Test 2 Review

1. Test 2 Review The test will consist of 3 sections. Section 1 is vocabulary matching. Section 2 is a Rate Per 100 problem. Section 3 is a Unit Rate Problem.

2. Test 2 ReviewVocabulary Matching Rate one part in 100 or in this context takes a quantity and calls that quantity part of a whole. If you divide that quantity into 100 pieces each piece would be worth 1%. Percent in this context is being used to identify either a whole or part of a whole. Quantity is the amount of work or task than can be accomplished in a given time

3. Test 2 Review John checks for bad hard drives on an assembly line. He saw 570 hard drives today. 45 of the hard drives were bad. What percent of the hard drives were bad? What percent of the hard drives were good?

4. Percent review you can skip to slide10 if you don’t need this100% • This square is a 10 x 10 square. Each square is 1% of the total. • 10 Squares are 10% of the total. If I had $100.00 each square would be worth $1.00 $1. $1. $1. $1. $1. $1. $1. $1. $1. $1.

5. If I had $200.00 each square would be worth $2.00. • The $2.00 is found by dividing the whole by 100. 20 Squares are 10% of the Total and would be worth $20.00 If the whole or 100% is $200.00 If I had $100.00 each square would be worth $1.00 $2. $2. $2. $2. $2. $2. $2. $2. $2. $2.

6. It doesn’t matter what the whole is. If you divide the whole by 100 you will always find 1% 342 100 = 3.42 3.42 = 1% or 1 square of the whole or big square. In terms of $100.00 each square is worth $3.42 $3.42

7. Move the decimal • The nice thing about knowing that any number can be divided by 100 and you will find 1% is that you don’t have to do long division to solve it. Just take the 100% and move the decimal over two spaces to the left and you will Have 1%. $3.42

8. Move the decimal 100% = 1. 10% =.1 1% =.01 So if 542 = 100% 54.2 =10% 5.42=1% $3.42

9. Move the decimal 100% = 1. 10% =.1 1% =.01 542 = 100% 542 or you could say 54.2 X 10 = 542 54.2 10% 54.2 10% 54.2 10% 54.2 10% 54.2 10% 54.2 10% 54.2 10% 54.2 10% 54.2 10% 54.2 10%

10. Move the decimal 100% = 1. 10% =.1 1% =.01 542 = 100% If we divided each of the 54.2 boxes by 10 we would have 1% of the big box or 5.42% therefore 5.42 x 100 =542 and 5.42 = 54.2 54.2 10% 54.2 10% 54.2 10% 54.2 10% 54.2 10% 54.2 10% 54.2 10% 54.2 10% 54.2 10% 54.2 10%

11. Move the decimal 100% = 1. 10% =.1 1% =.01 542 = 100% Thinking about mathematical relationships if we divide 542 by 100 we get 5.42. Using the inverse operation can be useful. 54.2 10% 54.2 10% 54.2 10% 54.2 10% 54.2 10% 54.2 10% 54.2 10% 54.2 10% 54.2 10% 54.2 10%

12. Solving the problem • 570 hard drives = 100% So: 100% = 570 10% = 57 1% = 5.7 We want to know the percent that were bad so we need to know how many of the 1% squares 45 hard drives equal. The small red square is both 1% and 5.7 hard drives. We need to Find how many of these 1% squares total up to 45 hard drives.

13. Solving the problem Your probably thinking that you could just add 5.7 until you get to 45 and that would give you the percentage. You would be correct! However if we remember our mathematical relationships unit we know that addition and subtraction are inverses of one another so we could also just subtract 5.7 from 45 and count the number of times we did so to get the answer. This would also work. A faster way would be to recognize that division is repeated subtraction so we could just divide 5.7 into 45 and that would solve the problem for us.

14. Solving the problem So: Divide 5.7 into 45. To do this move the decimal to the right for both the 5.7 and the 45 hard drives. . Therefore you will have 57 450.

15. Long Division 7. 89 % Therefore you will have 57 450.00 -399 51 0 - 456 540 As you can see we can continue to divide, but we can say we have approximately 7.89% of the hard drives that are bad. Or you could round up to approximately 8%.

16. Finishing up • Once we know that approximately 8% of the hard drives are bad we then can subtract 8% from the 100% total and we can say that approximately 92 % of the hard drives are good. • Complete sentence answers would be: • Approximately 8% of the hard drives are bad. • Approximately 925 of the hard drives are good.

17. Unit Rate Problems If it took 3.5 hours to mow 6 lawns, then at that rate, how many lawns could be mowed in 20 hours? How many lawns could be mowed in 20 minutes? How could we use a ratio to solve this problem? Try to build a model to solve this problem. Use 5 methods to solve this problem.

18. Method 1Traditional Approach • The ratio is 6 lawns: 3.5 hours 6 divided by 3.5 is approx 1. 71 lawns per hour 1.71 lawns per hour multiplied by 20 hours = 34.2 lawns. Therefore approx. 34.2 lawns can be mowed in 20 hours.

19. Traditional approach continued • Now that you have solved what can be done in 20 hours lets solve the 20 minute question. • Based on what we have found already we know that we can do approx. 1.71 lawn per hour. • There are 3 20 minute intervals in an hour. Therefore we can divide 1.71 by 3 and we get .57 lawns per each twenty minute period.

20. Method 2 Bar Model 6 lawns 3.5 hours The top model has been divided by 3 to show the increments in the lower model. 1.71 lawns 1 hour 1.71 lawns 1 hour 1.71 lawns 1 hour .855 lawns Per Half hour 34.2 lawns In 20 hours

21. Method 2 Bar Model 6 lawns 3.5 hours 1.71 lawns 1 hour 1.71 lawns 1 hour 1.71 lawns 1 hour .855 lawns Per Half hour The top model has been divided by 3 to show the increments in the lower model. 1.71 lawns 1 hour The 1 hour block has been divided into three parts to show the Twenty minute increments which are each .57 of a lawn in ½ hour. 20 Min .57 lawns

22. Number Line Model Move of 2.5 hours Move of 3.5 hours LAWNS 0 .57 lawns 6 12 18 24 30 34.2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 HOURS 20 minutes

23. Table

24. Ratio Table Min 20 60 210 420 630 840 1050 1200 Hours 1/3 1 3.5 7 10.5 14 17.5 20 Lawns .57 1.71 6 12 18 24 30 34.2 Approximately 34.2 lawns can be mowed in 20 hours. Approximately .57 lawns can be mowed in 20 minutes.