Standards: 7.RP.1, 7.NS.2d, 7.NS.3, 7.EE.4a, 7.G.1
Resource: Connected Math Program 2
Comparing and Scaling: Investigation 3.3
Ratio, Proportion, and Percent
Investigation #3- CMP2







Examine & Connect the idea of unit rate to what you
already know about ratios and about linear
relationships (3.1)
Further develop understanding of unit rates and how
to compute and interpret them (3.2)
Work with the important application of rates to miles
per hour (speed) (3.2)
Introduce the concept of “average” or “steady” rate of
progress (3.2)
Introduce and formalize the meaning of unit rate and
computation strategies for computing unit rates (3.3)
Relate unit rate to the slope of the line representing
the equation of the underlying relationship (3.3)
Confront the issue of what it means to divide in rate
situations


Introduce and formalize the meaning of unit
rate and computation strategies for
computing unit rates
Relate unit rate to the slope of the line
representing the equation of the underlying
relationship
The ads below use rates to describe sale
prices. To compare prices in sales such as
these, it’s often useful to find a unit rate. A
unit rate is a rate in which one of the numbers
being compared is 1 unit. The comparisons “45
miles per gallon,” “$3.50 per hour,” “8.5
kilometers per hour,” and “two sandwiches for
each person” are all unit rates. “Per gallon”
means “for one gallon” and “per hour” means
“for one hour.”
MUSIC CITY
CD Sale!
5 for $49.95
CD WORLD
Huge Savings!
7 for $65.80
Use unit rates to compare the ad prices and to
find the costs of various numbers of CDs at
each store.
A. Which store has the lower price per CD?
B. For each store, write an equation (a rule)
that you can use to calculate the cost c for
any purchase of n compact discs.
C. Use the equations you just wrote for
Question B. Write new equations to include
5% sales tax on any purchase.
D.
E.
Suppose a Web site sells CDs for $8.99 per
disc. There is no tax, but there is a shipping
charge of $5 for any order. Write an
equation to give the cost c of any order for
n discs from the Web site.
Use your equation from Question C or make
a rate table to answer each question.
1. How many discs do you have to order from the Web site to
get a better deal than buying from Music City?
2. How many discs do you have to order from the Web site to
get a better deal than buying from CD World?


What are the variables in the situation, and
what letters are good representations for the
variables?
Which seems to be the independent variable,
and which the dependent variable?



Explain what a rate is and give some
examples of different kinds of rates.
What does unit rate mean? What are some
examples where a unit rate is useful?
What variables were you dealing with in the
various parts of the problem? How did you
decide which was the independent and which
was the dependent variable?




How do the dependent and the independent
variables show up in an equation?
What are some ways of making comparisons
among the options for buying CD?
How did you figure out the answers to Q. E?
If you made a graph for numbers of CDs and
prices for each of the three companies, what
would each graph look like? Are they straight
lines? Do they go through the origin?
A.C.E
Application, Connections, & Extensions
#9, 11, 24, 25
Copy your answers in your math workbook