GEOMETRY CONTENT ACADEMY Three-Dimensional Figures SOL G.13, G.14 February 19, 2015 & March 5, 2015

REPORTING CATEGORY: POLYGONS, CIRCLES, AND THREE-DIMENSIONAL FIGURES

PACING

FORMULAS What formulas do students need to know related to Three- Dimensional Figures (SOL G.13 and G.14)? What formulas are provided on the formula sheet related to Three-Dimensional Figures?

CURRICULUM FRAMEWORK – G.13

HENRICO CURRICULUM GUIDE

PERFORMANCE ANALYSIS COMPARISON SOL G – None 2013 – None The student will use formulas for surface area and volume of three- dimensional objects to solve real-world problems.

2014 SPBQ DATA – G.13

Students need additional practice determining surface area and volume of three dimensional composite figures. A statue consists of a square pyramid and a rectangular prism with congruent bases. Specific measurements of the statue are shown in this figure. What is the total surface area of the statue represented by this composite figure? [Figure is not drawn to scale.] SUGGESTED PRACTICE FOR SOL G square inches Slant height can be found using the Pythagorean Theorem: 3² + x ² = 5² x = 4 10 in 6 in 5 in x Common Errors ? Misconceptions?

SUGGESTED PRACTICE FOR SOL G.13 What is the volume of this figure rounded to the nearest cubic inch? 10 in 6 in 5 in a The height, a, can be calculated using the Pythagorean Theorem, where 3 is half the length of the base and 4 is the slant height: Common Errors ? Misconceptions?

CURRICULUM FRAMEWORK – G.14

HENRICO CURRICULUM GUIDE

PERFORMANCE ANALYSIS COMPARISON SOL G – 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 – 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 – 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.

2014 SPBQ DATA – G.14

Students need additional practice determining the relationship between changes that affect one dimension (linear), changes that affect two dimensions (area), and changes that affect three dimensions (volume), particularly when figures are not provided. A rectangular prism has a volume of 36 cm³. a)If the height of the prism is tripled and the other dimensions do not change, what is the volume of the new rectangular prism? 108 cm 3 b)If all dimensions of the original rectangular prism are tripled, what is the volume of the new rectangular prism? 972 cm SUGGESTED PRACTICE FOR SOL G.14 Common Errors ? Misconceptions?

A cylinder has a surface area of 96 square inches. If all dimensions of this cylinder are multiplied by to create a new cylinder, what will be the surface area of the new cylinder? 24 square inches SUGGESTED PRACTICE FOR SOL G.14 Common Errors ? Misconceptions?

Students need additional practice determining how changes in dimensions of a geometric object affect surface area and volume, and how changes in surface area and volume affect its dimensions. Students also need additional practice determining these relationships for similar geometric objects. Example Using Ratios: Two similar rectangular prisms have side lengths with a ratio of 1:3. a)What is the ratio of their surface areas? 1:9 b)What is the ratio of their volumes? 1: SUGGESTED PRACTICE FOR SOL G.14 Common Errors ? Misconceptions?

Example Using Scale Factors: The dimensions of a triangular prism with a surface area of cm² are multiplied by a scale factor of 2.5 to create a similar triangular prism. a)What is the surface area of the new triangular prism? Extension: What is the relationship between the volume of the original prism and the volume of the new prism? The new volume is times the volume of the original prism SUGGESTED PRACTICE FOR SOL G.14 Common Errors ? Misconceptions?

Relationship Between Volume and Dimensions: Cathy has two cylinders that are the same height, but the volume of the second cylinder is 16 times the volume of the first cylinder. The radius of the second cylinder is – A.2 times the radius of the first cylinder. B.4 times the radius of the first cylinder. C.8 times the radius of the first cylinder. D.16 times the radius of the first cylinder SUGGESTED PRACTICE FOR SOL G.14 Common Errors ? Misconceptions?

Relationship Between Volume and Dimensions: Cathy has two cylinders with radii the same length, but the volume of the second cylinder is 16 times the volume of the first cylinder. The height of the second cylinder is – A.2 times the height of the first cylinder. B.4 times the height of the first cylinder. C.8 times the height of the first cylinder. D.16 times the height of the first cylinder SUGGESTED PRACTICE FOR SOL G.14 Common Errors ? Misconceptions?

Students need additional practice developing an understanding of the relationship between the linear, area, and volume ratios of similar geometric objects. Given: Objects A and B are three-dimensional. Object A is similar to object B. The height of object A is 24 inches and the height of object B is 36 inches. 1.What is the ratio of the surface area of object A to the surface area of object B in simplest form? 2.What is the ratio of their volumes in simplest form? 4:9 8: SUGGESTED PRACTICE FOR SOL G.14 Common Errors ? Misconceptions?

Students need additional practice using any given ratio of a pair of similar figures (linear, surface area, or volume) to determine the other two ratios. Pyramid S is similar to Pyramid T. If the ratio of the volume of Pyramid S to Pyramid T is 64:125, complete the table by finding the ratio of their side lengths and the ratio of their surface areas. Pyramid SPyramid T Side Length to Surface Areato Volume 64 to SUGGESTED PRACTICE FOR SOL G.14 Common Errors ? Misconceptions?

The ratio of the surface areas of two spheres is 1:9. 1.What is the ratio of the lengths of their radii? What is the ratio of their volumes? The ratio of the lengths of the radii is 1:3 and the ratio of the volumes is 1:27. 2.If the volume of the smaller sphere is 64 cubic inches, what is the volume of the larger sphere? The volume of the larger sphere is 1,728 cubic inches SUGGESTED PRACTICE FOR SOL G.14 Common Errors ? Misconceptions?

INSTRUCTIONAL RESOURCES HCPS Math Website – G Check out the Skills problems on the Mathematics Assessment Project link!

INSTRUCTIONAL RESOURCES HCPS Math Website – G

INSTRUCTIONAL RESOURCES 1.ExamView BanksExamView Banks 2.NextLesson.orgNextLesson.org  Surface Area and Volume Surface Area and Volume 3.HCPS Math Website  VDOE Enhanced Scope and Sequence Lessons  Skills - JMU Pivotal Items 4.ExploreLearning Teaching Strategies Student Engagement Activities