1. This set of tiles represents x² + 4x + 4. Can you arrange this set of tiles to make a square? What algebraic expression could be used to represent this? Completing the Square x 1 x²x 1 1 xx 1

2. x² + 4x + 4 = (x + 2)² Completing the Square Task Turn these expressions into complete squares: 1)x² + 6x + 9 2)x² + 8x + 16 3)x² + 10x + 25 What would the next expression in this sequence be? Explain. Challenge Can you turn the expression 4x² + 12x + 9 into a square? 1 1 1 1 xx x x x²

3. Completing the Square Task Turn these expressions into complete squares: 1)x² + 6x + 9 2)x² + 8x + 16 3)x² + 10x + 25 What would the next expression in this sequence be? Explain. Challenge Can you turn the expression 4x² + 12x + 9 into a square? (x + 3)² (x + 4)² (x + 5)² The next expression would be (x + 6)². The coefficient of x is going up in 2s and the constant is a square number. (2x + 3)² x²x²x²xxx x²x²x²x²xxx xx111 xx111 xx111

4. This set of tiles represents x² + 4x + 3. What happens if you try to arrange these into a square? Completing the Square x 1 x²x 1 1 xx

5. Completing the Square x 1 x²x 1 1 x x We are short of one red tile to make a complete square. We would need to “borrow” this one tile… (x + 2)² - 1

6. x²xxxx x1111 x1111 x1111 x1 We need to borrow 3: (x + 4)² - 3 Let’s try these together: x² + 6x + 4 x² + 8x + 13 Completing the Square x²xxx x111 x1 x We need to borrow 5: (x + 3)² - 5

7. This set of tiles represents x² + 2x + 4. What happens if you try to arrange these into a square? Completing the Square x 1 x²x 1 1 1

8. Completing the Square x 1 x² 1 1 x We have three extra red tiles that we can’t fit into the square. (x + 1)² + 3 1

9. Completing the Square Task Complete the square for the following expressions: 1)x² + 4x + 2 2)x² + 6x + 5 3)x² + 8x + 3 4)x² + 4x + 14 5)x² + 2x + 6 6)x² + 8x + 15 Challenge Complete the square for these expressions. You may need to adapt your diagrams slightly… 1)x² + x + 1 2)x² + 3x + 4 (x + 2)² - 2 (x + 3)² - 4 (x + 4)² - 13 (x + 2)² + 10 (x + 1)² + 5 (x + 4)² - 1 (x + ½)² + ¾ (x + 1½)² + 1¾