1. Solving Percent Problems

2. Learning Goal We are learning:
Shade 10 x 10 grids to represent percent, and determine the percent of a grid that is shaded
Determine the value represented by one square in a 10 x 10 grid, and determine the value of a grid given the value of one square
Use a 10 by 10 grid to solve percent problems
Use proportions to solve percent problems
Use decimals to solve percent problems

3. What is a percent?
a number as a fraction out of 100
per= for every; cent= 100 (for every 100)
written with percent symbol (%)

4. Strategies: Using a grid
10 x 10 grid represents 100%
Shading indicates % out of 100
Percents can be less than 1 and greater than 100
Shade in the percents to the right on your grid

5. Strategies: Using a grid
The unit square (10 x 10 grid) can be used to represent given amounts and used to determine the value of one of the small squares (1 percent)
Like sharing given amount equally among the 100 parts of the unit square

6. Strategies: Using a grid
Example: if the unit square represents 400 people (400 people represents 100% in some situation), then each small square represents 4 people

7. Strategies: Using a grid
Example: if the unit square represents 85 pounds, then each small square has a value of 0.85 pounds

8. Strategies: Using a grid
Example: if the unit square represents 162 days, then each small square has a value of days

9. Strategies: Using a grid
Conversely, if you are given the value of one or more small squares, you can determine the value of the unit square (grid)

10. Strategies: Using a grid
Example: If one square represents centimeters, then unit square has value of 75 centimeters (0.75 x 100)

11. Strategies: Using a grid
Example: If 12 small squares have a value of 30, then one small square has a value of 2.5 ( 30 ÷ 12 = 2.5), and the unit square has a value of 250

12. Strategies: Using a grid
Example: If 12 small squares have a value of 30, then one small square has a value of 2.5 ( 30 ÷ 12 = 2.5), and the unit square has a value of 250

13. Try It Out
25 acres of land are donated to a community, but the donor states that 6 acres of this land should be developed as a playground.
Use a percent grid to represent this situation.
What percent of the land is to be used for the playground?

14. Try It Out Unit square represents 25 acres
Divide by 100, so each square = or ¼ acres
So 4 small squares = 1 acre
24 small squares = 6 acres
(6 ÷ 0.25 = 24)
Therefore, 24% of the land is to be used for the playground

15. Try It Out
The school Population at Calderstone is135 percent of the school’s population from the year before. The new student population is How many students did the school have the previous year?

16. Try It Out
Current population can be represented by 135 small squares, so each small square represents 756 ÷ 135 = 5.6 students
School population for the year before is the value of one unit square, so # of students is 100 x 5.6 = 560

17. Strategies: Using a proportion
Solving a proportion: percent amount over 100 = _____ over total.
Ex.: x 0.42 =
Solving a Proportion: part over whole/total = _____ over 100 Ex
/2.4 =

18. Strategies: Multiplying by an equivalent decimal
turn the percent into a decimal and multiply by the total amount
Ex. 14% = or 0.14
= 0.14 x 42
= 5.88