Experiences with Area Assessment Materials
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- Suzanna Owen
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1 Experiences with Area Assessment Materials 1. Jenny bought a rectangular rug that had an area of 24 square feet and a perimeter of 20 feet. Which model shows the correct dimensions of the rug? A. 8 feet 3 feet B. 4 feet 6 feet C. 2 feet 12 feet D. 1 foot 24 feet 2. What is the perimeter of the rectangle? A. 18 units B. 18 square units C. 20 units D. 20 square units 3. What is the approximate area of the circle? A. 20 square units B. 24 square units C. 28 square units D. 36 square units Experiences with Area Assessment Materials Page 1 of 14
2 4. Jesse s birthday cake has chocolate frosting on the top of the cake. The cake is cut into different sized rectangular pieces. Each piece has frosting on the top. Jesse wants a piece of cake with the most frosting. Which piece has the most frosting? A. A piece with a top 5 inches wide and 2 inches long. B. A piece with a top with an area of 12 square inches and a perimeter of 14 inches. C. A piece with a top with an area of 7 square inches and a perimeter of 16 inches. D. A piece with a top 3 inches wide and 3 inches long. 5. What is the approximate area of the triangle? A. 6 square units B. 10 square units C. 14 square units D. 16 square units 6. Sam is designing a vegetable garden, and is going to surround the garden with a wooden fence. He doesn t have very much wood, so he wants to design a garden that would use the least amount of wood in the surrounding fence. Which garden design should Sam use? A. A square garden with an area of 100 square feet and a perimeter of 40 feet. B. A rectangular garden with an area of 117 square feet and a perimeter of 42 feet. C. A circular garden with an area of 113 square feet and a perimeter (circumference) of 38 feet. D. A triangular garden with an area of 90 square feet and a perimeter of 49 feet. Experiences with Area Assessment Materials Page 2 of 14
3 7. Draw a rectangle with a perimeter of 20 units and an area of 24 square units. Label the length and width. Experiences with Area Assessment Materials Page 3 of 14
4 8. Suzy planted a vegetable garden with three rows for carrots. Each row was twelve feet wide and three feet long. 3 feet 3 feet 3 feet 12 feet What was the total area of all three rows? Show how you got your answer using words, numbers, or pictures. What was the total area of all three rows? Experiences with Area Assessment Materials Page 4 of 14
5 9. Mark wants to paint the ceiling in his bedroom. His dad did some measurements and told him that the area of the ceiling is 120 square feet, and the perimeter is 44 feet. Which measurement will Mark need to use in order to buy the paint he needs to paint his ceiling? Explain your reasoning. Which measurement will Mark need? Explain your reasoning: Experiences with Area Assessment Materials Page 5 of 14
6 10. Lindsey put in a tile patio in her backyard. Each square tile measured 1 square foot. The patio is 8 feet wide by 16 feet long. Lindsey also wants to put a fence around the patio. Lindsey s Patio 8 feet 16 feet Find out how many tiles are needed to cover the patio floor Find out how many feet of fencing are needed to surround the patio Show your work using words, numbers, or pictures. Additional work space Additional work space. More work space on the next page Experiences with Area Assessment Materials Page 6 of 14
7 How many tiles are needed to cover the patio floor? How many feet of fencing are needed to surround the patio? Experiences with Area Assessment Materials Page 7 of 14
8 Experiences with Area Assessment Rubrics 1. Jenny bought a rectangular rug that had an area of 24 square feet and a perimeter of 20 feet. Which model shows the correct dimensions of the rug? A. 8 ft B. 4 ft 3 ft 6 ft C. 7 ft 3 ft D. 1 ft 24 ft The correct answer is B. Answer A shows a rug with an area of 24 sq ft, but a perimeter of 22 feet Answer C shows a rug with a perimeter of 20 feet, but an area of 21 sq ft Answer D shows a rug with an area of 24 sq ft, but a perimeter of 50 feet 2. What is the perimeter of the rectangle? A. 18 units B. 18 square units C. 20 units D. 20 square units The correct answer is A. Answer B is the correct number (18), but uses the incorrect unit (square units instead of units) Answer C uses the correct unit (units instead of square units) but the number 20 is the area, not perimeter Answer D is the area of the rectangle Experiences with Area Assessment Materials Page 8 of 14
9 3. What is the approximate area of the circle? A. 20 square units D. 24 square units C. 28 square units B. 36 square units The correct answer is C. Answer A is only the number of whole squares found inside of the circle Answer B is the number of whole squares found inside the circle plus 4 squares that are almost completely inside of the circle, but does not include several squares that are partially inside of the circle Answer D is the number of every square shown, counting those that are partially outside of the circle as full squares. 4. Jesse s birthday cake has chocolate frosting on the top of the cake. The cake is cut into different sized rectangular pieces. Each piece has frosting on the top. Jesse wants a piece of cake with the most frosting. Which piece has the most frosting on top? A. A piece that has a top 5 inches wide and 2 inches long. B. A piece with a top with an area of 12 square inches and a perimeter of 14 inches. C. A piece with a top with an area of 7 square inches and a perimeter of 16 inches. D. A piece with a top 3 inches wide and 3 inches long. The correct answer is B. The cake with the most frosting will be that with the greatest area of frosting. Answer A has an area of 10 square units, which is not the greatest area Answer C has the greatest perimeter, but the smallest area Answer D has an area of 9 square units, which is not the greatest area Experiences with Area Assessment Materials Page 9 of 14
10 5. What is the approximate area of the triangle? A. 6 square units B. 10 square units C. 16 square units D. 20 square units The correct answer is B. Answer C counts every square that is even partially covered by the triangle as a whole square unit Answer A counts only the squares that are completely covered by the triangle and ignores the rest Answer D is the result of multiplying the base times the height 6. Sam is designing a vegetable garden, and is going to surround the garden with a wooden fence. He doesn t have very much wood, so he wants to design a garden that would use the least amount of wood in the surrounding fence. Which garden design should Sam use? A. A square garden with an area of 100 square feet and a perimeter of 40 feet. B. A rectangular garden with an area of 117 square feet and a perimeter of 42 feet. C. A circular garden with an area of 113 square feet and a perimeter (circumference) of 38 feet. D. A triangular garden with an area of 90 square feet and a perimeter of 49 feet. The correct answer is C. The garden with the least amount of wood will be that with the smallest perimeter Answer A has more fence and less garden than C Answer B has more fence and more garden than C Answer D has the smallest area, but not the smallest perimeter Experiences with Area Assessment Materials Page 10 of 14
11 Item 7 7. Draw a rectangle with a perimeter of 20 units and an area of 24 square units. Label the length and width. Strand: Measurement ME01 Learning Target: (Attributes and Dimensions) Demonstrate understanding of the concept of area and perimeter 2-point response: The student shows understanding of the concept of area and perimeter by doing the following: Draws a rectangle with an area of 24 square units and a perimeter of 20 units (a 6 x 4 rectangle) Length and width are clearly 6 units by 4 units (with either numbers or tile drawings, etc.) 1-point response: The student does one of the following: Draws a rectangle with an area of 24 square units Draws a rectangle with a perimeter of 20 units Draws a rectangle with an area of 24 square units and a perimeter of 20 units but does not show the length and width as 6 units by 4 units 0-point response: The student shows very little or no understanding of the concept of area and perimeter. Experiences with Area Assessment Materials Page 11 of 14
12 Item 8 8. Suzy planted a vegetable garden with three rows for carrots. Each row was twelve feet wide and three feet long. 3 feet 3 feet 3 feet What was the total area of all three rows? Show how you got your answer using words, numbers, or pictures. Strand: Measurement 12 feet ME03 Learning Target: (Procedures) Use systematic procedures to measure, describe, and compare the area of rectangles identify area as the attribute to be measured, select and use appropriate units of measurement for area, select and use tools that match the unit chosen, count to determine the number of units 2-point response: The student shows understanding of determining the area of a rectangle by doing the following: Writes 108 square feet (108 ft 2 ) Shows an appropriate procedure to find the total area of all three rows 1-point response: The student does one or both of the following: Writes 108 Shows an appropriate procedure to find the total area of all three rows 0-point response: The student shows very little or no understanding of determining the area of a rectangle. Experiences with Area Assessment Materials Page 12 of 14
13 Item 9 9. Mark wants to paint the ceiling in his bedroom. His dad did some measurements and told him that the area of the ceiling is 120 square feet, and the perimeter is 44 feet. Which measurement will Mark need to use in order to buy the paint he needs to paint his ceiling? Explain your reasoning. Which measurement will Mark need? Explain your reasoning: Strand: Communicates Understanding CU02 Learning Target: (Represent and share information) Use everyday and mathematical language and/or notation to express ideas involving measurement; explain or represent mathematical ideas and information to familiar people in a context that is relevant to fifth grade students and involves measurement ME01 Learning Target: (Attributes and Dimensions) Demonstrate understanding of the concept of area and perimeter 2-point response: The student shows understanding of the concept of area and perimeter, and communicates that understanding by doing the following: Writes area (120 square feet) Clearly communicates why area is the measurement needed to buy paint for a ceiling 1-point response: The student does one of the following: Writes area (120 square feet) Clearly communicates why area is the measurement needed to buy paint for a ceiling 0-point response: The student shows very little or no understanding of the concept of area and perimeter, or communicating mathematical ideas Experiences with Area Assessment Materials Page 13 of 14
14 Item Lindsey put in a tile patio in her backyard. Each square tile measured 1 square foot. The patio is 8 feet wide by 16 feet long. Lindsey also wants to put a fence around the patio. Lindsey s Patio 8 feet 16 feet Find out how many tiles are needed to cover the patio floor Find out how many feet of fencing are needed to surround the patio Show your work using words, numbers, or pictures. Strand: Measurement ME01 Learning Target: (Attributes and Dimensions) Demonstrate understanding of the concept of area and perimeter ME03 Learning Target: (Procedures) Use systematic procedures to measure, describe, and compare the area of rectangles identify area as the attribute to be measured, select and use appropriate units of measurement for area, select and use tools that match the unit chosen, count to determine the number of units 4-point response: The student shows understanding of the concept of area and perimeter by doing the following: Writes 128 tiles Shows an appropriate procedure to find the total number of tiles needed Writes 48 feet of fencing Shows an appropriate procedure to find the total feet if fencing needed 3-point response: The student does three of the four things required for 4 points. 2-point response: The student does two of the four things required for 4 points. 1-point response: The student does one of the four things required for 4 points. 0-point response: The student shows very little or no understanding of solving the problem. NOTE: Allow for one computation error with answer that is consistent with the error. Experiences with Area Assessment Materials Page 14 of 14
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