Virginia Mathematics Checkpoint Assessment GEOMETRY G.14. Topic: Three-Dimensional Figures
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1 Virginia Mathematics Checkpoint Assessment GEOMETRY G.14 Topic: Three-Dimensional Figures Standards of Learning Blueprint Summary Reporting Category Geometry SOL Number of Items Reasoning, Lines, and G.1(a-d), G.2(a-c), G.3(a-d), 18 Transformations G.4(a-g) Triangles G.5(a-d), G.6, G.7, G.8 14 Polygons, Circles, and Three- G.9, G.10, G.11(a-c), G.12, 18 Dimensional Figures G.13, G.14(a-d) Excluded from Testing None Number of Operational Items 50 Number of Field-Test Items 10 Total Number of Items on Test 60 Virginia Mathematics SOL Test Cut Scores Failing Scores Passing Scores Test Basic Proficient Advanced Minimum Minimum Minimum Minimum # correct % correct # correct % correct # correct % correct Math 3 16 of 40 40% 26 of 40 65% 36 of 40 90% Math 4 17 of 50 34% 31 of 50 62% 45 of 50 90% Math 5 18 of 50 36% 31 of 50 62% 45 of 50 90% Math 6 16 of 50 32% 28 of 50 56% 45 of 50 90% Math 7 17 of 50 34% 31 of 50 62% 45 of 50 90% Math 8 17 of 50 34% 31 of 50 62% 46 of 50 92% Algebra I n/a n/a 25 of 50 50% 45 of 50 90% Geometry n/a n/a 25 of 50 50% 44 of 50 88% Algebra II n/a n/a 27 of 50 54% 43 of 50 86% Geometry Checkpoint G.14 Page 1
2 Checkpoint Items 1. Directions: After showing your thinking, write your answer in the boxes. What is the ratio of volume of pyramid B to volume of pyramid A? : Geometry Checkpoint G.14 Page 2
3 2. Directions: After showing your thinking, write your answer in the box. If the volume of the larger cylinder is 2,250 π square units, what is the radius of the larger cylinder? r = 5 r =? h =10 Radius = units Geometry Checkpoint G.14 Page 3
4 3. Directions: After showing your thinking, write your answer in the box. If the diameter of the cylinder is doubled, how many times bigger is the volume? Diameter = 16 Height = 12 times bigger Geometry Checkpoint G.14 Page 4
5 4. Directions: After showing your thinking, write your answer in the box. The radius of this sphere is 20 centimeters. If the radius is tripled, how many times bigger is the volume than the original volume? r = 20 times as big Geometry Checkpoint G.14 Page 5
6 5. Directions: Circle the box you want to select. In parallelogram EFGH, EF = 15 cm, FG = 17 cm, and the height is 13 cm. How will the area of the parallelogram change if FG is doubled? E H F 17 G The area will be 1 as big 2 The area will be the same The area will be twice as big The area will be four times as big Geometry Checkpoint G.14 Page 6
7 6. Directions: After showing your thinking, complete the missing information in the table below. The volume of this rectangle prism is changed from its current volume to 1,225 cubed units by changing one measurement Length Width Height Volume ,225 Geometry Checkpoint G.14 Page 7
8 7. Directions: After showing your thinking, write your answer in the box. If the volume of the cone after the height is changed is 384 π cubed units, what is the new height? h = 8 r = 4 Height = Geometry Checkpoint G.14 Page 8
9 8. Directions: After showing your thinking, write your answer in the box. The area of this circle after the radius is multiplied by 8 is 5,184 π square units. What is the original radius of the circle? Radius = Geometry Checkpoint G.14 Page 9
10 9. Directions: After showing your thinking, write your answer in the box. Two similar cylindrical canisters are being used for storage in the kitchen. If the second canister will hold 1 as much material as the first canister, what is 4 the height of the second canister? Height = Geometry Checkpoint G.14 Page 10
11 10. Directions: After showing your thinking, write your answer in the box. A 4 x 6 photograph is being enlarged to be placed in a larger frame. If the width of the enlarged picture is 14 inches, what is the length? Length = Geometry Checkpoint G.14 Page 11
12 Checkpoint Solutions SOL G.14 The student will use similar geometric objects in two- or three-dimensions to a) compare ratios between side lengths, perimeters, areas, and volumes; b) determine how changes in one or more dimensions of an object affect area and/or volume of the object; c) determine how changes in area and/or volume of an object affect one or more dimensions of the object; and d) solve real-world problems about similar geometric objects. Essential Knowledge and Skills a. Compare ratios between side lengths, perimeters, areas, and volumes, given two similar figures b. Describe how changes in one or more dimensions affect other derived measures (perimeter, area, total surface area, and volume) of an object c. Describe how changes in one or more measures (perimeter, area, total surface area, and volume) affect other measures of an object d. Solve real-world problems involving measured attributes of similar objects Item Answer/Solution SOL/EKS Code 1 125:512 G.14aa 2 15 G.14aa 3 4 G.14bb 4 27 G.14bb 5 The area will be twice as big G.14bb 6 Length Width Height Volume ,225 G.14cc 7 24 G.14cc 8 9 G.14cc 9 10 G.14dd G.14dd Essential Knowledge and Skills Compare ratios between side lengths, perimeters, areas, and volumes, given two similar figures Compare ratios between side lengths, perimeters, areas, and volumes, given two similar figures Describe how changes in one or more dimensions affect other derived measures (perimeter, area, total surface area, and volume) of an object Describe how changes in one or more dimensions affect other derived measures (perimeter, area, total surface area, and volume) of an object Describe how changes in one or more dimensions affect other derived measures (perimeter, area, total surface area, and volume) of an object Describe how changes in one or more measures (perimeter, area, total surface area, and volume) affect other measures of an object Describe how changes in one or more measures (perimeter, area, total surface area, and volume) affect other measures of an object Describe how changes in one or more measures (perimeter, area, total surface area, and volume) affect other measures of an object Solve real-world problems involving measured attributes of similar objects Solve real-world problems involving measured attributes of similar objects Geometry Checkpoint G.14 Page 12
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