1. Solving Equations Using Models
Math 8 - Linear Equations & Graphing

2. Investigate
With a partner, write an equation for the following statement:
“Marie received three $100 savings bonds on her first birthday. Her grandmother promised to give her 2 savings bonds each year after that for her birthday. How old will Marie be when she has 13 savings bonds?”
Let “n” represent Marie’s age in years.
Use the tiles to represent your equation.
13 = (n)
13 = 3(100) + 2(n)

3. Reflect & Share
Compare your equation and it’s solution with another group at your table.
Did you write the same equation?
Yes – find another way to write the equation.
No – are both equations correct?
How do you know?
Share what you did with the tiles.

4. To solve algebraic equations using models.
Learning Intention
To solve algebraic equations using models.

5. Solving Equations Using Models
We will be solving equations using tiles.
Remember:
Yellow tiles = +1
Red tiles = -1
Yellow Double tiles (stacked) = positive variable (n)
Red Double tiles (stacked) = negative variable (-n) OR
White small square = +1
Red small square = -1
Green Rectangle = positive variable (n)
Red Rectangle = negative variable (-n)

6. Example 1
Jodee is a contestant in the spell-a-thon. A contestant receives 3 points for every word spelled correctly. Because of a technical penalty, Jodee loses 5 points. She now has 19 points. How many words has Jodee spelled correctly?

7. Example 1
Let “j” represent the number of words Jodee has spelled correctly.
Then, the number of points she receives is 3j.
When the penalty is considered, the number of points is 3j-5.
So, the equation is:
3j – 5 = 19

8. Example 1
model

9. Example 1
Verify

10. Example 2
Herman is in the last round of a spell-a- thon in his school. A contestant receives 3 points for every word spelled correctly. Herman has 42 points. How many words has he spelled correctly?

11. Example 2
Let h represent the number of words Herman has spelled correctly.
Then, the number of points is 3 times h, or 3h.
Since Herman has 42 points the algebraic equation is:
3h = 42

12. Example 2 With tiles, model Herman’s equation.
Draw it in or have a student draw it in after they have tried it.

13. Example 3 Use tiles to solve: 8 = -6 – 2x Verify the solution.
Let them try first.

14. Example 3

15. Example 3

16. Example 3
Verify

17. Discussion
In Example 1 (Jodee), we had 19 on the right hand side. Could we have switched it?
In Example 2 (Herman), we used h to represent the number of words Herman spelled correctly. Could we use a different letter? Why?

18. Practice Time!

19. Supplemental Problems
Workbook:
Pages 138 – 141
Workbook is on D2L if you have lost your book or need to print new pages.