NAME ________________________________________________ DATE ____________________ PERIOD ___________
Lesson 1
(continued)
Use a problem-solving model to solve each problem.
1 The table shows the number of muffins
Ana baked. She wants to put the oatmeal,
banana, and blueberry muffins in rows with
the same number of each type of muffin.
What is the greatest number of muffins in
each row? 6.NS.4, MP 2
Muffins
Type
Number
Oatmeal
16
Banana
12
Raisin
10
Blueberry
20
A
2 muffins
B
4 muffins
C
12 muffins
D
20 muffins
Beads
Type
4
Number per Pack
Glass
6
Wooden
3
Pottery
5
H.O.T. Problem Suppose the LCM of
three numbers is 20, the GCF is 2, and the
sum of the three numbers is 16. What are the
three numbers? 6.NS.4, MP 7
Course 1 • Chapter 1 Ratios and Rates
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
3 Carlos has three pieces of fabric. The yellow
fabric is 45 inches wide, the blue fabric is
36 inches wide, and the red fabric is
27 inches wide. Carlos wants to cut all
three pieces into equal width strips that are
as wide as possible. How many strips of
each color will he have? 6.NS.4, MP 4
2
2 Maria will use all the glass, wooden, and
pottery beads she buys to make a necklace.
The table shows the number of beads that
come in each pack. Maria wants to use the
same number of each type of bead. What is
the least number of each type of bead she
will buy? The cost per pack is $1. How much
will she spend? 6.NS.4, MP 4
NAME ________________________________________________ DATE ____________________ PERIOD ___________
Lesson 2
Chapter 1
Multi-Step Problem Solving
Multi-Step Example
The table shows the types of sandwiches sold on Friday. What is
the denominator when the ratio of veggie sandwiches to the total
number of sandwiches is written as a fraction in simplest form?
6.RP.1, MP 1
Sandwich
Turkey
Tuna
Number Sold
9
11
Veggie
6
Chicken
14
Use a problem-solving model to solve this problem.
Analyze
Read the problem. Circle the information you know.
Underline what the problem is asking you to find.
Plan
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
What will you need to do to solve the problem?
Write your plan in steps.
Step 1
Determine the total number of sandwiches sold.
Step 2
Express the ratio of veggie sandwiches to total
sandwiches as a fraction in simplest form.
Solve
Use your plan to solve the problem. Show your steps.
The total number of sandwiches sold is
or
+
+
+
sandwiches.
The ratio of veggie to total sandwiches is
So, the simplified denominator is
or
.
.
Justify and Evaluate
How do you know your solution is accurate?
Course 1 • Chapter 1 Ratios and Rates
3
NAME ________________________________________________ DATE ____________________ PERIOD ___________
Lesson 2
(continued)
Use a problem-solving model to solve each problem.
1 The table shows the types of breakfasts sold
on Thursday. What is the denominator of the
simplified ratio of oatmeal orders to total
orders? 6.RP.1, MP 1
2 How many blue counters must be added
so that the ratio of yellow counters to total
counters is 1:6? 6.RP.1, MP 4
R
Breakfast
Number Sold
Omelets
14
Pancakes
17
Waffles
11
Oatmeal
8
Y
R
R
Y
B
H.O.T. Problem The ratio of blue circles
to total circles is 4 to 5. There are more than
10 circles. Describe what this group of circles
might look like. Explain. 6.RP.1, MP 3
Types of Music
9%
Jazz
38%
Pop
22%
Rap
26%
Rock
4
Course 1 • Chapter 1 Ratios and Rates
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
4
R
B
B
3 Cantrise surveyed 100 students about their
favorite type of music. After she makes the
graph, she receives two more votes for rap.
What is the new ratio of rap to total types
of music? 6.RP.1, MP 1
5%
Classical
B
NAME ________________________________________________ DATE ____________________ PERIOD ___________
Lesson 3
Chapter 1
Multi-Step Problem Solving
Multi-Step Example
Zariah is training for a 5-kilometer run, which is about 3 miles. She
begins her training by running 1 mile each day for 5 days. She records
the number of minutes it takes her to run a mile, as seen in the table.
What is her average time in feet per second? 6.RP.2, MP 1
Day
Time (min)
1
15
2
13
3
16
A
0.16 ft/sec
4
14
B
5.87 ft/sec
5
12
C
6.29 ft/sec
D
18.86 ft/sec
Use a problem-solving model to solve this problem.
Analyze
Read the problem. Circle the information you know.
Underline what the problem is asking you to find.
Plan
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
What will you need to do to solve the problem? Write your plan in steps.
Step 1
Determine the average time in minutes.
Convert to seconds.
Step 2
Divide the number of feet in a mile by the seconds.
Solve
Use your plan to solve the problem. Show your steps.
The average time is
14 minutes × 60 =
15 + 13 + 16 + 14 + 12
__
or
5
minutes.
seconds
So, Zariah runs an average of 5,280 ÷ 840 or about
Choice
feet per second.
is correct. Fill in that answer choice.
Justify and Evaluate
How do you know your solution is accurate?
Course 1 • Chapter 1 Ratios and Rates
5
NAME ________________________________________________ DATE ____________________ PERIOD ___________
Lesson 3
(continued)
Use a problem-solving model to solve each problem.
1 Adam records his biking speed for five
consecutive days in a table. There are
5,280 feet in a mile. Determine his average
rate in feet per minute. 6.RP.2, MP 1
Day
Speed
(miles per hour)
1
12
2
15
3
13
4
16
5
17
A
1,232 ft/min
B
1,276 ft/min
C
1,285 ft/min
D
1,320 ft/min
6
Company
Cost
A
20 shirts for $38.40
B
25 shirts for $48.75
C
30 shirts for $57.00
4
y yards
_
H.O.T. Problem Using the rate m minutes ,
predict what will happen to the value of the
ratio for each scenario in the table below.
Explain your reasoning. 6.RP.3, MP 7
y
m
increases
unchanged
unchanged
increases
decreases
unchanged
unchanged
decreases
value of ratio
Course 1 • Chapter 1 Ratios and Rates
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
3 Carmine is in charge of buying shirts for the
senior class. She contacted three companies
and recorded their pricing information in the
table below. What is the best price per shirt?
6.RP.3b, MP 1
2 At a grocery store, a 24-pack of 16.9-ounce
water bottles is sold for $4.99. There are
128 ounces in a gallon. Determine the
price per gallon. Round to the nearest
penny. 6.RP.3b, MP 1
NAME ________________________________________________ DATE ____________________ PERIOD ___________
Lesson 4
Chapter 1
Multi-Step Problem Solving
Multi-Step Example
Marybeth makes money babysitting. She charges a flat rate of
$5 plus $5 per hour for each child. The rule 5(n) + 5 can be used
to calculate her fee per hour, where n is the number of children.
Complete the table to find the ratios of the number of children
to the fee. Write each ratio in simplest form. 6.RP.3, MP 1
A
B
_1 , _2 , _3 , _4 , _1
10 15 20 25 6
_1 , _1 , _3 , _2 , _1
1
2
3
4
5
3
4
5
Babysitting fee
per hour ($)
20 _
25 6
_10, _15, _
, ,_
1 2 3 4 1
_1 , _2 , _3 , _4 , _1
C
D
11 6 13 7 3
Number of
children
10 15 20 25 30
Use a problem-solving model to solve this problem.
Analyze
Read the problem. Circle the information you know.
Underline what the problem is asking you to find.
Plan
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
What will you need to do to solve the problem? Write your plan in steps.
Step 1
Use the rule to determine each fee.
Step 2
Express each ratio in simplest form.
Solve
Use your plan to solve the problem. Show your steps.
Complete the table.
The number of children is the numerator and the fee is the
denominator. Simplify if necessary.
The ratios are
Choice
,
,
,
,
Number of
children
1
2
Babysitting fee
per hour ($)
.
is correct. Fill in that answer choice.
Justify and Evaluate
How do you know your solution is accurate?
Course 1 • Chapter 1 Ratios and Rates
7
NAME ________________________________________________ DATE ____________________ PERIOD ___________
Lesson 4
(continued)
Use a problem-solving model to solve each problem.
1 A rental car company charges $0.25 a mile.
Use a table like the one below to find the
ratios of the cost to the number of miles in
simplest form. 6.RP.3, MP 1
Cost ($)
Number of
Miles
A
B
C
D
5
10
15
2 The tables below show the swimming
speeds of the King penguin and the Emperor
penguin. Determine which table shows an
equivalent ratio. Write the equivalent ratio in
miles per hour rounded to the hundredths
place. 6.RP.3, MP 6
20
King Penguin
Distance (ft)
_5, _5, _15, _5
4 2 4 1
_4, _4, _4, _4
1 1 1 1
_1 , _1 , _1 , _1
4 4 4 4
_1 , _2, _3 , _5
Time (min)
860
1,300
1,740
1
2
3
4
Emperor Penguin
Distance (ft)
412
824
1,236
1,648
Time (min)
1
2
3
4
25 5 75 1
Number of
Pizzas
5
7
9
Number of
People
15
21
27
4
H.O.T. Problem On the blueprint
below, 1 inch represents 2.5 feet of the
house. Complete a table that shows the
corresponding number of feet of the house
for each length on the blueprint. 6.RP.3a, MP 2
3.75 in.
1 in.
1.5 in.
0.25 in.
1 in.
0.5 in.
0.5 in.
1.25 in.
1 in.
Course 1 • Chapter 1 Ratios and Rates
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
3 Joshua is trying to determine the number of
pizzas to order. The table below shows the
number of people pizzas will feed. If each
pizza costs $7, how much will it cost to feed
36 people? 6.RP.3, MP 1
8
440
NAME ________________________________________________ DATE ____________________ PERIOD ___________
Lesson 5
Chapter 1
Multi-Step Problem Solving
Multi-Step Example
The height of a tree over time is an equivalent ratio. Which statement
best describes the graph of the ratio table? 6.RP.3a, MP 1
Time (yr)
Height (ft)
3
4.2
A
For every one unit right, the line goes up three units.
5
7
B
The line appears to pass through (1, 2).
8
11.2
C
The line decreases from left to right.
D
The line appears to pass through the origin.
Use a problem-solving model to solve this problem.
Analyze
Read the problem. Circle the information you know.
Underline what the problem is asking you to find.
Plan
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
What will you need to do to solve the problem? Write your
plan in steps.
Step 1
Graph the ordered pairs.
Step 2
Determine which statement is true based on the graph..
Solve
Use your plan to solve the problem. Show your steps.
Graph the ordered pairs.
The line appears to increase from left to right, so C is incorrect.
The line also does not pass through (1, 2), so B is incorrect.
For every unit right, the line goes up 1.4 units, so A is incorrect.
Since the line appears to pass through the origin, choice
is correct. Fill in that answer choice.
Justify and Evaluate
How do you know your solution is accurate?
Course 1 • Chapter 1 Ratios and Rates
9
NAME ________________________________________________ DATE ____________________ PERIOD ___________
Lesson 5
(continued)
Use a problem-solving model to solve each problem.
1 The number of bricks is an equivalent ratio
to the height of a wall. Which statement
describes the pattern in the graph of the
ordered pairs? 6.RP.3a, MP 1
Number of Bricks
Height of Wall (ft)
48
4
84
7
108
9
A
As the height of the wall increases by
1 foot, there are 12 more bricks in the wall.
B
For every 48 bricks, the wall increases
by 3 feet.
C
For every 36 bricks, the wall increases
by 4 feet.
D
As the height of the wall increases by
2 feet, there are 48 more bricks in the wall.
10
4
H.O.T. Problem The table below shows
the hours and wages for two friends who
babysit. Use a graph to determine if they
make the same hourly rate. Explain why or
why not. 6.RP.3a, MP 3
Zoe
Felix
Hours
3
5
Wages
$21
$30
Course 1 • Chapter 1 Ratios and Rates
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
3 Five yards of material is needed to make
2 curtains. This represents an equivalent
ratio. If the equivalent ratio (curtains,
material) were graphed, what would the
y-coordinate be if the x-coordinate was 7?
6.RP.3a, MP 4
2 The perimeter of an equilateral triangle is an
equivalent ratio to the length of the sides. An
equilateral triangle with a side length of 3 cm
has a perimeter of 9 cm, and an equilateral
triangle with a side length of 5 cm has a
perimeter of 15 cm. What is the perimeter of
a triangle with a side length of 7 cm?
6.RP.3, MP 8
NAME ________________________________________________ DATE ____________________ PERIOD ___________
Chapter 1
Lesson 6 Multi-Step Problem Solving
Multi-Step Example
Luna wants to burn as many Calories as possible per minute
of exercise. Which exercise should Luna choose? 6.RP.3, MP 1
Exercise
Calories
Minutes
Walking
300
60
A
walking
Jump rope
110
10
B
jump rope
Biking
270
30
C
biking
Aerobics
160
20
D
aerobics
Use a problem-solving model to solve this problem.
Analyze
Read the problem. Circle the information you know.
Underline what the problem is asking you to find.
Plan
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
What will you need to do to solve the problem? Write your plan in steps.
Step 1
Determine the unit rate for each exercise.
Step 2
Compare the unit rates.
Solve
Use your plan to solve the problem. Show your steps.
Walking:
Biking:
300
_
=
Jump rope:
60
270
_
=
Aerobics:
30
The unit rate
110
_
=
10
160
_
=
20
Calories per minute is the greatest.
So, Luna should
. Choice
is correct. Fill in that answer choice.
Justify and Evaluate
How do you know your solution is accurate?
Course 1 • Chapter 1 Ratios and Rates
11
NAME ________________________________________________ DATE ____________________ PERIOD ___________
Lesson 6
(continued)
Use a problem-solving model to solve each problem.
1 Santiago needs to buy apples to make
applesauce. He is looking for a better price
than $1.29 per pound. Which store has a
better price per pound? 6.RP.3, MP 4
Store
Price ($)
Weight (lb)
Store A
4.08
3
Store B
5.04
4
Store C
12.88
7
Store D
7.35
5
A
Store A
B
Store B
C
Store C
D
Store D
12
30 ft
25 ft
?
4
5 in.
H.O.T. Problem Jacob bought 5 pencils
for 80¢. At this same rate, how many pencils
can he buy for 40¢? Explain why this answer
does not make sense. 6.RP.3b, MP 3
Course 1 • Chapter 1 Ratios and Rates
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
3 Riley and Magdalena bought beads to make
a necklace. The beads that Riley bought cost
48¢ for 12. Magdalena bought 20 beads for
$1.00. How much less do 15 of Riley’s beads
cost than 15 of Magdalena’s beads?
6.RP.3b, MP 4
2 Josh is making a scale model of his
grandfather’s airplane. Given the information
in the diagram, how many inches are the
wings of the model? 6.RP.3, MP 2
NAME ________________________________________________ DATE ____________________ PERIOD ___________
Chapter 1
Lesson 7 Multi-Step Problem Solving
Multi-Step Example
The table shows the results of a survey of a group of people about
their favorite animal. If 600 people were asked about their favorite
animal, predict how many more people would prefer dogs than cats.
6.RP.3, MP 1
A
B
6
C
285
D
Favorite Animal
Animal
Number of
Responses
Bird
5
195
Cat
13
90
Dog
19
Iguana
3
Use a problem-solving model to solve this problem.
Analyze
Read the problem. Circle the information you know.
Underline what the problem is asking you to find.
Plan
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
What will you need to do to solve the problem? Write your plan in steps.
Step 1
Determine the total number of people surveyed.
Step 2
Set up equivalent ratios.
Step 3
Subtract to determine how much more.
Solve
Use your plan to solve the problem. Show your steps.
There were 5 + 13 + 19 + 3 or 40 people surveyed.
Dogs:
19
?
_
=_
40
Cats:
600
40
600
=
=
So, 285 - 195 or
13
?
_
=_
more people chose dogs than cats. Choice
is correct.
Fill in that answer choice.
Justify and Evaluate
How do you know your solution is accurate?
Course 1 • Chapter 1 Ratios and Rates
13
NAME ________________________________________________ DATE ____________________ PERIOD ___________
Lesson 7
(continued)
Use a problem-solving model to solve each problem.
1 The table shows the results of a survey of a
group of people about their favorite sport.
If 100 people were asked about their favorite
sport, predict how many more people would
prefer hockey than volleyball. 6.RP.3, MP 1
2 Keshia rides her bike 10 miles per hour. At
this rate, how many more minutes will it take
her to ride 30 miles than 25 miles?
6.RP.3b, MP 2
Favorite Sport
Sport
Baseball
Soccer
A
3
B
10
C
30
D
70
Number of
Responses
7
10
Volleyball
5
Hockey
8
H.O.T. Problem Jamal is helping a friend
4
with her homework. Look at his friend’s work
to determine and explain the error she made
finding the answer to the problem.
6.RP.3, MP 3
If 3 dogs eat 4 pounds of food per day, how
many dogs eat 15 pounds of food?
_3 = _15
4
?
Multiply numerator and denominator by 5.
Therefore, 20 dogs eat 15 pounds of food.
14
Course 1 • Chapter 1 Ratios and Rates
Copyright © McGraw-Hill Education. Permission is granted to reproduce for classroom use.
3 Marisol pays $12 for 4 notebooks. How many
notebooks could she buy with $62?
6.RP.3b, MP 2