 5 each time
  • Next number: 20 + 5 = 25
  • Then: 25 + 5 = 30

Answer: Rule: Add 5; Next two: 25, 30

3
Worked Example

A colour pattern has the core [🔴 🔵 🟢]. The pattern has 20 colours. How many times does the core repeat completely? What colour is the 18th position?

Solution
  • Core length = 3 colours
  • 20 ÷ 3 = 6 remainder 2
  • Core repeats completely 6 times (18 colours)
  • Remainder 2 means 2 more colours from the core
  • 1st extra = 🔴, 2nd extra = 🔵
  • So 18th colour is the last of the 6th complete core = 🟢
  • Actually, 6 cores = 6 × 3 = 18 colours
  • 18th colour is the 3rd of the core = 🟢

Answer: 6 complete repeats; 18th colour is 🟢

Key Points

  • Colour patterns use repeating colours like 🔴🔵🔴🔵
  • Number patterns follow a rule like "add 3" or "subtract 2"
  • To find a number rule, subtract two numbers next to each other
  • The difference tells you what is being added (or subtracted)
  • Patterns help us predict what comes next
  • Colour and number patterns are connected — colours can represent numbers!

Completing Patterns and Creating Own Patterns

What does completing patterns mean?

Completing patterns means finding the missing part of a pattern. Sometimes the pattern has a gap in the middle or at the end. You need to use the pattern rule to fill in what's missing!

What does creating own patterns mean?

Creating your own patterns is fun! You can design your own repeating sequences using shapes, colours, numbers, or anything you like. You are the pattern maker!

How to complete patterns:

SituationStrategyExample
Missing at endContinue the core●■●■●■? → add ●
Missing in middleLook before and after▲?▲▲?▲ → core is [▲▲]
Missing at startLook at what follows?□■□■□ → core [□■], so ?=□

How to create your own patterns:

  • Step 1: Choose what to use (shapes, colours, numbers)
  • Step 2: Decide the core (2-5 items works well)
  • Step 3: Repeat the core at least 3 times
  • Step 4: Check that it follows the rule
Figure — Completing Patterns and Creating Own Patterns
Patterns Colour: Red, Blue, Red, Blue… Shape: ? ← What comes next? Number: 246 810 __ ← skip count by 2!
1
Worked Example

Complete the pattern: 2, 4, 6, __, 10, 12

Solution
  • Look at the numbers: 2, 4, 6, ?, 10, 12
  • Find the rule: 4-2=2, 6-4=2, so add 2 each time
  • After 6 comes 6+2=8
  • Check: 8+2=10 ✓, 10+2=12 ✓
  • The missing number is 8

Answer: 8

2
Worked Example

Create a pattern using shapes where the core is [△ □ ○] and repeat it 4 times.

Solution
  • Core = [△ □ ○]
  • Repeat 4 times:

- 1st core: △ □ ○

- 2nd core: △ □ ○

- 3rd core: △ □ ○

- 4th core: △ □ ○

  • Full pattern: △ □ ○ △ □ ○ △ □ ○ △ □ ○
  • Total length: 4 × 3 = 12 shapes

Answer: △ □ ○ △ □ ○ △ □ ○ △ □ ○

3
Worked Example

A pattern has a missing part in the middle: ★ ● ■ ★ ? ■ ★ ● ■. Find the missing shape and explain the rule.

Solution
  • Write positions: 1:★, 2:●, 3:■, 4:★, 5:?, 6:■, 7:★, 8:●, 9:■
  • Look for the core: Compare positions 1-3 and 7-9: both are [★ ● ■]
  • So core is [★ ● ■] (length 3)
  • Position 4 is the start of the 2nd core: should be ★ (matches ✓)
  • Position 5 should be the 2nd of core: ●
  • Position 6 should be the 3rd of core: ■ (matches ✓)
  • So missing shape is ●
  • Check full pattern: ★ ● ■ ★ ● ■ ★ ● ■ ✓

Answer: ●

Key Points

  • Completing patterns uses the pattern rule to fill missing parts
  • Look for the core to understand the pattern
  • You can find patterns missing at the beginning, middle, or end
  • Creating patterns lets you be a pattern designer
  • A good pattern has a clear core that repeats
  • Always test your pattern to make sure it follows the rule!