1. Splash Screen Chapter 4 Lesson 4-2

2. A.A B.B C.C D.D Express the ratio in simplest form: 6 grape candies out of a package of 24 (over Lesson 4-1) A. B. C. 4 D. 6

3. 1.A 2.B 3.C 4.D A.4:3 B.3:4 C.3:2 D.2:3 Express the ratio is simplest form: 3 cups to 2 pints (over Lesson 4-1)

4. 1.A 2.B 3.C 4.D A.$27/pizza B.$21/pizza C.$6/pizza D.$4.50/pizza Express the rate as a unit rate: $27 for 6 pizzas (over Lesson 4-1)

5. proportional nonproportional Identify proportional and nonproportional relationships.

6. Preparation for Standard 7AF3.4 Plot the values of quantities whose ratios are always the same (e.g., cost to the number of an item, feet to inches, circumference to diameter of a circle). Fit a line to the plot and understand that the slope of the line equals the quantities.

7. Identify Proportional Relationships HOUSE CLEANING A house-cleaning service charges by the hour. For the 1 st hour they charge $45. Each hour after that costs $30 more. The service completes a cleaning in 4 hours. Is the fee proportional to the number of hours worked? Make a table of values to solve. Begin by making a table to display numbers and cost. Find the fee for 1, 2, 3, and 4 hours worked and place this data into the table.

8. Identify Proportional Relationships Yesterday we worked with ratios. Today we will use our knowledge of ratios to help us determine whether the data in the table shows a proportional relationship or not. Watch & observe how I check to find whether the fee for services is “proportional” to the cost. *There will be two different ways or “Methods” to solve this type of problem. 45 1 75 2 Method 1 90 75 No, the fee & hours worked is not proportional.

9. Method 1 45 1 75 2 90 75 As I said, the fees & hours worked aren’t proportional. 75 2 105 3 225 210 105 3 135 4 420 405

10. 45 1 75 2 90 75 2 105 3 225 210 105 3 135 4 420 405 So why aren’t the fees proportional to the hours worked? The fees aren’t proportional to the hours worked because……… Method 1

11. Let’s use another method to determine whether the hours worked are proportional to the fees charged.

12. 45 1 = 4 51 75 2 = 7 52 3 7. 5 105 3 = 1 0 53 3 5 Once again I have proven the fees & hours worked aren’t proportional. Method 2

13. So why aren’t the fees proportional to the hours worked? The fees aren’t proportional to the hours worked because……… 45 1 = 4 51 75 2 = 7 52 3 7. 5 105 3 = 1 0 53 3 5 Method 2

14. We used two methods to determine whether the fees were proportional to the hours worked. Method 1 45 1 75 2 90 75 In method 1 we created two ratios and crossed multiplied. The products weren’t equal, therefore the ratio’s weren’t PROPORTIONAL. 45 1 = 4 51 75 2 = 7 52 3 7. 5 Method 2 In method 2 we created two ratios then divided the ratios out. The quotients weren’t equal, therefore the ratio’s weren’t PROPORTIONAL.

15. So which method do you like? Let’s take a poll. How many like Method 1 “Cross Multiplying”? How many like Method 2 “Dividing Out”? How many would use either one depending on the data you were working with?

16. Let’s Try One Out. You Pick the Method You Want To Use.

17. 1.A 2.B A.yes B.no PLUMBING A plumbing company charges $50 for the first hour and $40 for each additional hour. Suppose a service call is estimated to last 4 hours. Is the fee proportional to the number of hours worked?

18. 1.A 2.B A.yes B.no PLUMBING A plumbing company charges $50 for the first hour and $40 for each additional hour. Suppose a service call is estimated to last 4 hours. Is the fee proportional to the number of hours worked? Hours1234 Cost$50$90$130$170

19. 1.A 2.B A.yes B.no PLUMBING A plumbing company charges $50 for the first hour and $40 for each additional hour. Suppose a service call is estimated to last 4 hours. Is the fee proportional to the number of hours worked?