SUPERMARKET BOXES Assessment

Transcription

1 SUPERMARKET BOXES Assessment 1. Sally wants to build some gift boxes from attractive cardboard. She needs them to be different sizes and wants to have a formula to use for the surface area of the open box. The cardboard currently measures 10 inches by 20 inches. Sally is going to cut square pieces of length out of each corner and fold up the sides. What s the formula for the surface area of her open box? A. A = 200 4d 2 B. A = 200d C. A = 4d 3 60d d D. A = d 2. Which shape has the largest volume? A. Cylinder B. Cube C. Isosceles right triangular prism D. Square prism A. Cylinder B. Cube C. Triangular prism D. Square prism Supermarket Boxes Assessment Page 1 of 15

2 3. The ratio of the side lengths of two squares is 4:5. The ratio of their areas is: A. 64:125 B. 16:25 C. 4:5 D. 2: 5 4. The ratio of the altitudes of two similar triangles is 3:7. The ratio of their perimeters is: A. 27:343 B. 9:49 C. 3:7 D. 3: 7 5 The side lengths of a rectangle have been doubled. This means that the area has been A. Reduced by a factor of 2. B. Increased by a factor of 2 C. Increased by a factor of 4 D. Increased by a factor of 8 6. A very large can has a height of 4 feet and a diameter of 2 feet. A different can has a height of 4 feet and a diameter of 3 feet. The volume of the larger can is A. 1.5 times the volume of the smaller can B times the volume of the smaller can. C times the volume of the smaller can. D. 4 times the volume of the smaller can. 7. A storage building is 20 ft total across the front (shown) 12 feet is a rectangular solid and 8 feet of the floor is a lean-to. It is also 10 feet tall and 15 feet deep. The heating system can raise the temperature at a rate of 5 degrees for 600 cubic feet per minute. How long will it take to raise the temperature of the entire building by 5 degrees? A. 16 seconds B. 4 minutes C. 20 minutes D. 24 minutes Supermarket Boxes Assessment Page 2 of 15

3 8. Jim has a box which measures 2ft x 3ft x 4ft. He needs to carry 1 cubic yard of dirt. Is the box large enough? Show work to support your answer using words, numbers and/or diagrams. Supermarket Boxes Assessment Page 3 of 15

4 9. Jim wants to fill a pan with brownie mix. The box asks for a pan that is 8x8x2 inches. Jim has a circular pan with a diameter of 9 inches and a height of 2.25 inches. Will his circular pan hold as much batter as the square pan? Show work to support your answer using words, numbers and/or diagrams. Supermarket Boxes Assessment Page 4 of 15

5 10. A ramp is being built for a wheelchair. The builders want to make it out of concrete. The ramp is 1 ft in elevation and 12 feet long. The width of the ramp is 2.5 feet. What is the volume of the ramp How many cubic yards of concrete are needed? Show work to support your answer using words, numbers and/or diagrams. Supermarket Boxes Assessment Page 5 of 15

6 11. Potato chips are packed in cans that are 10 inches high and have a radius of 2 inches. The cans are placed into boxes that hold 24 cans, arranged in 4 rows of six cans each. The box is just big enough to hold the cans of chips. The cans touch the box on all 6 sides of the box. What volume of the the box that is not taken up by the cans? What percent of the entire box is empty space (not filled with cans)? Show work to support your answer using words, numbers and/or diagrams. Supermarket Boxes Assessment Page 6 of 15

7 12. A company that makes sports balls is redesigning their packaging. Option A is to use a cylinder, Option B is to use a rectangular prism and Option C uses a triangular prism. The balls are all 9 inches in diameter. Cylinder A The cylinder is 6 balls high and the diameter of one ball. The material for the lateral area costs 10-cents/square foot and the material for each base costs 30- cents/square foot. Option B The rectangular prism is the height of two balls, the length of three balls and the depth of one ball. The material for the entire package costs 12-cents/square foot. Option C The triangular prism has the balls in three layers. The base edge of the isosceles triangle is 4 balls wide, the height of the triangle is 3.5 balls and the depth of the prism is one ball. The material for this box costs 18-cents/square foot. Which box has the lowest cost for material? Show work to support your answer using words, numbers and/or diagrams. (Work space on page 8.) Supermarket Boxes Assessment Page 7 of 15

8 The packaging with the lowest cost is the Supermarket Boxes Assessment Page 8 of 15

9 Additional Work Space for #12 Supermarket Boxes Assessment Page 9 of 15

10 Supermarket Boxes Assessment Rubrics Note: Students may use a formula sheet for this assessment. 1. GLE 1.2.5) Use formulas to determine measurements related to right prisms, cylinders, cones, or pyramids. A. Difference in area of original board and the area of each removed square B. Calculate given numbers (10)(20)(d) with no real understanding of the question C. Calculate volume rather than surface area. D. Calculate surface area, but lid included. 2. (GLE 1.2.5) Use formulas to determine measurements related to right prisms, cylinders, cones, or pyramids. B..Cylinder volume is 502 cm3 Cube is 512 cm 3. Triangular Prism is 384 cm 3 Square Prism is 360 cm 3 A Triangular prism volume miscalculated (failure to 2) C Used the longest edge length D Used the largest surface area Students may consider that the cube and the cylinder are the largest shapes and just compare the volume of those two. 3. (GLE 1.3.1) Understand the properties of and the relationships among 1-dimensional, 2-dimensional, and 3-dimensional shapes and figures. B A C D square the ratio of the linear measurements cube the ratio maintained the same ratio square root the ratio Supermarket Boxes Assessment Page 10 of 15

11 4. GLE 1.3.1) Understand the properties of and the relationships among 1-dimensional, 2-dimensional, and 3-dimensional shapes and figures. C A B D both are linear measurements and have the same ratio cube the ratio square the ratio Square root the ratio Is height or altitude of the triangle preferred? 5. GLE 1.3.1) Understand the properties of and the relationships among 1-dimensional, 2-dimensional, and 3-dimensional shapes and figures. C Use the factor 2 2 = 4 A Divided by the factor (2) B Change area by the same factor (2) D Used the factor for volume rather than area (8) 6. GLE 1.2.1) Understand the relationship between change in one or two linear dimension(s) and corresponding change in perimeter, area, surface area, and volume. C the ratio of the areas is 1 2 :1.5 2 or a factor of 2.25 A B D Kept the same ratio as the diameter ratio. Used the ratio for surface area Squared the value of the first diameter 7. GLE (1.2.3) Apply unit conversions within measurement systems, U.S. or metric, to maintain an appropriate level of precision. B ( )(15)/600 = 4 minutes A divided surface area by 600 ft 3 C found 4 minutes, but multiplied by 5. D found correct cubic feet, but divided by 100 instead of 600. Supermarket Boxes Assessment Page 11 of 15

12 8. GLE (1.2.3) Apply unit conversions within measurement systems, U.S. or metric, to maintain an appropriate level of precision. 2-point response: The student shows understanding of how to convert the volume from cubic feet to cubic yards by doing all of the following: Volume of box: 2ft x 3ft x 4ft = 24 ft 3. Dividing by a cubic yard, which is 27 cubic feet. Stating The box is not large enough. Note: An error with the calculation of volume, but correct division by 27 cubic feet is allowed, even if this changes the response to the box IS large enough. 1-point response: The student shows understanding of the problem by doing one of the following: Finds the volume of box: 2ft x 3ft x 4ft = 24 ft 3 and shows some understanding of a cubic yard. States that a cubic yard is 27 cubic feet. Finds the volume of the box and states that the box is not large enough. 0-point response: The students shows very little or no understanding, or if the volume of the box is divided by 3 or 9 ft ((GLE 1.2.5) Use formulas to determine measurements related to right prisms, cylinders, cones, or pyramids. 2-point response: The student shows understanding of how to calculate the volume of a rectangular prism and of a cylinder by doing all of the following: The rectangular pan has a volume of 8x8x2 = 128 in 3. The circular pan has a volume of (4.5) 2 (π) (2.25)= 143 in 3. The circular pan is large enough for the brownie mix. Note: Allow one computational error as long as conceptual understanding is clear. 1-point response: The student shows understanding of the problem by doing two of the following: The rectangular pan has a volume of 8x8x2 = 128 in 3. The circular pan has a volume of (4.5) 2 (π) (2.25)= 143 in 3. The circular pan is large enough for the brownie mix. 0-point response: The students shows very little or no understanding. Supermarket Boxes Assessment Page 12 of 15

13 10. GLE 1.2.5) Use formulas to determine measurements related to right prisms, cylinders, cones, or pyramids. 2-point response: The student shows understanding of how to calculate the volume of a triangular prism and convert that value to cubic yards by doing all of the following: The volume of the ramp is (0.5)(1)(12)(2.5) = 15 ft 3. One yard = 27 ft 3. The ramp requires about 0.6 yards of concrete. Note: Allow one computational error as long as conceptual understanding of the volume formula is clear. The volume of concrete may be referred to as yards rather than cubic yards as is done in business 1-point response: The student shows understanding of the problem by doing one of the following: The volume of the ramp is (0.5)(1)(12)(2.5) = 15 ft 3. The ramp requires about 0.6 yards of concrete. Note: Allow one computational error as long as conceptual understanding of the volume formula is clear. The volume of concrete may be referred to as yards rather than cubic yards as is done in business 0-point response: The students shows very little or no understanding of the formula for the volume of the prism. 11. ((GLE 1.2.5) Use formulas to determine measurements related to right prisms, cylinders, cones, or pyramids. 2-point response: The student shows understanding of The volume of each can is 40π or in cans have a volume of 960π or in 3. The box has dimensions of 4(4 in) x 6(4 in) x (10 in) = 3840 in 3. The extra space in the box is = in 3. The percent of the space is 825.6/3840 = or 21.5% of the volume of the box. Note: Allow one computational error as long as conceptual understanding is clear. 1-point response: The student shows 3 or 4 of the following: The volume of each can is 40π or in cans have a volume of 960π or in 3. The box has dimensions of 4(4 in) x 6(4 in) x (10 in) = 3840 in 3. The extra space in the box is = in 3. The percent of the space is 825.6/3840 = or 21.5% of the volume of the box. 0-point response: The students shows very little or no understanding. Supermarket Boxes Assessment Page 13 of 15

14 12. (GLE 1.2.5) Use formulas to determine measurements related to right prisms, cylinders, cones, or pyramids. 4-point response: The student shows understanding of Shows work to calculate the surface area and cost of the cylinder Basel area = in 2 = ft 2. Cost = $ Lateral area = in 2 = 10.6 ft 2. Cost = $ 1.06 Total cost = $1.33 Shows work to calculate the surface area and cost of the rectangular prism. Surface area = 1728 in 2 = ft 2. Cost = $ 1.44 Show work to calculate the surface area and cost of the triangular prism. Surface area = 817 in 2 = 5.67 ft 2. Cost = $ 1.02 Selects Option C, the triangular prism, as the least costly package Note: Allow one computational error as long as conceptual understanding is clear. 3-point response: The student does three of the following: Shows work to calculate the surface area and cost of the cylinder Basel area = in 2 = ft 2. Cost = $ Lateral area = in 2 = 10.6 ft 2. Cost = $ 1.06 Total cost = $1.33 Shows work to calculate the surface area and cost of the rectangular prism. Surface area = 1728 in 2 = ft 2. Cost = $ 1.44 Show work to calculate the surface area and cost of the triangular prism. Surface area = 817 in 2 = 5.67 ft 2. Cost = $ 1.02 Selects Option C, the triangular prism, as the least costly package. Note: Allow one computational error as long as conceptual understanding is clear. 2-point response: The student does two of the following: Shows work to calculate the surface area and cost of the cylinder Basel area = in 2 = ft 2. Cost = $ Lateral area = in 2 = 10.6 ft 2. Cost = $ 1.06 Total cost = $1.33 Shows work to calculate the surface area and cost of the rectangular prism. Surface area = 1728 in 2 = ft 2. Cost = $ 1.44 Show work to calculate the surface area and cost of the triangular prism. Surface area = 817 in 2 = 5.67 ft 2. Cost = $ 1.02 Selects the triangular prism as the least costly package. Supermarket Boxes Assessment Page 14 of 15

15 Note: Allow one computational error as long as conceptual understanding is clear. 1-point response: The student does one of the following: Shows work to calculate the surface area and cost of the cylinder Basel area = in 2 = ft 2. Cost = $ Lateral area = in 2 = 10.6 ft 2. Cost = $ 1.06 Total cost = $1.33 Shows work to calculate the surface area and cost of the rectangular prism. Surface area = 1728 in 2 = ft 2. Cost = $ 1.44 Show work to calculate the surface area and cost of the triangular prism. Surface area = 817 in 2 = 5.67 ft 2. Cost = $ 1.02 Selects the triangular prism as the least costly package. Note: Allow one computational error as long as conceptual understanding is clear. 0-point response: The students shows very little or no understanding. Supermarket Boxes Assessment Page 15 of 15