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I hope that you find this resource helpful in your classroom. Please feel free to contact me with any questions as you implement this in your class.
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M A N E U V E R I N G T H E M I D D L E .C O M
PA G E T W O
SURFACE AREA
Students will be able to solve real-world problems involving the surface area of prisms and cylinders.
Ideas for Implementation: This performance task is an excellent summative assessment for your students. It can be given in the form of an assignment, group project or extra credit. It brings the concepts of the unit together and allows students to see a real-world application of surface area.
You could assign everyone the same block dimensions using the first set of dimensions provided, or you can cut out the dimension cards and give different dimensions to students. Note that the example answer key was made by using the first set of block dimensions provided.
While the answer key was made by choosing a total of 30 blocks, the students will choose their own quantity of blocks between 30 – 45. Therefore, answers may vary.
Notes: It may be helpful for students to work in partners or as a group of three. I would also encourage students to show their work on a separate piece of notebook paper.
There are different rubrics included so that you can choose one that best meets your needs and grading preferences.
©Maneuvering the Middle LLC, 2017
Performance Task
8.7B Use previous knowledge of surface area to make connections to the formulas for lateral and total surface area and determine solutions for problems involving rectangular prisms, triangular prisms, and cylinders.
Name _____________________________________Date ______________________________Pd______
Unit: Surface AreaPerformance Task
SURFACE AREA PERFORMANCE TASKYou are helping a toy company design and paint a set of children’s blocks to sell. The company would like the set of blocks to meet the following requirements:
• The total number of blocks in a set must be between 30 – 45
• A set of blocks must contain triangular prisms, rectangular prisms and cylinders
• The set of blocks should have the same number of each type of block
• Each type of block will be painted its own color (red, blue or yellow)
©Maneuvering the Middle LLC, 2017
STEP 1: DIMENSIONS, QUANTITY & COLORBased on your block base dimensions card, label the dimensions of the blocks in your set below. Then, determine the quantity of each type of block and the color the block will be painted.
QUANTITY: ________COLOR: ________
QUANTITY: ________COLOR: ________
QUANTITY: ________COLOR: ________
STEP 2: SETTING UP SURFACE AREAAnswer the questions below in order to prepare to find the surface area of your blocks.
1. What is the perimeter of the base in the triangular prism block? Explain.
2. What is the area of the base in the triangular prism block? Explain.
3. What is the perimeter of the base in the rectangular prism block? Explain.
4. What is the area of the base in the rectangular prism block? Explain.
5. What measurements will you need from the cylindrical block in order to find its surface area?
STEP 3: CALCULATING SURFACE AREAUse each table to find the surface area of one of each type of block as well as the total surface area for the number of blocks in the entire set.
©Maneuvering the Middle LLC, 2017
Use this space to explain how you calculated the total surface area for
the entire set of blocks:
STEP 4: PAINT ORDERThe toy company wants to produce 100 sets of the blocks you’ve designed. One gallon of paint will cover 5,760 square inches. Use the table to determine how many gallons of each paint color will need to be ordered.
Use this space to explain how you calculated the number of gallons needed for each paint color:
TYPE OF BLOCKSURFACE AREA
(1 SET)SURFACE AREA
(100 SETS)PAINT COLOR
GALLONS NEEDED
TRIANGULAR PRISM
RECTANGULAR PRISM
CYLINDER
TRIANGULAR PRISMS
FORMULA
PLUG IN VALUES
SURFACE AREA (one block)
SURFACE AREA (entire set)
RECTANGULAR PRISMS
FORMULA
PLUG IN VALUES
SURFACE AREA (one block)
SURFACE AREA (entire set)
CYLINDERS
FORMULA
PLUG IN VALUES
SURFACE AREA (one block)
SURFACE AREA (entire set)
1 GAL =5,760 IN.2
BLOCK BASE DIMENSIONS
THE HEIGHT OF EACH PRISM/CYLINDER
SHOULD BE 4 INCHES
©Maneuvering the Middle LLC, 2017
©Maneuvering the Middle LLC, 2017
BLOCK BASE DIMENSIONS
THE HEIGHT OF EACH PRISM/CYLINDER SHOULD BE 4 INCHES
BLOCK BASE DIMENSIONS
THE HEIGHT OF EACH PRISM/CYLINDER SHOULD BE 4.5 INCHES
BLOCK BASE DIMENSIONS
THE HEIGHT OF EACH PRISM/CYLINDER SHOULD BE 5 INCHES
BLOCK BASE DIMENSIONS
THE HEIGHT OF EACH PRISM/CYLINDER SHOULD BE 4.5 INCHES
3 in.
2.5
in.
4 in.
2.5
in.
4 in.
2 in.
2.5
in.
4 in.
3.5
in.
3 in.
2 in.
1.8 in.
4 in.
3 in.
5 in.
3 in.
2.5
in.
4.5 in.
2 in.
4 in.
Unit: Surface AreaPerformance Task
Name___________________________________________ Date ___________________________________ Pd _____
ABOVE STANDARD
METSTANDARD
BELOW STANDARD
MATHEMATICALCONTENT
Uses formulas and calculates surface area of prisms and cylinders with no errors.
40 points
Uses formulas and calculates surface area of prisms and cylinders with few errors.
30 points
Uses formulas and calculates surface area of prisms and cylinders with multiple errors.
20 points
MATHEMATICALTHINKING
Provides clear, descriptive and thorough reasoning for answered questions.
15 points
Provides some reasoning for answered questions but could use more explanation.
10 points
Does not provide reasoning for answered questions.
5 points
PARTICIPATION
Participates fully.
15 points
Participates with minor redirects from teacher.
10 points
Participates with major redirects from teacher.
5 points
SHOWS WORK
Showed work for 100% of the questions.
15 points
Showed the work for 80% or more of the questions.
10 points
Showed work for less than 80% of the questions.
5 points
FOLLOWSDIRECTIONS
Followed directions and criteria fully.
15 points
Followed directions and criteria with few errors.
10 points
Followed directionsand criteria with multiple errors.
5 points
TOTAL POINTS:
©Maneuvering the Middle LLC, 2017
TEACHER NOTES:
SURFACE AREA PERFORMANCE TASK
Unit: Surface AreaPerformance Task
Name___________________________________________ Date ___________________________________ Pd _____
ABOVE STANDARD
METSTANDARD
BELOW STANDARD
MATHEMATICALCONTENT
Uses formulas and calculates surface area of prisms and cylinders with no errors.
____ points
Uses formulas and calculates surface area of prisms and cylinders with few errors.
____ points
Uses formulas and calculates surface area of prisms and cylinders with multiple errors.
____ points
MATHEMATICALTHINKING
Provides clear, descriptive and thorough reasoning for answered questions.
____ points
Provides some reasoning for answered questions but could use more explanation.
____ points
Does not provide reasoning for answered questions.
____ points
PARTICIPATION
Participates fully.
____ points
Participates with minor redirects from teacher.
____ points
Participates with major redirects from teacher.
____ points
SHOWS WORK
Showed work for 100% of the questions.
____ points
Showed the work for 80% or more of the questions.
____ points
Showed work for less than 80% of the questions.
____ points
FOLLOWSDIRECTIONS
Followed directions and criteria fully.
____ points
Followed directions and criteria with few errors.
____ points
Followed directionsand criteria with multiple errors.
____ points
TOTAL POINTS:
©Maneuvering the Middle LLC, 2017
TEACHER NOTES:
SURFACE AREA PERFORMANCE TASK
SURFACE AREA PERFORMANCE TASK RUBRICName_________________________________________
Total Points ___________________________________
ABOVE STANDARD MET STANDARD BELOW STANDARD
MATHEMATICALCONTENT
Uses formulas and calculates surface area of prisms and cylinders with no errors.
40 points
Uses formulas and calculates surface area of prisms and cylinders with few errors.
30 points
Uses formulas and calculates surface area of prisms and cylinders with multiple errors.
20 points
MATHEMATICALTHINKING
Provides clear, descriptive and thorough reasoning for answered questions.
15 points
Provides some reasoning for answered questions but could use more explanation.
10 points
Does not provide reasoning for answered questions.
5 points
PARTICIPATION
Participates fully.
15 points
Participates with minor redirectsfrom teacher.
10 points
Participates with major redirects from teacher.
5 points
SHOWS WORK
Showed work for 100% of the questions.
15 points
Showed the work for 80% or more of the questions.
10 points
Showed work for less than 80% of the questions.
5 points
FOLLOWSDIRECTIONS
Followed directions and criteria fully.
15 points
Followed directions and criteria with few errors.
10 points
Followed directions and criteria with multiple errors.
5 points
Name_________________________________________
Total Points ___________________________________
©M
aneuveri
ng the M
iddle
LLC
, 2017
ABOVE STANDARD MET STANDARD BELOW STANDARD
MATHEMATICALCONTENT
Uses formulas and calculates surface area of prisms and cylinders with no errors.
40 points
Uses formulas and calculates surface area of prisms and cylinders with few errors.
30 points
Uses formulas and calculates surface area of prisms and cylinders with multiple errors.
20 points
MATHEMATICALTHINKING
Provides clear, descriptive and thorough reasoning for answered questions.
15 points
Provides some reasoning for answered questions but could use more explanation.
10 points
Does not provide reasoning for answered questions.
5 points
PARTICIPATION
Participates fully.
15 points
Participates with minor redirectsfrom teacher.
10 points
Participates with major redirects from teacher.
5 points
SHOWS WORK
Showed work for 100% of the questions.
15 points
Showed the work for 80% or more of the questions.
10 points
Showed work for less than 80% of the questions.
5 points
FOLLOWSDIRECTIONS
Followed directions and criteria fully.
15 points
Followed directions and criteria with few errors.
10 points
Followed directions and criteria with multiple errors.
5 points
SURFACE AREA PERFORMANCE TASK RUBRIC
Name_________________________________________
Total Points ___________________________________
ABOVE STANDARD MET STANDARD BELOW STANDARD
MATHEMATICALCONTENT
Uses formulas and calculates surface area of prisms and cylinders with no errors.
____ points
Uses formulas and calculates surface area of prisms and cylinders with few errors.
____ points
Uses formulas and calculates surface area of prisms and cylinders with multiple errors.
____ points
MATHEMATICALTHINKING
Provides clear, descriptive and thorough reasoning for answered questions.
____ points
Provides some reasoning for answered questions but could use more explanation.
____ points
Does not provide reasoning for answered questions.
____ points
PARTICIPATION
Participates fully.
____ points
Participates with minor redirectsfrom teacher.
____ points
Participates with major redirects from teacher.
____ points
SHOWS WORK
Showed work for 100% of the questions.
____ points
Showed the work for 80% or more of the questions.
____ points
Showed work for less than 80% of the questions.
____ points
FOLLOWSDIRECTIONS
Followed directions and criteria fully.
____ points
Followed directions and criteria with few errors.
____ points
Followed directions and criteria with multiple errors.
____ points
Name_________________________________________
Total Points ___________________________________
©M
aneuveri
ng the M
iddle
LLC
, 2017
ABOVE STANDARD MET STANDARD BELOW STANDARD
MATHEMATICALCONTENT
Uses formulas and calculates surface area of prisms and cylinders with no errors.
____ points
Uses formulas and calculates surface area of prisms and cylinders with few errors.
____ points
Uses formulas and calculates surface area of prisms and cylinders with multiple errors.
____ points
MATHEMATICALTHINKING
Provides clear, descriptive and thorough reasoning for answered questions.
____ points
Provides some reasoning for answered questions but could use more explanation.
____ points
Does not provide reasoning for answered questions.
____ points
PARTICIPATION
Participates fully.
____ points
Participates with minor redirectsfrom teacher.
____ points
Participates with major redirects from teacher.
____ points
SHOWS WORK
Showed work for 100% of the questions.
____ points
Showed the work for 80% or more of the questions.
____ points
Showed work for less than 80% of the questions.
____ points
FOLLOWSDIRECTIONS
Followed directions and criteria fully.
____ points
Followed directions and criteria with few errors.
____ points
Followed directions and criteria with multiple errors.
____ points
SURFACE AREA PERFORMANCE TASK RUBRIC
SURFACE AREA PERFORMANCE TASK RUBRIC
Name _____________________________________Date ______________________________Pd______
Unit: Surface AreaPerformance Task
SURFACE AREA PERFORMANCE TASKYou are helping a toy company design and paint a set of children’s blocks to sell. The company would like the set of blocks to meet the following requirements:
• The total number of blocks in a set must be between 30 – 45
• A set of blocks must contain triangular prisms, rectangular prisms and cylinders
• The set of blocks should have the same number of each type of block
• Each type of block will be painted its own color (red, blue or yellow)
©Maneuvering the Middle LLC, 2017
STEP 1: DIMENSIONS, QUANTITY & COLORBased on your block base dimensions card, label the dimensions of the blocks in your set below. Then, determine the quantity of each type of block and the color the block will be painted.
QUANTITY: ________COLOR: ________
QUANTITY: ________COLOR: ________
QUANTITY: ________COLOR: ________
STEP 2: SETTING UP SURFACE AREAAnswer the questions below in order to prepare to find the surface area of your blocks.
1. What is the perimeter of the base in the triangular prism block? Explain.
2. What is the area of the base in the triangular prism block? Explain.
3. What is the perimeter of the base in the rectangular prism block? Explain.
4. What is the area of the base in the rectangular prism block? Explain.
5. What measurements will you need from the cylindrical block in order to find its surface area?
Sample Key
10 10 10
2.5
in.
4 in.
4 in.
4 in.
4 in.2.5 in.3 in.
Red Blue Yellow
9 inches; I added the three sides of the triangular base.
3.75 square inches; I multiplied (1/2)(3)(2.5)
13 inches; I added the 4 sides of the rectangular base.
10 square inches; I multiplied 2.5(4)
The radius (2 inches) and the height (4 inches).
STEP 3: CALCULATING SURFACE AREAUse each table to find the surface area of one of each type of block as well as the total surface area for the number of blocks in the entire set.
©Maneuvering the Middle LLC, 2017
Use this space to explain how you calculated the total surface area for
the entire set of blocks:
STEP 4: PAINT ORDERThe toy company wants to produce 100 sets of the blocks you’ve designed. One gallon of paint will cover 5,760 square inches. Use the table to determine how many gallons of each paint color will need to be ordered.
Use this space to explain how you calculated the number of gallons needed for each paint color:
TYPE OF BLOCKSURFACE AREA
(1 SET)SURFACE AREA
(100 SETS)PAINT COLOR
GALLONS NEEDED
TRIANGULAR PRISM 435 in.2 43,500 in.2 Red 7.55 gallons
RECTANGULAR PRISM 720 in.2 72,000 in.2 Blue 12.5 gallons
CYLINDER 75.36 in.2 75,360 in.2 Yellow 13.1 gallons
TRIANGULAR PRISMS
FORMULA Ph + 2B
PLUG IN VALUES 9(4) + 2(3.75)
SURFACE AREA (one block) 43.5 in.2
SURFACE AREA (entire set) 435 in.2
RECTANGULAR PRISMS
FORMULA Ph + 2B
PLUG IN VALUES 13(4) + 2(10)
SURFACE AREA (one block) 72 in.2
SURFACE AREA (entire set) 720 in.2
CYLINDERS
FORMULA 2πrh + 2πr2
PLUG IN VALUES 2(3.14)(2)(4) + 2(3.14)(22)
SURFACE AREA (one block) 75.36 in.2
SURFACE AREA (entire set) 753.6 in.2
1 GAL =5,760 IN.2
I multiplied the surface area of one block times 10, the quantity of each type of block in the set.
I divided the surface area of 100 sets by the number of square inches that one gallon of paint will cover.