🎨 Patterns - Grade 3
Understanding Patterns!
Patterns are arrangements or sequences that follow a certain rule or order! Patterns are everywhere around us - in nature, art, music, and math!
Types of Patterns:
• Repeating Patterns - A core unit repeats over and over
• Growing Patterns - The pattern increases by a rule
• Shrinking Patterns - The pattern decreases by a rule
🔄 Repeating Patterns
What is a Repeating Pattern?
A repeating pattern has a group of items (called the core or unit) that repeats over and over again!
Core (Unit) → Core → Core → Core...
Parts of a Repeating Pattern:
• Core (Unit): The part that repeats
• Term: Each individual element in the pattern
• Rule: What repeats and in what order
Types of Repeating Patterns:
AB Pattern
Two different items alternate back and forth.
Example: ⭐ 🌙 ⭐ 🌙 ⭐ 🌙
Core: ⭐ 🌙
Pattern Type: AB
AAB Pattern
One item appears twice, then another item once.
Example: ❤️ ❤️ 💙 ❤️ ❤️ 💙
Core: ❤️ ❤️ 💙
Pattern Type: AAB
ABB Pattern
One item appears once, then another item twice.
Example: 🟢 🔵 🔵 🟢 🔵 🔵
Core: 🟢 🔵 🔵
Pattern Type: ABB
ABC Pattern
Three different items appear in sequence.
Example: 🔴 🟡 🟢 🔴 🟡 🟢
Core: 🔴 🟡 🟢
Pattern Type: ABC
AABB Pattern
Two items each appear twice.
Example: 🟨 🟨 🟪 🟪 🟨 🟨 🟪 🟪
Core: 🟨 🟨 🟪 🟪
Pattern Type: AABB
Number Patterns:
Example 1: 2, 5, 2, 5, 2, 5...
Core: 2, 5
Pattern Type: AB
Example 2: 1, 1, 3, 1, 1, 3, 1, 1, 3...
Core: 1, 1, 3
Pattern Type: AAB
💡 Key Point: In repeating patterns, the same group repeats without changing!
✏️ Complete a Repeating Pattern
How to Complete a Pattern:
- Find the core (repeating unit)
- See how many times the core repeats
- Figure out where you are in the core
- Fill in the missing part
Examples:
Example 1: Fill in the Blank
Pattern: 🔺 ⭕ 🔺 __ 🔺 ⭕
What shape goes in the blank?
Step 1: Find the core: 🔺 ⭕
Step 2: The pattern is: 🔺 ⭕ | 🔺 __ | 🔺 ⭕
Step 3: After 🔺 comes ⭕
Answer: ⭕ ✓
Example 2: Number Pattern
Pattern: 3, 7, 3, 7, __, 7, 3
What number goes in the blank?
Step 1: Find the core: 3, 7
Step 2: Pattern: 3, 7 | 3, 7 | __, 7 | 3
Step 3: The blank is the first position in the core
Answer: 3 ✓
Example 3: AAB Pattern
Pattern: ⬛ ⬛ ⬜ ⬛ __ ⬜ ⬛ ⬛ ⬜
What shape goes in the blank?
Step 1: Find the core: ⬛ ⬛ ⬜
Step 2: Pattern: ⬛ ⬛ ⬜ | ⬛ __ ⬜ | ⬛ ⬛ ⬜
Step 3: The blank is the second position (second A)
Answer: ⬛ ✓
🎨 Make a Repeating Pattern
Steps to Create Your Own Pattern:
- Choose your items - Pick 2 or 3 different shapes, colors, or numbers
- Decide the core - Arrange them in an order (AB, AAB, ABC, etc.)
- Repeat the core - Copy the core at least 3 times
- Check your pattern - Make sure it repeats correctly!
Pattern Ideas:
Using Shapes
AB Pattern: 🟦 🟥 🟦 🟥 🟦 🟥
ABC Pattern: ⭐ 🌙 ☀️ ⭐ 🌙 ☀️
AABB Pattern: 🔴 🔴 🟢 🟢 🔴 🔴 🟢 🟢
Using Numbers
AB Pattern: 5, 8, 5, 8, 5, 8...
AAB Pattern: 2, 2, 9, 2, 2, 9...
ABC Pattern: 1, 4, 7, 1, 4, 7...
Using Letters
AB Pattern: A, B, A, B, A, B...
AAB Pattern: X, X, Y, X, X, Y...
ABB Pattern: M, N, N, M, N, N...
💡 Creative Tip: You can make patterns with sounds, movements, or even claps!
📈 Growing Patterns
What is a Growing Pattern?
A growing pattern (also called an increasing pattern) is one that gets bigger by following a rule! Each term increases by a fixed amount or in a specific way.
Term 1 → Term 2 → Term 3 → Term 4...
(Each term is BIGGER than the previous one!)
Parts of a Growing Pattern:
• Term: Each step or position in the pattern
• Rule: How the pattern increases (what gets added)
• Starting Term: The first term in the pattern
Types of Growing Patterns:
Number Patterns (Adding)
Example 1: Add 3 each time
Pattern: 5, 8, 11, 14, 17...
Rule: Add 3 each time
Next term: \(17 + 3 = 20\) ✓
Formula: Next term = Previous term + 3
Skip Counting Patterns
Example 2: Count by 5s
Pattern: 10, 15, 20, 25, 30...
Rule: Add 5 each time
Next term: \(30 + 5 = 35\) ✓
Shape Patterns (Adding Objects)
Example 3: Add one circle each time
Term 1: ⭕
Term 2: ⭕ ⭕
Term 3: ⭕ ⭕ ⭕
Term 4: ⭕ ⭕ ⭕ ⭕
Rule: Add 1 circle each time
Next term (Term 5): ⭕ ⭕ ⭕ ⭕ ⭕ ✓
Building Patterns
Example 4: Staircase pattern
Term 1: 🟦
Term 2: 🟦 🟦
Term 3: 🟦 🟦 🟦
Term 4: 🟦 🟦 🟦 🟦
Rule: Add 1 square each time
Pattern: 1, 2, 3, 4, 5... blocks
Finding the Rule:
- Look at the first two terms
- Find the difference - How much was added?
- Check with other terms - Does the same rule work?
- State the rule - "Add ___ each time"
Example: Find the rule for 7, 10, 13, 16...
Step 1: \(10 - 7 = 3\)
Step 2: \(13 - 10 = 3\)
Step 3: \(16 - 13 = 3\)
Rule: Add 3 each time ✓
🔍 Find the Next Shape in a Pattern
How to Find the Next Shape:
- Identify the pattern type - Is it repeating or growing?
- Find the rule - What repeats or what gets added?
- Apply the rule - Use the rule to find the next shape
- Draw or name the next shape
Examples:
Example 1: Repeating Shape Pattern
Pattern: 🔴 🔵 🟡 🔴 🔵 🟡 🔴 __
What comes next?
Step 1: This is a repeating pattern
Step 2: Core: 🔴 🔵 🟡
Step 3: After 🔴 comes 🔵
Answer: 🔵 ✓
Example 2: Growing Shape Pattern
Pattern:
Term 1: ⭐
Term 2: ⭐ ⭐
Term 3: ⭐ ⭐ ⭐
What is Term 4?
Step 1: This is a growing pattern
Step 2: Rule: Add 1 star each time
Step 3: Term 4 has 4 stars
Answer: ⭐ ⭐ ⭐ ⭐ ✓
Example 3: Growing by 2
Pattern:
Term 1: 🟢
Term 2: 🟢 🟢 🟢
Term 3: 🟢 🟢 🟢 🟢 🟢
What is Term 4?
Step 1: Growing pattern
Step 2: Count: 1, 3, 5... (Add 2 each time)
Step 3: Next: \(5 + 2 = 7\) circles
Answer: 🟢 🟢 🟢 🟢 🟢 🟢 🟢 ✓
📊 Find the Next Row in a Growing Pattern
What are Row Patterns?
In row patterns, each row builds on the previous one by adding more items in a specific way!
How to Find the Next Row:
- Count items in each row
- Find the pattern in the numbers
- Determine the rule
- Apply the rule to create the next row
Examples:
Example 1: Triangle Pattern
Pattern:
Row 1: 🔺
Row 2: 🔺 🔺
Row 3: 🔺 🔺 🔺
Row 4: ?
Count: 1, 2, 3, ?
Rule: Add 1 triangle to each row
Next row: \(3 + 1 = 4\) triangles
Answer: 🔺 🔺 🔺 🔺 ✓
Example 2: Square Pattern
Pattern:
Row 1: 🟦
Row 2: 🟦 🟦 🟦
Row 3: 🟦 🟦 🟦 🟦 🟦
Row 4: ?
Count: 1, 3, 5, ?
Pattern: Odd numbers (add 2 each time)
Next row: \(5 + 2 = 7\) squares
Answer: 🟦 🟦 🟦 🟦 🟦 🟦 🟦 ✓
Example 3: L-Shape Pattern
Pattern:
Row 1: ⭐ ⭐ (2 stars in L-shape)
Row 2: ⭐ ⭐ ⭐ ⭐ (4 stars in L-shape)
Row 3: ⭐ ⭐ ⭐ ⭐ ⭐ ⭐ (6 stars in L-shape)
Row 4: ?
Count: 2, 4, 6, ?
Pattern: Even numbers (add 2 each time)
Next row: \(6 + 2 = 8\) stars
Answer: 8 stars in L-shape ✓
Example 4: Number Pattern in Rows
Pattern:
Row 1: 5
Row 2: 5, 10
Row 3: 5, 10, 15
Row 4: ?
Rule: Each row adds the next multiple of 5
Next number: 20
Answer: 5, 10, 15, 20 ✓
📝 Important Pattern Rules Summary
Repeating Patterns:
Core (Unit) repeats over and over
Find the core → Repeat it → Pattern complete!
Growing Patterns:
Next Term = Previous Term + Rule
Example: If rule is "add 4"
\(\text{Next Term} = \text{Previous Term} + 4\)
Finding the Rule:
Rule = Second Term − First Term
Example: 7, 12, 17, 22...
Rule: \(12 - 7 = 5\) (Add 5 each time)
Common Pattern Types:
| Pattern Type | Example | Core/Rule |
|---|---|---|
| AB Repeating | 1, 2, 1, 2, 1, 2 | Core: 1, 2 |
| ABC Repeating | A, B, C, A, B, C | Core: A, B, C |
| Growing by 1 | 3, 4, 5, 6, 7 | Rule: +1 |
| Growing by 5 | 5, 10, 15, 20, 25 | Rule: +5 |
💡 Quick Learning Tips
- ✓ Repeating patterns: Same core over and over!
- ✓ Growing patterns: Get bigger by a rule!
- ✓ To find the core: Look for what repeats
- ✓ To find the rule: Subtract consecutive terms
- ✓ AB pattern = two different items alternating
- ✓ ABC pattern = three different items in order
- ✓ AAB pattern = first item twice, second once
- ✓ Skip counting makes growing patterns (2, 4, 6, 8...)
- ✓ Each position in a pattern is called a term
- ✓ Count carefully to find the pattern rule
- ✓ Check your answer by continuing the pattern
- ✓ Patterns can use shapes, numbers, colors, or letters
- ✓ Look for patterns in nature, art, and everyday life!
- ✓ Practice making your own patterns!
- ✓ Growing patterns can grow by any number (1, 2, 3, 5, 10...)