Basic Pre Algebra
Intervention Program
This 9 lesson Intervention Plan is designed to provide extra practice
lessons and activities for students in Pre Algebra. The skills covered
are basics that must be mastered in order to ensure success in Pre
Algebra. These lessons are not meant to be 90 minute full class lessons
(although some could be used that way and some might last that long).
Intervention works best when students work in small, targeted groups
with a teacher.
This is a small piece of a larger, 35 lesson, full Pre Algebra Intervention Plan.
Created by: Lindsay Perro
©2011
1
Basic Pre Algebra
Intervention Program
LESSON
A
B
TOPIC
Order of Operations




No Calculator
Order of Operations
with Decimals
No Calculator
C
PLAN
Expanded Form
No Calculator











D
Rules of Exponents
No Calculator


Warm-up A
Notes on Order of Operations
Order of Operations Notes & Practice
Independent Practice Order of Operations
Bingo – Students solve the problems
independently. Bingo can be played if time
permits.
Exit ticket A
Warm up B
Decimal Operations Notes & Review
Puzzle – with partners
Exit Ticket B
Warm up C
Expanded Form Notes
Independent Practice - Form is Important
Worksheet
Exit Ticket C
Warm up D
Review of Exponents – Exponents Practice
Worksheet
Rules of Exponents Notes & Practice
Exponents Versa Tiles Activity - Independent
(Must have Versa Tiles for students to use)
E
Review Expanded
Form & Laws of
Exponents
No Calculator
 Exit Ticket D
 Warm up E
 Expanded Form with Decimals and Fractions
Worksheet
 Exponents Matching Game
Should be played like the game “Memory”.
 Exit Ticket E
2
LESSON
F
TOPIC
Fractions, Decimals &
Percents
No Calculator
G
Percent of a Number
H
Proportions and Unit
Rates
I
Proportions and Scale
LESSON
 Warm up F
 Fractions, Decimals and Percents Guided
Practice and Pairs Practice
 Silly Face Worksheet – Independent Practice
 Exit Ticket F
 Warm up G
 Percent of a Number Guided Practice
 Percent of a Number Coloring Sheet –
Independent Practice
 Exit Ticket G
 Warm up H
 Proportions and Unit Rate Notes and Guided
Practice
 Proportions and Unit Rate Coloring Sheet –
Independent Practice
 Exit Ticket H
 Warm up I
 Candy Bar Scale/Proportions Activity
 Exit Ticket I
3
Name _____________
Warm Up A
List as many words as you can that signal each operation.
1)
Addition
2)
Subtraction
3)
Multiplication
4)
Division
Name ___KEY________
Warm Up A
List as many words as you can that signal each operation.
1) Addition
Sum, more than, increased, plus
3)
Multiplication
Of, product, per
2)
Subtraction
Less than, difference, decreased
4)
Division
Quotient, per, divided by/into
4
Lesson A Notes
Give the students notes on the order of operations. Feel free to use PEMDAS, however stress to
them that Multiplication and Division are done from left to right – same with Addition and
Subtraction. Have them copy down the following graphic organizer, or have it copied for them.
ORDER OF OPERATIONS
PARENTHESIS
EXPONENTS
MULTIPLICATION
ADDITION
OR
DIVISION
OR
SUBTRACTION
5
Lesson A Notes and Practice
Name: _______________________________
Date: ______________
Order of Operations Notes & Practice
P_____________________________ ( )
Remember
E _____________________________
M/D___________________________
3
x/÷
A/S____________________________ + / -
Multiplication and
Division are solved
from left to right
Addition and
Subtraction are
solved from left to
right
Solve each problem. Show your work for each step.
EX. 10 − 2 x 3
10 – 6
4
1. 22 – 4 x 4
2. 30 – 20 ÷ 5
3. (15 – 6) ÷ 3
4. 35 – 12 ÷ 4 + 10
5. 10 x (8 – 4)
5. 6( 12 - 4 )
7. 15 - 4 x 2 + 5
8. 45 – 3 x 10
6
9. 2×7−2×5
10. 2 + 3 (5 − 4)
11. 6 ÷ 2 + 3 × 5
12. 8 + 12 ÷ 2 x 3
13. 5 × 1 − 4 ÷ 2
14. 11 + 5 × 4 − 4
15. 24 ÷ 6 + 5 x 2
16. 45 ÷ 5 + (4 x 2)
17. 2 x 5 + 5 x 2
Bonus! (7 - 5 + 3 – 2) ÷ 3 + 4 x 8 ÷ 2
7
Name: _______KEY____________________
Date: ______________
Order of Operations Notes & Practice
P______PARENTHESIS____________ ( )
Remember
E ______EXPONENTS_____________
M/D_MULTIPLICATION / DIVISION___
3
x/÷
A/S_ADDITION / SUBTRACTION _____ + / -
Multiplication and
Division are solved
from left to right
Addition and
Subtraction are
solved from left to
right
Solve each problem. Show your work for each step.
a. 10 − 2 x 3
10 – 6
4
1. 22 – 4 x 4
22 – 16
6
2. 30 – 20 ÷ 5
30 - 4
26
3. (15 – 6) ÷ 3
9÷3
3
4. 35 – 12 ÷ 4 + 10
35 – 3 + 10
33 + 10
43
5. 10 x (8 – 4)
10 x 4
40
5. 6( 12 - 4 )
6(8)
48
7. 15 - 4 x 2 + 5
15 – 8 + 5
7+5
12
8. 45 – 3 x 10
45 – 30
15
8
9. 2×7−2×5
14 – 2 x 5
14 – 10
4
10. 2 + 3 (5 − 4)
2 + 3(1)
2+3
5
11. 6 ÷ 2 + 3 × 5
3+3x5
3 + 15
18
12. 8 + 12 ÷ 2 x 3
8+6x3
8 + 18
26
13. 5 × 1 − 4 ÷ 2
5–4÷2
5–2
3
14. 11 + 5 × 4 − 4
11 + 20 – 4
31 – 4
27
15. 24 ÷ 6 + 5 x 2
4+5x2
4 + 10
14
16. 45 ÷ 5 + (4 x 2)
9 + (4 x 2)
9+8
17
17. 2 x 5 + 5 x 2
10 + 5 x 2
10 + 10
20
Bonus! (7 - 5 + 3 – 2) ÷ 3 + 4 x 8 ÷ 2
(2 + 3 – 2) ÷ 3 + 4 x 8 ÷ 2
(5 – 2) ÷ 3 + 4 x 8 ÷ 2
3÷3+4x8÷2
1+4x8÷2
1 + 32 ÷ 2
1 + 16
17
9
Lesson A Independent Practice / Game
Name_______________________________________
Date _________________________
Order of Operations BINGO!
Solve each problem. When you are finished, Bingo will be played!
B
I
N
G
O
16 – 8 ÷ 2 x 4
16 ÷ 4 + 3 (9-7)
3(7-5+1)
5(3) - 3(4)
42 ÷ (5-3)
2 x 3 + 16 ÷ 4
27 ÷ 3 – 5 + 12
10 x 3+ 4 x 5
42 ÷ 7 + 8 - 6
5(8 - 4)
12 x 2 - (6 x 2)
13 - 5
2+2
81 ÷ 9 x 9 - 10
100 – 5 x 4 x 3
16 + 84
11 + 9
3(3) + 3
3(3) - 3
(12 - 3) x 2
6(5) - 3(5)
6(6) + 3 x 2
10 x 4 – 4 x 4
24 - 4(2)
7(4-3)
15 – 2 x 3 + 2
4(2) + 4 x 3
2(3 + 6)
2x3
(3 x 4 x 5) - 4(5)
3(4 + 2)
3x3
15(7 - 4)
2[2 + (10 - 4) ÷ 3]
10[ 3(1 + 4) - 6(2) ]
10
Name____________KEY______________________
Date ____________________________
Order of Operations BINGO!
Solve each problem. When you are finished, Bingo will be played!
B
I
N
G
O
16 – 8 ÷ 2 x 4
16 ÷ 4 + 3 (9 - 7)
3( 13 – 5 + 1)
7(3) - 3(4)
42 ÷ (5-3)
0
10
27
9
21
2 x 5 + 16 ÷ 4
27 ÷ 3 – 5 + 12
10 x 3+ 4 x 5
77 ÷ 7 + 8 – 6
5(8 - 4)
14
16
50
13
20
12 x 2 - (6 x 2)
13 - 5
2+2
81 ÷ 9 x 9 – 10
100 – 6 x 4 x 3
16 + 84
11 + 9
12
2
71
28
5
3(3) + 3
6(2)
(12 - 3) x 2
6(5) - 3(5)
6(6) + 3 x 2
10 x 4 – 4 x 4
1
18
15
42
24
44 - 4(2)
7(4-3)
15 – 2 x 3 + 2
5(2) + 4 x 3
2(3 + 6)
2x3
36
7
11
22
3
(3 x 4 x 5) - 4(5)
5(4 + 2)
3+2
15(7 - 4)
2[2 + (10 - 4) ÷ 3]
10[ 3(1 + 4) - 6(2) ]
40
6
45
8
30
11
Name _____________
Exit Ticket A
1) 5 + 4 ( 3 – 1)
2)
3x3–4x2
3) 15 ÷ 5 x 3 + 2
4)
4 x 3+8
8÷2
Name ____ KEY _____
Exit Ticket A
1) 5 + 4 ( 3 – 1)
2)
3x3–4x2
13
3) 15 ÷ 5 x 3 + 2
11
1
4)
4 x 3+8
8÷2
5
12
Name _____________
Warm Up B
Use < or > to make each statement true.
1)
-6
-8
2)
3
-1
3)
-17
-15
4)
0
-9
5)
-100
2
6)
-19
7)
-3
-2
8)
3
-36
-3
Name ___ KEY _____
Warm Up B
Use < or > to make each statement true.
1)
-6
3)
-17
5)
-100
7)
-3
2)
3
-1 >
4)
0
-9 >
2 <
6)
-19
-2 <
8)
3
-8 >
-15 <
-3 6 >
-3 >
13
Name _________________________
Lesson B Notes and Review
DECIMAL OPERATIONS REVIEW
Complete the following table about decimal rules. Put a check mark in the box to show a rule applies to the given operation.
Adding Decimals
Subtracting
Decimals
Multiplying
Decimals
Dividing
Decimals
Line up the
decimals
Drop down the
decimal into your
answer (Or Float it
up)
Count the number
of decimal places
for your answer
Move the decimal
so you have a
whole number
Practice!
1. 4.5 x 0.56
5. 22.3 x 4.6
2. 125 ÷ 0.5
6. 40.5 ÷ 1.5
3. 4.5 + 15
7. 162.234 + 19.2
4. 156.43 – 42.1
8. 5,124 – 10.75
14
Word Problems - Read each problem carefully. These are REAL LIFE situations – you need to
know how to set up and solve each of these!
1. Morgan purchased $30.46 worth of groceries. She paid the cashier with a $50 bill. How
much change should she receive?
2. Aileen worked 35.5 hours last week. She earns $7.75 per hour. How much money did
she make last week?
3. Reggie has a piece of lumber that is 9 feet long. He needs to cut it into .75 foot sections.
How many pieces will he have after he makes his cuts?
4. Aralynn is making a quilt. She has used 5.5 balls of yarn and will need 8 more. How many
balls of yarn will she have used when she’s finished?
5. Coffee costs $3.59 per pound. How much would 5.7 pounds of coffee cost?
6. Carl ran the 100 meter dash in 15.454 seconds. Jeremy ran it in 16.05 seconds. How
much faster did Carl run than Jeremy?
15
Name ________KEY_____________
DECIMAL OPERATIONS REVIEW
Complete the following table about decimal rules. Put a check mark in the box to show a rule applies to the given operation.
Adding Decimals
Subtracting
Decimals
Multiplying
Decimals
Line up the
decimals
Drop down the
decimal into your
answer (Or Float it
up)
Count the number
of decimal places
for your answer
Move the decimal
so you have a
whole number
Dividing
Decimals
You can’t have a decimal
divisor
Practice!
1. 4.5 x 0.56 = 2.52
5. 22.3 x 4.6 = 102.58
2. 125 ÷ 0.5 = 250
6. 40.5 ÷ 1.5 = 27
3. 4.5 + 15 = 19.5
7. 162.234 + 19.2 = 181.434
4. 156.43 – 42.1 = 114.33
8. 5,124 – 10.75 = 5113.25
16
Word Problems - Read each problem carefully. These are REAL LIFE situations – you need to
know how to set up and solve each of these!
1. Morgan purchased $30.46 worth of groceries. She paid the cashier with a $50 bill. How
much change should she receive?
$19.54
2. Aileen worked 35.5 hours last week. She earns $7.75 per hour. How much money did
she make last week?
$275.13
3. Reggie has a piece of lumber that is 9 feet long. He needs to cut it into .75 foot sections.
How many pieces will he have after he makes his cuts?
12 pieces
4. Aralynn is making a quilt. She has used 5.5 balls of yarn and will need 8 more. How many
balls of yarn will she have used when she’s finished?
13.5 balls of yarn
5. Coffee costs $3.59 per pound. How much would 5.7 pounds of coffee cost?
$20.46
6. Carl ran the 100 meter dash in 15.454 seconds. Jeremy ran it in 16.05 seconds. How
much faster did Carl run than Jeremy?
.596 seconds
17
Lesson B Activity – Puzzle. Pre Cut!
4.05
6.72
3−1
3.1 x 8.3 – 4.7
21.03
3.5 + 2 x 3.8
11.1
0.8
13.3 ÷ 2.1 - 6
3.03
8+6.2+4
3 + 4.1 (9 – 3.5)
15.6
1.27
6[5.2 (4.1 – 3.6)]
13.15
15.2 – 4.1 ÷ 2
2.08
32 + 6 + 1.3
13 – (4.2 x 2.6)
8−2
25.55
0.86
3.1−2.3 𝑥 0.6
4÷2
14.096
6.1−4.3
6−4
14 ÷ 2.2 + 6
13.
1
14 –
6 + 3.5 (2 + 4.1 ÷ 2)
20.175
18 + (14 – 12)
3.5 + 2 – 1.2
4 + 8 (2.3 x 3.6)
70.24
1.56
3.9 ÷ 3 x 1.2
4.2736
5.2 – 1.1 + 3.3
7.4
7.48
2.2 (4 – 3 x 0.2)
4.1 + 6 ÷ 2
3.2−1.6
18.5
9.7 + 7.6 – 3 + 4.2
5.005
( 4 – 3.5) 6 + 4
(5.5 x 8.7 – 2.8) ÷ 9
3.23
18 – 3 + 2 x 4
18
Name _____________
Exit Ticket B
1)
2.5 + 4 ( 5.5 – 0.5)
2) 3.2 x 3 – 4.1 x 2
3)
15.5 ÷ 5 x 0.3 + 2.5
4)
2.4 x 0.5 + 0.8
8.8 ÷ 4.4
Name ___ KEY ____
Exit Ticket B
1)
2.5 + 4 ( 5.5 – 0.5)
2) 3.2 x 3 – 4.1 x 2
22.5
3)
15.5 ÷ 5 x 0.3 + 2.5
3.43
1.4
4)
2.4 x 0.5 + 0.8
8.8 ÷ 4.4
1
19
Name _____________
Warm Up C
1) Order the following numbers from
least to greatest.
2) Order the following numbers from
least to greatest.
1 2 3 1
0.43, 0.5, 0.57, 0.202
, , ,
5 3 8 4
3) Order the following numbers from
greatest to least.
4) Order the following numbers from
least to greatest.
1 1 3 3
, , ,
3
3
5
10
0.5, , 0.35,
2 8 5 4
Name ___ KEY _____
Warm Up C
1) Order the following numbers from
least to greatest.
0.43, 0.5, 0.57, 0.202
0.202, 0.43, 0.5, 0.57
2) Order the following numbers from
least to greatest.
1 2 3 1
, , ,
5 3 8 4
1 1 3 2
, , ,
4) Order the following numbers from
least to greatest.
5 4 8 3
3) Order the following numbers from
greatest to least.
1 1 3 3
, , ,
2 8 5 4
3 3 1 1
3
4 5 2 8
10
, , ,
3
3
5
10
0.5, , 0.35,
, 0.35, 0.5,
3
5
20
Lesson C Notes
Name _____________________________________________
Date_______________________
Expanded Form Notes
There are TWO different ways to write numbers in expanded form. One way is to use place value, and the other
is to use fractions. You need to be familiar with both ways.
Place Value
Guided Practice
Write 31.024 in expanded form.
Step 1: Identify the place value of each number.

The 3 is in the _______________ place.

The 2 is in the _______________ place.

The 1 is in the _______________ place.

The 4 is in the _______________ place.

Skip any zeros.
Step 2: Multiply each number by the decimal for its place value.
(3 x 10) + (1 x 1) + (2 x 0.01) + (4 x 0.001)
Independent Practice
Write 5.106 in expanded form.
Step 1: Identify the place value of each number.

The 5 is in the ________________ place.

Skip any zeros.

The 1 is in the _________________ place.

The 6 is in the ________________ place.
Step 2: Multiply each number by the decimal for its place value.
Write 152.026 in expanded form.
Write 25.0603 in expanded form.
21
Place Value Using Fractions
Guided Practice
Write 31.024 in expanded form.
Step 1: Identify the place value of each number.

The 3 is in the _______________ place.

The 2 is in the _______________ place.

The 1 is in the _______________ place.

The 4 is in the _______________ place.

Skip any zeros.
Step 2: Multiply each number by the fraction for its place value.
(3 x 10) + (1 x 1) + (2 x
𝟏
𝟏𝟎𝟎
) + (4 x
𝟏
𝟏𝟎𝟎𝟎
)
Independent Practice
Write 5.106 in expanded form.
Step 1: Identify the place value of each number.

The 5 is in the ________________ place.

Skip any zeros.

The 1 is in the _________________ place.

The 6 is in the ________________ place.
Step 2: Multiply each number by the fraction for its place value.
Write 152.026 in expanded form.
Write 25.0603 in expanded form.
Bring it all together. Write each of the following numbers in expanded form using place value and fractions.
Write 0.075 in expanded form.
Write 120.005 in expanded form.
22
Name ___________KEY_____________________________
Date_______________________
Expanded Form Notes
There are TWO different ways to write numbers in expanded form. One way is to use place value, and the other
is to use fractions. You need to be familiar with both ways.
Place Value
Guided Practice
Write 31.024 in expanded form.
Step 1: Identify the place value of each number.

The 3 is in the ___TENS______ place.

The 2 is in the __HUNDREDTHS___ place.

The 1 is in the ___ONES_______ place.

The 4 is in the _THOUSANDTHS___ place.

Skip any zeros.
Step 2: Multiply each number by the decimal for its place value.
(3 x 10) + (1 x 1) + (2 x 0.01) + (4 x 0.001)
Independent Practice
Write 5.106 in expanded form.
Step 1: Identify the place value of each number.

The 5 is in the ___ONES______ place.

Skip any zeros.

The 1 is in the ____TENTHS_______ place.

The 6 is in the _THOUSANDTHS__ place.
Step 2: Multiply each number by the decimal for its place value.
( 5 X 1) + ( 1 X 0.1) + ( 6 X .001)
Write 152.026 in expanded form.
(1 X 100) + (5 X 10) + (2 X 1) + (2 X .01) + (6 X .001)
Write 25.0603 in expanded form.
(2 X 10) + (5 X 1) + (6 X .01) + (3 X .0001)
23
Place Value Using Fractions
Guided Practice
Write 31.024 in expanded form.
Step 1: Identify the place value of each number.

The 3 is in the ___TENS______ place.

The 2 is in the __HUNDREDTHS___ place.

The 1 is in the ___ONES_______ place.

The 4 is in the _THOUSANDTHS___ place.

Skip any zeros.
Step 2: Multiply each number by the fraction for its place value.
(3 x 10) + (1 x 1) + (2 x
𝟏
𝟏𝟎𝟎
) + (4 x
𝟏
𝟏𝟎𝟎𝟎
)
Independent Practice
Write 5.106 in expanded form.
Step 1: Identify the place value of each number.

The 5 is in the ___ONES______ place.

Skip any zeros.

The 1 is in the ____TENTHS_______ place.

The 6 is in the _THOUSANDTHS__ place.
Step 2: Multiply each number by the fraction for its place value.
1
1
( 5 X 1) + ( 1 X 10 ) + ( 6 X 1000 )
Write 152.026 in expanded form.
Write 25.0603 in expanded form.
1
1
(1 X 100) + (5 X 10) + (2 X 1) + (2 X 100 ) + (6 X 1000 )
1
1
(2 X 10) + (5 X 1) + (6 X 100 ) + (3 X . 10000 )
Bring it all together. Write each of the following numbers in expanded form using place value and fractions.
Write 0.075 in expanded form.
( 7 X .01) + ( 5 X .001)
1
1
(7 X 100 ) + ( 5 X 1000 )
Write 120.005 in expanded form.
(1 X 100) + (2 X 10) + ( 5 X .001)
1
(1 X 100) + ( 2 X 10) + ( 5 X 1000 )
24
Lesson C Independent Practice
Name __________________________________
Date ________________
Form Is Important
Write the given decimal in standard form, and expanded form using decimals.
Written Form
Standard Form
Expanded Form using Decimals
EX: Three and fifteen hundredths
3.15
(3 x 1) + (1 x 0.1) + (5 x .01)
Four and ninety three thousandths
Eighty six hundredths
One hundred twenty and four tenths
Six and one thousandth
One thousand four and sixteen hundredths
Ninety and five tenths
Complete the table by writing each decimal in the missing form.
Written Form
Standard Form
Expanded Form using Decimals
142.06
(4 x 1,000) + (2 x 10) + (6 x 0.001)
3.07
1,006.08
(9 x 1) + (4 x .01) + (5 x .001)
700.007
(5 x 10,000) + (3 x 100) + (4 x .1)
25
Name __________KEY____________________
Date _________________
Form Is Important
Write the given decimal in standard form, and expanded form using decimals.
Written Form
Standard Form
Expanded Form using Decimals
EX: Three and fifteen hundredths
3.15
(3 x 1) + (1 x 0.1) + (5 x .01)
Four and ninety three thousandths
4.093
(4 x 1) + (9 x .01) + (3 x .001)
Eighty six hundredths
0.86
(8 x .1) + (6 x .01)
One hundred twenty and four tenths
124.4
(1 x 100) + ( 2 x 10) + (4 x 1) + (4 x .1)
Six and one thousandth
6.001
(6 x 1) + (1 x .001)
One thousand four and sixteen hundredths
1,004.16
(1 x 1,000) + (4 x 1) + (1 x .1) + (6 x .01)
Ninety and five tenths
9.5
(9 x 1) + (5 x .1)
Complete the table by writing each decimal in the missing form.
Written Form
Standard Form
Expanded Form using Decimals
One hundred forty two and six hundredths
142.06
(1 x 100) + (4 x 10) + (2 x 1) + (6 x .01)
Four thousand twenty and six thousandths
4,020.006
(4 x 1,000) + (2 x 10) + (6 x 0.001)
Three and seven hundredths
3.07
(3 x 1) + (7 x .01)
One thousand six and eight hundredths
1,006.08
(1 x 1,000) + (6 x 1) + (8 x .01)
Nine and forty five thousandths
9.045
(9 x 1) + (4 x .01) + (5 x .001)
Seven hundred and seven thousandths
700.007
(7 x 100) + (7 x .001)
Fifty thousand, three hundred and four
tenths
50,300.4
(5 x 10,000) + (3 x 100) + (4 x .1)
26
Name _____________
Exit Ticket C
1) Write in expanded form using place value.
2) Write in expanded form using fractions.
2,002.004
5.276
3) Write in expanded form using place value.
4) Write in expanded form using fractions.
23.23
505.050
Name ____KEY_____
Exit Ticket C
1) Write in expanded form using place value.
2) Write in expanded form using fractions.
2,002.004
(2 x 1,000) + (2 x 1) + (4 x .001)
3) Write in expanded form using place value.
505.050
(5 x 100) + (5 x 1) + (5 x .01)
5.276
(5 x 1) + (2 x
1
10
) + (7 x
1
100
) + (6 x
1
1,000
)
4) Write in expanded form using fractions.
23.23
(2 x 10) + (3 x 1) + (2 x
1
10
) + (3 x
1
100
)
27
Name _____________
Warm Up D
1) Simply. Write your answer as an exponent.
75
2) Simply. Write your answer as an exponent.
43 • 43
73
3) Simply. Write your answer as an exponent.
84
4) Simply. Write your answer as an exponent.
82 • 85
81
Name ___ KEY ______
Warm Up D
1) Simply. Write your answer as an exponent.
75
73
72
3) Simply. Write your answer as an exponent.
84
81
83
2) Simply. Write your answer as an exponent.
43 • 43
46
4) Simply. Write your answer as an exponent.
82 • 85
87
28
Lesson D Review
Name ___________________________
Date ___________
Exponents Practice
Fill in the missing parts of the table.
Words
Expanded Form
Standard Form
Three cubed
3•3•3
27
4•4•4•4
Six to the 2nd power
Four squared
Seven to the 4th power
2•2•2•2•2•2
Three to the 4th power
Three squared plus 2
cubed
3•3+2•2•2
5•5•5+4•4
Two squared plus ten
squared
2•2+6•6•6•6
29
Name _________KEY__________
Date ___________
Exponents Practice
Fill in the missing parts of the table.
Words
Expanded Form
Standard Form
Three cubed
3•3•3
27
Four to the 4th power
4•4•4•4
256
Six to the 2nd power
6•6
36
Four squared
4•4
16
Seven to the 4th power
7•7•7•7
2,401
Two to the 6th power
2•2•2•2•2•2
64
Three to the 4th power
3•3•3•3
81
Three squared plus 2
cubed
3•3+2•2•2
17
Five cubed plus four
squared
5•5•5+4•4
141
Two squared plus ten
squared
2 • 2 + 10 • 10
104
Two squared plus six to
the fourth power
2•2+6•6•6•6
1,300
30
Lesson D Notes
Name _____________________________________________
Date_______________________
Rules of Exponents Notes
Rule
Definition
Example
What is an
Exponent?
An exponent tells us how many times we
multiply a number by itself. We never
multiply the base by the exponent!
8³ = 8 x 8 x 8
Product Rule
When multiplying two powers that have
the same base, you can add the exponents.
5³ x 5² = 53 + 2 = 55
Quotient Rule
We can divide two powers with the same
base by subtracting the exponents.
Zero Rule
Any nonzero number raised to the power of
zero equals 1.
(not 8 x 3)
97
95
= 97−5 = 92
𝑥0 = 1
Product Rule Let’s try some! Write each answer as an exponent.
1. 3³ x 3¹
3. 45 x 45
2. 74 x 75
4. 𝑥 𝑚 • 𝑥 𝑛
31
Quotient Rule Let’s try some! Write each answer as an exponent.
1.
2.
36
3.
32
24
4.
21
BCR Practice
87
84
10 9
10 5
912
96
Part A:
Reduce the given fraction. Write you answer as an exponent.
Part B:
Use what you know about the laws of exponents to explain why your answer is
correct. Use words, numbers and/or symbols in your explanation.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
32
Name __________KEY_______________________________
Date_______________________
Rules of Exponents Notes
Rule
Definition
Example
What is an
Exponent?
An exponent tells us how many times we
multiply a number by itself. We never
multiply the base by the exponent!
8³ = 8 x 8 x 8
Product Rule
When multiplying two powers that have
the same base, you can add the exponents.
5³ x 5² = 53 + 2 = 55
Quotient Rule
We can divide two powers with the same
base by subtracting the exponents.
Zero Rule
Any nonzero number raised to the power of
zero equals 1.
(not 8 x 3)
97
95
= 97−5 = 92
𝑥0 = 1
Product Rule Let’s try some! Write each answer as an exponent.
1. 3³ x 3¹
2. 74 x 75
34
79
3. 45 x 45
4. 𝑥 𝑚 • 𝑥 𝑛
410
𝑥 𝑚 +𝑛
33
Quotient Rule Let’s try some! Write each answer as an exponent.
1.
2.
36
32
24
21
=
=2
BCR Practice
34
3.
3
4.
87
84
= 83
10 9
10 5
= 104
912
96
Part A:
Reduce the given fraction. Write you answer as an exponent. 96
Part B:
Use what you know about the laws of exponents to explain why your answer is
correct. Use words, numbers and/or symbols in your explanation.
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
___________________________________________________________________
34
Lesson D Independent Practice
Name ___________________________________________
Date _____________________________
Exponents & Square Roots VersaTiles© Activity
Solve each problem by following the given directions. Find your answer in the box below. Using the VersaTiles,
place the problem number over the letter that corresponds to your answer below. WRITE YOUR ANSWER ON
THIS SHEET AS WELL!
Simplify. Write your answer using exponents.
98
?
6
12
?
1.
94
=9
2.
5 •5
=5
3.
5
?
10
4 •4 =4
4.
75
= 7?
75
Write in standard form.
5.
53
6.
42
7.
33
8.
26
Simplify.
9.
225
81
10.
64
11.
12.
144
Answer Box
A
B
8
G
C
125
H
5
D
4
I
15
E
1
J
9
F
12
K
27
64
L
18
16
35
Name ____________
KEY_______________________
Date _____________________________
Exponents & Square Roots VersaTiles© Activity
Solve each problem by following the given directions. Find your answer in the box below. Using the VersaTiles,
place the problem number over the letter that corresponds to your answer below. WRITE YOUR ANSWER ON
THIS SHEET AS WELL!
Simplify. Write your answer using exponents.
98
?
6
12
?
1.
94
=9
2.
5 •5
4
=5
18
3.
5
?
10
4 •4 =4
5
4.
75
75
= 7?
0
Write in expanded form.
5.
53
6.
125
42
7.
16
33
8.
26
27
64
Simplify.
225
9.
15
81
10.
9
64
11.
8
12.
144
12
Answer Box
36
Name _____________
Exit Ticket D
1) Solve.
3
4
3) Simplify using exponents.
512
54
2) Write using exponents.
6•6•6•6
4) Simplify using exponents.
73 • 75
Name ____KEY_____
Exit Ticket D
1) Solve.
34
81
3) Simplify using exponents.
512
54
58
2) Write using exponents.
6•6•6•6
64
4) Simplify using exponents.
73 • 75
78
37
Name _____________
Warm Up E
5) Write in expanded form using place value.
6) Write in expanded form using fractions.
154.004
7) Solve.
203.704
8) Write using exponents.
5•5•5•5•5
4
4
Name ___ KEY ____
Warm Up E
1) Write in expanded form using place value.
154.004
2) Write in expanded form using fractions.
203.704
1
(1 x 100) + (5 x 10) + (4 x 1) + (4 x .001)
(2 x 100) + (3 x 1) + (7 x
3) Solve.
4) Write using exponents.
5•5•5•5•5
4
4
256
10
) + (4 x
1
1,000
)
55
38
Lesson E Worksheet
Name ____________________________________
Date ____________________________________
Expanded Form with Decimals and Fractions
Use the digits in the given number to fill in the place value chart.
Then write each number in expanded form using decimals and expanded form using fractions.
Example:
305.047
hundreds
Tens
Ones
•
Tenths
100
10
1
.1 /
3
0
5
0
Hundredths
𝟏
𝟏𝟎
.01 /
Thousandths
𝟏
.001 /
𝟏𝟎𝟎
4
𝟏
𝟏,𝟎𝟎𝟎
7
(3x100) + (5 x 1) + (4 x .01) + (7 x .001)
(3x100) + (5 x 1) + (4 x
1
100
) + (7 x
1
1,000
)
Your Turn!
48.65
hundreds
Tens
Ones
100
10
1
•
Tenths
.1 /
𝟏
𝟏𝟎
Hundredths
.01 /
𝟏
𝟏𝟎𝟎
Thousandths
.001 /
𝟏
𝟏,𝟎𝟎𝟎
75.08
hundreds
Tens
Ones
100
10
1
•
Tenths
.1 /
𝟏
𝟏𝟎
Hundredths
.01 /
𝟏
𝟏𝟎𝟎
Thousandths
.001 /
𝟏
𝟏,𝟎𝟎𝟎
39
Each number is given in expanded notation. Break it down by using the given table.
Then write each number in standard form.
Example:
(5 x 10) + (4 x
hundreds
Tens
Ones
100
10
1
𝟏
𝟏𝟎
•
) + (6 x
Tenths
.1 /
5
𝟏
𝟏,𝟎𝟎𝟎
)
Hundredths
𝟏
.01 /
𝟏𝟎
𝟏
𝟏𝟎𝟎
4
Thousandths
.001 /
𝟏
𝟏,𝟎𝟎𝟎
6
Fill in the empty spaces with zeros.
50.406
Your Turn!
(9 x 100) + (6 x
hundreds
Tens
Ones
100
10
1
(8 x
𝟏
𝟏𝟎
Tens
Ones
100
10
1
) + (8 x
𝟏𝟎𝟎
•
Tenths
.1 /
) + (4 x
hundreds
𝟏
•
𝟏
𝟏𝟎
𝟏
𝟏𝟎
) + (5 x
Tenths
.1 /
𝟏
𝟏𝟎
𝟏
𝟏,𝟎𝟎𝟎
)
Hundredths
𝟏
.01 /
𝟏
𝟏,𝟎𝟎𝟎
𝟏𝟎𝟎
.001 /
𝟏
𝟏,𝟎𝟎𝟎
)
Hundredths
.01 /
Thousandths
𝟏
𝟏𝟎𝟎
Thousandths
.001 /
𝟏
𝟏,𝟎𝟎𝟎
40
Independent Practice
Write each number in expanded form using decimals.
1. 625.03
____________________________________________________
2. 100.005
____________________________________________________
3. 45.76
____________________________________________________
4. 190.405
____________________________________________________
Write each number in expanded form using fractions.
5. 14.7
____________________________________________________
6. 1,000.506
____________________________________________________
7. 55.98
____________________________________________________
8. 210.006
____________________________________________________
Write each number in standard form.
9. (5 x 10) + (9 x
10. (7 x
1
10
) + (1 x
1
10
) + (6 x
1
100
) + (3 x
1
1,000
)
______________________________
)
______________________________
1
1,000
11. (9 x 1,000) + (5 x 100) + (6 x
12. (2 x 100) + (9 x 10) + (3 x
1
10
1
100
)
) + (4 x
______________________________
1
100
)
______________________________
41
Name __________KEY_______________
Date ____________________________________
Expanded Form with Decimals and Fractions
Use the digits in the given number to fill in the place value chart.
Then write each number in expanded form using decimals and expanded form using fractions.
Example:
305.047
hundreds
Tens
Ones
•
Tenths
100
10
1
.1 /
3
0
5
0
𝟏
𝟏𝟎
Hundredths
𝟏
.01 /
𝟏𝟎𝟎
4
Thousandths
.001 /
𝟏
𝟏,𝟎𝟎𝟎
7
(3x100) + (5 x 1) + (4 x .01) + (7 x .001)
(3x100) + (5 x 1) + (4 x
1
100
) + (7 x
1
1,000
)
Your Turn!
48.65
hundreds
Tens
Ones
•
Tenths
100
10
1
.1 /
4
8
6
𝟏
𝟏𝟎
Hundredths
.01 /
𝟏
𝟏𝟎𝟎
Thousandths
.001 /
𝟏
𝟏,𝟎𝟎𝟎
5
( 4 x 10 ) + ( 8 x 1 ) + ( 6 x 𝟎. 𝟏 ) + ( 5 x 𝟎. 𝟎𝟏)
𝟏
𝟏
( 4 x 10 ) + ( 8 x 1 ) + ( 6 x 𝟏𝟎 ) + ( 5 x 𝟏𝟎𝟎)
75.08
hundreds
Tens
Ones
100
10
1
7
5
•
Tenths
.1 /
𝟏
𝟏𝟎
Hundredths
.01 /
𝟏
𝟏𝟎𝟎
Thousandths
.001 /
𝟏
𝟏,𝟎𝟎𝟎
8
( 7 x 10 ) + ( 5 x 1 ) + ( 8 x 𝟎. 𝟎𝟏)
𝟏
( 7 x 10 ) + ( 5 x 1 ) + ( 8 x
)
𝟏𝟎𝟎
42
Each number is given in expanded notation. Break it down by using the given table.
Then write each number in standard form.
Example:
(5 x 10) + (4 x
hundreds
Tens
Ones
100
10
1
𝟏
𝟏𝟎
•
) + (6 x
Tenths
.1 /
5
𝟏
𝟏,𝟎𝟎𝟎
)
Hundredths
𝟏
.01 /
𝟏𝟎
𝟏
𝟏𝟎𝟎
4
Thousandths
.001 /
𝟏
𝟏,𝟎𝟎𝟎
6
Fill in the empty spaces with zeros.
50.406
Your Turn!
(9 x 100) + (6 x
hundreds
Tens
Ones
100
10
1
𝟏
) + (8 x
𝟏𝟎𝟎
•
Tenths
.1 /
𝟏
𝟏𝟎
𝟏
𝟏,𝟎𝟎𝟎
)
Hundredths
𝟏
.01 /
9
𝟏𝟎𝟎
6
Thousandths
.001 /
𝟏
𝟏,𝟎𝟎𝟎
8
900.068
(8 x
𝟏
𝟏𝟎
) + (4 x
hundreds
Tens
Ones
100
10
1
8
•
𝟏
𝟏𝟎
) + (5 x
Tenths
.1 /
4
𝟏
𝟏𝟎
𝟏
𝟏,𝟎𝟎𝟎
)
Hundredths
.01 /
𝟏
𝟏𝟎𝟎
Thousandths
.001 /
𝟏
𝟏,𝟎𝟎𝟎
5
80.405
43
Independent Practice
Write each number in expanded form using decimals.
1. 625.03
( 6 x 100) + ( 2 x 10) + ( 5 x 1 ) + ( 3 x .01)
2. 100.005
( 1 x 100) + ( 5 x .001)
3. 45.76
( 4 x 10) + ( 5 x 1) + ( 7 x .1 ) + ( 6 x .01)
4. 190.405
( 1 x 100) + ( 9 x 10) + ( 4 x .1 ) + ( 5 x .001)
Write each number in expanded form using fractions.
𝟏
5. 14.7
( 1 x 10 ) + ( 4 x 1 ) + ( 7 x
6. 1,000.506
( 1 x 1,000 ) + ( 5 x
7. 55.98
( 5 x 10 ) + ( 5 x 1 ) + ( 9 x
8. 210.006
( 2 x 100 ) + ( 1 x 10 ) + ( 6 x
𝟏
𝟏𝟎
𝟏𝟎
)
)+(6x
𝟏
𝟏𝟎
𝟏
𝟏,𝟎𝟎𝟎
)
)+(8x
𝟏
𝟏,𝟎𝟎𝟎
𝟏
𝟏𝟎𝟎
)
)
Write each number in standard form.
9. (5 x 10) + (9 x
10. (7 x
1
10
) + (1 x
1
10
) + (6 x
1
100
) + (3 x
1
1,000
)
50.906
)
0.713
1
1,000
11. (9 x 1,000) + (5 x 100) + (6 x
12. (2 x 100) + (9 x 10) + (3 x
1
10
1
100
)
) + (4 x
9,500.06
1
100
)
290.34
44
Lesson E Worksheet
Rules of Exponents Memory
Pre -cut the cards. To ensure students cannot see through the back, print on cardstock or darker paper.
𝟖𝟔
𝟖𝟐
𝟖𝟏𝟔
𝟖𝟒
𝟖
𝟖𝟏𝟐
𝟖𝟐 • 𝟖𝟏
𝟖𝟑
𝟖𝟑 • 𝟖𝟎 • 𝟖𝟒
𝟖𝟕
𝟖𝟓
𝟖𝟓
1
𝟖𝟗
𝟖𝟑
𝟖𝟔
𝟖𝟐 • 𝟖𝟐 • 𝟖𝟒
𝟖𝟖
𝟖𝟏 • 𝟖 𝟏
𝟖𝟐
𝟖𝟏𝟎
𝟖𝟓
𝟖𝟓
𝟖𝟏𝟐
𝟖𝟐
𝟖
𝟒
𝟏𝟎
45
Name _____________
Exit Ticket E
1) Write in expanded form using place value.
2) Write in expanded form using fractions.
200.06
7.007
3) Simplify using exponents.
615
65
4) Simplify using exponents.
31 • 32 • 33 • 34
Name ___ KEY ____
Exit Ticket E
1) Write in expanded form using place value.
200.06
(2 x 100) + (6 x .001)
3) Simplify using exponents.
615
65
610
2) Write in expanded form using fractions.
7.007
(7 x 1) + (7 x
1
1,000
)
4) Simplify using exponents.
31 • 32 • 33 • 34
310
46
Name _____________
Warm Up F
1) Put the following numbers in order from least to greatest.
1
3
1
, , 0.04, 3%
4
__________________________________
Use what you know about rational numbers to explain how you found your answer. Use words,
numbers, and/or symbols in your explanation.
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_________________________________________________________________________
_____________________________________________________
Name ___ KEY ___
Warm Up F
1) Put the following numbers in order from least to greatest.
1
3
1
, , 0.04, 3%
4
1
1
4
3
3% , 0.04 , ,
Use what you know about rational numbers to explain how you found your answer. Use words,
numbers, and/or symbols in your explanation.
Students should demonstrate their ability to convert the four numbers to all be in the same
form, and then compare them. They can show their work in this section to get credit if they
wish and if all work is shown.
47
Lesson F Guided & Group Practice
Name __________________________________
Date _____________
Fractions, Decimals and Percents
Use the chart below to help you convert among fractions, decimals and percents. You will need
this to change and compare these three forms of numbers!
48
Use the chart to help you complete the following problems.
2
2
1. The annual amount of rainfall in a given city is 35 inches. Convert 35 to a
5
5
decimal.
2. Put the following numbers in order from least to greatest.
1
, 0.202 , 30%
4
3. You scored an 80% on your math test. Express this number as a fraction and
as a decimal.
4. A new car loan comes with a 3.49% interest rate. Express this number as a
decimal.
5. Which number has the greatest value?
3
, 0.35 , 35% ,
5
5
15
49
Directions: Cut up the cards before giving them to students. The students (working individually or with
partners) will pick 5 cards from the pile. They must use a white board or sheet of paper to order the numbers
from least to greatest. If they are working with a partner, they must both agree on the answer before they can
pick 5 more cards.
1
2
3
4
3
5
1
5
7
8
3
8
2
5
1
4
1
3
2
3
1
8
5
8
0.2
0.55
0.85
0.18
0.5
0.33
0.45
0.13
50
0.9
0.16
0.12
0.75
50%
95%
15%
4.5%
72%
41%
5%
7.5%
55%
10%
0.67
0.8
0.26
3
10
7
10
1
10
51
Lesson F Independent Practice
52
53
Lesson F Exit Ticket
Name ______________________________
Exit Ticket F
SHOW YOUR WORK!
1. In Megan’s Science class there are 35
students. Fourteen are girls. What is
the ratio of girls to boys?
2. The ratio of number of cats to dogs in
the pound was 12:36. How is this ratio
represented as a fraction in simplest
form?
3. On a day it snowed, three-tenths of
the students wore snow boots. Write a
ratio to represent the number of
students who did wear boots
compared to the number of students
who did not.
4. Which of the following does not
represent 75%?
A.
1
75
B. 0.75
5. Carleigh took a survey of the students
in her art class to see what their
15
favorite color was. 25 students chose
150
C. 200
D.
6. Rewrite 0.15 as a fraction in simplest
form.
15
blue. What is 25 written as a percent?
54
Name _________KEY_______________
Exit Ticket F
SHOW YOUR WORK!
1. In Megan’s Science class there are 35
students. Fourteen are girls. What is
the ratio of girls to boys?
2. The ratio of number of cats to dogs in
the pound was 12:36. How is this ratio
represented as a fraction in simplest
form?
14 : 21
Reduced to
2:3
3. On a day it snowed, three-tenths of
the students wore snow boots. Write a
ratio to represent the number of
students who did wear boots
compared to the number of students
who did not.
1
3
4. Which of the following does not
represent 75%?
1
𝐴. 75
150
C. 200
B. 0.75
D.
3:7
5. Carleigh took a survey of the students
in her art class to see what their
15
favorite color was. 25 students chose
6. Rewrite 0.15 as a fraction in simplest
form.
15
blue. What is 25 written as a percent?
3
20
60%
55
Name _____________
Warm Up G
1) Re-write as a decimal and a percent.
3
5
2) Re-write as a fraction and a percent.
3) Re-write as a decimal and a fraction.
5%
4) Re-write as a fraction in simplest form.
0.03
125
200
Name ___ KEY ______
Warm Up G
1) Re-write as a decimal and a percent.
3
5
0.6 60%
3) Re-write as a decimal and a fraction.
5%
0.05
5
100
2) Re-write as a fraction and a percent.
0.03
3
3%
100
4) Re-write as a fraction in simplest form.
125
200
5
8
56
Lesson G Notes and Practice
Name _________________________________________
Date _______________________
Percent of a Number Guided Practice
To determine the percent of a number you need to remember two key points:
1) The word “of” means Multiply!
2) Percents must be changed to decimals before you can multiply with them.
Example:
What is 70% of 150?
Step 1: Change the percent to a decimal by moving the decimal two places to the left. Remember, the
decimal in a whole number is at the end – just like a period is at the end of a sentence.
70% = 0.70
Step 2: Multiply the percent (which is now a decimal) by the given number.
0.70 x 150
105
Try these:
What is 40% of 120?
Step 1: Change the percent to a decimal by moving the decimal two places to the left. Remember, the
decimal in a whole number is at the end – just like a period is at the end of a sentence.
40% = _________
Step 2: Multiply the percent (which is now a decimal) by the given number.
_______ x _______
_______
What is 60% of 70?
Step 1: Change the percent to a decimal by moving the decimal two places to the left. Remember, the
decimal in a whole number is at the end – just like a period is at the end of a sentence.
60% = _________
Step 2: Multiply the percent (which is now a decimal) by the given number.
_______ x _______
_______
57
On Your Own:
1) What is 30% of 250?
_________________________ = ___________________
Show your work here!
2) What is 40% of 55?
_________________________ = ___________________
Show your work here!
3) What is 10% of 780?
_________________________ = ___________________
Show your work here!
4) What is 20% of 1,300? _________________________ = ___________________
Show your work here!
5) What is 90% of 800?
_________________________ = ___________________
Show your work here!
6) The Smith family went out to dinner and received great service. They decided to leave a
20% tip for their waitress. If their dinner bill totaled $90, how much was the tip?
Think: You need to find what percent of what number?
Show your work!
7) Carlos just took a 40 question math test. He scored a 75%. How many questions did he
get correct on his test?
Show your work!
8) Marge ordered $320 worth of photographs from a website. She has to pay a 10% shipping
and handling fee. How much will the fee cost her?
Show your work!
9) April made $440 in tips last night waitressing. She had to give 20% of her tips to the boys
who clean the tables. How much money did she have to give them?
Show your work!
10)
You purchase a $1,500 television. You have to pay 6% sales tax. How much will
the tax be on your new television?
Show your work!
58
Name _________KEY___________________________
Date _______________________
Percent of a Number Guided Practice
To determine the percent of a number you need to remember two key points:
3) The word “of” means Multiply!
4) Percents must be changed to decimals before you can multiply with them.
Example:
What is 70% of 150?
Step 1: Change the percent to a decimal by moving the decimal two places to the left. Remember, the
decimal in a whole number is at the end – just like a period is at the end of a sentence.
70% = 0.70
Step 2: Multiply the percent (which is now a decimal) by the given number.
0.70 x 150
105
Try these:
What is 40% of 120?
Step 1: Change the percent to a decimal by moving the decimal two places to the left. Remember, the
decimal in a whole number is at the end – just like a period is at the end of a sentence.
40% = 0.40
Step 2: Multiply the percent (which is now a decimal) by the given number.
0.40 x 120
48
What is 60% of 70?
Step 1: Change the percent to a decimal by moving the decimal two places to the left. Remember, the
decimal in a whole number is at the end – just like a period is at the end of a sentence.
60% = 0.60
Step 2: Multiply the percent (which is now a decimal) by the given number.
0.60 x 70
42
59
On Your Own:
1) What is 30% of 250?
______0.30 x 250_______ = _____75_______
Show your work here!
2) What is 40% of 55?
______0.40 x 55_______ = _____22_______
Show your work here!
3) What is 10% of 780?
______0.10 x 780_______ = _____78_______
Show your work here!
4) What is 20% of 1,300? ______0.20 x 1,300_______ = _____260_______
Show your work here!
5) What is 90% of 800?
______0.90 x 800_______ = _____720_______
Show your work here!
6) The Smith family went out to dinner and received great service. They decided to leave a 20% tip
for their waitress. If their dinner bill totaled $90, how much was the tip?
Think: You need to
find what percent of what number?
Show your work!
0.20 x 90
$18 tip
7) Carlos just took a 40 question math test. He scored a 75%. How many questions did he get
correct on his test?
Show your work!
0.75 x 40
30 questions correct
8) Marge ordered $320 worth of photographs from a website. She has to pay a 10% shipping and
handling fee. How much will the fee cost her?
Show your work!
0.10 x 320
$32 fee
9) April made $440 in tips last night waitressing. She had to give 20% of her tips to the boys who
clean the tables. How much money did she have to give them?
Show your work!
0.20 x 440
$88
10) You purchase a $1,500 television. You have to pay 6% sales tax. How much will the tax be on
your new television?
Show your work!
0.06 x 1,500
$90 sales tax
60
Lesson G Independent Practice
Name _____________________________________
Date__________________
Percent of a Number
Solve each problem. Find your answer in one of the two answer boxes. Find the problem number on the coloring page
and color each section with the number the color that corresponds to your answer.
#
Problem
Answer 1
Answer 2
Answer 3
1
What is 10% of 47?
470
DARK GREEN
2
What is 20% of 82?
16.4
BLACK
4.7
LIGHT
GREEN
62
ORANGE
3
What is 150% of 50?
7.5
ORANGE
100
RED
75
YELLOW
4
What is 50% of 30?
15
ORANGE
80
YELLOW
60
RED
5
What is 10% of 9?
90
PINK
19
PURPLE
0.9
RED
6
A $400 TV is on sale for
25% off. What is the sale
price of the TV?
$100
GREEN
$300
BLUE
$375
YELLOW
7
A $65 purse is on sale for
10% off. How much money
will you save if you buy it?
$55.00
BLACK
$10.00
RED
$6.50
DARK GREEN
8
The cost of a movie ticket
increased by 15%. The old
price was $8. How much
are they now?
$23.00
LIGHT BLUE
$9.20
GRAY
$9.50
PINK
9
A $75 jacket is 50% off.
How much does the jacket
cost now?
$37.50
PURPLE
$40.00
GREEN
$25.00
RED
10
You leave a 20% tip on your
$70 dinner bill. How much
was the tip?
$5.00
ORANGE
$14.00
PINK
$90.00
YELLOW
37
YELLOW
164
BLUE
61
62
Name __________KEY_______________________
Date__________________
Percent of a Number
Solve each problem. Find your answer in one of the two answer boxes. Find the problem number on the coloring page
and color each section with the number the color that corresponds to your answer.
#
Problem
Answer 1
Answer 2
Answer 3
1
What is 10% of 47?
470
DARK GREEN
2
What is 20% of 82?
16.4
BLACK
4.7
LIGHT
GREEN
62
ORANGE
3
What is 150% of 50?
7.5
ORANGE
100
RED
75
YELLOW
4
What is 50% of 30?
15
ORANGE
80
YELLOW
60
RED
5
What is 10% of 9?
90
PINK
19
PURPLE
0.9
RED
6
A $400 TV is on sale for
25% off. What is the sale
price of the TV?
$100
GREEN
$300
BLUE
$375
YELLOW
7
A $65 purse is on sale for
10% off. How much money
will you save if you buy it?
$55.00
BLACK
$10.00
RED
$6.50
DARK GREEN
8
The cost of a movie ticket
increased by 15%. The old
price was $8. How much
are they now?
$23.00
LIGHT BLUE
$9.20
GRAY
$9.50
PINK
9
A $75 jacket is 50% off.
How much does the jacket
cost now?
$37.50
PURPLE
$40.00
GREEN
$25.00
RED
10
You leave a 20% tip on your
$70 dinner bill. How much
was the tip?
$5.00
ORANGE
$14.00
PINK
$90.00
YELLOW
37
YELLOW
164
BLUE
63
Name ______________________________
Exit Ticket G
SHOW YOUR WORK!
1. Daniel is shopping for a new TV. He
found one on sale for 25% off the
original price, which is $650. Write
an expression (don’t solve it) to find
out how much money he saved.
2. Corrine ordered a $120 couch and
needs to pay a 10% shipping charge.
How much will the shipping charge
be?
3. Stephanie’s test score was 50%
lower than Jonathan’s. If Jonathan
scored a 96 on his test, what did
Stephanie score?
4. Amber’s soccer team has scored 40
goals this season. Amber scored 10%
of the goals by herself. How many
goals has she scored?
5. Heather is reading a 450 page book.
She is 10% finished with the book.
How many pages has she read?
6. Kevin is jogging 20 miles today. He is
25% finished. How many miles has
he completed?
64
Name _______KEY___________________
Exit Ticket G
SHOW YOUR WORK!
1. Daniel is shopping for a new TV.
He found one on sale for 25%
off the original price, which is
$650. Write an expression (don’t
solve it) to find out how much
money he saved.
2. Corrine ordered a $120 couch and
needs to pay a 10% shipping charge.
How much will the shipping charge
be?
$12
650 x 0.25
3. Stephanie’s test score was 50%
lower than Jonathan’s. If Jonathan
scored a 96 on his test, what did
Stephanie score?
4. Amber’s soccer team has scored 40
goals this season. Amber scored 10%
of the goals by herself. How many
goals has she scored?
4 goals
48
5. Heather is reading a 450 page book.
She is 10% finished with the book.
How many pages has she read?
45 pages
6. Kevin is jogging 20 miles today. He is
25% finished. How many miles has
he completed?
5 miles
65
Name _____________
Warm Up H
1) You just purchased a $150 television. The
sales tax is 6%. How much will you pay in
sales tax?
3) You are planning to go to a theme park.
Admission is $45. You have a coupon for
10% off your admission fee. How much
money will you save by using the coupon?
2) How much will you pay all together for
the television in problem #1?
4) What will your new cost of admission be
in problem #3?
Name ____KEY______
Warm Up H
1) You just purchased a $150 television. The
sales tax is 6%. How much will you pay in
sales tax?
$9.00
3) You are planning to go to a theme park.
Admission is $45. You have a coupon for
10% off your admission fee. How much
money will you save by using the coupon?
$4.50
2) How much will you pay all together for
the television in problem #1?
$159.00
4) What will your new cost of admission be
in problem #3?
$41.50
66
Lesson H Notes and Practice
Name ______________________________________
Date _____________________________
Proportions and Unit Rate
PROPORTIONS NOTES

When setting up a proportion, first decide what two units you are comparing – miles to minutes, degrees
to hours, etc.
o Write your units as a proportion of their own.
 Example:
 You just traveled 40 miles in 30 minutes. How far will you travel in 45 minutes?
 We are comparing miles to minutes, therefore:
𝒎𝒊𝒍𝒆𝒔
𝒎𝒊𝒏𝒖𝒕𝒆𝒔
o Usually you will be given a ratio in the problem. Above we are told “You just traveled 40 miles
in 30 minutes”. This can be written as a ratio. Be sure to set it up the same was as the unit ratio.
𝒎𝒊𝒍𝒆𝒔
𝒎𝒊𝒏𝒖𝒕𝒆𝒔
=
𝟒𝟎 𝒎𝒊𝒍𝒆𝒔
𝟑𝟎 𝒎𝒊𝒏𝒖𝒕𝒆𝒔
o Next, look at the information you have left in the problem, and look to see WHAT you are trying
to find. We want to find out how far we will travel in 45 minutes.
We know two things:
1. We are trying to find out how far (distance – miles)
2. We know the minutes, 45.
Substitute what you KNOW into the proportion. Since we know the minutes, we must make sure
to put the 45 on the bottom of the fraction bar.
𝒎𝒊𝒍𝒆𝒔
𝒎𝒊𝒏𝒖𝒕𝒆𝒔

=
𝟒𝟎 𝒎𝒊𝒍𝒆𝒔
𝟑𝟎 𝒎𝒊𝒏𝒖𝒕𝒆𝒔
=
𝑵 𝒎𝒊𝒍𝒆𝒔
𝟒𝟓 𝒎𝒊𝒏𝒖𝒕𝒆𝒔
To solve the proportion you cross multiply, and divide.
𝟒𝟎 𝒎𝒊𝒍𝒆𝒔
𝟑𝟎 𝒎𝒊𝒏𝒖𝒕𝒆𝒔
=
𝑵 𝒎𝒊𝒍𝒆𝒔
𝟒𝟓 𝒎𝒊𝒏𝒖𝒕𝒆𝒔
o Multiply the 30 and N to get 30•N, and multiply the 40 and 45 to get 40•45. Set this up as an
equation.
o 30•N = 40•45
Solve as you would a regular equation
o 30•N = 1,800
30
30
o
N = 60 miles
67
Guided Practice

You just paid $30 for 12 gallons of gas. How much will it cost you to get an additional 4 gallons of gas?
o We are comparing cost to gallons. Write this as it’s own ratio.
o We know we paid $30 for 12 gallons. Write this as a ratio, set equal to the ratio from above.
o We know we are looking for the cost of 4 gallons. Write this as a ratio set equal to the proportion
you just wrote above.
o Now cross multiply and solve!
Independent Practice
1. It takes you 25 minutes to drive the 35 miles from school to your house. How long will it take you to
drive the 70 miles from your house to the beach – if you travel at the same rate of speed?
SHOW YOUR WORK!
2. You used 4 cups of chocolate chips to bake 90 batches of cookies. How many cups do you need if you
are planning to only bake 112.5 batches of cookies?
SHOW YOUR WORK!
68
UNIT RATE NOTES:

Determining Unit Rate is nothing more than finding the cost/mileage/etc. for ONE unit.
o Most unit rate questions will be given you information for more than one thing.
 Example:
You can purchase 6 boxes of tissues for $15. How much does each box cost?
o Write the information you have been given as a ratio.
𝟔 𝒃𝒐𝒙𝒆𝒔
$𝟏𝟓
o Next, set up a proportion to determine the cost of just one box of tissues. Don’t forget to write a
ratio using words first. We are comparing boxes to cost.
𝒃𝒐𝒙𝒆𝒔
𝒄𝒐𝒔𝒕
=
𝟔 𝒃𝒐𝒙𝒆𝒔
$𝟏𝟓
=
𝟏 𝒃𝒐𝒙
$𝑵
o To solve the proportion you cross multiply, and divide.
𝟔 𝒃𝒐𝒙𝒆𝒔
$𝟏𝟓
=
𝟏 𝒃𝒐𝒙
$𝑵
o Multiply the 6 and N to get 6•N, and multiply the 15 and 1 to get 15•1. Set this up as an
equation.
o 6•N = 15•1
Solve as you would a regular equation
o 6•N = 15
6
6
o N = $2.50
o You will see that you end up dividing the cost by the number of units. When you get better at
finding unit rate, you can solve that way.
Guided Practice

You just paid $45 for 12 gallons of gas. How much did each gallon of gas cost you?
o You paid $45 for 12 gallons of gas. Write this as a ratio.
$𝟒𝟓
𝟏𝟐 𝒈𝒂𝒍𝒍𝒐𝒏𝒔
o We want to find the cost of ONE gallon. We write this as another ratio.
𝒄𝒐𝒔𝒕
$𝟒𝟓
$𝑵
=
=
𝒈𝒂𝒍𝒍𝒐𝒏𝒔 𝟏𝟐 𝒈𝒂𝒍𝒍𝒐𝒏𝒔 𝟏 𝒈𝒂𝒍𝒍𝒐𝒏𝒔
o Now cross multiply and solve!
12•N = 45•1
12•N = 45
12
12
N = $3.75
69
INDEPENDENT PRACTICE
1. A pack of 5 books costs $18.75. A pack of 3 books $12.75. Which pack has the lowest cost per book?
(hint – find the unit rate for each pack, then compare)
SHOW YOUR WORK!
2. You found CDs on sale! Eight CDs would cost you $79.92. What is the cost per CD?
SHOW YOUR WORK!
3. You have the option of buying 20 tickets at the fair for $15 or 45 tickets for $27. Which is the best deal?
SHOW YOUR WORK!
4. You can buy 30 cans of soda for $6. What is the cost per can?
SHOW YOUR WORK!
70
Name __________KEY_________________
Date _____________________________
Proportions and Unit Rate

PROPORTIONS NOTES
When setting up a proportion, first decide what two units you are comparing – miles to minutes, degrees
to hours, etc.
o Write your units as a proportion of their own.
 Example:
 You just traveled 40 miles in 30 minutes. How far will you travel in 45 minutes?
 We are comparing miles to minutes, therefore:
𝒎𝒊𝒍𝒆𝒔
𝒎𝒊𝒏𝒖𝒕𝒆𝒔
o Usually you will be given a ratio in the problem. Above we are told “You just traveled 40 miles
in 30 minutes”. This can be written as a ratio. Be sure to set it up the same was as the unit ratio.
𝒎𝒊𝒍𝒆𝒔
𝒎𝒊𝒏𝒖𝒕𝒆𝒔
=
𝟒𝟎 𝒎𝒊𝒍𝒆𝒔
𝟑𝟎 𝒎𝒊𝒏𝒖𝒕𝒆𝒔
o Next, look at the information you have left in the problem, and look to see WHAT you are trying
to find. We want to find out how far we will travel in 45 minutes.
We know two things:
3. We are trying to find out how far (distance – miles)
4. We know the minutes, 45.
Substitute what you KNOW into the proportion. Since we know the minutes, we must make sure
to put the 45 on the bottom of the fraction bar.
𝒎𝒊𝒍𝒆𝒔
𝒎𝒊𝒏𝒖𝒕𝒆𝒔

=
𝟒𝟎 𝒎𝒊𝒍𝒆𝒔
𝟑𝟎 𝒎𝒊𝒏𝒖𝒕𝒆𝒔
=
𝑵 𝒎𝒊𝒍𝒆𝒔
𝟒𝟓 𝒎𝒊𝒏𝒖𝒕𝒆𝒔
To solve the proportion you cross multiply, and divide.
𝟒𝟎 𝒎𝒊𝒍𝒆𝒔
𝟑𝟎 𝒎𝒊𝒏𝒖𝒕𝒆𝒔
=
𝑵 𝒎𝒊𝒍𝒆𝒔
𝟒𝟓 𝒎𝒊𝒏𝒖𝒕𝒆𝒔
o Multiply the 30 and N to get 30•N, and multiply the 40 and 45 to get 40•45. Set this up as an
equation.
o 30•N = 40•45
Solve as you would a regular equation
o 30•N = 1,800
30
30
o
N = 60 miles
71
Guided Practice

You just paid $30 for 12 gallons of gas. How much will it cost you to get an additional 4 gallons of gas?
o We are comparing cost to gallons. Write this as it’s own ratio.
𝒄𝒐𝒔𝒕
𝒈𝒂𝒍𝒍𝒐𝒏𝒔
o We know we paid $30 for 12 gallons. Write this as a ratio, set equal to the ratio from above.
𝒄𝒐𝒔𝒕
$𝟑𝟎
=
𝒈𝒂𝒍𝒍𝒐𝒏𝒔 𝟏𝟐 𝒈𝒂𝒍𝒍𝒐𝒏𝒔
o We know we are looking for the cost of 4 gallons. Write this as a ratio set equal to the proportion
you just wrote above.
𝒄𝒐𝒔𝒕
$𝟑𝟎
𝑵 𝒄𝒐𝒔𝒕
=
=
𝒈𝒂𝒍𝒍𝒐𝒏𝒔 𝟏𝟐 𝒈𝒂𝒍𝒍𝒐𝒏𝒔 𝟒 𝒈𝒂𝒍𝒍𝒐𝒏𝒔
o Now cross multiply and solve!
12•N = 30•4
12•N = 120
12
12
N = $10
Independent Practice
3. It takes you 25 minutes to drive the 35 miles from school to your house. How long will it take you to
drive the 70 miles from your house to the beach – if you travel at the same rate of speed?
SHOW YOUR WORK!
𝒎𝒊𝒏𝒖𝒕𝒆𝒔
𝒎𝒊𝒍𝒆𝒔
=
𝟐𝟓 𝒎𝒊𝒏𝒖𝒕𝒆𝒔
𝟑𝟓 𝒎𝒊𝒍𝒆𝒔
=
𝑵 𝒎𝒊𝒏𝒖𝒕𝒆𝒔
𝟕𝟎 𝒎𝒊𝒍𝒆𝒔
35•N = 25•70
35•N = 1,750
35
35
N = 50 minutes
4. You used 4 cups of chocolate chips to bake 90 batches of cookies. How many cups do you need if you
are planning to only bake 112.5 batches of cookies?
SHOW YOUR WORK!
𝒄𝒖𝒑𝒔
𝒃𝒂𝒕𝒄𝒉𝒆𝒔
=
𝟒 𝒄𝒖𝒑𝒔
𝟗𝟎 𝒃𝒂𝒕𝒄𝒉𝒆𝒔
=
𝑵 𝒄𝒖𝒑𝒔
𝟏𝟏𝟐.𝟓 𝒃𝒂𝒕𝒄𝒉𝒆𝒔
90•N = 112.5•4
90•N = 450
90
90
N = 5 cups
72
UNIT RATE NOTES:

Determining Unit Rate is nothing more than finding the cost/mileage/etc. for ONE unit.
o Most unit rate questions will be given you information for more than one thing.
 Example:
You can purchase 6 boxes of tissues for $15. How much does each box cost?
o Write the information you have been given as a ratio.
𝟔 𝒃𝒐𝒙𝒆𝒔
$𝟏𝟓
o Next, set up a proportion to determine the cost of just one box of tissues. Don’t forget to write a
ratio using words first. We are comparing boxes to cost.
𝒃𝒐𝒙𝒆𝒔
𝒄𝒐𝒔𝒕
=
𝟔 𝒃𝒐𝒙𝒆𝒔
$𝟏𝟓
=
𝟏 𝒃𝒐𝒙
$𝑵
o To solve the proportion you cross multiply, and divide.
𝟔 𝒃𝒐𝒙𝒆𝒔
$𝟏𝟓
=
𝟏 𝒃𝒐𝒙
$𝑵
o Multiply the 6 and N to get 6•N, and multiply the 15 and 1 to get 15•1. Set this up as an
equation.
o 6•N = 15•1
Solve as you would a regular equation
o 6•N = 15
6
6
o N = $2.50
o You will see that you end up dividing the cost by the number of units. When you get better at
finding unit rate, you can solve that way.
Guided Practice

You just paid $45 for 12 gallons of gas. How much did each gallon of gas cost you?
o You paid $45 for 12 gallons of gas. Write this as a ratio.
$𝟒𝟓
𝟏𝟐 𝒈𝒂𝒍𝒍𝒐𝒏𝒔
o We want to find the cost of ONE gallon. We write this as another ratio.
𝒄𝒐𝒔𝒕
$𝟒𝟓
$𝑵
=
=
𝒈𝒂𝒍𝒍𝒐𝒏𝒔 𝟏𝟐 𝒈𝒂𝒍𝒍𝒐𝒏𝒔 𝟏 𝒈𝒂𝒍𝒍𝒐𝒏𝒔
o Now cross multiply and solve!
12•N = 45•1
12•N = 45
12
12
N = $3.75
73
INDEPENDENT PRACTICE
1. A pack of 5 books costs $18.75. A pack of 3 books $12.75. Which pack has the lowest cost per book?
(hint – find the unit rate for each pack, then compare)
SHOW YOUR WORK!
𝒃𝒐𝒐𝒌𝒔
𝒄𝒐𝒔𝒕
=
𝟓 𝒃𝒐𝒐𝒌𝒔
$𝟏𝟖.𝟕𝟓
=
𝟏 𝒃𝒐𝒐𝒌
𝒃𝒐𝒐𝒌𝒔
$𝑵
𝒄𝒐𝒔𝒕
5•N = 18.75•1
5•N = 18.75
5
5
N = $3.75 per book
=
𝟑 𝒃𝒐𝒐𝒌𝒔
$𝟏𝟐.𝟕𝟓
=
𝟏 𝒃𝒐𝒐𝒌
$𝑵
3•N = 12.75•1
3•N = 12.75
3
N = $4.25 per book
3
Lowest cost per book
2. You found CDs on sale! Eight CDs would cost you $79.92. What is the cost per CD?
𝑪𝑫𝒔
SHOW YOUR WORK!
𝒄𝒐𝒔𝒕
=
𝟖 𝑪𝑫𝒔
$𝟕𝟗.𝟗𝟐
=
𝟏 𝑪𝑫
$𝑵
8•N = 79.92•1
8•N = 79.92
8
8
N = $9.99 per CD
3. You have the option of buying 20 tickets at the fair for $15 or 45 tickets for $27. Which is the best deal?
SHOW YOUR WORK!
𝒕𝒊𝒄𝒌𝒆𝒕𝒔 𝟐𝟎 𝒕𝒊𝒄𝒌𝒆𝒕𝒔 𝟏 𝒕𝒊𝒄𝒌𝒆𝒕
=
=
𝒄𝒐𝒔𝒕
$𝟏𝟓
$𝑵
20•N = 15•1
20•N = 15
20
20
N = $0.75 per ticket
𝒕𝒊𝒄𝒌𝒆𝒕𝒔
𝒄𝒐𝒔𝒕
=
𝟒𝟓 𝒕𝒊𝒄𝒌𝒆𝒕𝒔
$𝟐𝟕
=
𝟏 𝒕𝒊𝒄𝒌𝒆𝒕
$𝑵
45•N = 27•1
45•N = 27
45
45
N = $0.60 per ticket
Best Deal
4. You can buy 30 cans of soda for $6. What is the cost per can?
SHOW YOUR WORK!
𝒄𝒂𝒏𝒔
𝒄𝒐𝒔𝒕
=
𝟑𝟎 𝒄𝒂𝒏𝒔
$𝟔
=
𝟏 𝒄𝒂𝒏
$𝑵
30•N = 6•1
30•N = 6
30 30
N = $0.20 per can
74
Lesson H Independent Practice
Name _______________________________
Date______________
Proportions & Unit Rates
Solve each problem. Find your answer in one of the two answer boxes. Find the problem number on the coloring page
and color each section with the number the color that corresponds to your answer.
#
1
2
3
4
5
6
7
8
9
10
Problem
Answer 1
Answer 2
It takes you 45 minutes to drive the 30 miles
from your house to the mall. How long will it
take you to drive the 75 miles to the beach?
50 minutes
RED
112.5 minutes
BLACK
A box of 6 matchbox cars costs $11.94. A box
of 4 matchbox cars costs $8.12. Which box
has the lowest cost per car?
Box of 6
DARK GREEN
Box of 4
LIGHT GREEN
You were able to purchase 5 gallons of gas
for $19.85. How many gallons did you buy if
you spent $47.64
189 gallons
GRAY
12 gallons
BLUE
You used 5 cups of flour to bake 80 cookies.
How many cups do you need if you are
planning to bake 144 cookies?
16 cups
BLACK
9 cups
BROWN
$287.64
PINK
$7.99
RED
9 songs
YELLOW
12 songs
ORANGE
Your family
GRAY
Their family
BROWN
$3.60
BLUE
$22.50
PURPLE
$15
RED
$1.75
PINK
4,900 ft²
ORANGE
100 ft²
YELLOW
You found DVDs on sale! Six DVDs would
cost you $47.94. What is the cost per DVD?
You have the option of downloading 12 songs
online for $10.68 or 9 songs for $7.38. Which
is the best deal?
You are taking a trip at the same time as
another family. Your family traveled 1,900
miles in 2 days, their family traveled 2,700
miles in 3 days. Who is traveling faster?
Carla purchases 4 books for $10. Amy
purchases 9 books. How much did Amy
spend if her books cost the same as Carla’s?
You can buy a 20 pound bag of dog food for
$35. What is the cost per pound?
Amy used 3 gallons of paint to cover 2,100 ft²
of wall space inside her house. How much
wall space can she paint with 7 gallons?
75
76
Name ________KEY________________
Date______________
Proportions & Unit Rates
Solve each problem. Find your answer in one of the two answer boxes. Find the problem number on the coloring page
and color each section with the number the color that corresponds to your answer.
#
1
2
3
4
5
6
7
8
9
10
Problem
Answer 1
Answer 2
It takes you 45 minutes to drive the 30 miles
from your house to the mall. How long will it
take you to drive the 75 miles to the beach?
50 minutes
RED
112.5 minutes
BLACK
A box of 6 matchbox cars costs $11.94. A box
of 4 matchbox cars costs $8.12. Which box
has the lowest cost per car?
Box of 6
Box of 4
DARK GREEN LIGHT GREEN
You were able to purchase 5 gallons of gas
for $19.85. How many gallons did you buy if
you spent $47.64
189 gallons
GRAY
12 gallons
BLUE
You used 5 cups of flour to bake 80 cookies.
How many cups do you need if you are
planning to bake 144 cookies?
16 cups
BLACK
9 cups
BROWN
$287.64
PINK
$7.99
RED
You have the option of downloading 12 songs
online for $10.68 or 9 songs for $7.38. Which
is the best deal?
9 songs
YELLOW
12 songs
ORANGE
You are taking a trip at the same time as
another family. Your family traveled 1,900
miles in 2 days, their family traveled 2,700
miles in 3 days. Who is traveling faster?
Your family
GRAY
Their family
BROWN
$3.60
BLUE
$22.50
PURPLE
$15
RED
$1.75
PINK
4,900 ft²
ORANGE
100 ft²
YELLOW
You found DVDs on sale! Six DVDs would
cost you $47.94. What is the cost per DVD?
Carla purchases 4 books for $10. Amy
purchases 9 books. How much did Amy
spend if her books cost the same as Carla’s?
You can buy a 20 pound bag of dog food for
$35. What is the cost per pound?
Amy used 3 gallons of paint to cover 2,100 ft²
of wall space inside her house. How much
wall space can she paint with 7 gallons?
77
Name ______________
Exit Ticket H
1) After buying 8 movie tickets for $36, you
realize you need to buy one more ticket.
How much will one ticket cost you?
3) You paid $8.40 for 7 sodas at the movie
theater. How much did each soda cost?
2) It takes you 60 minutes to drive 45 miles.
If you drive at the same pace, how long
should it take you to drive an additional 15
miles?
4) You bought 10 pounds of chicken for
$13.00. How much did you pay per
pound?
Name ____KEY______
Exit Ticket H
1) After buying 8 movie tickets for $36, you
realize you need to buy one more ticket.
How much will one ticket cost you?
$4.50
3) You paid $8.40 for 7 sodas at the movie
theater. How much did each soda cost?
$1.20
2) It takes you 60 minutes to drive 45 miles.
If you drive at the same pace, how long
should it take you to drive an additional 15
miles?
20 minutes
4) You bought 10 pounds of chicken for
$13.00. How much did you pay per
pound?
$1.30
78
Name _____________
Warm Up I
1) 5 CDs cost $18.75. Find the cost of one
CD.
2) 3 gallons of gas costs $8.85. How
much would 12 gallons cost?
3) You can either buy 6 pairs of jeans for
$75 or 4 pairs of jeans for $52. Which is
the better buy?
4) You can download 12 songs for
$9. How many songs can you
download for $19.50?
Name ____ KEY ____
Warm Up I
1) 5 CDs cost $18.75. Find the cost of one
CD.
2) 3 gallons of gas costs $8.85. How
much would 12 gallons cost?
$3.75
$35.40
3) You can either buy 6 pairs of jeans for
$75 or 4 pairs of jeans for $52. Which is
the better buy?
6 pairs for $75
4) You can download 12 songs for
$9. How many songs can you
download for $19.50?
26 songs
79
Lesson I Activity
Candy Bar
Scale and Proportions
Adapted from “Honey I Blew Up The Candy Bar” found at www.okea.org
Materials:
 1 packet per student
 1 candy bar per student (fun size will work the best, and cost the least!)
o It will be better if various sized candy bars are available to the students.
 Rulers
 Crayons, Markers or Colored Pencils
80
Name ___________________________________
Date____________________
Candy Bar Scale and Proportions
You are going to find the scale factor between a miniature candy bar and an enlarged one.
1. Record the name of the candy bar you’ve been given. ______________________
2. Find the dimensions of the candy bar in millimeters.
Length _______________
Width _______________
Height_______________
3. Record your results in the table below under the column for “Original Size.”
4. Using a scale of 10mm : 3.5cm, determine the dimensions for a new candy bar. Record
these dimensions in the “New Size” column.
ORIGINAL
SIZE
(mm)
Show Your Work Here
10𝑚𝑚
Example
45 mm
3.5𝑐𝑚
=
NEW SIZE
(cm)
45𝑚𝑚
𝑥
10x = 45 • 3.5
10x = 157.5
x = 15.75
15.75 cm
LENGTH
WIDTH
HEIGHT
81
The scale factor is 1 : 3.5
Your new candy bar should be 3.5 times bigger than the original.
When you enlarge a candy bar, you also increase the amount of calories, fat, etc. Follow the directions below to
determine the nutritional content of your new candy bar.
1. Copy the nutritional information from your candy bar into the table below under the
“Original Size” column.
2. Set up and solve a proportion to determine the nutritional information in the new candy
bar. Use the scale factor (1 : 3.5) from above. An example has been done for you.
ORIGINAL SIZE
Show Your Work
Here
1
EXAMPLE:
240 grams
3.5
=
NEW SIZE
240
𝑥
1x = 240 • 3.5
X = 840
840 grams
Calories
Total Fat
Cholesterol
Sodium
Total
Carbohydrates
Protein
82
In the space below, create a drawing of the front your new candy bar.
Be sure to use the measurements you found on the first page of this activity.
Design it however you’d like – be sure to give it a name!
Be neat, colorful and creative!
83
Name _____________
Exit Ticket I
1) James bought a model car. The scale is 1cm :
20in. The length of the model car is 12.5cm.
What is the actual length, in inches, of the car?
2) A miniature house measures 4 inches tall.
Using a scale of 1.5 in : 5 feet, find the
height of the actual house.
3) The distance from your house to school on a map
is 0.25 inches. Using a scale of 0.5 inches : 1
mile, how far is your home from school, in
miles?
4) A football field measures 120 yards from
end zone to end zone. Using a scale factor
of 5 yards : 3 inches, how many inches
long would a model football field have to
be?
Name ____ KEY _____
Exit Ticket I
1) James bought a model car. The scale is 1cm :
20in. The length of the model car is 12.5cm.
What is the actual length, in inches, of the car?
2) A miniature house measures 4 inches tall.
Using a scale of 0.75 in : 6 feet, find the
height of the actual house.
250 inches
32 feet
3) The distance from your house to school on a map
is 0.25 inches. Using a scale of 0.5 inches : 1
mile, how far is your home from school, in
miles?
4) A football field measures 120 yards from
end zone to end zone. Using a scale factor
of 5 yards : 3 inches, how many inches
long would a model football field have to
be?
0.5 mile
72 inches
84