Summer Packet for Students Entering 7th Grade



2016-2017 (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 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 beginning of the first week back. 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. [pic] =

13. [pic] = 14. 15 – 13 – (-9) = 15. [pic] =

17. [pic] = 18. [pic] =

19. [pic] 20. [pic] 21. [pic]

22. [pic] 23. [pic] 24. [pic]

Order of Operations

25. 32 + (18 [pic] 3 [pic] 3)[pic] 9 26. 30 – 3(15 – 12)2 27. 5[6 + 4 - 8]3 – 12

28. 3(4 + 7) – 42 29. 15 [pic] 5 [pic] 7 – 18 30. 6 + 4(7 – 4) [pic] 6

|Work to Both Sides | Fact Family |Check: |

| | | |

|5x – 3 = 12 |5x – 3 = 12 |Does 5(3) – 3 = 12? |

|+ 3 +3 |5x = 12 + 3 |15 – 3 = 12 |

|5x = 15 |5x = 15 |12 = 12 ✓ |

|5 5 |x = 15 [pic] 5 | |

|x = 3 |x = 3 | |

Solving Equations: Here is an example: The check is a required step!

Solve the equation. Must solve using either fact family method or doing work to both sides. Include a check.

31. [pic] 32. [pic] 33. [pic]

34. [pic] 35. 6x – 12 = 48 36. x + 5.5 = 7.2

37. [pic] 38. [pic] 39. 3x + 7 = 19

|Work to Both Sides | Fact Family |Check: |

| | | |

|5x – 3 = 12 |5x – 3 = 12 |Does 5(3) – 3 = 12? |

|+ 3 +3 |5x = 12 + 3 |15 – 3 = 12 |

|5x = 15 |5x = 15 |12 = 12 ✓ |

|5 5 |x = 15 [pic] 5 | |

|x = 3 |x = 3 | |

Solving Inequalities: Here is an example:

|Work to Both Sides | Fact Family |Graph: |

| | | |

|5x – 3 < 12 |5x – 3 < 12 | |

|+ 3 +3 |5x < 12 + 3 | |

|5x < 15 |5x < 15 | |

|5 5 |x < 15 [pic] 5 | |

|x < 3 |x < 3 | |

Solve the inequality. Must solve using either fact family method or doing work to both sides. Graph your solution.

40. [pic] 41. [pic] 42. [pic]

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 [pic] 0.12 49) 5.6 [pic] 3 50) 1.89 [pic] 1.3

Surface Area and Volume

51. Find the surface area and volume of the rectangular prism

52. Find the surface area of the triangular prism.

Mean Median and Mode

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.

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 beginning of the first week back to school.

Parent Signature

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