Basic Math

Patterns | Third Grade

12 months ago
6 mins

🎨 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:

  1. Find the core (repeating unit)
  2. See how many times the core repeats
  3. Figure out where you are in the core
  4. 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:

  1. Choose your items - Pick 2 or 3 different shapes, colors, or numbers
  2. Decide the core - Arrange them in an order (AB, AAB, ABC, etc.)
  3. Repeat the core - Copy the core at least 3 times
  4. 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:

  1. Look at the first two terms
  2. Find the difference - How much was added?
  3. Check with other terms - Does the same rule work?
  4. 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:

  1. Identify the pattern type - Is it repeating or growing?
  2. Find the rule - What repeats or what gets added?
  3. Apply the rule - Use the rule to find the next shape
  4. 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:

  1. Count items in each row
  2. Find the pattern in the numbers
  3. Determine the rule
  4. 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 TypeExampleCore/Rule
AB Repeating1, 2, 1, 2, 1, 2Core: 1, 2
ABC RepeatingA, B, C, A, B, CCore: A, B, C
Growing by 13, 4, 5, 6, 7Rule: +1
Growing by 55, 10, 15, 20, 25Rule: +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...)
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