1. 5 Minute Check

4. Simplify 2. 3 2 3

5. 5 Minute Check

8. Simplify 4. 4 1 4

9. 5 Minute Check

10. Friday, Jan 9 Lesson 7.1.3/7.1.4 Convert Unit Rates/ Proportional and Nonproportional Relationships

11. Convert Unit Rates Objective: To convert units of measure between derived units to solve problems.

12. Convert Unit Rates The relationships among some commonly used customary and metric units are shown in the tables below.

13. Convert Unit Rates Each of the relationships in the tables can be written as a unit ratio. A unit ratio, like a unit rate, has a denominator of one unit.

14. Convert Unit Rates A remote control car travels at a rate of 10 feet per second. How many inches per second is this? How to Convert Unit Rates Step 1 – Write the complete rate as a fraction with units.

15. Convert Unit Rates A remote control car travels at a rate of 10 feet per second. How many inches per second is this? 10 ft 1 s How to Convert Unit Rates Step 1 – Write the complete rate as a fraction with units.

16. Convert Unit Rates A remote control car travels at a rate of 10 feet per second. How many inches per second is this? 10 ft 1 s How to Convert Unit Rates Step 2 – Determine the units of the answer and write as a fraction.

17. Convert Unit Rates A remote control car travels at a rate of 10 feet per second. How many inches per second is this? 10 ft in 1 s = 1 s How to Convert Unit Rates Step 2 – Determine the units of the answer and write as a fraction. Leave space for the conversion rate.

18. Convert Unit Rates A remote control car travels at a rate of 10 feet per second. How many inches per second is this? 10 ft in 1 s = 1 s How to Convert Unit Rates Step 3 – Determine the units of the conversion rate(s). Leave space for the conversion rate.

19. Convert Unit Rates A remote control car travels at a rate of 10 feet per second. How many inches per second is this? 10 ft in in 1 s ft = 1 s How to Convert Unit Rates Step 3 – Determine the units of the conversion rate(s). conversion rate.

20. Convert Unit Rates A remote control car travels at a rate of 10 feet per second. How many inches per second is this? 10 ft in in 1 s ft = 1 s The conversion rate units are determined by the original rate units and the answer units. In the above case, we need to cancel the “ft” units and replace with “in” units. Notice the conversion rate has “ft” in the denominator, so it will cancel the “ft” of the original rate. conversion rate.

21. Convert Unit Rates A remote control car travels at a rate of 10 feet per second. How many inches per second is this? 10 ft in in 1 s ft = 1 s How to Convert Unit Rates Step 4 – Complete the conversion rate(s). Eg. How many inches in how many feet? conversion rate.

22. Convert Unit Rates A remote control car travels at a rate of 10 feet per second. How many inches per second is this? 10 ft 12 in in 1 s 1 ft = 1 s How to Convert Unit Rates Step 4 – Complete the conversion rate(s). conversion rate.

23. Convert Unit Rates A remote control car travels at a rate of 10 feet per second. How many inches per second is this? 10 ft 12 in in 1 s 1 ft = 1 s How to Convert Unit Rates Step 5 – Multiply and cancel units.

24. Convert Unit Rates A remote control car travels at a rate of 10 feet per second. How many inches per second is this? 10 ft 12 in 120 in 1 s 1 ft = 1 s How to Convert Unit Rates Step 5 – Multiply and cancel units.

25. Convert Unit Rates A swordfish can swim at a rate of 60 miles per hour. How many feet per hour is this? Step 1 - ?

26. Convert Unit Rates A swordfish can swim at a rate of 60 miles per hour. How many feet per hour is this? 60 mile 1 h Step 2 - ?

27. Convert Unit Rates A swordfish can swim at a rate of 60 miles per hour. How many feet per hour is this? 60 mile ft 1 h = 1 h Step 3 – ?

28. Convert Unit Rates A swordfish can swim at a rate of 60 miles per hour. How many feet per hour is this? 60 mile ft ft 1 h mile = 1 h Remember – we want to cancel the “mile” unit in the numerator of the original rate. In order to do so, the conversion rate must have a “mile” unit in the denominator. Step 4 – ?

29. Convert Unit Rates A swordfish can swim at a rate of 60 miles per hour. How many feet per hour is this? 60 mile 5280 ft ft 1 h 1 mile = 1 h How many feet in how many miles? Step 5 – ?

30. Convert Unit Rates A swordfish can swim at a rate of 60 miles per hour. How many feet per hour is this? 60 mile 5280 ft 316, 800 ft 1 h 1 mile = 1 h

31. Convert Unit Rates A gull can fly at a speed of 22 miles per hour. How many feet per hour can the gull fly? Do this on your own.

32. Convert Unit Rates A gull can fly at a speed of 22 miles per hour. How many feet per hour can the gull fly? 22 miles 5280 ft 116,160 ft 1 h 1 mile = 1 h

33. Convert Unit Rates Marvin is walking at a speed of 7 feet per second. How many feet per hour is this? Do this on your own.

34. Convert Unit Rates Marvin is walking at a speed of 7 feet per second. How many feet per hour is this? 7 ft 60 s 420 ft 1 s 1 min = 1 min 420 ft 60 min 25,200 ft 1 min 1 h = 1 h Or you can create one large conversion rate…

35. Convert Unit Rates Marvin is walking at a speed of 7 feet per second. How many feet per hour is this? 7 ft 60 s · 60 min 25,200 ft 1 s 1 min · 1 h = 1 h

36. Proportional and Nonproportional Relationships Objective: To identify and understand proportional and nonproportional relationships.

37. Proportional and Nonproportional Relationships Two quantities are proportional if they have a constant ratio or rate. All of the ratios above are equivalent ratios because they all have the same value.

38. Proportional and Nonproportional Relationships For relationships in which the ratio is not constant, the two quantities are nonproportional.

39. Proportional and Nonproportional Relationships Andrew earns $18 per hour for mowing lawns. Is the amount of money he earns proportional to the number of hours he spends mowing? Explain. How to Determine if a Rate or Ratio is Proportional. Step 1 – Make a table.

40. Proportional and Nonproportional Relationships Andrew earns $18 per hour for mowing lawns. Is the amount of money he earns proportional to the number of hours he spends mowing? Explain. How to Determine if a Rate or Ratio is Proportional. Step 1 – Make a table.

41. Proportional and Nonproportional Relationships Andrew earns $18 per hour for mowing lawns. Is the amount of money he earns proportional to the number of hours he spends mowing? Explain. How to Determine if a Rate or Ratio is Proportional. Step 2 – Simplify the rates or ratios.

42. Proportional and Nonproportional Relationships Andrew earns $18 per hour for mowing lawns. Is the amount of money he earns proportional to the number of hours he spends mowing? Explain. How to Determine if a Rate or Ratio is Proportional. Step 2 – Simplify the rates or ratios.

43. Proportional and Nonproportional Relationships Andrew earns $18 per hour for mowing lawns. Is the amount of money he earns proportional to the number of hours he spends mowing? Explain. How to Determine if a Rate or Ratio is Proportional. Step 2 – Simplify the rates or ratios. Since all rates can be simplified to 18, they are proportional.

44. Proportional and Nonproportional Relationships Uptown Tickets charges $7 per baseball ticket plus a $3 processing fee per order. Is the cost of an order proportional to the number of tickets ordered? Explain. Step 1 - ?

45. Proportional and Nonproportional Relationships Uptown Tickets charges $7 per baseball ticket plus a $3 processing fee per order. Is the cost of an order proportional to the number of tickets ordered? Explain. Step 2 - ? (It doesn’t matter which unit is top or bottom)

46. Proportional and Nonproportional Relationships Uptown Tickets charges $7 per baseball ticket plus a $3 processing fee per order. Is the cost of an order proportional to the number of tickets ordered? Explain. Since all rates do not simplify to the same, they are nonproportional.

47. Proportional and Nonproportional Relationships You can use recipe shown to make fruit punch. Is the amount of sugar used proportional to the amount of mix used? Explain. Do this on your own.

48. Proportional and Nonproportional Relationships You can use recipe shown to make fruit punch. Is the amount of sugar used proportional to the amount of mix used? Explain. Since all rates can be simplified to 0.5, they are proportional.

49. Proportional and Nonproportional Relationships The tables shown represent the number of pages Martin and Gabriel read over time. Which situation represents a proportional relationship between the time spent reading and the number of pages read? Explain. Do this on your own.

50. Proportional and Nonproportional Relationships

51. The Vista Marina rents boats for $25 per hour. In addition to the rental fee, there is a $12 charge for fuel. Is the number of hours you rent the boat proportional to the total cost? Explain. Do this on your own.

52. Proportional and Nonproportional Relationships The Vista Marina rents boats for $25 per hour. In addition to the rental fee, there is a $12 charge for fuel. Is the number of hours you rent the boat proportional to the total cost? Explain. No, The cost to times ratios are not the same.

53. Proportional and Nonproportional Relationships Which situation represents a proportional relationship between the number of laps run by each student and their time?

54. Proportional and Nonproportional Relationships Which situation represents a proportional relationship between the number of laps run by each student and their time? Desmond’s time is proportional. It takes him 73s for every lap.

55. Proportional and Nonproportional Relationships Plant A is 18 inches tall after 1 week, 36 inches after 2 weeks, 56 inches after 3 weeks. Plant B is 18 inches tall after 1 week, 36 inches after 2 weeks, 54 inches after 3 weeks. Which represents a proportional relationship between the height and number of weeks?

56. Proportional and Nonproportional Relationships Plant A is 18 inches tall after 1 week, 36 inches after 2 weeks, 56 inches after 3 weeks. Plant B is 18 inches tall after 1 week, 36 inches after 2 weeks, 54 inches after 3 weeks. Which represents a proportional relationship between the height and number of weeks? Plant APlant B Plant B grows at 18 inches per week. Height183656 Weeks123 Height183654 Weeks123

57. Proportional and Nonproportional Relationships Johanna’s parents give her $10 per week for lunch money. Blake ran laps around the gym. His times are shown in the table. Blake is trying to decide whether the number of laps is proportional to the time. Find his mistake and correct it.

58. Proportional and Nonproportional Relationships Johanna’s parents give her $10 per week for lunch money. Blake ran laps around the gym. His times are shown in the table. Blake is trying to decide whether the number of laps is proportional to the time. Find his mistake and correct it. They are not proportional. The 1 st min was 25 sec per lap, the 2 nd min was 33 sec per lap.

59. Proportional and Nonproportional Relationships Johanna’s parents give her $10 per week for lunch money. True or false? If a function rule has only multiplication and/or division it is a proportional relationship. Give examples to support your answer.

60. Proportional and Nonproportional Relationships Johanna’s parents give her $10 per week for lunch money. True or false? If a function rule has only multiplication and/or division it is a proportional relationship. Give examples to support your answer. If a simplified function rule has only multiplication and/or division it is a proportional relationship. Proportional Nonproportional x3x 13 26 39 x3x +2 15 28 311

61. Proportional and Nonproportional Relationships Agenda Notes Complete the Mid-Chapter Check on page 44 and bring to my desk. Homework – Homework Practice 7.1.3 and 7.1.4 Due Mon, Jan 12 Mid-Chapter 7.1 Quiz - Monday, Jan 12