Number Patterns

Identifying, Analyzing, and Applying Patterns in Mathematics

CAPS Grade 10 Mathematical Literacy

Number Patterns serve as a foundational concept for grasping how variables change in practical contexts. This document outlines identifying types of patterns, predicting subsequent terms, articulating relationships, and interpreting patterns in tabular form.

1. Identifying the Type of Pattern

Constant Difference (Linear)

Increases or decreases by a fixed amount each time.

Example: 15, 30, 45, 60 (+15 each time)

Constant Ratio

Multiplying or dividing by a consistent factor.

Example: 2, 4, 8, 16, 32 (×2 each time)

Square/Geometric Patterns

Patterns based on square numbers.

Example: 1, 4, 9, 16, 25 (1², 2², 3², 4², 5²)

Identify Pattern Types

3 Questions
1 3, 6, 9, 12, ... What type of pattern?
Constant Difference
Constant Ratio
Square Pattern
None
2 2, 4, 8, 16, 32, ... What type of pattern?
Constant Difference
Constant Ratio
Square Pattern
None
3 1, 4, 9, 16, 25, ... What type of pattern?
Constant Difference
Constant Ratio
Square Pattern
None
0/3

2. Finding the "Next Term"

1

Find Difference

Subtract first term from second

2

Apply Pattern

Add difference to last term

Example: 5, 10, 15, ? → difference = 5 → next = 20
Ratio Example: 3, 6, 12, ? → ratio = ×2 → next = 24

Next Term Challenge

Sequence: 2, 5, 8, 11, ?
Hint: Find the difference between terms

3. Describing the Pattern in Words

Writing Pattern Descriptions

Example: "For every additional litre of petrol bought, the total price increases by R22.50."

Key Elements:

1

Identify the independent variable

2

State the rate of change

3

Mention any starting value

Describing Patterns

2 Questions
1 R50, R75, R100, R125. Best description?
Increases by R25 each time
Increases by R50 each time
Doubles each time
Decreases by R25 each time
2 3, 6, 12, 24. Best description?
Adds 3 each time
Multiplies by 2 each time
Adds 6 each time
Multiplies by 3 each time
0/2

4. Direct vs. Inverse Patterns

Direct Pattern

As one variable increases, the other increases.

Example: Cost of apples increases as weight increases.

Inverse Pattern

As one variable increases, the other decreases.

Example: More workers = fewer days to complete a job.

5. Patterns in Tables

Input (Top Row)

Independent variable (e.g., Number of People)

Output (Bottom Row)

Dependent variable (e.g., Total Cost)

Table Patterns

3 Questions
1 Pattern 1: 4 matches, P2: 7, P3: 10. Matches for P5?
13
16
19
22
2 Input: 1,2,3,4,5 | Output: 5,10,15,?,25. Missing?
16
18
20
22
3 Differences: +3, +5, +7. What pattern?
Linear
Quadratic
Constant ratio
No pattern
0/3

Exam Tip: Always check if the pattern is constant difference or constant ratio first. Write down the differences between consecutive terms to help identify the pattern.

Final Assessment

6 Questions
1 7, 11, 15, 19, ... Next term?
21
22
23
24
2 3, 9, 27, 81, ... Pattern type?
Constant difference
Constant ratio (×3)
Square numbers
Fibonacci
3 2 workers=12 days, 4 workers=6 days. This is:
Direct proportion
Inverse proportion
Constant
Random
4 Pattern 1:2 tiles, P2:5, P3:8. Tiles for P6?
14
15
16
17
5 R120, R110, R100, R90. Best description?
Increases by R10
Decreases by R10
×0.9 each time
+10% each time
6 Table: n:1,2,3,4,5 | Value:1,4,9,16,? Missing?
20
24
25
36
0/6

Conclusion

Mastering number patterns is crucial for understanding how variables interact in real-world scenarios. By identifying types of patterns, predicting subsequent terms, and interpreting data in tables, students develop a strong foundation in mathematical reasoning.