Tiling And Filling The Pool Assessment Materials for Student

Transcription

1 Tiling And Filling The Pool Assessment Materials for Student You have been hired to design the outside of a tissue box for a new company. The base of the box is 10 inches by 4 inches. The height of the box is 3 inches. The bottom of the box is to be left blank for logos and pricing by the company. (Questions #1-4 are in reference to this given scenario.) 1) How many faces (flat surface of a 3-D figure) are left for you to design? a) 2 b) 3 c) 5 d) 6 2) What is the surface area of the sides (faces) that you will be designing? a) 124 square inches b) 124 cubic inches c) 184 square inches d) 184 cubic inches 3) What is the volume of the tissue box that you are designing? a) 120 cubic inches b) 120 square inches c) 164 cubic inches d) 164 square inches 4) The company decided to increase the volume of the box so that it could hold more tissue. They doubled the height of the box so that it is now 6 inches. How many of the sides have had their area changed by this doubling of the height? a) 2 b) 3 c) 4 d) 5 Tiling And Filling The Pool Assessment Materials Page 1 of 14

2 5) The local children s museum is designing a new activity room for small children. They want to cover this large foam cube with fabric on all sides so the children can play with it. How much fabric will they need to purchase to cover the cube? (You do not need to account for seams.) c) 27 square meters d) 27 cubic meters a) 54 square meters 3 meters b) 54 cubic meters 6) Find the area of the shaded figure. 10 centimeters a) 16 square centimeters b) 40 square centimeters 5 centimeters c) 50 square centimeters d) 60 square centimeters (inside rectangle 5cm x 2cm) 7) Sue figured out the surface area and volume of the box for her diorama project. The only problem is that she did not label her work. When she came back to the project the next day, she couldn t remember which number was the surface area and which was the volume. Look at the box and help Sue solve her problem. 8 inches 10 inches a) volume = 480 cubic inches surface area = 376 square inches b) volume = 480 square inches surface area = 376 cubic inches c) volume = 480 cubic inches surface area = 188 square inches d) volume = 480 square inches surface area = 188 cubic inches 6 inches Tiling And Filling The Pool Assessment Materials Page 2 of 14

3 8) The gift box below has a surface area of 504 square inches and a volume of 720 cubic inches 6 inches 12 inches 10 inches If you double the length of the box from 12 inches to 24 inches, what is new surface area and volume be? Show your work using words, numbers and/or diagrams. The new surface area is square inches. The new volume is cubic inches. Tiling And Filling The Pool Assessment Materials Page 3 of 14

4 9) Grandma is mailing a box full of gifts to Aunt Sally. The dimensions of the box are 24 inches long by 20 inches wide by 12 inches deep. Grandpa sticks a book into the box while Grandma isn t looking. The book has dimensions of 10 inches by 8 inches by 2 inches. What is the volume left in the box after Grandpa has stuck the book in? Show your work using words, numbers and/or diagrams. The volume left in the box is cubic inches. Tiling And Filling The Pool Assessment Materials Page 4 of 14

5 10) One brick has a height of 2 inches, a length of 8 inches, and a width of 3 inches. 2 inches 3 inches 8 inches Determine the volume of one brick. Determine the total volume of three bricks stacked on top of each other. Be sure to include accurate the appropriate units in your answers. Show your work using words, numbers and/or diagrams. The volume of one brick is. The volume of three bricks stacked is. Tiling And Filling The Pool Assessment Materials Page 5 of 14

6 Tiling And Filling The Pool Assessment Materials with Solutions You have been hired to design the outside of a tissue box for a new company. The base of the box is 10 inches by 4 inches. The height of the box is 3 inches. The bottom of the box is to be left blank for logos and pricing by the company. (Questions #1-4 are in reference to this given scenario.) 1) How many faces (flat surface of a 3-D figure) are left for you to design? a) 2 *misconception of front and back b) 3 *number of sides with different dimensions or three dimensions listed c) 5 *correct response d) 6 *requires students to understand that a rectangular prism has 6 sides (faces), but that they need to subtract the base 2) What is the surface area of the sides (faces) that you will be designing? a) 124 square inches *correct response b) 124 cubic inches *numeric calculation is correct, but error of square versus cubic units c) 184 square inches *the base 10 x 4 x 4 sides (common error to not recognize that 2 of the sides have a different dimension of 10 x 3 ) d) 184 cubic inches *same as a plus the error of square versus cubic units 3) What is the volume of the tissue box that you are designing? a) 120 cubic inches *correct response b) 120 square inches *error of square versus cubic units c) 164 cubic inches *this is the surface area and then listed as cubic inches d) 164 square inches *this is the surface area Tiling And Filling The Pool Assessment Materials Page 6 of 14

7 4) The company decided to increase the volume of the box so that it could hold more tissue. They doubled the height of the box so that it is now 6 inches. How many of the sides have had their area changed by this doubling of the height? a) 2 *does not account for ends b) 3 *there are three pairs of rectangles with different dimensions, error in not realizing that bottom and top have not changed c) 4 *correct response d) 5 *focus on five sides being designed and does not focus on dimensions 5) The local children s museum is designing a new activity room for small children. They want to cover this large foam cube with fabric on all sides so the children can play with it. How much fabric will they need to purchase to cover the cube? (You do not need to account for seams.) 3 meters a) 27 square meters *calculated volume and mislabeled b) 27 cubic meters *calculated volume c) 54 square meters *correct response d) 54 cubic meters *numeric calculation is correct, but error of cubic versus square units Tiling And Filling The Pool Assessment Materials Page 7 of 14

8 6) Find the area of the shaded figure. 10 centimeters 5 centimeters (inside rectangle 5cm x 2cm) a) 40 square centimeters *correct response b) 16 square centimeters * calculated the perimeters and subtracted c) 50 square centimeters *did not subtract the inside figure d) 60 square centimeters *added the area of the two figures 7) Sue figured out the surface area and volume of the box for her diorama project. The only problem is that she did not label her work. When she came back to the project the next day, she couldn t remember which number was the surface area and which was the volume. Look at the box and help Sue solve her problem. 8 inches 10 inches 6 inches a) volume = 480 cubic inches surface area = 376 square inches b) volume = 480 square inches surface area = 376 cubic inches c) volume = 480 cubic inches surface area = 188 square inches d) volume = 480 square inches surface area = 188 cubic inches *correct response *label reversed *did not account for 6 sides on rectangular prism, only three *did not account for 6 sides on rectangular prism, only three, and reversed the labels Tiling And Filling The Pool Assessment Materials Page 8 of 14

9 8) The gift box below has a surface area of 504 square inches and a volume of 720 cubic inches. 6 inches 10 inches 12 inches If you double the length of the box from 12 inches to 24 inches, what is the new surface area and volume? Show your work using words, numbers and/or diagrams. surface area ( 24inches x 10 inches) x 2 = 480 square inches ( 24inches x 6 inches) x 2 = 288 square inches ( 6 inches x 10 inches) x 2 = 120 square inches = 888 square inches volume 6 inches x 24 inches x 10 inches = 1440 cubic inches The new surface area is 888 square inches. The new volume is 1440 cubic inches. Tiling And Filling The Pool Assessment Materials Page 9 of 14

10 Scoring Rubric- #8 ME01 (Attributes and Dimensions) Demonstrates understanding of the concepts of volume and surfaces area of rectangular prisms. (GLE 1.2.1) ME03 (Procedures) Use systematic procedures to measure, describe, and compare the area of rectangles and right triangles and the volume of rectangular prisms identify area or volume as the attribute to be measured, select and use appropriate unit for area or volume, select and use appropriate unit for area or volume, select and use tool that matches the unit chosen, count to determine the number of units; use formulas to find the perimeter and area of rectangles and right triangles. (GLE1.2.4 and 1.2.5) Items may ask students to use surface area and volume to describe a rectangular prism. Items may ask students to identify the volume for a given rectangular prism from a picture or model. Items may ask students to use and/or describe procedures for measuring length, perimeter, and area of a rectangle or right triangle and/or the volume of a rectangular prism: identify the attribute to be measured; select and use appropriate unit of measurement; select and use a tool that matches the unit chosen; count or compare the attribute to the units on the tool to determine the number of units. 2-point response: The student shows an understanding of how doubling the length changes the surface area and volume of the gift box by doing the following: Indicates that the new surface area of the gift box is 888 square inches Shows work and/or explanation supporting 888 square inches Indicates that the new volume of the gift box is 1440 cubic inches Shows work and/or explanation supporting 1440 cubic inches 1-point response: The student does two or three of the following: Indicates that the new surface area of the gift box is 888 square inches Shows work and/or explanation supporting 888 square inches Indicates that the new volume of the gift box is 1440 cubic inches Shows work and/or explanation supporting 1440 cubic inches 0-point response: The student shows little or no understanding of how to find the new surface area or volume. Tiling And Filling The Pool Assessment Materials Page 10 of 14

11 9) Grandma is mailing a box full of gifts to Aunt Sally. The dimensions of the box are 24 inches long by 20 inches wide by 12 inches deep. Grandpa sticks a book into the box while Grandma isn t looking. The book has dimensions of 10 inches by 8 inches by 2 inches. What is the volume left in the box after Grandpa has stuck the book in? Show your work using words, numbers and/or diagrams. volume of box 24 inches x 20 inches x 12 inches = 5760 cubic inches volume of book 10 inches x 8 inches x 2 inches = 160 cubic inches 5760 cubic inches 160 cubic inches = 5600 cubic inches The volume left in the box is 5600 cubic inches. Tiling And Filling The Pool Assessment Materials Page 11 of 14

12 Scoring Rubric- #9 ME03 (Procedures) Use systematic procedures to measure, describe, and compare the area of rectangles and right triangles and the volume of rectangular prisms identify area or volume as the attribute to be measured, select and use appropriate unit for area or volume, select and use appropriate unit for area or volume, select and use tool that matches the unit chosen, count to determine the number of units; use formulas to find the perimeter and area of rectangles and right triangles. (GLE and 1.2.5) SR 02 (Constructs Solutions) Select and organize relevant information: use appropriate concepts and procedures from number sense, measurement, geometric sense, and probability and statistics. (GLE 2.2.2) Items may ask students to use and/or describe procedures for measuring length, perimeter, and area of a rectangle or right triangle and/or the volume of a rectangular prism: identify the attribute to be measured; select and use appropriate unit of measurement; select and use a tool that matches the unit chosen; count or compare the attribute to the units on the tool to determine the number of units. Items may ask students to solve a problem by doing the following: show understanding of the problem by selecting and organizing relevant information; use strategies and procedures appropriately to construct a solution; answer the problem with a viable solution that is mathematically correct and answers the question(s) asked. 2-point response: The student shows an understanding of how to calculate volume given dimensions for two 3-Dimensional objects and that you must subtract to find the remaining volume by doing the following: Indicates that the volume of the box is 5760 cubic inches and that the volume of the book is 160 cubic inches Shows work and/or explanation supporting 5760 cubic inches and 160 cubic inches Indicates that the remaining volume of the box is 5600 cubic inches Shows work and/or explanation supporting 5600 cubic inches 1-point response: The student does two or three of the following: Indicates that the volume of the box is 5760 cubic inches and that the volume of the book is 160 cubic inches Shows work and/or explanation supporting 5760 cubic inches and 160 cubic inches Indicates that the remaining volume of the box is 5600 cubic inches Shows work and/or explanation supporting 5600 cubic inches 0-point response: The student shows little or no understanding of how to calculate volume and/or construct the solution. Tiling And Filling The Pool Assessment Materials Page 12 of 14

13 10) One brick has a height of 2 inches, a length of 8 inches, and a width of 3 inches 2 inches 3 inches 8 inches Determine the volume of one brick. Determine the total volume of three bricks stacked on top of each other. Be sure to include accurate the appropriate units in your answers. Show your work using words, numbers and/or diagrams. volume of one brick 2 inches x 8 inches x 3 inches = 48 cubic inches volume of three bricks stacked (2 inches x 8 inches x 3 inches) x 3 = 144 cubic inches or 6 inches x 8 inches x 3 inches = 144 cubic inches The volume of one brick is 48 cubic inches. The volume of three bricks stacked is 144 cubic inches. Tiling And Filling The Pool Assessment Materials Page 13 of 14

14 Scoring Rubric- #10 ME01 (Attributes and Dimensions) Demonstrates understanding of the concepts of volume and surfaces area of rectangular prisms. (GLE 1.2.1) ME03 (Procedures) Use systematic procedures to measure, describe, and compare the area of rectangles and right triangles and the volume of rectangular prisms identify area or volume as the attribute to be measured, select and use appropriate unit for area or volume, select and use appropriate unit for area or volume, select and use tool that matches the unit chosen, count to determine the number of units; use formulas to find the perimeter and area of rectangles and right triangles. (GLE and 1.2.5) Items may ask students to identify the volume for a given rectangular prism from a picture or model. Items may ask students to label measurements of rectangular prism to show understanding of the relationships among linear dimensions, surface area, and volume of rectangular prisms and that area is measured in square units and volume in cubic units. Items may ask students to use and/or describe procedures for measuring length, perimeter, and area of a rectangle or right triangle and/or the volume of a rectangular prism: identify the attribute to be measured; select and use appropriate unit of measurement; select and use a tool that matches the unit chosen; count or compare the attribute to the units on the tool to determine the number of units. 2-point response: The student shows an understanding of how to calculate volume from a picture and that changing one dimension impacts the new volume by doing the following: Indicates that the volume of one brick is 48 cubic inches and labels it correctly in answer Shows work and/or explanation supporting 48 cubic inches Indicates that the volume of three bricks stacked is 144 cubic inches and labels it correctly in answer Shows work and/or explanation supporting 144 cubic inches 1-point response: The student does two or three of the following: Indicates that the volume of one brick is 48 cubic inches Shows work and/or explanation supporting 48 cubic inches Indicates that the volume of three bricks stacked is 144 cubic inches Shows work and/or explanation supporting 144 cubic inches 0-point response: The student shows little or no understanding of how to calculate volume and/or construct the solution. Tiling And Filling The Pool Assessment Materials Page 14 of 14