Square, Triangular & Index Numbers
Year 6 Mathematics Exploring number patterns and notation
Learning Intentions & Success Criteria
Learning Intention: We are learning to identify and use squared numbers, triangular numbers, and index (power) notation Success Criteria: I can identify squared numbers and triangular numbers Success Criteria: I can use index notation to represent and explain numbers
I Do: What are Square Numbers?
Square numbers are made by multiplying a number by itself 1² = 1 × 1 = 1 2² = 2 × 2 = 4 3² = 3 × 3 = 9 4² = 4 × 4 = 16 We can arrange them in perfect square shapes!
We Do: Building Square Numbers
Work with your partner to build the next three square numbers Use counters or draw dots to show: 5², 6², and 7² Calculate: 5 × 5 = ? Calculate: 6 × 6 = ? Calculate: 7 × 7 = ? Check your square patterns!
I Do: Discovering Triangular Numbers
Triangular numbers form triangle patterns 1st triangular number: 1 2nd triangular number: 1 + 2 = 3 3rd triangular number: 1 + 2 + 3 = 6 4th triangular number: 1 + 2 + 3 + 4 = 10 Each adds one more row to the triangle!
Think & Share
What would the 5th triangular number be? How would you calculate it? Can you draw the triangle pattern? Discuss with your neighbor!
I Do: Introduction to Index Notation
Index notation is a short way to write repeated multiplication Instead of 2 × 2 × 2, we write 2³ The small number (index/power) tells us how many times to multiply 2³ = 2 × 2 × 2 = 8 3⁴ = 3 × 3 × 3 × 3 = 81 Read 2³ as 'two to the power of three'
We Do: Index Notation Practice
{"left":"Write in index form:\n2 × 2 × 2 × 2 × 2\n5 × 5 × 5\n10 × 10","right":"Calculate the value:\n3³\n4²\n2⁵"}
You Do: Number Pattern Challenge
Complete the square number sequence: 1, 4, 9, 16, __, __, __ Find the next two triangular numbers after 10: __, __ Write in index notation: 6 × 6 × 6 × 6 Calculate: 5² + 3² Challenge: Can you find a number that is both square and triangular?
Lesson Summary
Square numbers: multiply a number by itself (n²) Triangular numbers: add consecutive numbers starting from 1 Index notation: short way to write repeated multiplication These patterns help us understand number relationships!