algebra 1 summer skills packet

8/12/2019 Algebra 1 Summer Skills Packet

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(For Students Entering Algebra I-Fall 2014)

Medford Public Schools

Department of Mathematics


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edford Public Schools489 Winthrop Street, Medford, Massachusetts 02155

Carolyn A. Joy [email protected]

K-12 Director of Mathematic s and Science 781-393-2214

June 13, 2014

Dear Student/Parent/Guardian:

Welcome to your Summer Mathematics Review Packet. In order to help you/your child meet

with success in Algebra I, you are being provided with a packet of mathematics problems

that include topics that have been studied in middle school. In todays environment of

rigorous academic standards with the newly implemented Common Core, students will need

to have an understanding of core topics in order to progress and move forward in theirmathematical learning. This packet is intended to help you retain the basic skills you have

learned.

If you need to review howto complete the work, there are excellent, easy-to-understand set

of tutorials on line. Most of the tutorials are under 10 minutes long. You will see referencesto different sites as you progress through the packet. The sitewww.khanacademy.orgis very

popular with many topics you can scroll down and click on ORuse a search box search for

video or topic. Enter the topic you are working on for the day and you will get a list of

video tutorials to choose from. Watch as many as you need to help you complete the packetproblems. There is also an opportunity to ask questions and get some online feedback. You

will find useful information there if you take the time to read it.

It is suggested that you work on the packet at the rate of about 2-3 pages per week throughoutthe summer. At this rate, you will have it completed in time for the start of school. Your

algebra teacher will give you instructions on the due date, how you will receive credit and

any consequences for not completing the packet. Please remember, the packet is designed tohelp you as you transition to high school algebra.

All work should be neatly shown on the packet. You should show ALL steps in yourprocess, including work in which you may have used a calculator. If you need to do work on

separate paper, make sure you include the title of the page and the problem number.

Good luck as you enter high school.

Sincerely,

Carolyn A. Joy, DirectorMs. Elizabeth Burns, teacher

Ms. Rebecca Jacobs, teacher

Ms. Megan LeClair, teacher
mailto:[email protected]:[email protected]://www.khanacademy.org/http://www.khanacademy.org/http://www.khanacademy.org/http://www.khanacademy.org/mailto:[email protected]


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Algebra 1 Name:_____________________________

Summer Packet

2014 Middle School:_____________________________

Order of OperationsNeed a refresher? Order of Operations Video:

https://www.khanacademy.org/math/arithmetic/order-of-operations/order_of_operations/v/order-of-operations

1. Determine which step you would do first in the following problems. The first problem has been done for

you.

a) 14 + 7 40 87

7 40because it is the first

multiplication when reading left to

right.

b) 50 5 + (7 2) 9 + 4 c) (11 5)2 + 7 + 36 9

d) 16 8 + 27 35 5 e) 76 + 14 2 8 f) 14 8 + 5 9 + 27 3


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2. Simplify the expression. The first problem has been done for you.

a) (34 4) 3 6

30 3 6

30 3 36

10 36

26

b) (2 + 2)+(12 6) c) (96 6) (9 + 6)

d) (10 + 5)+(15 3) e) (74 + 3) 7 f) (65 5) (15 + 5)

g) (26 8) 10 h) 4(12 + 4)+ 5 i) (30 2) 22

Order of Operations Extra Practice:

https://www.khanacademy.org/math/arithmetic/order-of-operations/order_of_operations/e/order_of_operations_2

https://www.khanacademy.org/math/arithmetic/order-of-operations/order_of_operations/e/order_of_operations

https://www.khanacademy.org/math/arithmetic/order-of-operations/order_of_operations/e/order_of_operations


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Operations with Integers

3. Solve each problem; use the number line if needed. The first problem has been done for you.

a)

8 +(6)= 2

b)

(11) (8)=

c)

12 + (6)=

d)

14 (1)=

e)

(5)+(14)=

f)

1 8 =

g)

86 =

h)

9 + 7 =

i)

414 =

j)

2639 =

k)

677798 =

l)

4 (8) =

4. Solve each problem. The first problem has been done for you.

a) 45 (9)= 5 b) 6 2 = c) 5 8 =

d) 9 8 = e) 9 1 = f) 24 8 =

Operations with Integers Extra Practice:

http://cdn.kutasoftware.com/Worksheets/PreAlg/Dividing%20Integers.pdf

http://cdn.kutasoftware.com/Worksheets/PreAlg/Multiplying%20Integers.pdf

http://cdn.kutasoftware.com/Worksheets/PreAlg/Dividing%20Integers.pdf


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Operations with Rational NumbersNeed a refresher? Operations with Rational Numbers Video:

https://www.khanacademy.org/math/arithmetic/fractions/fractions-unlike-denom/v/adding-and-subtracting-fractions

https://www.khanacademy.org/math/arithmetic/fractions/multiplying_fractions/v/multiplying-negative-and-positive-fractions

https://www.khanacademy.org/math/arithmetic/fractions/div-fractions-fractions/v/conceptual-understanding-of-dividing-fractions-

by-fractions

5. Perform the indicated operation on the rational number. The first problem has been done for you.

a)6

7

7

21=

18

21

7

21=

11

21

b)2

3

3

10=

c)2

3

8

42=

d)12

14

4

8=

e) 13

54

1

9=

f) 1

4

4

20=

g) 5

6

2

4=

h) 10

22

5

11=

i)5

8

1

6

=

=5

8

6

1=

5 6

8 1

=30

8 =

15

4

j)1

3

1

4

=

k)1

2

2

3

=

l)3

6

1

2

=

m)5

7

1

3=

n)3

5

7

10=

o)1

2

5

7=

p)1

3

1

2=

Operations with Rational Numbers Extra Practice:

https://www.khanacademy.org/math/arithmetic/fractions/fractions-unlike-denom/e/adding_and_subtracting_fractions

https://www.khanacademy.org/math/arithmetic/fractions/multiplying_fractions/e/multiplying_fractions

https://www.khanacademy.org/math/arithmetic/fractions/div-fractions-fractions/e/dividing_fractions_2

http://cdn.kutasoftware.com/Worksheets/PreAlg/Add%20and%20Subtracting%20Fractions%20and%20Mixed%20Numbers.pdf

http://cdn.kutasoftware.com/Worksheets/PreAlg/Multiplying%20and%20Dividing%20Fractions%20and%20Mixed%20Numbers.pdf


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Evaluating Expressions with Given Values

Need a refresher? Evaluating Expressions with Given Values Video:

https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-expressions-and-variables/cc-6th-evaluating-

expressions/v/variables-and-expressions-1

6. Find the value of the given expression. The first problem has been done for you.

a)

3 + 5 , = 1, = 23(1)+ 5(2)

3 + 10

7

b)

4 + 21 , = 7, = 7c)

2 +6

,3 = 2, = 6

d)

( 2)+ 3,

= 1, = 1

e)

)6 ,( = 9, = 2 f)3 + + , = 5, = 2

Evaluating Expressions with Given Values Extra Practice:

http://cdn.kutasoftware.com/Worksheets/PreAlg/Evaluating%20Variable%20Expressions.pdf

http://cdn.kutasoftware.com/Worksheets/PreAlg/Evaluating%20Variable%20Expressions.pdf


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Number Sense

Need a refresher? Number Sense Video:

https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/comparing-decimals-pre-alg/v/comparing-decimals-1-example

https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/comparing-decimals-pre-alg/v/ordering-decimals-example

7. Fill in the place holder with, or =. The first problem has been done for you.

a)

4.5 > 4.5

b)

0.707________07.07

c)

18.2________18.0

d)

3.21________ 3.12

e)

0.3________ 0.33

f)

0.06________0.6

8. Arrange and write the decimals in increasing order. The first problem has been done for you

a)

14.367, 28.7784, 213.22, 361.238, 5.2, 5.33

361.238, 28.7784, 5.33, 5 .2, 14.367, 213.22

b)

11.111, 111.11, 1.11, 11.1, 11.1, 1.11

c)

8.1, 67.3, 82.55, 121.91, 2.2, 46.76

Number Sense Extra Practice:

https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/comparing-decimals-pre-alg/v/comparing-decimals-1-example

https://www.khanacademy.org/math/pre-algebra/decimals-pre-alg/comparing-decimals-pre-alg/v/ordering-decimals-example


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Properties of Real Numbers

Need a refresher? Properties of Real Numbers Video:

https://www.khanacademy.org/math/arithmetic/order-of-operations/arithmetic_properties/v/commutative-law-of-addition

9. Choose the best answer about properties of real numbers. The first problem has been done for you.

a) Which property is used in the following

expression?(6 9) 9 = 9 (8 6)

a) Associative Property of Addition

b) Distributive Property of Multiplication

c) Commutative Property of Addition

d) Associative Property of Multiplication

b) The value of any nonzero number will be changed

by_____________

a) Multiplying by zero

b) Adding zero

c) Multiplying by one

d) Dividing by one

c) Which property of addition is used in the

following?2 + 9) + 4 = 2 + (9 + 4)

a) Identity Propertyb) Associative Property

c) Distributive Property

d) Commutative Property

d) Which is an example of the Associative Property

of Addition?

a) 6 + (6)= 0b) (3 + 9) + 7 = 3 + (9 + 7)c) 3 + 2 = 2 + 3

d) 5 + 0 = 5

e) Which is an example of the Identity Property of

Addition?

a) 9 + 0 = 9b) 7 + 6 = 6 + 7c) 8 1 = 8

d) (6 + 2)+ 3 = 6 + (2 + 3)

f) Which equation shows the Commutative Property

of Multiplication?

a) 7 4 = 4 7b) 6 9 5 9 =(6 5) 3c) 3 3 = 3 + 3 + 3

d) 8 1 = 8

g) Which property would you use to simplify thefollowing expression?3( + 9)a) Associative Property

b) Commutative Property

c) Distributive Property

d) Multiplication Property of Zero

h) Which operation will not change the value of anynonzero number?

a) Dividing by zero

b) Multiplying by one

c) Multiplying by zero

d) Adding one

10. Find the property used in each question. The first problem has been done for you.

a)

4 + 9 = 9 + 4

Commutative Property of Addition

b)

2 1

2

= 1

c)

9 (8 + 2)= 9 8 + 9 2

d)

11 (7 5)=(11 7) 5

e)

2 + 0 = 2

f)

6 + 4 = 4 + 6

g)

5 1 = 5

h)

3 + 3 = 0

i)

15 + 0 = 15


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Properties of ExponentsNeed a refresher? Properties of Exponents Video:

https://www.khanacademy.org/math/pre-algebra/exponents-radicals/exponent-properties/v/exponent-rules-part-1

https://www.khanacademy.org/math/pre-algebra/exponents-radicals/exponent-properties/v/exponent-rules-part-2

https://www.khanacademy.org/math/pre-algebra/exponents-radicals/exponent-properties/v/exponent-properties-involving-

quotients

https://www.khanacademy.org/math/pre-algebra/exponents-radicals/negative-exponents-tutorial/v/negative-exponents

If there is a negative it is NOT being raised to that power unless

there are parenthesis.

Example:1 = 1, 2 = 1, (7) = 1

11. Evaluate the exponents. The first problem has been done for you.

a)

(2) =(2)(2)=

= 4

b)

5 =c)

(10) =

d)

(3) =e)

(5) =f)

8 =


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Solving Equations with One VariableNeed a refresher? Solving Equations with One Variable Video:

https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/why-of-algebra/v/one-step-equation-

intuition

https://www.khanacademy.org/math/algebra/solving-linear-equations-and-inequalities/why-of-algebra/v/why-we-do-the-same--

thing-to-both-sides--two-step-equations

13. Solve the one-step equations. The first problem has been done for you.

a)

15 = 22

+15 + 15

= 7

b)

21 = 105

c)

12= 11

d) + 9 = 25 e) 7 = 1 f)4

= 5

14. Solve the two-step equations, round your answers to the nearest hundredth if needed. The first problem

has been done for you.

a)

159 = 3

+15 + 15

9 = 18

9 9

= 2

b)6

22 = 16

c)

7 +2

7= 20

d)3

7 17 = 11

e)

5 28 = 11

f)

18 25 + = 6

g)21

28 = 12

h)7 +20

= 24

i)16

18 = 2

Solving Equations with One Variable Extra Practice:

http://cdn.kutasoftware.com/Worksheets/PreAlg/One-Step%20Equations%20With%20Integers.pdf

http://cdn.kutasoftware.com/Worksheets/PreAlg/Two-Step%20Equations%20With%20Integers.pdf


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The Coordinate PlaneNeed a refresher? The Coordinate Plane Video:

https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/coordinate-plane/v/the-coordinate-plane

15. Tell what point is located at each ordered pair. The first problem has been done for you.

a) (9, 4)

C

b) (4,7) c) (8, 2) d) (8, 3)

e) (1,3) f) (3, 5) g) (9,3) h) (1,1)

16. Write the ordered pair for each given point. The first problem has been done for you.

a) S

(8, 5)

b) M c) X d) F

e) Y f) Q g) G h) A

17. Plot the following points on the coordinate grid.

a)

(3,5)

b)

(7, 2)

c)

(3,5)

d) (3, 1)e)

(6,8)

f) ((0,7 g) (6, 8) h) (8,3)


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SlopeNeed a refresher? Slope Video:

https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/slope-and-intercepts/v/slope-of-a-line

18. Find the slope of each line. The first problem has been done for you.

a)

Slope:

b)

Slope:

c)

Slope:

d)

Slope:

e)

Slope:

f)

Slope:

19. Find the slope from the pair of points. The first problem has been done for you.

a)

(4,4)(0,2)

4 2

4 0=

2

4=

1

2

b)

(3, 4)(4,2)

c)

(5,0) (5,2)

d)

(5, 4)(5,3)

e)

(2, 5) (1,5)

f)

(5, 2)(5,0)

g)

(1,0) (2,5)

h)

(3,0) (0, 3)

Slope Extra Practice:

https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/slope-and-intercepts/e/slope_of_a_line

http://cdn.kutasoftware.com/Worksheets/PreAlg/Slope.pdf


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Slope Intercept Form of Linear EquationsNeed a refresher? Slope Intercept Form of Linear Equations Video:

https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/graphing-slope-intercept/v/graphing-a-line-in-slope-

intercept-form

20. Find the slope and the-intercept of the linear equation. The first problem has been done for you.a)

= 14 2

14

= 2

b)

= 13 1

c)

= 27 + 1

d)

= 34 + 3

21. Write the slope-intercept form of the equation, and plot the equation of each line given the slope and-intercept.

a) b)


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22. Sketch the graph of each line.

a) = 4 b) = + 1 c) = 3

d) = + 3 e) = + 5 f) = 2


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23. Write the equation form each line. The first problem has been done for you.

a)

43

b) c)

d) e) f)

Slope Intercept Form of Linear Equations Extra Practice:

http://cdn.kutasoftware.com/Worksheets/PreAlg/Graphing%20Lines%20in%20Slope-Intercept%20Form.pdf

https://www.khanacademy.org/math/algebra/linear-equations-and-inequalitie/graphing-slope-intercept/v/graphing-a-line-in-slope-

intercept-form

algebra 1 summer skills packet

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