Name ___________________________
Period__________
Date ___________
UNIT 5: RATIO, PROPORTION, AND PERCENT
WEEK 17: Student Packet
17.1 Proportional Reasoning
• Use sense-making strategies to solve proportional reasoning
problems.
• Solve problems that involve whole numbers and decimals.
• Use measurement expressed as a product to solve problems.
1
17.2 Understanding Percents
• Convert fractions to decimals and percents.
• Find percents of numbers.
5
17.3 Ratios, Rates, and Proportions
• Introduce terminology and notations for ratio, rate, and proportion.
• Solve proportions using equivalent fractions.
• Review math concepts from prior lessons.
• Demonstrate competency in multiplication and division of fractions
(highlighted review).
10
Unit 5: Ratio, Proportion, and Percent (Student Packet)
Week 17 – SP
FOCUS ON VOCABULARY 17
Unscramble the words to reveal words from the word bank. Then, write their definitions
or give examples.
Example:
oairt
ratio: (example) The ratio 12:4 can also be written as 12 to 4.
1. tera _______________________________________________________________
___________________________________________________________________
2. niut erta ____________________________________________________________
___________________________________________________________________
3. inut ecirp ___________________________________________________________
___________________________________________________________________
4. otoopnirrp __________________________________________________________
___________________________________________________________________
5. eptencr ____________________________________________________________
___________________________________________________________________
Word Bank
unit price
unit rate
percent
Unit 5: Ratio, Proportion, and Percent (Student Packet)
proportion
rate
Week 17 – SP0
17.1 Proportional Reasoning
PROPORTIONAL REASONING
Ready (Summary)
Set (Goals)
We will use sense-making strategies to
solve proportional reasoning problems.
• Use sense-making strategies to
solve proportional reasoning
problems.
• Solve problems that involve whole
numbers and decimals.
• Use measurement expressed as a
product to solve problems.
Go (Warmup)
Solve each pencil problem in two ways. Show your work.
1. If 1 pencil costs $0.17, then what is the
cost of 4 pencils?
2. If 5 pencils cost $1.15, then what is the
cost of 1 pencil?
Method 1:
Method 1:
Method 2:
Method 2:
Answer: 4 pencils cost $ ________ .
Answer: 1 pencil costs $ _________ .
Unit 5: Ratio, Proportion, and Percent (Student Packet)
Week 17 – SP1
17.1 Proportional Reasoning
PENCIL PROBLEMS
Solve each pencil problem in two ways. Show your work.
1. If 3 pencils cost $0.57, then what is the
cost of 6 pencils?
2. If 4 pencils cost $1.08, then what is the
cost of 10 pencils?
Method 1:
Method 1:
Method 2:
Method 2:
Answer:
Answer:
3. How much will 4 pencils cost if 6
pencils cost $1.68?
4. How much will 2 pencils cost if 7
pencils cost $1.82?
Method 1:
Method 1:
Method 2:
Method 2:
Answer:
Answer:
Unit 5: Ratio, Proportion, and Percent (Student Packet)
Week 17 – SP2
17.1 Proportional Reasoning
PENCIL PROBLEMS (continued)
Solve each pencil problem in two ways. Show your work.
5. If it costs $1.89 for 9 pencils, then how
many pencils can be purchased for
$2.52?
6. How many pencils can be purchased
for $0.48 if the cost of 6 pencils is
$1.44?
Method 1:
Method 1:
Method 2:
Method 2:
Answer:
Answer:
7. How much will 5 pencils cost if 8
pencils cost $4.40?
8. If 18 pencils cost $3.24, then how
much do 12 pencils cost?
Method 1:
Method 1:
Method 2:
Method 2:
Answer:
Answer:
Unit 5: Ratio, Proportion, and Percent (Student Packet)
Week 17 – SP3
17.1 Proportional Reasoning
PAINTING A FENCE
The work required to paint a fence can be measured in painter-hours.
number of painter-hours
number of hours it takes one painter to paint the
=
needed to paint the fence
fence
number of painter-hours
number of painters it takes to paint the fence in one
=
needed to paint the fence
hour
Example: If it takes 6 painters 3 hours to paint a fence,
then it takes 18 painter-hours to paint the fence.
Suppose painting a fence requires 40 painter-hours of labor.
Suppose a painter charges $12 per hour (i.e. the cost is $12 per painter-hour).
1. How many hours does it take 2 painters to paint the fence?
2. How many hours does it take 5 painters to paint the fence?
3. If a fence must be painted in 4 hours, how many painters should be hired to paint it?
4. How much will it cost to paint the fence?
5. If a contractor hires 4 painters to paint the fence, how much will it cost the contractor
per hour to have the fence painted?
Unit 5: Ratio, Proportion, and Percent (Student Packet)
Week 17 – SP4
17.2 Understanding Percents
UNDERSTANDING PERCENTS
Ready (Summary)
Set (Goals)
We will learn sense-making strategies
for finding percents of numbers.
• Convert fractions to decimals and
percents.
• Find percents of numbers.
Go (Warmup)
Complete the table. Use mental math when possible. If another method is used, show
the work clearly. Be prepared to explain your methods.
Fraction
1.
1
2
2.
7
10
Decimal
3.
0.06
4.
0.3333333…
Percent
5.
25%
6.
40%
Unit 5: Ratio, Proportion, and Percent (Student Packet)
Week 17 – SP5
17.2 Understanding Percents
PERCENTS OF CONTAINERS
Complete the problems below.
1. About how full is each container? Give estimates using percents.
Container A
Container B
Container C
Container D
2. You are now given the information that, when full, each container holds 800 ounces
of liquid. How many ounces do you estimate to be in each container?
3. A correction is made to the above information. These containers actually hold 900
ounces of liquid. Now how many ounces do you estimate to be in each container?
The container below holds 600 ounces of liquid when full.
Determine how much liquid would make it:
4. 50% full ___________
5. 25% full ___________
6. 75% full ___________
7. 10% full ___________
8. 20% full ___________
Unit 5: Ratio, Proportion, and Percent (Student Packet)
Week 17 – SP6
17.2 Understanding Percents
PERCENTS OF OTHER ITEMS 1
Complete each sentence.
A dollar is _____ cents. Find the following percents of a dollar.
1. 5% of a dollar is _____ cents.
2. 34% of a dollar is _____ cents.
3. 10% of a dollar is _____ cents .
4. 76% of a dollar is _____ cents.
5. A meter is _____ centimeters. The rectangle below represents a meter stick. Write
some numbers on the meter stick to represent centimeters. The left edge of the
meter stick represents 0 centimeters.
Going from left to right, write the letter on the meter stick above that represents each
of the following:
A.
100% of the way
F.
10% of the way
B.
50% of the way
G. 20% of the way
C. 25% of the way
H. 0% of the way
D. 75% of the way
I.
80% of the way
E.
J.
55% of the way
5% of the way
6. How are finding percents and finding centimeters on a meter stick related?
___________________________________________________________________
___________________________________________________________________
Unit 5: Ratio, Proportion, and Percent (Student Packet)
Week 17 – SP7
17.2 Understanding Percents
PERCENTS OF OTHER ITEMS 2
Complete each sentence.
1. Finding 100% of something is the same as finding __________ of it.
So 100% of $40 is __________.
2. Finding 50% of something is the same as finding __________ of it.
This is the same as dividing by__________. So 50% of $40 is __________.
3. Finding 25% of something is the same as finding __________ of it.
This is the same as dividing by __________. So 25% of $40 is __________.
4. Finding 10% of something is the same as finding __________ of it.
This is the same as dividing by__________. So 10% of $40 is __________.
5. Finding 10% can help with finding other percents as well. Use your answer for 10%
of $40 to find 20% of $40. Explain your strategy.
___________________________________________________________________
___________________________________________________________________
6. Find 5% of $40. Explain your strategy.
___________________________________________________________________
___________________________________________________________________
Unit 5: Ratio, Proportion, and Percent (Student Packet)
Week 17 – SP8
17.2 Understanding Percents
MONEY AND OTHER ITEMS
Complete the charts below.
Money
1.
$30
2.
$42
3.
$16
4.
$150
5.
$500
Items
6.
80 games
7.
60 apples
8.
40 balloons
9.
120 students
10.
12 cars
More Money
11.
$1,000
12.
$150
13.
$7,500
Find 10%
Find 5%
Find 15%
Find 20%
Find 10%
Find 5%
Find 50%
Find 25%
Find 1%
Find 0.5%
Find 1.5%
Find 150%
Unit 5: Ratio, Proportion, and Percent (Student Packet)
Week 17 – SP9
17.3 Ratios, Rates, and Proportions
SKILL BUILDER 1A
Complete the problems.
1. A ratio is a comparison of _________________________________________________ .
Here are some stars and squares:
Show each ratio in three different ways.
2.
Number of stars to
number of squares.
to
:
3.
Number of squares to
total number of figures.
to
:
4.
Number of stars to
number of stars.
to
:
Express each ratio as a fraction.
5.
2 to 3 ___________
6.
7 to 10 ___________
7.
5:5 ______________
8. A rate is a special ratio that compares _______________________________________ .
9. We generally include the ___________ when writing rates.
Use fractions to express each rate.
10. You earned $3 in one day. What is the rate per day? ____________________________
11. You read 5 books in 2 weeks. What is the rate per week? ________________________
12. You grew 3 inches in 11 weeks. What is the rate per week? ______________________
Unit 5: Ratio, Proportion, and Percent (Student Packet)
Week 17 – SP10
17.3 Ratios, Rates, and Proportions
SKILL BUILDER 1B
Complete the problems.
13. A proportion is ____________________________________________________________ .
14.
2
4
=
may be written as 2:5 = ____ : _____
5
10
Find the missing number in the proportions.
4
n
n
3
=
16.
=
15.
5
35
12
4
18.
5
n
=
15
3
19.
5
30
=
9
n
17.
16
4
=
n
5
20.
3
n
=
11 33
21. The ratio of boys to girls is 5:4. If there are 12 girls in the class, how many boys are there?
__________________________________________________________________________
22. Cynthia wrote the following on her paper.
6
6+6
12
=
=
10
10 + 6
16
Explain what is wrong with her work, and correct her work.
Unit 5: Ratio, Proportion, and Percent (Student Packet)
Week 17 – SP11
17.3 Ratios, Rates, and Proportions
SKILL BUILDER 2
Here are some triangles and stars:
Show the ratios in three different ways:
Number of stars to
1. total number of
figures.
Number of triangles
2. to total number of
figures.
3.
Number of triangles
to number of stars.
4. There are 12 marbles in a jar. Five are red and the rest are blue. What is the ratio of red
marbles to blue marbles? __________________________________________________
5. Dan got 13 problems correct. There were 20 problems on the test. What is the ratio of
correct problems to total problems? __________________________________________
Compute.
6. A portion of popcorn is
3
cup. How many portions of popcorn can be made from 5 cups
4
of popcorn?
3
2
miles from his grandmother. He bikes
of the way, and then stops to
5
3
rest. How far did Keto bike before he stopped?
7. Keto lives 2
Unit 5: Ratio, Proportion, and Percent (Student Packet)
Week 17 – SP12
17.3 Ratios, Rates, and Proportions
SKILL BUILDER 3A
Give the ratios or rates as fractions. Include units on the rates.
1. You made 7 hits in 10 tries. What is the ratio of hits to tries? ___________________
What is the ratio of hits to misses? _______________________________________
2. A map legend says 1 inch = 2 miles. Write this as a ratio in three different ways.
___________________________________________________________________
Find the missing number in each proportion.
n
8
10
5
3.
=
4.
=
6
12
50
n
6.
15
n
=
3
6
Compute.
9.
18.46 ÷ 0.02
7.
10.
n
30
=
6
12
354.3 ÷ 10
Unit 5: Ratio, Proportion, and Percent (Student Packet)
5.
20
2
=
n
3
8.
4
n
=
9
18
11.
2.004 × 1.2
Week 17 – SP13
17.3 Ratios, Rates, and Proportions
SKILL BUILDER 3B
Compute.
5 3
×
12.
6 4
13.
6
1
1
×1
2
2
Complete the table.
Fraction
1
15.
25
14.
Decimal
16.
4 1
÷
5 4
Percent
0.15
17.
7%
18.
115%
19. Fill in the table, graph the values, connect the points, and write an equation for the line.
There are 16 ounces in 1 pound.
Pounds (x)
0
1
2
Ounces (y)
0
16
32
3
4
5
x
Write the rule using words: ____________________
_________________________________________
Write the rule using symbols:
y = ______________________________________
Unit 5: Ratio, Proportion, and Percent (Student Packet)
Week 17 – SP14
17.3 Ratios, Rates, and Proportions
SKILL BUILDER 3C
20. Use square tiles to create all the rectangles that have an area of 16 square units. Record
the dimensions of each rectangle you found. Let the vertical distance be the length and
let the horizontal distance be the width.
Length
Width
Area
Area
Width
21. Make a graph of width vs. length and area vs. length.
Length
Length
Compute.
-7 + -5
22.
23.
8 − 15
Unit 5: Ratio, Proportion, and Percent (Student Packet)
24.
-12 ÷ -4
Week 17 – SP15
17.3 Ratios, Rates, and Proportions
TEST PREPARATION 17
Show your work on a separate sheet of paper and choose the best answer.
1. If 3 pencils cost $0.78, then what will 7 pencils cost?
A.
$0.26
B.
$0.82
C.
$1.26
D.
$1.82
G.
60 apples
H.
6 apples
2. What is 150% of 40 apples?
E.
6,000 apples
F.
600 apples
3. The ratio of boys to girls is 6:5. If there are 25 girls in the class, how many boys are
there?
A.
20
B.
4. What is the product of 8
E.
25
C.
30
D.
35
5
2
and 1 ?
6
4
10
24
F.
13
1
4
G.
8
10
12
H.
13
20.5
B.
22.5
C.
225
D.
2.25
8
10
12
5. 4.5 × 5
A.
6. If 5 paper petals are needed to make 1 paper flower, which of these describes the
relationship between the number of paper petals (x) and the number of paper
flowers (y)?
E.
y =
1
x
5
F.
y = 5x
Unit 5: Ratio, Proportion, and Percent (Student Packet)
G.
y = x +5
H.
x = y +5
Week 17 – SP16
17.3 Ratios, Rates, and Proportions
KNOWLEDGE CHECK 17
Show your work on a separate sheet of paper and write your answers on this page.
17.1 Proportional Reasoning
Solve each pencil problem in two ways. Show your work.
1. How much will 4 pencils cost if 6 pencils cost $1.74?
2. If it costs $3.24 for 9 pencils, then how many pencils can be purchased for $6.48?
17.2 Understanding Percents
Find the following percents.
Amount
3.
$60
4.
40 pencils
Find 10%
Find 5%
Find 15%
Find 20%
17.3 Ratios, Rates, and Proportions
Find the missing number (n) in each proportion.
5.
n
3
=
25
5
6.
30
3
=
10
n
Highlighted Review: Fractions: Multiplication and Division
Compute.
7.
2
1
× 3
5
2
Unit 5: Ratio, Proportion, and Percent (Student Packet)
8.
1
3
÷ 5
7
Week 17 – SP17
17.3 Ratios, Rates, and Proportions
Home-School Connection 17
Here are some questions from this week’s lessons to review with your young mathematician.
1. If 4 pencils cost $0.92, how much will 9 pencils cost?
2. Complete the table.
Find 10%
Find 5%
Find 50%
Find 25%
240 students
3. Find the missing number in
n
6
.
=
4
12
Parent (or Guardian) signature ____________________________
Selected California Mathematics Content Standards
NS 5.1.2 Interpret percents as a part of a hundred; find decimal and percent equivalents for common fractions
and explain why they represent the same value; compute a given percent of a whole number.
NS 6.1.2 Interpret and use ratios in different contexts (e.g., batting averages, miles per hour) to show the
relative sizes of two quantities, using appropriate notations (a/b, a to b, a:b).
NS 6.1.3 Use proportions to solve problems (e.g., determine the value of N if 4/7 = N/21, find the length of a
side of a polygon similar to a known polygon). Use cross-multiplication as a method for solving such
problems, understanding it as the multiplication of both sides of an equation by a multiplicative
inverse.
NS 7.1.3 Convert fractions to decimals and percents and use these representations in estimations,
computations, and applications.
AF 7.4.2 Solve multistep problems involving rate, average speed, distance, and time or a direct variation.
MR 7.1.0 Students make decisions about how to approach problems.
Unit 5: Ratio, Proportion, and Percent (Student Packet)
Week 17 – SP18