Entering ALL sections of Algebra I in The Middle School

Summer Math Packet

This packet is designed for you to review all of your pre-algebra skills and make sure you

are well prepared for the start of Algebra I or Honors Algebra I in the Middle School this

fall. We anticipate this packet will take about 7 hours to complete.

Please SHOW ALL WORK neatly in the space provided or attached on a separate sheet of

paper. This assignment is due on the first day of class in the fall.

*Please show all of your work as you were required to do during the entire school year.

Remember No Work-No Credit.

We are really looking forward to the upcoming school year and hope you are too!

Questions? Email us at:

alexandra.spitzer@stewardschool.org

diane.maiese@stewardschool.org

corbin.orgain@stewardschool.org

Entering Algebra I (all levels) in the Middle School Summer Review Packet

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I. Integers

Watch the videos for a review of this topic:

https://www.khanacademy.org/math/pre-algebra/pre-algebra-negative-numbers/pre-algebra-add-and-

sub-integersss/v/adding-integers-with-different-signs?modal=1

https://www.khanacademy.org/math/pre-algebra/pre-algebra-negative-numbers/pre-algebra-sub-neg-

intro/v/adding-and-subtracting-negative-number-examples?modal=1

https://www.khanacademy.org/math/pre-algebra/pre-algebra-negative-numbers/pre-algebra-mult-divide-

negatives/v/multiplying-positive-and-negative-numbers?modal=1

https://www.khanacademy.org/math/pre-algebra/pre-algebra-negative-numbers/pre-algebra-mult-divide-

negatives/v/dividing-positive-and-negative-numbers?modal=1

Compute without a calculator.

1) -15 + -35 2) -11 + -14

3) -13 – (-6) 4) -18 – (-3)

5) 32 – 68 6) 17 – 46

7) 45 – (-14) 8) 13 – (-12)

9) -143 + 31 10) -17 + 80

11) -34 + 12 – (-9) – 10 12) -8 – 12 + 3 – (-7)

13) 70 7 14) 48 ( 8)

15) (-9)(7) 16) (-5)(-12)

17) 12 3 4 18) 8 9 2

Entering Algebra I (all levels) in the Middle School Summer Review Packet

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II. Fractions

Watch the videos for a review of this topic:

https://www.khanacademy.org/math/pre-algebra/pre-algebra-fractions/pre-algebra-add-sub-

fractions/v/adding-small-fractions-with-unlike-denominators?modal=1

https://www.khanacademy.org/math/pre-algebra/pre-algebra-fractions/pre-algebra-add-sub-

fractions/v/adding-small-fractions-with-unlike-denominators?modal=1

https://www.khanacademy.org/math/pre-algebra/pre-algebra-fractions/pre-algebra-add-sub-mix-num-w-

unlike-den/v/adding-subtracting-mixed-numbers-1-ex-1?modal=1

https://www.khanacademy.org/math/pre-algebra/pre-algebra-fractions/pre-algebra-add-sub-mix-num-w-

unlike-den/v/adding-subtracting-mixed-numbers-1-ex-2?modal=1

https://www.khanacademy.org/math/pre-algebra/pre-algebra-fractions/pre-algebra-multiply-

fractions/v/multiplying-fractions?modal=1

https://www.khanacademy.org/math/pre-algebra/pre-algebra-fractions/pre-algebra-mult-mixed-

num/v/multiplying-mixed-numbers?modal=1

https://www.khanacademy.org/math/pre-algebra/pre-algebra-fractions/pre-algebra-dividing-

fractions/v/another-dividing-fractions-example?modal=1

Compute without calculator.

1) 5 1

8 2 2)

2 3

3 4

3) 3 7

2 9 4)

8 1

7 3

5) 3

9 27

6) 5 1

4 36 4

Entering Algebra I (all levels) in the Middle School Summer Review Packet

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7) 3 2

7 54 3 8)

1 28 9

3 5

9) 1 1

1 22 2 10)

1 13 5

4 4

11) 3 7

4 9 12)

5 1

6 2

13) 1 1

3 22 5

14) 1 1

2 53 4

15) 7

58

16) 14

315

17) 6 3

11 4 18)

3 7

4 8

Entering Algebra I (all levels) in the Middle School Summer Review Packet

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III. Order of Operations

To evaluate numerical expressions containing more than one operation, use the rules for order of

operations. The rules are often summarized using the expression GEMDAS.

Watch the videos for a review of this topic:

https://www.khanacademy.org/math/pre-algebra/pre-algebra-arith-prop/pre-algebra-order-of-

operations/v/introduction-to-order-of-operations?modal=1

https://www.khanacademy.org/math/pre-algebra/pre-algebra-arith-prop/pre-algebra-order-of-

operations/v/order-of-operations?modal=1

Evaluate each expression.

1) 250 [5 (3 7 4)] 2) 2 250 (12 3 ) (6 1)

3) 2126 3

2 4) 28 (2 8) 2

5) 2 25 4 5 4

5(4)

6)

22 4 8 2

(5 2) 2

Entering Algebra I (all levels) in the Middle School Summer Review Packet

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IV. Evaluating Algebraic Expressions

To evaluate algebraic expressions, first replace the variables with their values. Then, use order of

operations to calculate the value of the resulting numerical expression.

Watch the video for a review of this topic:

https://www.khanacademy.org/math/algebra/introduction-to-algebra/alg1-substitution/v/evaluating-

expressions-in-two-variables?modal=1

Evaluate each expression.

1) 25 4 24x y y when x and y 2) 2 4( ) 2 4

5z x x when x and z

3) 3 4

2 37

xywhen x and y

x

4)

2 2212, 9, 4

y zwhen x y and z

x y z

Entering Algebra I (all levels) in the Middle School Summer Review Packet

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V. The Real Number System

The Real number system consists of two main sub-­‐groups Rational numbers and Irrational numbers.

The set of rational numbers includes several subsets: natural numbers, whole numbers, and integers.

Real Numbers-­‐ any number on the number line.

o Rational Numbers-­‐ a number that can be written as the ratio of two integers

(this includes decimals that have a definite end or repeating pattern)

• Examples: 3 7

2, 5, , 2 , 0.253, 0.34 8

• Integers--- positive and negative whole numbers and 0 • Examples: -5, -3, 0, 8, …

Whole Numbers --- the counting numbers from 0 to infinity

• Examples: {0, 1, 2, 3, 4, ….}

Natural Numbers --- the counting numbers from 1 to infinity • Examples: {1, 2, 3, 4, …}

o Irrational Numbers --- Non-terminating, non-repeating decimals

(including , and the square root of any number that is not a perfect square.)

• Examples: 2 , 3, 20, 3.21793156...

Name all the sets of which each number belongs. 1) -4.2

2) 8

3) 25

4) 5

3

5) 0

6) 12

4

Entering Algebra I (all levels) in the Middle School Summer Review Packet

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VI. The Distributive Property

The Distributive Property states for any number a, b, and c:

a(b + c) = ab + ac or (b + c)a = ba + ca

a(b − c) = ab − ac or (b − c)a = ba – ca

Watch the video for a review of this topic:

https://www.khanacademy.org/math/algebra-basics/alg-basics-algebraic-expressions/alg-basics-

distributive-property/v/distributive-property-with-variables-exercise

Rewrite each expression using the distributive property.

1) 7( 4)x 2) 3(2 5)x

3) 4(5 9)x 4) 1

(14 6 )2

y

5) 23(7 3 2)x x 6) 1

(16 12 4 )4

x y z

Entering Algebra I (all levels) in the Middle School Summer Review Packet

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VII. Combining Like Terms

Terms in algebra are numbers, variables or the product of numbers and variables. In algebraic

expressions terms are separated by addition (+) or subtraction (-) symbols. Terms can be combined

using addition and subtraction if they are like terms.

Like terms have the same variables to the same power.

Example of like-­‐terms: 5x2

and −6x2

Example of terms that are NOT like-­‐terms: 9x2

and 15x

Although both terms have the variable x, they are not being raised to the same power

Watch the videos for a review of this topic:

https://www.khanacademy.org/math/algebra/introduction-to-algebra/alg1-manipulating-

expressions/v/combining-like-terms?modal=1

https://www.khanacademy.org/math/algebra/introduction-to-algebra/alg1-manipulating-

expressions/v/combining-like-terms-and-the-distributive-property?modal=1

Simplify each expression

1) 5x − 9x + 2 2) 3q2

+ q − q2

3) c2

+ 4d 2

− 7d 2

4) 5x2

+ 6x −12x2

− 9x + 2

5) 2(3x − 4y) + 5(x + 3y) 6) 10x − 4(x + 2)

Entering Algebra I (all levels) in the Middle School Summer Review Packet

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VIII. Solving Equations

Watch the videos for a review of this topic:

https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-two-steps-equations-

intro/v/equations-2?modal=1

https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-two-steps-equations-

intro/v/solving-equations-1?modal=1

Solve each equation.

1) 98 = b + 34 2) −14 + y = −2

3) 8k = −64 4) 2

5x = 6

5) 14n − 8 = 34 6) 5 3 38n

Entering Algebra I (all levels) in the Middle School Summer Review Packet

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7) 4 15 21m 8) 12 75

d

9) 8 123

n 10) 12 9

2

x

11) 3( 4) 15x 12) 9 4 5 8x x

IX. Writing Algebraic Expressions

In algebraic expressions, letters such as x and w are called variables. A variable represents an

unspecified number or value.

Watch the video for a review of this topic:

https://www.khanacademy.org/math/algebra/introduction-to-algebra/alg1-writing-

expressions/v/writing-expressions-1?modal=1

Write an algebraic expression for each verbal expression.

1) Four times a number decreased by twelve

2) Three more than the product of five and a number

3) The quotient of two more than a number and eight

4) Seven less than twice a number

Entering Algebra I (all levels) in the Middle School Summer Review Packet

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X. Solving Word Problems

Watch the videos for a review of this topic:

https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-linear-eq-word-

probs/v/basic-linear-equation-word-problem?modal=1

https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-linear-eq-word-

probs/v/application-problems-with-equation-in-one-variable?modal=1

https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-linear-eq-word-

probs/v/linear-equation-word-problem-example?modal=1

Write an algebraic equation to model each situation. Then solve the equation and answer

the question.

1) A video store charges a one‐time membership fee of $11.75 plus $1.50 per video rental.

How many videos did Stewart rent if he spends $71.75?

2) Nick is 30 years less than 3 times Ray’s age. If the sum of their ages is 74, how old are each of

the men?

3) Three‐fourths of the student body attended the pep‐rally. If there were 1230 students at the pep

rally, how many students are there in all?

4) Sarah drove 3 hours more than Michael on their trip to Texas. If the trip took 37 hours, how

long did Sarah and Michael each drive?

Entering Algebra I (all levels) in the Middle School Summer Review Packet

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Answers to Odd problems

I. Integers

1) -50 3) -7 5) -36

7) 59 9) -112 11) -23

13) 10 15) -63 17) -9

II. Fractions

1) 1

8 3)

41 52

18 18

5) 46 4

67 7 7)

513

12

9) -1 11) 7

12

13) 77 7

710 10

15) 35 3

48 8

17) 8

11

III. Order of Operations

1) 2 3) 4 5) 1

IV. Evaluating Algebraic Expressions

1) 1896 3) 1

V. The Real Number System

1) rational and real

3) natural, whole, integer, rational, real

5) whole, integer, rational, real

VI. The Distributive Property

1) 7 28x 3) 20 36x 5) 221 9 6x x

VII. Combing Like Term

1) 4 2x 3) 2 23c d 5) 11 7x y

VIII. Solving Equations

1) 64b 3) 8k 5) 3n

7) 9m 9) 60n 11) 9x

IX. Writing Algebraic Expressions

1) 4 12x 3) 2

8

x

X. Solving Word Problems

1) 40 videos 3) 1640 students