Grade 7 Open Response Problems by Strand

Number Sense

2008 Spring Release, Mathematics - Grade 7
Question 22: Open-Response
Reporting Category: Number Sense and Operations
Standard: 7.N.9 - Select and use appropriate operations—addition, subtraction, multiplication, division, and positive integer exponents—to solve problems with rational numbers (including negatives). This standard is intentionally the same as standard 8.N.12.

Drew's goal was to earn $150 during a four-week period in the summer.
  1. The first week, Drew earned 50% of his goal amount. What was the total amount of money that Drew earned the first week? Show or explain how you got your answer.
  2. The second week, Drew earned 50% of the part of his goal amount that he had left to earn after the first week. What was the total amount of money that Drew earned the second week? Show or explain how you got your answer.
  3. The third week, Drew earned 50% of the part of his goal amount that he had left to earn after the second week. What was the total amount of money that Drew earned the third week? Show or explain how you got your answer.
  4. The fourth week, Drew earned exactly enough money to reach his goal amount. What percent of Drew's original goal amount did he earn in the fourth week? Show or explain how you got your answer.

2007 Spring Release, Mathematics - Grade 7
Question 9: Open-Response
Reporting Category: Number Sense and Operations
Standard: 7.N.9 - Select and use appropriate operations—addition, subtraction, multiplication, division, and positive integer exponents—to solve problems with rational numbers (including negatives). This standard is intentionally the same as standard 8.N.12.

Sandy purchased three trees.

  • The price of the first tree was $63.50.
  • The price of the second tree was equal to twice the price of the first tree.
  • The price of the third tree was equal to of the price of the second tree.

a. / What was the price of the second tree? Show or explain how you got your answer.
b. / What was the price of the third tree? Show or explain how you got your answer.
c. / What was the total of the prices of all three trees? Show or explain how you got your answer.
d. / Sandy had to pay sales tax of 5% on her purchase. What was the total amount of Sandy's purchase of three trees, including tax? Show or explain how you got your answer.

2006 Spring Release, Mathematics - Grade 7
Question 22: Open-Response
Reporting Category: Number Sense and Operations
Standard: 7.N.9 - Select and use appropriate operations—addition, subtraction, multiplication, division, and positive integer exponents—to solve problems with rational numbers (including negatives). This standard is intentionally the same as standard 8.N.12.

Jeremy had some bricks that he was going to use to build a short wall on his patio, next to his garden.

  1. Each brick is 8 inches long, as shown below. What is the total length of a row of 4 bricks? Show your work or explain how you got your answer.
  1. Each brick is 2 inches high, as shown below. What is the total height of a stack of 4 bricks? Show your work or explain how you got your answer.

To build the wall, Jeremy first spread a -inch layer of mortar, then placed a layer of bricks, then spread another -inch layer of mortar, and so on. Five layers of bricks, with mortar, are pictured below. (A finished brick wall has bricks, not mortar, on top.)

Mortar
(Each layer is in. high) /
  1. How many layers of bricks, with mortar, did Jeremy need in order to make the wall a total of 21 inches high? Show or explain how you got your answer.

Patterns Relations and Algebra

2010 Spring Release, Mathematics - Grade 7
Question 17: Open-Response
Reporting Category: Patterns, Relations, and Algebra
Standard: 7.P.3 - Create and use symbolic expressions for linear relationships and relate them to verbal, tabular, and graphical representations.

An almanac states that it is possible to determine the temperature by counting the number of times a cricket chirps. To use cricket chirps to determine the temperature in degrees Celsius, the almanac gives the steps below.

  • Count the number of times a cricket chirps in 25 seconds.
  • Divide that number by 3.
  • Then add 4 to get the temperature in degrees Celsius.
  1. Use the information from the almanac to show that when a cricket chirps 27 times in 25 seconds, the temperature is 13 degrees Celsius.
  2. In your Student Answer Booklet, copy the table below, and fill in the missing numbers using the information from the almanac. Show or explain how you got your answers.

Number of
Chirps in
25 Seconds / Temperature
(degrees Celsius)
27 / 13
48 / ?
? / 28
  1. Based on your table, write an expression that can be used to calculate the temperature in degrees Celsius when a cricket chirps n times in 25 seconds.

2008 Spring Release, Mathematics - Grade 7
Question 9: Open-Response
Reporting Category: Patterns, Relations, and Algebra
Standard: 7.P.3 - Create and use symbolic expressions for linear relationships and relate them to verbal, tabular, and graphical representations.

The label on the can of paint that Chang bought stated that 1 gallon of paint will cover 300 square feet.
  1. In your Student Answer Booklet, copy the table below. (Do not use the grid for the table.) Based on the information on the label, complete the table for the numbers of gallons listed. Show or explain how you got each answer.

Paint Coverage
Number of Gallons / Area Covered
(in square feet)
1 / 300
2
3
4
  1. Write an expression that represents the number of square feet that g gallons will cover.
  2. On the grid in your Student Answer Booklet, graph the relationship between the number of gallons of paint used and the area covered by the paint using the data from your table in part (a). Be sure to title your graph and label your axes.

2007 Spring Release, Mathematics - Grade 7
Question 22: Open-Response
Reporting Category: Patterns, Relations, and Algebra
Standard: 7.P.3 - Create and use symbolic expressions for linear relationships and relate them to verbal, tabular, and graphical representations.

Mary took 7 hours to read a biography that had 210 pages.

a. / What was Mary's average reading rate, in pages per hour? Show or explain how you got your answer.
b. / In your Student Answer Booklet, copy the table below, and complete it using Mary's average reading rate from part (a).

Mary's Reading Rate

Number of
Hours (x) / Number of
Pages (y)
1
2
3
4
c. / Write an equation that represents the relationship between x, the number of hours Mary read, and y, the number of pages she read.
d. / How long will it take Mary to read 80 pages at the same average reading rate? Show or explain how you got your answer.

2006 Spring Release, Mathematics - Grade 7
Question 39: Open-Response
Reporting Category: Patterns, Relations, and Algebra
Standard: 7.P.3 - Create and use symbolic expressions for linear relationships and relate them to verbal, tabular, and graphical representations.

Danny saved money to buy a bike that cost a total of $150. He saved the same amount of money each week until he had enough money to pay for the bike. The table below shows how much money Danny still needed at the end of each of the first five weeks of saving.

Money Still Needed for Bike
at End of Week

Week Number / Money Needed
1 / $135
2 / $120
3 / $105
4 / $90
5 / $75
  1. How much money did Danny save each week? Show or explain how you got your answer.
  2. On the grid in your Student Answer Booklet, graph the data from the table. Be sure to title your graph and label the axes.
  3. How much money did Danny still need to save after he had saved for 7 weeks? Show or explain how you got your answer.
  4. Write an equation that could be used to find a, the amount of money Danny still needed to save after he saved for w weeks.

Geometry

2009 Spring Release, Mathematics - Grade 7
Question 14: Open-Response
Reporting Category: Geometry
Standard: 7.G.3 - Demonstrate an understanding of the relationships of angles formed by intersecting lines, including parallel lines cut by a transversal. This standard is intentionally the same as standard 8.G.3.

Parallel lines n and p are intersected by transversal lines q and m, as shown in the figure below.

Lines q, m, and p intersect at a common point.

  1. What is the degree measure of 1? Show or explain how you got your answer.
  2. What is the degree measure of 2? Show or explain how you got your answer.
  3. What is the degree measure of 3? Show or explain how you got your answer.
  4. What is the degree measure of 4? Show or explain how you got your answer.

2008 Spring Release, Mathematics - Grade 7
Question 39: Open-Response
Reporting Category: Geometry
Standard: 7.G.6 - Predict the results of translations and reflections of figures on unmarked or coordinate planes and draw the transformed figure.

On the grid in your Student Answer Booklet, copy the x-axis, the y-axis, and triangle LMN shown below.

  1. On your grid, draw the image of triangle LMN after it is translated 4 units to the left. Label the image PQR. List the coordinates for points P, Q, and R.
  2. On your grid, draw the image of triangle LMN after it is translated 6 units up and 3 units to the right. Label the image TUV. List the coordinates for points T, U, and V.
  3. On your grid, draw the image of triangle LMN after it is reflected over the x-axis. Label the image XYZ. List the coordinates for points X, Y, and Z.

2007 Spring Release, Mathematics - Grade 7
Question 39: Open-Response
Reporting Category: Geometry
Standard: 7.G.4 - Graph points and identify coordinates of points on the Cartesian coordinate plane (all four quadrants).
Standard 7.G.4 is intentionally the same standard as 6.G.4, which is not currently being assessed at grade 6. Standard 7.G.4 will be assessed at grade 7.

Copy the x-axis and y-axis shown below onto the grid in your Student Answer Booklet.

a. / Plot and label point P(4, 6) and point Q(4, 2) on your grid.
b. / Line segment PQ is one side of a rectangle. On your grid, draw rectangle PQRS with a length of 4 units and a width of 2 units.
  • Label point R and point S.
  • Write the coordinates of point R and point S.

c. / On your grid, draw the two diagonals of rectangle PQRS. What are the coordinates of the point where the two diagonals intersect?

2006 Spring Release, Mathematics - Grade 7
Question 9: Open-Response
Reporting Category: Geometry
Standard: 7.G.6 - Predict the results of translations and reflections of figures on unmarked or coordinate planes and draw the transformed figure.

Copy the x-axis and the y-axis, as shown below, onto the grid in your Student Answer Booklet.

The coordinates of three of the four vertices of rectangle PQRS are given below.

  • Point P: (2, 5)
  • Point Q: (6, 5)
  • Point R: (6, 2)
  1. On your grid, plot and label points P, Q, and R.
  2. On your grid, locate and plot the fourth vertex of the rectangle and label it S. Draw rectangle PQRS.
  3. On your grid, draw the reflection of rectangle PQRS over the x-axis.
  4. Based on the reflection you performed in part (c), write the coordinates of the point that is the image of point P.

Measurement

2009 Spring Release, Mathematics - Grade 7
Question 17: Open-Response
Reporting Category: Measurement
Standard: 7.M.3 - Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms and cylinders. Use technology as appropriate.

Ray had a block of wood in the shape of a rectangular prism. The block and its dimensions are shown below.

  1. Ray painted the front face of the block red. What is the area, in square inches, of the face he painted red? Show or explain how you got your answer.
  2. Ray painted the top and bottom faces of the block black. What is the area, in square inches, of the faces he painted black? Show or explain how you got your answer.
  3. Ray painted the other faces of the block white. What is the area, in square inches, of the faces he painted white? Show or explain how you got your answer.

2008 Spring Release, Mathematics - Grade 7
Question 28: Open-Response
Reporting Category: Measurement
Standard: 7.M.1 - Select, convert (within the same system of measurement), and use appropriate units of measurement or scale. This standard is intentionally the same as standard 8.M.1.

A park near Jon's house has a jogging trail that is 2640 yards long.

  1. What is the length, in feet, of the jogging trail? Show or explain how you got your answer.
  2. Using your answer from part (a), determine the length, in miles, of the jogging trail. Show or explain how you got your answer. (1 mile=5280 feet)
  3. The jogging trail starts at the entrance to the park and ends at a pond. The trail starts with a sign, ends with a sign, and has a sign posted along the trail every mile. What is the total number of signs along the trail from the beginning to the end? Show or explain how you got your answer.

2007 Spring Release, Mathematics - Grade 7
Question 29: Open-Response
Reporting Category: Measurement
Standard: 7.M.3 - Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms and cylinders. Use technology as appropriate.

The figure below is a rectangle with a semicircle at one of its ends.

The radius of the semicircle is 5 feet, and the dimensions of the rectangle are 10 feet by 16 feet.

a. / What is the diameter, in feet, of the semicircle? Show or explain how you got your answer.
b. / What is the length, in feet, of the curved part of the semicircle? Show or explain how you got your answer. (Use 3.14 for π.)
c. / What is the perimeter, in feet, of the figure? Show or explain how you got your answer.

2006 Spring Release, Mathematics - Grade 7
Question 28: Open-Response
Reporting Category: Measurement
Standard: 7.M.3 - Demonstrate an understanding of the concepts and apply formulas and procedures for determining measures, including those of area and perimeter/circumference of parallelograms, trapezoids, and circles. Given the formulas, determine the surface area and volume of rectangular prisms and cylinders. Use technology as appropriate.

A park has a rose garden with the dimensions shown below. A 36-inch-wide sidewalk surrounds the rose garden.

  1. What are the total length and the total width, in feet, of the park? Show or explain how you got your answers.
  2. What is the perimeter, in feet, of the park? Show or explain how you got your answer.
  3. What is the area, in square feet, of the entire sidewalk? Show or explain how you got your answer.

Data, Statistics and Probability

2010 Spring Release, Mathematics - Grade 7
Question 8: Open-Response
Reporting Category: Data Analysis, Statistics, and Probability
Standard: 7.D.3 - Use tree diagrams, tables, organized lists, and area models to compute probabilities for simple compound events, e.g., multiple coin tosses or rolls of number cubes.

Madison plans to sew one button and one ribbon on a clown costume. She has one each of the following colors of buttons in her pocket:

  • black
  • green
  • red
  • white

All the buttons are the same size and shape.Madison will select one button from her pocket without looking.

  1. What is the probability that she will select a red button? Show or explain how you got your answer.

Madison has one each of the following colors of ribbon in a bag:

  • black
  • white
  • yellow

All the ribbons are the same size and material. She will select one button from her pocket and one ribbon from her bag without looking.

  1. Make an organized list or a tree diagram showing all the possible color combinations that Madison could select.
  2. What is the probability that Madison will select a black button and a black ribbon? Show or explain how you got your answer.
  3. What is the probability that Madison will select a button and a ribbon that are different colors from each other? Show or explain how you got your answer.

2008 Spring Release, Mathematics - Grade 7
Question 29: Open-Response
Reporting Category: Data Analysis, Statistics, and Probability
Standard: 7.D.2 - Find, describe, and interpret appropriate measures of central tendency (mean, median, and mode) and spread (range) that represent a set of data. Use these notions to compare different sets of data. This standard is intentionally the same as standard 8.D.3.

The table below shows the state sales tax rates on purchased goods in the year 2005 for the six New England states.
2005 Sales Tax Rates
in New England States
States / Sales Tax Rate
Connecticut / 6%
Maine / 5%
Massachusetts / 5%
New Hampshire / 0%
Rhode Island / 7%
Vermont / 6%
  1. What was the range of 2005 sales tax rates for the New England states? Show or explain how you got your answer.
  2. What was the mean sales tax rate in 2005 for the New England states? Show or explain how you got your answer.
  3. What was the median sales tax rate in 2005 for the New England states? Show or explain how you got your answer.
  4. A newspaper reporter stated that the mode of the 2005 sales tax rates for the New England states was 5%. Was the reporter correct? Explain your reasoning.