G6 U3 Constructed Response
Name: ________________________________________ Date:_______________
Grade 6 Unit 3 Constructed Response Graphing TASK 1: Ordered Pairs, Points on a Plane (CCSS 6.NS.6, 6.NS.8; SMP 1, 2, 4, 6)
1. Use the coordinate grid below to graph and label each point: y
Graph and label the points: a. S(−8, −4) b. T(5, −1)
7 6
U
5 4 3 2
Name the ordered pair for each point
1 −7
−6
−5
−4
V
−3
−2
−1 −1 −2 −3
1
2
3
4
5
6
7
x
c. U _________ d. V _________
−4 −5 −6 −7
e. In complete sentences, explain each step necessary to plot an ordered pair on a coordinate grid.
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Grade 6 Unit 3 Constructed Response Graphing 2. Draw a coordinate grid. Label the x and y-axes with a reasonable range and scale. Plot and label each point provided in the box below.
{ (
) (
) (
) (
) (
a. Identify the quadrant each point is located in. Point
Quadrant
Copyright © Swun Math Grade 6 Unit 3 Constructed Response, Page 2
) (
)}
Grade 6 Unit 3 Constructed Response Graphing 3. a. Explain how you chose the range and scale for the x and y-axes in question.
b. How do question 1 and 2 connect to other mathematical concepts that you have learned? How were these concepts useful in helping you understand the coordinate plane?
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Grade 6 Unit 3 Constructed Response Graphing TASK 2: Symmetry, Rational Numbers and the Coordinate Plane (CCSS: 6.NS.6, 6.NS.8; SMP: 1, 2, 4, 6)
4. a. Draw a coordinate grid. Label the x and y-axes with a reasonable range and scale. Plot and label each group of ordered pairs provided in the box below. { ( { (
) ( ) (
)} )}
b. Analyze the coordinate grid you created. Identify the quadrants in which the ordered pairs are located and describe their relationship. Use the mathematical language you have learned to describe this relationship.
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Grade 6 Unit 3 Constructed Response Graphing 5. Draw a coordinate grid. Label the x and y-axes with a reasonable range and scale. Plot and label each point provided in the box below. { (
) (
) (
) (
) (
) (
)}
6. a. After graphing the ordered pairs, identify and describe the type of numbers that you worked with. How do they compare to the numbers you worked with in questions 1 and 2?
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Grade 6 Unit 3 Constructed Response Graphing b. Was the process for placing these points on the coordinate grid the same as working with integers?
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Grade 6 Unit 3 Constructed Response Graphing TASK 3: Absolute Value and Polygons on the Coordinate Plane (CCSS: 6.NS.6, 6.NS.8, 6.G.3; SMP: 1, 2, 3, 4, 5, 7)
7. Stan was asked to find the distance between the two points on the coordinate grid below: y Stan’s work:
7 6
(
5
) (
)
4 3 2 1 −7
−6
−5
−4
−3
−2
−1 −1
1
2
3
4
5
6
7
x
−2 −3 −4
J
−5
K
−6 −7
a. After analyzing the coordinate grid and Stan’s work, write a critique in which you determine if Stan’s process is correct for finding the distance between the points. Identify and explain any errors in his work. Correct any errors you may find.
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Grade 6 Unit 3 Constructed Response Graphing b. If Stan was incorrect, show the correct process for finding the distance between the two points.
Answer: ____________________ 8. a. Draw a coordinate grid. Label the x and y-axes with a reasonable range and scale. The points P, Q, and R, are all points of a rectangle. Plot and label each point and find the missing point of the rectangle. Label it with the letter S. { (
) (
) (
)}
Answer: S (___ , ____)
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Grade 6 Unit 3 Constructed Response Graphing b. Find the perimeter and the area of the rectangle you created in your coordinate grid above. Show your work and give your answer for each in the table below. Perimeter
Answer: _______________
Area
Answer: _______________
b. Explain the process you used to find the perimeter and the area of the rectangle from the coordinate grid. What formulas were important in this process?
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Grade 6 Unit 3 Constructed Response Graphing 9. Use the grid below to construct a coordinate grid. Use the information given and your knowledge of polygons to answer the following questions. Gina and her mom are taking their friend Charlene out for her Birthday. Gina’s house is located at (−7, −5). They head north 8 miles toward Charlene’s home. a. Represent the locations of Gina’s and Charlene’s homes on the grid with a scale of 1 mile. Name the ordered pairs for each person’s house. Connect the points with line segments. b. After picking up Charlene, they drove 5½ miles east to a bookstore. Plot and label the location of Charlene’s home and the bookstore.
c. From the bookstore they can either go to the restaurant 4½ miles north, or to an antique shop 6½ miles east. Plot and label the two places they could travel to.
d. The ladies decide that they are going to go the antique shop first. Connect the points with line segments. Write an absolute value equation to show the distance between Charlene’s home and the antique shop. Answer: ___________________________ Copyright © Swun Math Grade 6 Unit 3 Constructed Response, Page 10
Grade 6 Unit 3 Constructed Response Graphing e. Once they arrive at the antique shop, how many miles have Gina and her mom traveled altogether? Show your work.
Answer: __________________ f. After shopping at the antique store, they decide to head to the restaurant for dinner. From the restaurant they make one last stop at the bookstore before heading back to Charlene’s home. Connect their stop with line segments. g. The roads connecting the bookstore, the antique shop, and the restaurant are the perimeter of a newly renovated park. Find the area of the park. Show your work and round to the nearest hundredth if necessary.
Answer: __________________
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Grade 6 Unit 3 Constructed Response Graphing TASK 1: Ordered Pairs, Points on a Plane (CCSS 6.NS.6, 6.NS.8; SMP 1, 2, 4, 6)
1. Use the coordinate grid below to graph and label each point: y
Graph and label the points: a. S(−8, −4) b. T(5, −1)
7 6
U
5 4 3 2
Name the ordered pair for each point
1 −7
−6
−5
−4
V
−3
−2
−1 −1 −2 −3
1
2
3
4
5
6
7
x
c. U _________ d. V _________
−4 −5 −6 −7
e. In complete sentences, explain each step necessary to plot an ordered pair on a coordinate grid.
Copyright © Swun Math Grade 6 Unit 3 Constructed Response, Page 1
Grade 6 Unit 3 Constructed Response Graphing 2. Draw a coordinate grid. Label the x and y-axes with a reasonable range and scale. Plot and label each point provided in the box below.
{ (
) (
) (
) (
) (
a. Identify the quadrant each point is located in. Point
Quadrant
Copyright © Swun Math Grade 6 Unit 3 Constructed Response, Page 2
) (
)}
Grade 6 Unit 3 Constructed Response Graphing 3. a. Explain how you chose the range and scale for the x and y-axes in question.
b. How do question 1 and 2 connect to other mathematical concepts that you have learned? How were these concepts useful in helping you understand the coordinate plane?
Copyright © Swun Math Grade 6 Unit 3 Constructed Response, Page 3
Grade 6 Unit 3 Constructed Response Graphing TASK 2: Symmetry, Rational Numbers and the Coordinate Plane (CCSS: 6.NS.6, 6.NS.8; SMP: 1, 2, 4, 6)
4. a. Draw a coordinate grid. Label the x and y-axes with a reasonable range and scale. Plot and label each group of ordered pairs provided in the box below. { ( { (
) ( ) (
)} )}
b. Analyze the coordinate grid you created. Identify the quadrants in which the ordered pairs are located and describe their relationship. Use the mathematical language you have learned to describe this relationship.
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Grade 6 Unit 3 Constructed Response Graphing 5. Draw a coordinate grid. Label the x and y-axes with a reasonable range and scale. Plot and label each point provided in the box below. { (
) (
) (
) (
) (
) (
)}
6. a. After graphing the ordered pairs, identify and describe the type of numbers that you worked with. How do they compare to the numbers you worked with in questions 1 and 2?
Copyright © Swun Math Grade 6 Unit 3 Constructed Response, Page 5
Grade 6 Unit 3 Constructed Response Graphing b. Was the process for placing these points on the coordinate grid the same as working with integers?
Copyright © Swun Math Grade 6 Unit 3 Constructed Response, Page 6
Grade 6 Unit 3 Constructed Response Graphing TASK 3: Absolute Value and Polygons on the Coordinate Plane (CCSS: 6.NS.6, 6.NS.8, 6.G.3; SMP: 1, 2, 3, 4, 5, 7)
7. Stan was asked to find the distance between the two points on the coordinate grid below: y Stan’s work:
7 6
(
5
) (
)
4 3 2 1 −7
−6
−5
−4
−3
−2
−1 −1
1
2
3
4
5
6
7
x
−2 −3 −4
J
−5
K
−6 −7
a. After analyzing the coordinate grid and Stan’s work, write a critique in which you determine if Stan’s process is correct for finding the distance between the points. Identify and explain any errors in his work. Correct any errors you may find.
Copyright © Swun Math Grade 6 Unit 3 Constructed Response, Page 7
Grade 6 Unit 3 Constructed Response Graphing b. If Stan was incorrect, show the correct process for finding the distance between the two points.
Answer: ____________________ 8. a. Draw a coordinate grid. Label the x and y-axes with a reasonable range and scale. The points P, Q, and R, are all points of a rectangle. Plot and label each point and find the missing point of the rectangle. Label it with the letter S. { (
) (
) (
)}
Answer: S (___ , ____)
Copyright © Swun Math Grade 6 Unit 3 Constructed Response, Page 8
Grade 6 Unit 3 Constructed Response Graphing b. Find the perimeter and the area of the rectangle you created in your coordinate grid above. Show your work and give your answer for each in the table below. Perimeter
Answer: _______________
Area
Answer: _______________
b. Explain the process you used to find the perimeter and the area of the rectangle from the coordinate grid. What formulas were important in this process?
Copyright © Swun Math Grade 6 Unit 3 Constructed Response, Page 9
Grade 6 Unit 3 Constructed Response Graphing 9. Use the grid below to construct a coordinate grid. Use the information given and your knowledge of polygons to answer the following questions. Gina and her mom are taking their friend Charlene out for her Birthday. Gina’s house is located at (−7, −5). They head north 8 miles toward Charlene’s home. a. Represent the locations of Gina’s and Charlene’s homes on the grid with a scale of 1 mile. Name the ordered pairs for each person’s house. Connect the points with line segments. b. After picking up Charlene, they drove 5½ miles east to a bookstore. Plot and label the location of Charlene’s home and the bookstore.
c. From the bookstore they can either go to the restaurant 4½ miles north, or to an antique shop 6½ miles east. Plot and label the two places they could travel to.
d. The ladies decide that they are going to go the antique shop first. Connect the points with line segments. Write an absolute value equation to show the distance between Charlene’s home and the antique shop. Answer: ___________________________ Copyright © Swun Math Grade 6 Unit 3 Constructed Response, Page 10
Grade 6 Unit 3 Constructed Response Graphing e. Once they arrive at the antique shop, how many miles have Gina and her mom traveled altogether? Show your work.
Answer: __________________ f. After shopping at the antique store, they decide to head to the restaurant for dinner. From the restaurant they make one last stop at the bookstore before heading back to Charlene’s home. Connect their stop with line segments. g. The roads connecting the bookstore, the antique shop, and the restaurant are the perimeter of a newly renovated park. Find the area of the park. Show your work and round to the nearest hundredth if necessary.
Answer: __________________
Copyright © Swun Math Grade 6 Unit 3 Constructed Response, Page 11
