MathIsimple
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Lesson 5-3

Number & Shape Patterns

Identify and extend number patterns and geometric patterns using algebraic thinking. Master pattern recognition through detective agency activities.

Learning Scenario: Pattern Detective Agency

Scenario: You're a pattern detective! You need to solve these mysteries: What comes next in the sequence 2, 5, 8, 11, ? And what's the next shape in the pattern △, □, △, □, ? You also need to find the rule for the pattern 3, 6, 9, 12, ? and predict what the 10th number will be.

This detective work will teach you to spot patterns, find rules, and make predictions using algebraic thinking!

Number Patterns

Number patterns are sequences where each number follows a rule. Look for the pattern to predict what comes next.

Example:

2, 5, 8, 11, ? → Rule: add 3 each time → Next: 14

Shape Patterns

Shape patterns repeat in a cycle. Identify the repeating unit to predict what comes next.

Example:

△, □, △, □, ? → Pattern: triangle, square, repeat → Next: △

Step-by-Step Learning
1

Look for the Pattern

Examine the sequence carefully. What's happening from one number to the next? Is it adding, subtracting, multiplying, or dividing?

Example: 3, 6, 9, 12 → Look: 3+3=6, 6+3=9, 9+3=12 → Rule: add 3

2

Test the Rule

Apply your rule to see if it works for all the numbers in the sequence. If it doesn't work, look for a different pattern.

Example: Rule "add 3" works: 3+3=6, 6+3=9, 9+3=12 ✓

3

Make Predictions

Use your rule to predict the next numbers in the sequence or find any specific position.

Example: Next number: 12 + 3 = 15. 10th number: 3 + (9 × 3) = 30

Interactive Activities

Activity 1: Number Pattern Detective

Find the rule and next numbers:

  • • 1, 4, 7, 10, ?
  • • 2, 4, 8, 16, ?
  • • 5, 10, 15, 20, ?
  • • 3, 6, 12, 24, ?
  • • 100, 90, 80, 70, ?

Activity 2: Shape Pattern Detective

Find the next shapes:

  • • △, ○, △, ○, ?
  • • □, △, ○, □, △, ○, ?
  • • ★, ★, ○, ★, ★, ○, ?
  • • ◇, □, ◇, □, ?
  • • ▲, ▲, ▲, ○, ▲, ▲, ▲, ?
Practice Problems

Problem Set 1: Number Patterns

1. 2, 5, 8, 11, ? What's next?

2. 1, 3, 9, 27, ? What's next?

3. 4, 8, 12, 16, ? What's next?

4. 50, 45, 40, 35, ? What's next?

Problem Set 2: Pattern Rules

5. What's the rule for 2, 4, 6, 8, 10?

6. What's the rule for 1, 4, 7, 10, 13?

7. What's the rule for 3, 6, 12, 24, 48?

8. What's the rule for 100, 90, 80, 70, 60?

Problem Set 3: Advanced Patterns

9. What's the 10th number in 2, 5, 8, 11, ...?

10. What's the 8th number in 1, 3, 9, 27, ...?

11. What's the next shape in △, □, ○, △, □, ○, ?

12. What's the 15th shape in ★, ★, ○, ★, ★, ○, ...?

Common Mistakes to Avoid

❌ Not checking if the rule works for all numbers

Wrong: Seeing 2, 4, 6 and thinking "add 2" without checking

Correct: Check: 2+2=4, 4+2=6 ✓ (rule works)

❌ Confusing number patterns with shape patterns

Wrong: Looking for mathematical operations in shape patterns

Correct: Look for repeating cycles in shape patterns

Key Takeaways

Look for patterns by examining what happens between consecutive terms

Test your rule to make sure it works for all numbers in the sequence

Use the rule to make predictions about future terms

Shape patterns repeat in cycles, while number patterns follow mathematical rules