1. AIM: How do we solve 2 step equations using algebra tiles? OBJECTIVE: S.W.B.A.T. use algebra tiles or the puzzle method to solve 2 step equations Homework: 2 -step Equations Day 1 worksheet October 10, 2007 DO NOW Scales balance when the weights on them are equal. Which equation is represented by the balance scale below ?

2. Using the properties of equality to solve equations –Do Now debrief OR x + x + -1 = x + 1 + 1 + 1 + 1 + 1 2x – 1 = x + 5

3. Using algebra tiles to solve equations In Addition to puzzles we can also use algebra tiles to solve 2-step equations. However we must first know how to use the tiles and what they stand for. negative x positive x positive 1 negative 1

4. Using algebra tiles to solve equations - The rules negative x positive x + = 0

5. Using algebra tiles to solve equations – The rules + = 0 positive 1 negative 1

6. Using algebra tiles to solve equations – Example 1 Solve - 5 = 2x + 1 Goal: Variables on 1 side, numbers on other side

7. Using algebra tiles to solve equations – Example 1 continued Now we need to move all numbers to the left. -5 = 2x + 1 Add a red box to each side of the fence Red and yellow cancel out -6 = 2x

8. Using algebra tiles to solve equations – Example 1 continued -6 = 2x Now we see that each green bar is equal to 3 red rectangles so we can remove half of each side

9. Using algebra tiles to solve equations – Example 1 continued -3 = x Done! Now we see that one green bar is equal to 3 red rectangles

10. Using algebra tiles to solve equations – Example 1 continued Now let’s check x = -3 using the original equation - 5 = 2x + 1

11. Using algebra tiles to solve equations – Example 2 Solve -5 = - 3 x + 7

12. Using algebra tiles to solve equations – Example 2 continued – 5 -3x + 7 Goal is to get all variables on one side of the fence Add three green bars to both sides to eliminate the red bars on the right

13. Using algebra tiles to solve equations – Example 2 continued 3x + -5 7 Goal is to get one variable alone on the left All variables on the right cancel each other out.

14. Using algebra tiles to solve equations – Example 2 continued 12 Now add five yellows to both sides to get rid of the numbers on the left. 3x Reds and yellows cancel

15. Using algebra tiles to solve equations – Example 2 continued 12 Now we can see that each green bar is equal to four yellows 3x

16. Using algebra tiles to solve equations – Example 2 continued x 4 Goal is to get one x on one side of the fence x = 4. Done ! Now let’s check using the original equation -5 = - 3 x + 7

17. Using the Puzzle method to solve equations – Example 3 Let’s Solve - 5 = 2x + 1 using the puzzle method I’m thinking of a number. x Multiply the number by 2 2x Add 1 2x + 1 You get -5 2x + 1 = -5 What number am I ? -5 – 1 -2 Work backwards!