Math CC7/8 – Nov. 7 Key Word: Things Needed Today (TNT) Unit Rate, Constant of Proportionality Things Needed Today (TNT) Pencil/Math Notebook/Calculator Math Book –Comparing & Scaling Math Notebook: Topic: Unit Rate & Constant of Proportionality HW: CS pg. 53 #9 pg. 55 #12 & 13 pg. 56 #24 & Worksheet

What’s Happening? HW Questions Quick Warm Up Lesson- C&S 2.3! Begin HW?

Warm Up Simplify the following problems -6(x – 7) 5 + 4 (x-5) Answers -6x + 42 4x – 15 -2x -3

Finish 2.2

Royal: P = 12n Howdy’s: P = 13n 1. If you know the price of one pizza, how can you find the price of additional numbers of pizzas?. B If you know the price of one pizza, you can multiply that price by any number of pizzas to find the total cost. 2. For each pizza place, use your strategy from part (1) to write an equation for the total price P for any number of pizzas n. Royal: P = 12n Howdy’s: P = 13n

Royal: P = 12n 400 = 12n n = 400 ÷ 12 33.333 About 33 pizzas

Entries in delivery line are $5 more than pick up Howdy’s listed price is valid only if you pick up the pizza. If you request delivery, they charge a flat $5 fee for any number of pizzas. 1) a. Complete the table on labsheet 2.2. Find the prices for Howdy’s pizzas if you pick up and if they deliver. Both rows increase by 13 Entries in delivery line are $5 more than pick up Pick Up line can be scaled up Delivery line cannot be scaled up!

This does NOT show up in the delivery line. That equation would be: Howdy’s: P = 13n The 13 in the equation shows up in the increase in the pick up line. This does NOT show up in the delivery line. That equation would be: D = 13n + 5 D= delivery

Both graphs are straight lines Use 2 different colors to graph..1 color for the delivery and another color for the pick up. Both graphs are straight lines The lines are parallel The pick up line starts at (0, 0) The delivery line starts at (0, 5) Use labsheet 2.2 to graph b. How are the graphs similar? How are they different?

Zero Pizza Delivery: (0, 5) Pick Up: (0, 0) One Pizza Delivery: C. For each graph, which coordinate pair represents how much one pizza costs? How much zero pizzas cost? One Pizza Delivery: (1, 18) Pick Up: (1, 13) Zero Pizza Delivery: (0, 5) Pick Up: (0, 0)

Amount of pizza per person Number of people per pizza Price per pizza Add to notes In Comparing Bits & Pieces (CC 6), you found unit rates. Recall that a unit rate is a rate in which the second quantity is 1 unit. The rates 45 miles per gallon and $3.50 per hour are unit rates because “per gallon” means “for one gallon” and “per hour” means “for one hour.” You may have used the following unit rates in previous problems: Amount of pizza per person Number of people per pizza Price per pizza

C = 13n The unit rate for the price of one pizza at Howdy’s is $13. The equation C = 13n relates cost of pizza and number of pizzas. This equation represents a proportional relationship 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. Add to notes C = 13n Constant of proportionality When a delivery charge of $5 is added to the cost, the relationship is no longer proportional: C = 13n + 5 is not a proportional relationship. ? How can you recognize a proportional relationship from a table or graph?

How can you find a unit rate in: Question How can you find a unit rate in: a description an equation a table Or a graph ?

n = 5C C = 0.2n 5 oranges per dollar $0.20 per orange

Do Not Graph, just share and analyze

(1, 5) = 5 oranges for $1 (1, 0.20) = $0.20 for one orange

g gallons d = 30 miles d miles 600 miles 1 gallon 20 gallons

Unit Rate: 30 miles per gallon

3. What equation relating d and g does the graph represent?

1 gallon = 30 miles (1, 30) 0 gallons = 0 miles (0, 0)

x = 120 miles x miles Both are correct! 600 miles 20 gallons x miles You could also look at the graph, make a rate table, or use the equation, d = 30g and substitute 4 for g!

If time…

If time… FreshFoo ds! $0.83 for one box ($0.03 less than MFYM)

Homework pg. 53 #9 pg. 55 #12 & 13 pg. 56 #24 Worksheet