Linear Patterns: Tables, Rules, Graphs

Year 9 Mathematics Exploring patterns through multiple representations New Zealand Curriculum

What Are Linear Patterns?

Year 9 Mathematics Exploring patterns through multiple representations New Zealand Curriculum

Spot the Pattern

Look at this sequence: 3, 7, 11, 15, 19... What comes next? How much does each number increase by? Work with a partner to find the pattern

Tables of Values

Organize patterns in rows and columns Term number (position) vs Value Calculate differences between consecutive values Constant difference = Linear pattern

From Patterns to Rules

{"left":"In Words: Start with 3, add 4 each time\nIn Algebra: Value = 4n - 1","right":"Check: When n=1, Value = 4(1)-1 = 3 ✓\nCheck: When n=2, Value = 4(2)-1 = 7 ✓"}

Graphing Linear Patterns

Think and Discuss

Why do linear patterns create straight lines when graphed? What would happen if the differences weren't constant? How does the steepness of the line relate to the constant difference?

Key Takeaways

Linear patterns have constant differences Tables, rules, and graphs show the same pattern differently Algebraic rules help us predict any term Straight line graphs = linear relationships Next lesson: Non-linear patterns and how they differ