1. Quiz #5 ½ point of the equation, ½ point for the solution. 2. A heavy equipment (cranes, road graders, etc.) has a base salary of 32,500. If his total income was $74,000 last year, salary of 32,500. If his total income was $74,000 last year, and if he earns $1100 for every heavy machine he sells, and if he earns $1100 for every heavy machine he sells, how many did he sell ? how many did he sell ? 1.Your club wants to sell pizzas to make money. You charge $12 for every large pizza and $7 for every small pizza. A business decides to buy pizza for all of their employees to help your club make money. They have a budget of $150. They decide to buy 7 large pizzas. charge $12 for every large pizza and $7 for every small pizza. A business decides to buy pizza for all of their employees to help your club make money. They have a budget of $150. They decide to buy 7 large pizzas. How many small pizzas can they buy and stay within How many small pizzas can they buy and stay within their budget? their budget?

2. CP Math Lesson #6 More Word Problems and Unit Conversion

3. Homework  Worksheet on the blog.

4. Unit conversion Essential skill for Word Problems

5. We need to talk about units. Unit: how a real world quantity is measured. What are 3 units for distance? Time  “seconds”, “hours”, “days” feetmilesmeters Quantity: something in the real world item that can be “quantified” (to have a number describe the quantity). “quantified” (to have a number describe the quantity).

6. Your turn: Give an example of the unit of measure for each of the following quantities. 1. How hot it is. 2. How many __________ are on sale. 3. How large an angle is.

7. Units Treat units like variables when doing the math.

8. Units

9. Units

10. Your turn: Simplify the following expressions. 4. 5. 6. 7.

11. Unit conversions Unit conversion is an essential skill. Example: You are traveling 20 miles per hour. How far do you travel in 5 minutes? do you travel in 5 minutes? Example: You are traveling 20 miles per hour. How far do you travel in 5 minutes? do you travel in 5 minutes?

12. Conversion Factor: a number that equals ‘1’ (always) Comes from equilvalent measurements Conversion factor

13. Your turn: Write the two conversion factors for the following units 8. Convert between seconds and minutes 9. Convert between days and years

14. Unit conversions pick which unit conversion factor to multiply by. Conversion factors: Convert 49 inches into feet Multiply by the correct conversion factor  unit you want to convert to in the numerator. unit you want to convert to in the numerator.

15. Examples:

16. Your turn: Write the two conversion factors for the following units 10. Convert one year into days. 11. Convert 25 feet into yards.

17. Multi-step unit conversion Just use the unit conversion factor to eliminate the units you don’t want in your final answer. you don’t want in your final answer.

18. Your turn: 12. 1 billion seconds is how many years? 13. 1 mile is how many inches? (5280 ft/mile)

19. Rate (“____ per ____”)  Miles per hour  $ per gallon  Apples per person  Televisions per household These are all units of rates

20. Speed/Distance Model: (involves time) Distance = (speed) (time) Speed is a “rate” Speed is a “rate” (distance per unit time) This is a ‘gotcha.’ All units (hours, minutes, feet, miles, etc., MUST be CONSISTENT throughout the problem!!!! d = r*t

21. Speed/Distance Model: (involves time) Distance = (speed) (time) Example: d = r*t It takes you 5 hours to drive to St. George. St. George is 300 miles away. How fast were you going? 1. Write the formula 2.Identify the quantities from the formula that are given in the problem: d = ?, r = ?, t = ? the problem: d = ?, r = ?, t = ? d = 300 miles, r = ?, t = 5 hours d = r*t 3. Replace the values given into the formula. 300 miles = r * 5 hours 4. Solve for the unknown variable. 300 miles = r * 5 hours ÷ 5 hours ÷ 5 hours

22. Speed/Distance Model: (involves time) Distance = (speed) (time) Example: d = r*t A plane flew at a speed of 300 miles/hr for 7 hours. How far did it fly? 1. Write the formula 2.Identify the quantities from the formula that are given in the problem: d = ?, r = ?, t = ? the problem: d = ?, r = ?, t = ? d = ?, r = 300 miles/hr, t = 7 hours d = r*t 3. Replace the values given into the formula. d= 300 miles/hr * 7 hours 4. Solve for the unknown variable.

23. Speed/Distance Model: (involves time) Distance = (speed) (time) Example: d = r*t A plane flew 4000 miles in 6 hours. What was its speed? 1. Write the formula 2.Identify the quantities from the formula that are given in the problem: d = ?, r = ?, t = ? the problem: d = ?, r = ?, t = ? d = 4000, r = x Miles/hr, t = 6 hours d = r*t 3. Replace the values given into the formula. 4000 = x miles/hr * 6 hours 4. Solve for the unknown variable.

24. Your turn ½ point of the equation, ½ point for the solution. Distance = (speed) (time) 14. What would the speed have to be to travel 1000 14. What would the speed have to be to travel 1000 miles in 6 hours? miles in 6 hours? d = r*t 15. How long would it take to travel 1500 miles if your speed was 200 miles per hour? speed was 200 miles per hour?

25. Two people traveling (1) Same direction You leave Roy and travel south at 65 mph. Your You leave Roy and travel south at 65 mph. Your friend leaves 2 hours later. How long would she have to friend leaves 2 hours later. How long would she have to travel to catch up to you if she is going 75 mph? travel to catch up to you if she is going 75 mph? d = r*t How do we relate her distance to your distance?

26. Two people traveling (1) Same direction You leave Roy and travel south at 65 mph. Your You leave Roy and travel south at 65 mph. Your friend leaves 2 hours later. How long would she have to friend leaves 2 hours later. How long would she have to travel to catch up to you if she is going 75 mph? travel to catch up to you if she is going 75 mph? d = r*t How do we relate her travel time to your travel time?

27. Two people traveling (1) Same direction d = r*t Replace the variables with numbers from the problem. If there are 2 unknown variables, you need to find a way to relate the two. For example: to relate the two. For example: When you have only one variable, you can solve for it.

28. Your turn (1) Same direction 16. Your friend travels north at 20 mph for an hour, then you 16. Your friend travels north at 20 mph for an hour, then you follow at 30 mph. How long will it take to catch up? follow at 30 mph. How long will it take to catch up? d = r*t 17. Your friend travels east at 50 mph for 3 hours, then you 17. Your friend travels east at 50 mph for 3 hours, then you follow. It takes you 5 hours to catch up. How fast were you follow. It takes you 5 hours to catch up. How fast were you going? going?

29. Two people traveling (2) Opposite direction You leave Roy and travel south at 65 mph. Your You leave Roy and travel south at 65 mph. Your friend travels north at 50 mph. How long will it be until you are friend travels north at 50 mph. How long will it be until you are 350 miles apart? 350 miles apart? d = r*t 350 miles Total distance problem. How do we relate her travel time to your travel time?

30. Two people traveling (2) Opposite direction d = r*t Replace the variables with numbers from the problem. If there are 2 unknown variables, you need to find a way to relate the two. For example: to relate the two. For example: When you have only one variable, you can solve for it.

31. Two people traveling (2) Opposite direction 18. You and your friend both leave Roy at the same time in 18. You and your friend both leave Roy at the same time in opposite directions. Your speed is 30 mph and his speed opposite directions. Your speed is 30 mph and his speed is 55 mph. How long will it be until you are 280 miles apart? is 55 mph. How long will it be until you are 280 miles apart? d = r*t 19. You and your friend both leave Roy at the same time in 19. You and your friend both leave Roy at the same time in opposite directions. Your speed is 50 mph. After 8 hours opposite directions. Your speed is 50 mph. After 8 hours you are 600 miles apart. What was his speed? you are 600 miles apart. What was his speed?

32. Homework.