Download Summer Packet EnteringGrade7

2014-2015 (entering) Grade 7 Summer Math Packet
Dear Students and Parents:
The purpose of this packet is to review math concepts as you look forward to pre-algebra next
year. All concepts in this packet have been previously covered in 6th grade. Please use this
summer to assure all pre-requisite concepts have been understood. This packet will be checked
for completion by the end of the first week back in September (9/15). Show all your work for
each problem.
Have a wonderful summer!
Operations with Integers
Evaluate each expression.
Remember that - (-) = +. There must be no number between the two negatives.
1. -8 – (-5) =
2. 12 – 18 =
3. -7 – 12 + 5 =
4. –(-4) + 8 =
5. 10 – (-4) =
6. -9 – 12 – (-15) =
For #7-9, Substitute the given value for the variable and evaluate. x = - 2, y = -5
7. x + y =
8. y – x =
9. 2x + 3y =
10. 18 – (-20) =
11. -45 ÷ 5 =
12.
-36
=
12
14. 15 – 13 – (-9) =
15.
-4
=
2
13.
-4
=
-4
1
16.
=
19. 12 - 3
22. 5
5
7
2
2
-3
5
7
1
3
17. 3 -1
4 =
9
1 1
2 15
20. 13 ×1
23. 2
3 1
¸5
7 5
æ 2ö æ 5ö
18. ç 4 ÷ ¸ ç1 ÷ =
è 3ø è 9ø
1
8
21. 3 + 5
5
6
24. 4
2 1
2
+3 +2
6
9
3
Order of Operations
25.
32 + (18  3 3)  9
28. 3(4 + 7) – 42
26. 30 – 3(15 – 12)2
29. 15
5 7 – 18
27. 5[6 + 4 - 8]3 – 12
30. 6 + 4(7 – 4)
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Solving Equations: Here is an example: The check is a required step!
Work to Both Sides
Fact Family
5x – 3 = 12
+ 3 +3
5x = 15
5
5
x=3
5x – 3 = 12
5x = 12 + 3
5x = 15
x = 15 5
x=3
Check:
Does 5(3) – 3 = 12?
15 – 3 = 12
12 = 12 ✓
Solve the equation. Must solve using either fact family method or doing work to both
sides. Include a check.
3
1
2
1
31.
32. 2x + 4 = 28
33. 4x + = 3
x=2
4
3
3
2
34.
37.
2
2
x=
7
3
2x +1.5 = 3.7
35. 6x – 12 = 48
38.
3 1
x- =
5 2
36. x + 5.5 = 7.2
39. 3x + 7 = 19
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Solving Inequalities: Here is an example:
Work to Both Sides
5x – 3 < 12
+ 3 +3
5x < 15
5
5
x<3
Fact Family
Graph:
5x – 3 < 12
5x < 12 + 3
5x < 15
x < 15 5
x<3
Solve the inequality. Must solve using either fact family method or doing work to both
sides. Graph your solution.
40. 3x -12 £ 9
41. 5x + 7 > 32
42. 6x - 3 <15
Operations with Decimals – Use standard algorithm for multiplying and dividing. When
dividng, round to the hundredths place, if necessary.
43. 10.5 – 3.78
44. 13.2 + .007
45. 1.75 – 0.04
46. (4.5)(3.8)
46) (2.45)(1.2)
47) 3(1.74)
48) 32.7
49) 5.6
50) 1.89
0.12
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1.3
4
Surface Area and Volume
51. Find the surface area and volume of the rectangular prism
52. Find the surface area of the triangular prism.
Measures of Center and MAD
Follow these steps to find the mean absolute deviation
1) Find the mean of the data
2) Find the distance each number is from the mean
3) Take the average mean of the absolute value of the distances
For #s 53 – 57, use the following set of data: 5, 7, 8, 3, 5, 3, 10, 2, 5, 8
53. Find the mean.
54. Find the median.
55. Find the mode.
56. Find the range.
57. Find the Mean Absolute Deviation (MAD)
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Translating Expressions and Equations
Translate each sentence into an equation. Include let statements to define your variables.
58. The cost in dollars is equal to 16 times the number of people.
59. 40 miles per hour for a given number of hours must equal 350 miles.
60. Sales tax is 7% of the total purchase.
61. Deanna has $150 in her account. At the end of each week, she plans to take $15 out of her
account for her spending money. Write an equation to show the relationship between the
number of weeks and the balance in the account.
My child completed this packet over the summer and will be ready to submit it by the end
of the first week back to school in September. (9/15)
Parent Signature
_______________________________
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