1. Pre-Algebra 8-5 Estimating with Percents Pledge & Moment of Silence

2. Pre-Algebra 8-5 Estimating with Percents Pre-Algebra HOMEWORK Page 423 #31-38 & Spiral Review (#39-45)

3. Pre-Algebra 8-5 Estimating with Percents Our Learning Goal Students will be able to determine and construct fractions, decimals, and percents by understanding their relationships, solving for the unknown, solving increase and decrease, solving sales tax/total cost contextual problems and compute simple interest.

4. Our Learning Goal Assignments Learn to relate decimals, fractions, & percents (8-1) Learn to find percents (8-2) Learn to find a number when the percent is known (8-3) Learn to find percent increase and decrease (8-4) Learn to estimate with percents (8-5) Learn to find commission, sales tax, and withholding tax (8-6) Learn to compute simple interest (8-7)

5. Pre-Algebra 8-5 Estimating with Percents Learning Goal Scale Students are able to determine & construct fractions, decimals, & percents: 43210 Clear understanding their relationships Able to solve for the unknown Understands how to solve for increase & decrease Calculating solving sales tax/total cost contextual problems Computing simple interest Understands their relationships Some solving for the unknown Difficulty solving for increase & decrease Understands their relationships Difficulty solving for the unknown Some understanding their relationships Even with help, no understanding or skill demonstrated

6. Pre-Algebra 8-5 Estimating with Percents Student Learning Goal Chart

7. Pre-Algebra 8-5 Estimating with Percents 8-5 Estimating with Percents Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

8. Pre-Algebra 8-5 Estimating with Percents Warm Up Find each percent increase or decrease to the nearest percent. 1. from 1 to 0.62 2. from 162 to 177 3. from 16 to 22 4. from to 38% decrease 9% increase 38% increase Pre-Algebra 8-5 Estimating with Percents 5 8 3 4 17% decrease

9. Pre-Algebra 8-5 Estimating with Percents Problem of the Day If you enlarge a picture by 25%, by what percent do you need to reduce it to return it to its original size? (Hint: Try using a simple number for the original area of the picture.) 20%

10. Pre-Algebra 8-5 Estimating with Percents Today’s Learning Goal Assignment Learn to estimate with percents.

11. Pre-Algebra 8-5 Estimating with Percents Vocabulary estimate compatible numbers

12. Pre-Algebra 8-5 Estimating with Percents Some problems require only an estimate. Estimates involving percents and fractions can be found by using compatible numbers, numbers that go well together because they have common factors. 12 24  compatible 13 24 not compatible

13. Pre-Algebra 8-5 Estimating with Percents Estimate. A. 21% of 66 Additional Example 1A: Estimating with Percents Instead of computing the exact answer of 21%  66, estimate. 21% =  21 100 20 100 Use compatible numbers, 20 and 100.  1 5 Simplify. 66  65Use compatible numbers, 65 and 5. 1 5  65 = 13 Use mental math: 65 ÷ 5. So 21% of 66 is about 13.

14. Pre-Algebra 8-5 Estimating with Percents Estimate. A. 29% of 86 Try This: Example 1A Instead of computing the exact answer of 29%  86, estimate. 29% =  29 100 30 100 Use compatible numbers, 30 and 100.  3 10 Simplify. 86  90 Use compatible numbers, 90 and 10. 3 10  90 = 27 Use mental math: 90 ÷ 10. So 29% of 86 is about 27.

15. Pre-Algebra 8-5 Estimating with Percents Estimate. B. 36% of 120 Additional Example 1B: Estimating with Percents Instead of computing the exact answer of 36%  120, estimate. 36%  35%Round.  30% + 5%Break down the percent into smaller parts.  3  10% + 5% 35%  120 = (3  10% + 5%)  120 Set up an equation.

16. Pre-Algebra 8-5 Estimating with Percents Additional Example 1B Continued = 36 + 610% of 120 is 12, so 5% of 120 is 6. = 42 So 36% of 120 is about 42. = 3  10%  120 + 5%  120 Use Distributive Property.

17. Pre-Algebra 8-5 Estimating with Percents Estimate. B. 44% of 130 Instead of computing the exact answer of 44%  130, estimate. 44%  45%Round.  40% + 5%Break down the percent into smaller parts.  4  10% + 5% 45%  130 = (4  10% + 5%)  130 Set up an equation. Try This: Example 1B

18. Pre-Algebra 8-5 Estimating with Percents = 52 + 6.5 10% of 130 is 13, so 5% of 130 is 6.5. = 58.5 So 44% of 130 is about 58.5. = 4  10%  130 + 5%  130 Setup an equation. Try This: Example 1B Continued

19. Pre-Algebra 8-5 Estimating with Percents The diameter of the Moon is about 2160 miles. If the diameter of the Moon is about 27% of the diameter of Earth, what is the approximate diameter of Earth? Additional Example 2: Problem Solving Application

20. Pre-Algebra 8-5 Estimating with Percents Additional Example 2 Continued 1 Understand the Problem The answer is the approximate diameter of Earth. List the important information: The diameter of the Moon is about 2160 miles. The diameter of the Moon is about 27% of the diameter of the Earth. Let e represent the diameter of the Earth. 2160  27%  e Diameter of the Moon  27%  Diameter of Earth

21. Pre-Algebra 8-5 Estimating with Percents Use compatible numbers: 2160 is close to 2000; 27% is close to 25% 2 Make a Plan Think: The numbers 2160 and 27% are difficult to work with. Additional Example 2 Continued Find an equivalent ratio for 25%. 25% = = 25 100 1 4

22. Pre-Algebra 8-5 Estimating with Percents Solve 3 Think: 2000 is of what number? 1 4 4  2000 = e 8000 = e The diameter of Earth is approximately 8000 miles. Additional Example 2 Continued

23. Pre-Algebra 8-5 Estimating with Percents Look Back4 25% of 8000 mi is, or 2000 mi. This is the approximate diameter of the moon. 8000 4 Additional Example 2 Continued

24. Pre-Algebra 8-5 Estimating with Percents The length of a football field is 83% of the length of a soccer field. If a football field is 100 yards, what is the approximate length of a soccer field? Try This: Example 2

25. Pre-Algebra 8-5 Estimating with Percents 1 Understand the Problem The answer is the approximate length of a soccer field. List the important information: The length of a football is about 100 yards. The length of a football field is 83% of a soccer field. Try This: Example 2 Continued Let l represent the length of a soccer field. 100  83%  l Length of football field  83%  Length of soccer field

26. Pre-Algebra 8-5 Estimating with Percents Use compatible numbers: 83% is close to 80% 2 Make a Plan Think: The number 83% is difficult to work with. Try This: Example 2 Continued Find an equivalent ratio for 80%.80% = = 80 100 4 5

27. Pre-Algebra 8-5 Estimating with Percents Solve 3 Think: 100 is of what number? 4 5 125 = l The length of a soccer field is approximately 125 yards.  100 = l 5 4 Try This: Example 2 Continued

28. Pre-Algebra 8-5 Estimating with Percents Look Back4 Try This: Example 2 Continued 80% of 125 yards is  125, or 100 yards. This is the length of a soccer field. 4545

29. Pre-Algebra 8-5 Estimating with Percents Review Classwork Review & Grade Page 414 #1-17

30. Pre-Algebra 8-5 Estimating with Percents Lesson Quiz Estimate. 1. 34% of 12 2. 47 out of 236 3. 113% of 80 4. 22 out of 51 5. According to the last census, 33,871,648 people live in California, and 3,694,820 of those people live in Los Angeles. Estimate the percent of Californians who live in Los Angeles. 20% 4 90 40% 10% Possible answers: