Pledge & Moment of Silence

1. Pledge & Moment of Silence 

2. Pre-Algebra HOMEWORK Page 423 #31-38 & Spiral Review (#39-45)

3. 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. Learning Goal ScaleStudents are able to determine & construct fractions, decimals, & percents:

6. Student Learning Goal Chart

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

8. 8-5 Estimating with Percents 5 3 8 4 Pre-Algebra 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 17% decrease

9. 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. Today’s Learning Goal Assignment Learn to estimate with percents.

11. Vocabulary estimate compatible numbers

12. 12 24 13 24  not compatible compatible 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.

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

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

15. Additional Example 1B: Estimating with Percents Estimate. B. 36% of 120 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. Additional Example 1B Continued = 3  10%  120 + 5% 120 Use Distributive Property. = 36 + 6 10% of 120 is 12, so 5% of 120 is 6. = 42 So 36% of 120 is about 42.

17. Try This: Example 1B 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.

18. Try This: Example 1B Continued = 4  10%  130 + 5% 130 Setup an equation. = 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.

19. Additional Example 2: Problem Solving Application 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?

20. 1 Diameter of the Moon  27%  Diameter of Earth Understand the Problem Additional Example 2 Continued 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

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

22. 3 Solve Think: 2000 is of what number? 1 4 Additional Example 2 Continued 4  2000 = e 8000 = e The diameter of Earth is approximately 8000 miles.

23. 25% of 8000 mi is , or 2000 mi. This is the approximate diameter of the moon. 8000 4 4 Look Back Additional Example 2 Continued

24. Try This: Example 2 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?

25. 1 Length of football field  83%  Length of soccer field Understand the Problem Try This: Example 2 Continued 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. Let l represent the length of a soccer field. 100  83%  l

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

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

28. 80% of 125 yards is  125 , or 100 yards. This is the length of a soccer field. 4 5 4 Look Back Try This: Example 2 Continued

29. 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. Possible answers: 4 20% 90 40% 10%