MATH MESSAGE
Grade 6, Unit 1, Lessons 16 - 23
6TH GRADE MATH
Objectives of Lessons 16 - 23
Unit 1: Ratio and Unit Rates
Math Parent Letter
The purpose of this newsletter is to guide parents,
guardians, and students as students master the math
concepts found in the St. Tammany Public School’s
Guaranteed Curriculum aligned with the state
mandated Common Core Standards. Sixth grade
Unit 1 covers ratios, unit rates, and percent. This
newsletter will address concepts found in Unit 1,
Lessons 16 - 23, Unit Rates
The students will learn to…

Understand the concept of a unit rate a/b
associated with a ratio a:b with b ≠ 0, and
use rate language in the context of a ratio
relationship. For example, “This recipe has a
ratio of 3 cups of flour to 4 cups of sugar, so
there is 3/4 cup of flour for each cup of
sugar.” “We paid $75 for 15 hamburgers,
which is a rate of $5 per hamburger.”

Use ratio and rate reasoning to solve realworld and mathematical problems, for
example, by reasoning about tables of
equivalent ratios, tape diagrams, double
number line diagrams, or equations.
Words to know:



Ratio
Rate
Unit Rate



Ratio Table
Rate Unit
Value of a Ratio

Solve unit rate problems including those
involving unit pricing and constant speed.
For example, if it took 7 hours to mow 4
lawns, then at that rate, how many lawns
could be mowed in 35 hours? At what
rate were lawns being mowed?
Use ratio reasoning to convert
measurement units; manipulate and
transform units appropriately when
multiplying or dividing quantities.
Ratio – A pair of nonnegative numbers A:B, where
both are not zero, and that are used to indicate that
there is a relationship between two quantities such
that when there are A units of one quantity, there are
B units of the second quantity.
Rate – A rate indicates, for a proportional
relationship between two quantities, how many units
of one quantity there are for every 1 unit of the
second quantity. For a ratio of A:B between two
quantities, the rate is A/B units of the first quantity
per unit of the second quantity. For example, $10
for every 4 packs of diet cola is a rate because it is a
ratio of two quantities.
Ratio Table – A table listing pairs of numbers that
form equivalent ratios.
Rate Unit – the unit for the rate. For example, miles
per hour; words per minute; dollars per pound.
Unit Rate – The numeric value of the rate, for
example, in the rate 2.5 mph, the unit rate is 2.5.
The unit rate is 2.5 because it is the value of the
ratio.
Value of a Ratio – For the ratio A:B, the value of
the ratio is the quotient A/B.

LESSONS 16 – 23:
From Ratios to Rates
Students will recognize that they can associate a
ratio of two quantities, such as the ratio of miles per
hour to another quantity called the rate. Ratios can
be transformed to rates and unit rates. Given a
ratio, students precisely identify the associated rate.
They identify the unit rate and the rate unit.
Example Problem and Answer
At Foodworld, white seedless grapes cost $3.99 for 2
pounds. White seedless grapes are advertised at
Savemore for 3 pounds for $5. What is the unit price
of white seedless grapes at each grocery store? If
necessary, round to the nearest penny. Students are
encouraged to use a calculator on this problem.
Store
*
1 pound
2 pounds
3 pounds
Foodworld
$2*
$3.99
$6
Savemore
$1.67*
$3.34
$5
1.995 rounded to the nearest penny
**
1.
rounded to the nearest penny
The unit price for white seedless grapes at Foodworld
is $2 per pound. At Savemore the grapes are $1.67
per pound.
Example Problem and Solution
How many cups are in 7 quarts?
If your family wanted to save money, where should
they go to buy grapes? Why?
My family should buy grapes at Savemore because
the grapes cost less than they do at Foodworld.
How many centimeters are in 25 meters?
Example Problem and Answer
The owner of Sandwich King can make submarine
sandwiches at the rate of 3 per minute. What is the
ratio of sandwiches per minute? If she continues to
work at this rate for 5 minutes, how many
sandwiches will she make?
The ratio of sandwiches per minute is 3:1.
0
3
6
9
12
?
0
1
2
3
4
5
Sandwiches
Minutes
She will make 15 sandwiches in 5 minutes. I
drew a double number line with increments of 3
on the top, and increments of 1 at the bottom. If
I think about the “? “on the upper line, I can see
that 15 will line up with the 5 on the bottom line.
Students cross out any units that are in both the
numerator and the denominator in the expression
because they cancel out.
Students solve problems by analyzing different unit
rates given in tables, equations and graphs.
Example Problem and Solution
Sporting World and Golf City are both having a sale
on the same bestselling golf balls. Micah is trying to
decide which store has the better deal. Use the
information below to determine which store has the
better deal. Explain your thinking. Calculator use is
encouraged to divide the quantities. (Remember to
round your answers to the nearest penny)
Sporting World:
Number of Golf balls
12
24
36
Cost (dollars)
16
32
48
Finding a Rate by Diving Two Quantities
While there is no physical way to divide two different
quantities like (5 miles)/(2hours), students make use
of the structure of division and ratios to model
(5 miles)/(2hours) as a quantity 2.5 mph.
Interpreting a rate as a division of two quantities, or
a fraction, is the first step toward converting
measurement units.
Example Problem and Solution
For this problem, we will use the information from
the previous problem about Sandwich King. In order
to keep up with the large volume of customers during
a typical 90 minute lunch crowd, the owner needs to
make at least 250 sandwiches. If she continues to
make sandwiches at a rate of 3 sandwiches per
minute, will she be able to make enough sandwiches
during the 90 minute lunch crowd?
Golf City
where c represents the cost in dollars
and b represents the number of golf balls.
Sporting World has the better buy because one golf
ball is $1.33. Each golf ball at Golf City would be
$1.45, which is $ 0.12 more per golf ball.
Students will also solve problems using the formula,
Example Problem and Solution
After take-off, a commercial airplane cruised at an
average speed of 550 miles per hour for 5 hours.
About how far did it travel?
d = _____
Yes, the owner will be able to make at least 250
sandwiches in 90 minutes. At the rate of 3
sandwiches per minute, she can make 270
sandwiches in 90 minutes.
Students will apply this skill converting measures.
Students use rates between measurements to
convert measurement in one unit to measurement in
another unit. They transform units appropriately
when multiplying or dividing quantities.
● _____ hours
d = 550
● 5 hours
d = 550
● 5 hours
Cross out any units that are in both the numerator
and the denominator in the expression because they
cancel out.
d = 550 miles ● 5
d = 2,750 miles
The plane travelled 2,750 miles in 5 hours.