Transcript rttCS 2.3-Day 1 Per 4-Unit Rate Constant of Proportionality.pptx

CS 2.3: Finding Costs –
Unit Rate and Constant of Proportionality
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: What do these algorithms represent?
Answer this question using the algorithm:
verify: 400 = 12(33.33)
33 pizzas
96 = 12n
96 ÷ 12 = 8
verify:
96 = 12(8)
8 pizzas
Homework Review: CS 2.2 p. 8
CS 2.3: Finding Costs – Unit Rate and Constant of Proportionality
pkt p. 9
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 __________________
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
__________
__________________.
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.
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.
$ .20
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.
5 oranges
3. How many oranges can you buy for $5?
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
4. How much do 25 oranges cost?
If the price is $ .20 per orange.
Then 25 oranges costs 25 times as much as 1 orange.
.20 x 25 = $5.00
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?
n = 5C
The number of oranges will equal five times the dollars spent.
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
c. Identify the two unit rates in the equations.
What information do the unit rates give you?
C = 0.2n
n = 5C
0.2
5
No matter how many you buy,
each orange will always cost $ .20
No matter how many you buy, you will
get 5 oranges for every dollar spent.
d. How does the constant of proportionality relate to the unit rate?
constant of proportionality = unit rate
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
Equation:
C = 0.2n
(oranges, cost)  (x,y)
Cost of Oranges
Equation: n =
5C
(cost, oranges)  (x,y)
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
Equation:
C = 0.2n
(oranges, cost)  (x,y)
Cost of Oranges
Equation: n =
5C
(cost, oranges)  (x,y)
B. Noralie’s car uses 20 gallons of gas to go 600 miles.
300
315
Find the missing values in the table.
Find the unit rate (miles per gallon) by using the table:
unit rate = 30 miles per gallon
How can you tell by looking the table that this is a
proportional relationship?
The table increase by 30 miles for every gallon.
(Can you see the same scale factors
and all the equivalent fractions?)
300
315
Equation
Write the equation for this situation:
d = 30g
(d=distance, g=gallons)
How can you tell by looking the equation that this is a
proportional relationship?
For every gallon used, the distance will increase by 30 miles
Find the unit rate (miles per gallon) by
using the graph:
Unit Rate:
30 miles per gallon
(4, 120)
What does (1, 30) mean?
1 gallon = 30 miles
Use the graph to find how many miles she
can drive with 4 gallons of gas.
(4, 120)
= 120 miles
How can you tell by looking the graph that
this is a proportional relationship?
The rate moves in a straight line.
CS Exit Ticket #2
CS 2.3: Finding Costs –
Unit Rate and Constant of Proportionality
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