Download POWELL MATH STUDENTS Summer Math Skills

POWELL MATH STUDENTS
Summer Math Skills
_____________________________________________________________________________________
Dear Parents/Guardians and Math Students,
The Math teachers at Powell Middle School are looking forward to working with you to ensure a
productive school year! Powell Middle School maintains high expectations and we are expecting students
to practice and develop their skills over the summer to start the year off strong! We have put together
this packet with important information and valuable practice activities to prepare you for the beginning
of the school year. This work is to be completed prior to your first day of school. The skills packet is due
on Friday, September 9, 2016. It is expected that you complete this packet, as it will count as your first
formative assessment grade for the first semester of the 2016-2017 school year.
Enjoy your summer!
Powell Middle School Math Department
Mrs. Chriss
Mrs. Sloane
Mrs. Hart
Ms. Zito
Mrs. Morici
_____________________________________________________________________________________
DIRECTIONS:
• You should complete all the problems in this packet.
• YOU MUST SHOW ALL WORK FOR EACH PROBLEM IN ORDER TO RECEIVE CREDIT.
If you need help during the summer on this packet, use the websites included on the Resource Page at the
end of the packet. If you should misplace or lose your packet, you can download a copy from the Powell
Middle School web page. In addition, if you check our web page, and click on the summer math icon, you
will find dates and times where you can meet with a Powell math teacher for assistance.
Do your best to complete this math skills packet. Be sure to spend adequate time answering the
questions with accuracy. The more you prepare for this upcoming school year, the more
successful you will be! 
Online Resources (videos & practice problems)
Adding and subtracting rational numbers:
www.khanacademy.org/math/algebra-basics/core-algebra-foundations/core-algebra-foundations-negativenumbers/v/adding-and-subtracting-negative-number-examples
Adding and subtracting positive/negative fractions:
https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/fractions-unlike-denom-prealg/e/adding_and_subtracting_fractions
Multiplying positive/negative integers:
https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations/core-algebra-foundationsnegative-numbers/v/multiplying-positive-and-negative-numbers
Multiplying positive/negative fractions:
https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/multiplying-fractions-pre-alg/v/multiplyingnegative-and-positive-fractions
Dividing positive/negative integers:
https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations/core-algebra-foundationsnegative-numbers/v/dividing-positive-and-negative-numbers
Dividing positive/negative fractions:
https://www.khanacademy.org/math/arithmetic/fractions/div-fractions-fractions/e/dividing_fractions_2
Evaluating expressions:
https://www.khanacademy.org/math/algebra-basics/core-algebra-expressions/core-algebra-variables-andexpressions/e/evaluating_expressions_2
Order of operations:
https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations/algebra-foundations-order-ofoperations/e/order_of_operations
Combining Like Terms:
https://www.khanacademy.org/math/algebra-basics/core-algebra-expressions/core-algebra-manipulatingexpressions/e/combining_like_terms_2
One-Step Equations (positive/negative):
https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/core-algebrasolving-basic-equations/e/one_step_equations
One-Step Equations Decimals/Fractions:
https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-one-step-add-subequations/e/one-step-add-sub-equations-2
One-Step Equations Multiplication/Division:
https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/core-algebrasolving-basic-equations/e/linear_equations_1
One-Step Equations Multiplication/Division-Fractions and Decimals:
https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/core-algebrasolving-basic-equations/e/linear_equations_1
Graphing Rates/Proportional Relationships:
https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/core-algebrasolving-basic-equations/e/linear_equations_1
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/cc-8th-graphingprop-rel/v/graphing-proportional-relationships-example-2
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-ratio-proportion/cc-7th-equations-ofproportional-relationships/v/equations-of-proportional-relationships
Writing equations for proportional relationships:
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-ratio-proportion/cc-7th-equations-ofproportional-relationships/v/equations-of-proportional-relationships
Part 1: Adding Rational Number – Find each sum. Show all work and write all answers in simplest
form.
1. 9 + (-3) =
2. -12 + -5 =
3. -11 + 6 =
4. -12 + 7 + (-3) =
7
2
2
3
7. - + 3 =
4
5
5. - +
3
=
20
8. 7.23 + (-8.36) =
6
7
6. -8 + - =
9. -8.5 + (-9.38) =
Part 2: Subtracting Rational Number – Find each difference. Show all work and write all answers in
simplest form.
10. 4 – (-6) =
11. -10 – 4 =
12. 6 – (-6) – 9 =
1 5
=
6 12
14.
1
3
17. -12.41 – (-9.95) =
13. - -
9
4
16. - - - =
9
-3=
10
3
4
5
6
15. 5 - -4 =
18. 2 – 8.25 =
Part 3: Multiplying & Dividing Rational Number – Find each product or quotient. Show all work and
write all answers in simplest form.
19. 4 ∙ (-3) =
20. -6 ∙ 5 ∙ -2 =
21. -8(-2) =
22. 12 ÷ -6 =
25.
-21
=
-3
23. -35 ÷ -5 =
24.
-56
=
7
26. -1.2 ∙ 2.5 =
27. -3.7 ∙ -2.1 =
3
21
=
∙
14 12
29. -
28. -
3
10
∙ - =
4
9
30. -
3
÷
7
11
=
35
÷
5
6
31. 1 ¸ (-30) =
32. -
1
13
=
÷
9
30
33. -0.81 ÷ -0.9 =
Part 4: Order of Operations – Simplify each expression. Show all work.
34. -12 – 5 ∙ 2 =
35. (10 – 12)2 =
36. 10 – 4(-5 – 1) =
37. 18 ÷ -6 – 5 ∙ -2 =
38. 9 – 2(4 – 5 – 6) =
39. -4 ∙ 7 ÷ 14 ∙ -5 =
Part 5: Combining Like Terms – Simplify each expression.
40.
5x + 8 – 2x
41.
-12 + 6n – 3n + 7
42.
43.
45.
x2 + 3x + 5x + 2x2
44.
-14 + 3w – 9w + 10
4g – 7g + 6 + g
4n2 – 7n + 3 + 5n – 1
Part 6: Solving One-Step Equations – Solve each equation. Show all work and check each solution.
46.
x – 15 = 25
47.
n + -6 = 13
48.
-7b = 35
Check Step:
49.
Check Step:
x
=3
9
50.
Check Step:
-3r = -42
Check Step:
51.
-18 + c = 32
Check Step:
Check Step:
52.
12.5 + h = -31.6
p
= 14
-2
53.
Check Step:
54.
-4.2w = -8.4
Check Step:
Check Step:
55.
1
- x=9
3
56.
n – 19 = -21
Check Step:
Check Step:
57.
k – (-3.8) = 4.7
Check Step:
Part 7: Proportional Relationship Scenarios – Create a table, graph, and equation for each scenario.
Mrs. Chriss is taking her family up north. She drives an average of 65 miles per hour. Create a
table, graph, and equation to show the relationship between time, t, and distance, d.
61. Table:
62. Graph:
63. Equation:
Powell is selling t-shirts to raise money for a field trip to Cedar Point. They earn a profit of $5 for
every shirt they sell. Create a table, graph, and equation to show the relationship between the
number of shirts they sell, n, and their total profit, p.
64. Table:
65. Graph:
66. Equation:
Ethan planted a tree that is 20 inches tall. Create a table, graph, and equation to show the height
of the tree, h, after y years, if it grows an average of 3 inches every year.
67. Table:
68. Graph:
69. Equation:
Part 8: Proportional Relationships (Writing Equations) – Write an equation for each table and graph.
70.
71.
72.
Equation:
73.
Equation:
Equation:
74.
Equation:
75.
Equation:
Equation:
Online Resources (videos & practice problems)
Adding and subtracting rational numbers:
www.khanacademy.org/math/algebra-basics/core-algebra-foundations/core-algebra-foundations-negativenumbers/v/adding-and-subtracting-negative-number-examples
Adding and subtracting positive/negative fractions:
https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/fractions-unlike-denom-prealg/e/adding_and_subtracting_fractions
Multiplying positive/negative integers:
https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations/core-algebra-foundationsnegative-numbers/v/multiplying-positive-and-negative-numbers
Multiplying positive/negative fractions:
https://www.khanacademy.org/math/pre-algebra/fractions-pre-alg/multiplying-fractions-pre-alg/v/multiplyingnegative-and-positive-fractions
Dividing positive/negative integers:
https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations/core-algebra-foundationsnegative-numbers/v/dividing-positive-and-negative-numbers
Dividing positive/negative fractions:
https://www.khanacademy.org/math/arithmetic/fractions/div-fractions-fractions/e/dividing_fractions_2
Evaluating expressions:
https://www.khanacademy.org/math/algebra-basics/core-algebra-expressions/core-algebra-variables-andexpressions/e/evaluating_expressions_2
Order of operations:
https://www.khanacademy.org/math/algebra-basics/core-algebra-foundations/algebra-foundations-order-ofoperations/e/order_of_operations
Combining Like Terms:
https://www.khanacademy.org/math/algebra-basics/core-algebra-expressions/core-algebra-manipulatingexpressions/e/combining_like_terms_2
One-Step Equations (positive/negative):
https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/core-algebrasolving-basic-equations/e/one_step_equations
One-Step Equations Decimals/Fractions:
https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-one-step-add-subequations/e/one-step-add-sub-equations-2
One-Step Equations Multiplication/Division:
https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/core-algebrasolving-basic-equations/e/linear_equations_1
One-Step Equations Multiplication/Division-Fractions and Decimals:
https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/core-algebrasolving-basic-equations/e/linear_equations_1
Graphing Rates/Proportional Relationships:
https://www.khanacademy.org/math/algebra-basics/core-algebra-linear-equations-inequalities/core-algebrasolving-basic-equations/e/linear_equations_1
https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-linear-equations-functions/cc-8th-graphingprop-rel/v/graphing-proportional-relationships-example-2
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-ratio-proportion/cc-7th-equations-ofproportional-relationships/v/equations-of-proportional-relationships
Writing equations for proportional relationships:
https://www.khanacademy.org/math/cc-seventh-grade-math/cc-7th-ratio-proportion/cc-7th-equations-ofproportional-relationships/v/equations-of-proportional-relationships