_______________________________________________

(Name)

Math 7 Summer Review Packet For students entering Math 7

This summer math packet was developed to provide students an opportunity to review grade level math objectives and to improve math

performance.

DUE: FIRST WEEK OF SCHOOL

Dear student, Happy summer vacation! The start of the new school year is just around the corner. We want you to be as prepared as possible for the school year. It is important that you have a smooth transition to your new math class right at the beginning of the school year. With this in mind, we are providing a review summer packet of previously taught skills for you to complete over the summer. It is your responsibility to complete the packet before the start of the school year. Your new math teacher is expecting to see all work necessary to solve the problems in this packet. Work space is provided. However, if you use lined paper, please attach it to your packet. Your signature at the bottom of this page signifies that you have completed all work to the best of your ability and tried your best to complete the packet. If you have trouble on some of the information, seek assistance from a parent/guardian or other adult who may be able to assist you! Best wishes and we will see you soon!

Sincerely, FOMS Mathematics Department

Dear Parent/Guardian, It is important to us that your child has a smooth transition into a new math course. With this in mind, we are providing a practice workbook of previously taught skills for your child to complete over the summer. By doing so, it is our goal to increase your child’s retention of mathematics’ skills and to assure a clear understanding of expectations we have for students in the upcoming year in math. Please encourage and monitor your child’s completion of this workbook. Please make sure that ALL WORK IS SHOWN on each page or on attached paper. Remember, the goal is to work on it consistently throughout the summer and not to rush to finish it quickly. Students are to submit their workbooks to their math teachers within the first week of school. The packet will be assessed for a completion grade. Please sign and date the bottom of this document stating that your child has completed the summer math packet to the best of his/her ability. A list of suggested supplies and resources is also attached to this summer packet. The math department will be using graphing calculators for classroom instruction, homework completion, and MCPS assessments. Students may choose to purchase their own to bring back and forth to school. It is recommended that you purchase the graphing calculator during the summer so that your child can become acquainted with it before school starts in the fall. Thank you for your support! Suggested Math Supplies for a Math 7 Student: #2 pencils Paper (refill as needed)

Graph Paper Protractor- basic and clear

Compass Scientific Calculator

Sincerely, FOMS Mathematics Department

Please fill in the following information when the summer math packet is complete:

Student Signature Grade: Date:

Parent/Guardian Signature Date

Reading and Writing Numbers

HINTS: Place Value Chart

9 8 1 2 3 4 ● 5 6 7 8 9 100

T H O

U S A N

D S

10

T H O

U S A N

D S

T

H O U S

A N D S

H

U N D R

E D S

T

E N S

O

N E S

Dec. Pt.

A N

D

T

E N T H

S

H

U N D R

E D T H

S

T

H O U S

A N D T

H S

10

T H O

U S A N

D T H

S

100

T H O

U S A N

D T H

S

When you reach the decimal point of a problem, you do not say “point” you refer to the decimal point as “and”. Rounding General Rules:

If the number after the underlined number is 5 – 9, round the underlined number up 1 unit. If the number after the underlined number is 0 – 4, keep the underlined number the same and add zeros.

EX:

Number Written in Words Note

6,047.05 Six thousand forty seven and five hundredths When writing the decimal portion of a number, you find the last listed number ’s place value. For example, 5, the last number, is in the hundredths place. Ther efore, the decimal would be “and 5 hundredths.”

12.041 Twelve and Forty-One Thousandths One, the last number , is in the thousandths place. Therefore, the decimal would be “and 41 thousandths.”

1) Write the following number in words.

a) 560.8

b) 7.016

c) 24.47

d) 6.003

2) Write the number the name represents.

a) Forty-five thousandths

b) Seventeen and seven hundredths

c) Six million and five thousandths

d) Two hundred eight thousand, four

3) Round each number to the underlined place value. Number Rounded Answer

EXAMPLE: 42.5 43 (The 5 tells you to r ound the 2 up 1 unit.)

a) 712.04

b) 18.096

c) 45.481

d) 176.95

Number Rounded Answer

EXAMPLE: 12,547 12,500 (The 4 tells you to leave the 5 alone.)

e) 432,483

f) 1,387,216

g) 392,621

h) 38,721,830

Adding & Subtracting Whole Numbers

Hint: Adding Whole Numbers Adding numbers with different places requires lining up the units column. Your problem should always be justified on the r ight side. The key to

adding is regrouping. If a column adds up to more than ten, then the tens digit of the sum needs to be included in the next column.

Examples:

1 1

5 6 7 5 6 7 5 6 7 + 2 9 5 + 2 9 5 + 2 9 5

2 6 2 8 6 2

Hints: Subtracting Whole Numbers Subtracting numbers with different places requires lining up the units column. Your problem should always be justified on the r ight side. The key to adding is regrouping. If a column adds up to more than ten, then the tens digit of the sum needs to be included in the next column.

Examples:

3 16 2 13 2 3 4 6 3 4 6 3 4 6

- 1 5 7 - 1 5 7 - 1 5 7

9 8 9 1 8 9

Solve:

a)

6, 4 9 6 4, 1 1 3 + 3, 6 0 8

b)

5 4, 3 9 8 + 6 4, 5 0 8

c)

3, 2 5 4 7 5 4 + 6 9 0

d)

5 4, 6 7 8 + 7, 1 2 3

e) 98,455 – 9,770 f) 14,789 – 908 g) 37,805 – 8,979 h) 809 – 665

7 + 5 = 12 (I have to carry the 1)

1 + 6 + 9 = 16 (I have to carry the 1)

1 + 5 + 2 = 8 (I don’ t have to carry because my number is less than 10)

I cannot subtract 6 – 7, so I must

borrow from the 4 and make the 6 a 16.

I cannot subtract 3 – 5, so I must

borrow from the 3 and make the 3 a 13. I can subtract 2 – 1 so I do not have to

borrow.

Multiplying & Dividing Whole Numbers

Multiplying Hints: Step #1 Step #2 Step #3

Line up the numbers vertically (right justified). Multiply each digit in the top line by the ones digit in the bottom line (far right). Carry when necessary.

Write a 0 under the last term you multiplied by (3 in the example) as a place holder. Then multiply each digit of the top line by the tens digit in the bottom line.

Add the numbers together. Carry when necessary.

1 5 6 x 2 3 1 6 8 +

1 5 6 x 2 3 1 6 8 + 1 1 2 0

5 6 x 2 3

1 6 8 + 1 1 2 0 1 2 8 8

The answer is 1,120

Dividing Hints: You can always use this mnemonic device to help you remember the steps.

Daddy Mommy Sister Brother Then repeat the process over again! Step 1: Divide Step 2: Multiply Step 3: Subtract Step 4: Br ing down

Round 1 Round 2 Round 3

6

1 2 7 6 0 8 - 7 2 4 0

Div ide: 76 ÷ 12 is about 4

6 3

1 2 7 6 0 8 - 7 2 4 0 - 3 6 4 8

Div ide: 76 ÷ 12 is about 4

6 3 4

1 2 7 6 0 8 - 7 2 4 0 - 3 6 4 8 - 4 8

0

Div ide: 76 ÷ 12 is about 4

Multiply: 12 x 6 = 72

Multiply: 12 x 6 = 72

Multiply: 12 x 6 = 72

Subtract:

76 – 72 = 4

Subtract:

76 – 72 = 4

Subtract:

76 – 72 = 4

Br ing Down: Br ing the 0 down.

Br ing Down: Br ing the 0 down.

Br ing Down: Br ing the 0 down.

Repeat the steps! Repeat the steps! The final answer is 634!

Solve: (use lined paper if you do not have enough room on this sheet.)

a) 742 • 17 b) 659 x 7 c) 407(29) d) (25)(13)

Note: All of the problems listed above are multiplication problems. You will see multiplication written in many different ways next year!

a)

1333857

b)

2055

c)

384016

d)

37899

3 x 6 = 18

I place the 8 below and carry

the 1.

3 x 5 = 15 15 + 1 (carried) = 16. I write the 16 next to the 8.

0

P L A C E H O L D E

R

Multiply 2 x 6. P lace 2 below and carry the11. Multiply 2 x 5 and add the carried 1.

Adding Decimals Subtracting Decimals Write the problem up and down!

Line up the decimal points

Add. Remember to carry when needed.

Erase any extra zeros at the end of your final answer.

Write the problem up and down!

Line up the decimal points.

Subtract. Remember to borrow when needed.

Erase any extra zeros at the end of your final answer.

602.84 + 37.3 + 157.662 + 54.89 1 2 2 1

6 0 2 . 8 4 0

3 7 . 3 0 0

1 5 7 . 6 6 2

+ 5 4 . 8 9 0

8 5 2 . 6 9 2

852.962

803.25 – 32.73 7 10 2 12

8 0 3 . 2 5 - 3 2 . 7 3

7 7 0 . 5 2

770.52

Exercise: Add the decimal numbers.

1) 17.62 + 19.45 + 2.7 +3.946

+

2) 341.08 + 69.343 + 205.91 + 3.967

+

3) 6.835 + 27.31 +83.2 + 4.73

+

4) 936.84 – 274.61

–

5) 3007.92 – 1564.73

–

6) 827.56 – 343.927

–

7) 65.479 – 28.53

–

Decimals: Addition and Subtraction

Decimals: Multiplication

Multiplying Decimals Write the problem up and down.

DO NOT LINE UP YOUR DECIMALS!!!!! Multiply carefully!

Place the decimal in the final answer. Count the places to the right of the decimal point in each number. Count the same number of places from right to left in the answer, then place the decimal pt.

Sometimes you’ll need to fill places with zeroes.

167.5 x 0.14

2 3 2

1 6 7. 5 1 # after decimal

pt.

x 0. 1 4 2 #’s after

decimal pt.

6 7 0 0

+ 1 6 7 5 0

2 3. 4 5 0. Move decimal 3

spaces right.

23.450 = 23.45

Exercise: Multiply the decimal numbers.

1) 28.2 x 0.5 x

2) 32.1 x 8.2 x

3) 57.2 x 0.3 x

4) 12.4 x 1.02 x

5) 16.7 x 0.23 x

6) 6.7 x 0.43 x

Decimals: Division

Dividing Decimals Write the problem across. The first number goes into the “division symbol.” The second number goes outside of the house.

Dividing by Whole Numbers

1) Bring up the decimal point.

2) Divide until there is no remainder

Dividing by Decimals

1) Move both decimal points to the right until the outside number is whole.

2) Bring the moved decimal pt up.

3) Divide until there is no remainder

2 3 . 5 1 . 6 9 2

0 . 0 7 2

2 3 5 1 6 . 9 2 0

- 1 6 4 5

4 7 0

- 4 7 0

0

Exercise: Divide the decimals. Show all work.

1) 19.36 ÷ 0.8

2) 6.93 ÷ 0.21

3) 10.464 ÷ 1.2

4) 119.85 ÷ 5.1

5) 8.748 ÷ 0.4

6) 7.31 ÷ 0.017

Problem

1.692 ÷ 23.5 Answer

0.072

Integer Operations

Addition Subtraction Multiplication Division

Same Sign: You add Pos + Pos = Pos

Neg + Neg = Neg

Different Signs: You subtract The number that “looks bigger” deter mines whether the answer is negative or positive.

a) Keep the first number. b) Switch the minus sign to

a plus sign

c) Change the sign of the second number.

d) Then follow the rules of adding.

e) Positive x Positive = Positive f) Negative x Negative = Positive

g) Positive x Negative = Negative

h) Negative x Positive = Negative i) Anything x zero = zero

j) Positive ÷ Positive = Positive k) Negative ÷ Negative = Positive

l) Positive ÷ Negative = Negative

m) Negative ÷ Positive = Negative n) Anything ÷ zero = NOT POSSIBLE

o) Zero ÷ Anything = ZERO

Find each sum (add). Show all work!

a) -12 + -7

b) -20 + 25 c) -16 + 9 d) 10 + 27 e) -5 + 24

f) 23 + -9

g) -17 + -23 h) -3 + 12 i) 8 + -26 j) -1 + -8 + -11

Find each difference (subtract). Show all work!

a) -15 – -20

b) 14 – 20 c) -10 – 24 d) -21 – 4

e) 18 - -9

f) -24 - -15

g) -20 – 13 h) 21 – 17 i) -12 - -16 j) 9 – 30

Find each product (multiply). Show all work!

a) 8(11)

b) -4(12) c) -1 • -40 d) (-5)(-7) e) 7 x 3 x -2

f) 0 x -54

g) 23 • -2 h) (-10)(-10) i) -8 • -4 • 3 j) (-8)(12)

Note: All of the questions listed above involve multiplication. You can see multiplication written in many different ways!

Find each quotient (divide). Show all work!

a) -44 ÷ 4 b) 0 ÷ -5 c) 32 ÷ 8 d) -49 ÷ 7 e)

6

84

f) 80 ÷ -4 g) -64 ÷ -8

h) 6

90

i) 5

100

j)

5

215

Note: All of the questions listed above involve division. You can s ee division written in many different ways!

One-Step Equations

Helpful Hints

1) Get the variable (letter) by itself by doing the opposite operation on both sides of equal sign.

Addition: x + 7 = 9

x + 7 = 9

- 7 -7

x = 2

x = 2

Subtraction: x – 12 = 8

x - 12 = 8

+ 12 +12

x = 20

x = 20

Multiplication: 5x = 35

5 x = 35

5 5

x = 7

x = 7

Division: 246

x

6)24(6

6

x

x = 144

Solve each equation using the steps above.

a) y + 13 = 5 b) x – 12 = 15 c) x – 9 = 13

d) 4f = 28

e) 5

d = 7

f) y + 13 = 25

g) 8

a = 4

h) 5h = 65 i) 12 =

7

k

Reading and Creating Graphs- Part 1

Hints: Basic Graph Information Bar Graph

Bar Graphs compare data.

Circle Graph

Circle graphs show how a whole is broken into parts.

Line Graph

Line graphs measure change in

data over time.

Stem & Leaf Plot

Stem & Leaf Plots shows groups of

data arranged by place value

Hints: Measures of Central Tendency Measure of Variation

Mean Median Mode Range Sum of a set of numbers divided by the amount of numbers in the set

Middle number (when numbers are in order from least to greatest)

Number that appears most often

highest number minus lowest number

1) State what type of graph you would use for each question.

a) Lissy wants to display a graph to show the fraction of sixth grade expenses that go to outdoor education.

b) Elise wants to display a graph to show the comparison between movies liked in the United States and in Italy.

c) Harrison wants to display a graph to show his change in height over eight years.

2) Make a stem-and-leaf plot of the data showing phone call lengths. Don’t forget a title and key.

Phone Call Lengths

18 67 35 20 45

45 69 23 34 48

61 43 46 63 29

32 8 22 25 23

Find the mean, median, mode and range.

Mean

Median

Mode

Range

stem leaf

3) Use the stem and leaf plot to the right to answer the questions below.

a) Name the highest score on the test. a) 96 b) 94 c) 100 d) 97

b) Name the score that appears most often. a) 79 b) 97 c) 89 d) 98

c) What is the range?

a) 7 b) 25 c) 2 d) no range

Science Test Scores (Questions 1 – 3)

stem leaf

7 2 8 9 9 9 8 1 3 8 9 9 9 4 4 7

8/1 = 81%

Favorite Cola

180

200

220

240

260

280

300

Jive Cola Zippy Cola Cool Cola

Cola

Am

ou

nt

of

Peo

ple

Bank Stock Prices

40

50

60

70

80

90

100

Jan Apr Jul Oct

Monthes

Sto

ck P

rices

Reading and Creating Graphs- Part 2

4) Choose mode, median, mean, or range to best describe each statement below.

a) Most of the students have Ms. Hurren for math

b) The difference between the tallest and smallest child is 8 in.

c) Half of the students are on team 6-A.

d) The average amount of time spent on homework is 45minutes

5) Use the graph to choose the statement that is true.

a) Jive Cola is more than twice as popular as Cool Cola. b) Jive Cola is less than twice as popular as Cool Cola.

c) Jive Cola is 4 times as popular as Cool Cola d) Zippy Cola is the most favorite Cola chosen

6) Use the graph to answer the question below. A bank customer looks at the graph and states that the cost of

stocks in April was over twice the cost of stocks in July. What should the bank manager do to make this graph

accurate?

a) His origin is incorrect. He should have started at 0. b) He should have used a different scale.

c) He should have made a circle graph. d) He should have made a pictograph

7) Find the mean, median, mode, and range.

66, 46, 50, 42, 39, 64, 45, 51, 54, 57 Order: Least to Greatest

Mean

Median

Mode

Range

8) Find the mean, median, mode, and range.

17, 16, 13, 17, 17, 10, 10, 13, 10 Order: Least to Greatest

Mean

Median

Mode

Range

Plotting Points on a Coordinate Plane

Coordinate Plane Vocabulary Helpful Hints for Graphing

Steps to plot a point. Start at the origin (0, 0)

1. Move left or right to whatever number x is. sign direction

positive (+) r ight

negative (-) left

2. Move up or down to whatever number y is. sign direction

positive (+) up

negative (-) down

Definitions:

Ordered Pairs: set of 2 numbers.

The first number tells you to move left or r ight. The second number tells you to move up or down. Remember: CRAWL before you CLIMB!!!

Origin: the center point

You always start from (0, 0) and then move across and then up or down.

Use the graph below to answer the following questions.

A

B

CK

L

D E

F

GH

I

J

-10

-9

-8

-7

-6

-5

-4

-3

-2

-1

0

1

2

3

4

5

6

7

8

9

10

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

A) Name the Point for each ordered pair below

1) (1, -4) _____ 2) (0, 0) _____

3) (-3, -1) _____ 4) (4, 4) _____

5) (-5, 0) _____ 6) (-2, 2) _____

B) Write the ordered pair of each of the following points listed below.

1) Point G _____ 2) Point H _____

3) Point I _____ 4) Point J _____

5) Point K _____ 6) Point L _____

C) Place the following points on the coordinate plane above.

1) Label M at (-3, 1) 2) Label Point N at (-4, -4)

3) Label Point O at (-2, -6) 4) Label Point P at (3, 0)

Quadrant 1

Quadrant 4

Quadrant 2

Quadrant 3

Order of Operations

Helpful Hints- Order of Operations Example #1 Example #2 1) Underline the step you are completing.

2) Bring down all other numbers and operations.

Go in order! Remember:

Please Excuse My Dear Aunt Sally!

P Parenthesis

E Exponents

M D

Multiply or Divide

(Left to Right)

A S

Add or Subtract

(Left to Right)

3(2)³ (10 – 3 • 2) + 8 - 2 • 5 – 4

3(2)³ ÷ (10 – 6) + 8 – 2 • 5 – 4

3(2)³ ÷ 4 + 8 – 2 • 5 – 4

3(8) ÷ 4 + 8 – 2 • 5 – 4

24 ÷ 4 + 8 – 2 • 5 – 4

6 + 8 – 2 • 5 – 4

6 + 8 – 10 – 4

14 – 10 – 4

4 – 4

0

12 6 + 8 – 4 • 2 (5 – 1)

12 ÷ 6 + 8 – 4 • 2 ÷ 4

2 + 8 – 4 • 2 ÷ 4

2 + 8 – 8 ÷ 4

2 + 8 – 2

10 – 2

8

Simplify the following expressions using order of operations.

a) 45 ÷ 3² ÷ 5 b) 2² + 2(3)² ÷3 c) 50 – 5² - 5(7 – 2)

d) 2 + 2² • 3² ÷ 12 e) 25 – 3 • 2² f) (3 + 2²) • 2

g) 5 • 6 – 25 ÷ 5 – 2 h) (6 – 4)² i) (3 • 2) (4 – 2) + 6 • 2

Problem Solving- Part 1

Addition Subtraction Multiplication Division Sum

Positive Total

Plus

All together Incr eased by

Add

Addends

In all Deposit

Difference

Mor e than Gr eater than

Take away

Subtr act Less than

Minus

Withdraw

Decr eased by _____ less than

Product

Times In all

Multiply

Multiples Double (x 2)

Tr iple (x 3)

Tw ice (x 2)

Quotient

Divide Goes into

Factor s

Pieces or Parts Per

Shar e Equally

Divisible

Par t of

Show all steps to solve each problem.

1) Evan needs forks and spoons for a party. He needs 8.75 lbs. of forks and 7.25 lbs. of spoons. The silverware costs $5.40 per pound. What is the total cost of the silverware?

Final Answer:

2) David and Stefany arrived at RFK stadium with $56. Their tickets were $10 each and they spend $7 on snacks. Parking at RFK costs another $2. David lost $14, and Stefany got mad at

him. How much did they leave with?

Final Answer:

3) Luis bought groceries for a total of $29.35. If he handed the cashier two twenty dollar bills, how much change would he receive?

Final Answer:

4) In order to pay off the car she bought, Zoey had to make 34 payments of $145.75. What is the total cost of the car?

Final Answer:

5) Kyle’s uncle said, “If you add 10 to my age and then double the sum, the result is 90.” How old is Kyle’s uncle?

Final Answer: