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This page shows questions in the Math 7 Expressions and Equations public release module at MSDE. 7th Grade Math
"Math 7 Expressions and Equations"

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This is a multiple choice question that allows you to select several options.

Miguel eats a meal at a restaurant and leaves a 15 % tip for the server. The cost of the meal without the tip is p dollars.

Which expressions represent the total cost, in dollars, of the meal and the tip?

Select all that apply.

  1. A.
    1.15p
  2. B.
    15100p
  3. C.
    p+15
  4. D.
    p+0.15p
  5. E.
    p+1.15p
i1

To represent the tip, the student could have expressed the percent as the decimal 0.15. The amount of the tip for a breakfast that cost p dollars could be expressed at 0.15p. When the tip is added to the cost of the breakfast, the student could express the total cost as p + 0.15p. The distributive property could also be used to express the total cost as 1 × p + 0.15 × p = (1 + 0.15)p = 1.15p.i4

To represent the tip, the student could have expressed the percent as the decimal 0.15. The amount of the tip for a breakfast that cost p dollars could be expressed at 0.15p. When the tip is added to the cost of the breakfast, the student could express the total cost as p + 0.15p. The distributive property could also be used to express the total cost as 1 × p + 0.15 × p = (1 + 0.15)p = 1.15p.

This is a fill in the blank question that allows you to enter only numbers.

A certain three-dimensional figure has one base and 3 faces.

  • The area of each face is the same.
  • The area of the base is 5 square centimeters.
  • The total surface area of the figure, including the base, is 26 square centimeters.

What is the area of one face of the three-dimensional figure?

Enter your answer in the space provided.

square centimeters

To determine the area of one face, the student could first find the total area of the three faces by subtracting 5, the area of the base, from 26 which was 21. Since the area of each face is the same, the student could divide 21 by 3 and conclude that the area of one face is 7 square centimeters.

This is a drag and drop question that allows you to select text and place it in an appropriate answer space.

Consider the following expression.

−2(w−3)+5(6w+4)

Create an equivalent expression with exactly two terms.

Move a number into each box.

( −32 ) ( −28 ) ( −26 ) ( −14 ) 14 26 28 32

w+

To determine an equivalent expression, the student could apply the distributive property to each quantity in parentheses. The first quantity could be rewritten as (–2 × w) + (–2 × –3) = (–2w) + (6) = –2w + 6. The second quantity could be rewritten as (5 × 6w) + (5 × 4) = 30w + 20. The sum of the two quantities could then be written as–2w + 6 + 30w + 20 = –2w + 30w + 6 + 20 = (–2 + 30)w + 26 = 28w + 26.

This is a multiple choice question that allows you to select only one option.

A volunteer is planning to hold tutoring sessions next year to tutor students in math and science.

  • The volunteer will provide 4 tutoring sessions each month.
  • The number of hours the volunteer will tutor in each session is the same.
  • The volunteer will spend 1 hour of each session tutoring science.
  • The volunteer wants to spend at least 120 hours tutoring next year.

The inequality 48(x+1)≥120 can be used to represent this situation.

What is the meaning of the possible solutions for x in the inequality?

  1. A.
    the number of hours spent tutoring math per month
  2. B.
    the number of hours spent tutoring math per session
  3. C.
    the number of hours spent tutoring science per month
  4. D.
    the number of hours spent tutoring science per session
i2

Correcti1

Misrepresented the frequency of the tutoring sessionsi3

Misrepresented the subject and the frequency of the tutoring sessionsi4

Misrepresented the subject

This is a multiple choice question that allows you to select only one option.

At the end of the year 2010, a business had 140 stores in the United States. By the end of the year 2016, the number of stores in the United States had increased by 60%, and 114 of the total number of stores were located in California.

How many stores were located in California at the end of the year 2016 ?

Select one answer.

  1. A.
    6
  2. B.
    10
  3. C.
    14
  4. D.
    16
i4

To determine the exact number of stores at the end of 2016, the student could have found the increase in the number of stores in the United States by first expressing the percent of increase as 60/100 or 0.6. Then, solving 0.6 × 140, the student could conclude that the increase in the United States was 84 stores bringing the total number in the United States to 140 + 84 or 224 stores. To determine the number of stores located in California, the student could find (1/14) of 224 by solving (1/14) × 224, resulting in 16 stores. i1

Multiplied 0.6 and 1/14 first, then multiplied by 140 i2

Just found 1/14 of 140 i3

Added 60 and 140, then found 1/14 of 200 and rounded the answer