1. Learning Target: I can find the unit rate and the constant of proportionality from a graph, table, and equation. Homework: Complete notes on p.11 for the Zaption Video CS 2.3 Warm Up: CS 2.3: Finding Costs – Unit Rate and Constant of Proportionality What do these algorithms represent? Answer this question using the algorithm: verify: 400 = 12(33.33) 96 = 12n 96 ÷ 12 = 8 96 = 12(8) verify: 33 pizzas 8 pizzas

2. Homework Review: CS 2.2 p. 8

5. pkt p. 9 CS 2.3: Finding Costs – Unit Rate and Constant of Proportionality The unit rate of one pizza at Howdy’s is $13. The equation P = 13 n relates the price of the pizza and the number of pizzas. This equation represents a __________________ ___________________________, because you multiply one variable by a constant number to get the value of the other variable. The constant multiplier is called the __________ _____ __________________. constant of proportionality If a delivery charge of $5 is added to the cost, the relationship is no longer proportional. P = 13n + 5 is not a proportional relationship. proportional relationship

6. A.FreshFoods has oranges on sale at 10 for $2. This is a ratio or rate. 1. What is the cost per orange? This is a unit rate, because we are talking about the price of one orange. 2. How many oranges can you buy for $1? This is also a unit rate, because we are talking about how many oranges you can get for $1. $.20 5 oranges

7. 3. How many oranges can you buy for $5? 4. How much do 25 oranges cost? If the Unit Rate is: 5 oranges for $1. Then you can get 5 times as many oranges for $5 5 oranges x $5 = 25 oranges If the price is $.20 per orange. Then 25 oranges costs 25 times as much as 1 orange..20 x 25 = $5.00

8. 6. The equation n = 5C relates cost: C to number of oranges: n. a. What does this equation tell you about the relationship between the number of oranges and the cost of the oranges? b. What is another equation relating these same two variables? What information does this other equation give you? C = 0.2n The cost will equal $.20 times the number of oranges n = 5C The number of oranges will equal five times the dollars spent.

9. c. Identify the two unit rates in the equations. What information do the unit rates give you? d. How does the constant of proportionality relate to the unit rate? C = 0.2n No matter how many you buy, each orange will always cost $.20 n = 5C No matter how many you buy, you will get 5 oranges for every dollar spent. 0.2 5 constant of proportionality = unit rate

10. 7. Graph the two equations for the oranges problem on separate coordinate grids. a. Think about how to scale your graph on each axis before you start plotting points. b. Look at the tables that you created on page 9 so that you can find coordinates to plot. Cost of Oranges Cost of Oranges Equation: C = 0.2n Equation: n = 5C (oranges, cost)  (x,y) (cost, oranges)  (x,y)

11. 7. Graph the two equations for the oranges problem on separate coordinate grids. a. Think about how to scale your graph on each axis before you start plotting points. b. Look at the tables that you created on page 9 so that you can find coordinates to plot. Cost of Oranges Cost of Oranges Equation: C = 0.2n Equation: n = 5C (oranges, cost)  (x,y) (cost, oranges)  (x,y)

12. B. Noralie’s car uses 20 gallons of gas to go 600 miles. Find the missing values in the table. Find the unit rate (miles per gallon) by using the table: How can you tell by looking the table that this is a proportional relationship? 300 315 unit rate = 30 miles per gallon The table increase by 30 miles for every gallon. (Can you see the same scale factors and all the equivalent fractions?)

13. Equation Write the equation for this situation: How can you tell by looking the equation that this is a proportional relationship? 300 315 For every gallon used, the distance will increase by 30 miles d = 30g (d=distance, g=gallons)

14. Find the unit rate (miles per gallon) by using the graph: What does (1, 30) mean? Use the graph to find how many miles she can drive with 4 gallons of gas. How can you tell by looking the graph that this is a proportional relationship? Unit Rate: 30 miles per gallon 1 gallon = 30 miles (4, 120) = 120 miles The rate moves in a straight line. (4, 120)

15. CS Exit Ticket #2

16. Did I reach my Learning Target? I can find the unit rate and the constant of proportionality from a graph, table, and equation. Homework: Complete notes on p.11 for the Zaption Video CS 2.3 CS 2.3: Finding Costs – Unit Rate and Constant of Proportionality