

Content Area 
Grade Level 
Mathematics

7 
Unit Topic 
ThreeDimensional Shapes
Sub Topic 1 Nets of three dimensional shapes
Sub Topic 2 Volume of three dimensional shapes
Sub Topic 3 Surface Area of three dimensional shapes

Description of Unit 
The volume and surface area of prisms and cylinders can be calculated and applied to real world problems. Students will build threedimensional objects from twodimensional representations and draw two dimensional representations of three dimensional objects. Students will create models of nets of three dimensional figures (e.g., cube, rectangular prism, cylinder). Students will find the surface area of prisms using physical models. Students will determine the volume and surface areas of cylinders and prisms. Students will demonstrate the relationship between the area of the base and volume of prisms and cylinders.

Standard(s)/Benchmarks/Grade Level Expectations Addressed 
Geometry 7.G
Draw, construct, and describe geometrical figures and describe the relationships between them.
1.Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
3. Describe the twodimensional figures that result from slicing three dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
Solve reallife and mathematical problems involving angle measure, area, surface area, and volume.
4. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
6. Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Key Search Words 
Base
Height
Face
Net
Prisms
Cylinders
Surface Area
Volume

Discovery Education Resources
Draw, construct, and describe geometrical figures and describe the relationships between them.
1.Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
Video:
Introduction (CrossDimensional Representations)
Example 1: Scale DrawingsMaps
Example 2: BlueprintsMuseum
Recognizing Scale
Example 1: Proportion and ScaleCapitol Model
Example 2: Congruence and SimilarityFlags
Example 3: Proportionate GrowthSharks and Nautilus
Math Overview
Grades 0607: Scale Drawings
Grade 0708: Scale Drawings and Models
Math Explanation
Grades 0607: Scale Drawings: Using Scales to Find Area
Grades 0607: Scale Drawings: Matching a Scale Factor with Measurements
Grades 0607: Scale Drawings: Using Scales to Make a Diagram of a Real Object
Grades 0607: Ratios: Finding Ratios for Area in a Diagram
Grade 0708: Similar Solids: Using Ratio of Surface Area of Solids to Find Ratio of Volumes
Grade 0708: Ratios and Rates: Relating Ratio of Length to Ratio of Perimeter and Area
Grades 0607: Similar Polygons: Finding the Ratio of the Perimeter and Area of Similar Polygons
3. Describe the twodimensional figures that result from slicing three dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.
Video:
Example 3: Planar CrossSectionsEarth and MRI
Instructional Image
Hailstone; cross section
Math Explanation
Grade 0708: Volume of a Cylinder: Finding Area of Cross Section of Cylinder and Finding Volume
Solve reallife and mathematical problems involving angle measure, area, surface area, and volume.
4. Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.
Video:
Central Angle, Arc, & Circumference
Practice Problem: Angles & Circles
Section C: Circleville (Circumference of Circles)
Descriptions of Circles and Cylinders
Measurements of Circles: Circumference
Measurements of Circles: Diameter
Relationship Between Circumference and Diameter
Defining Circumference, Radius and Diameter
Solving Problems with Circles
Math Overview
Grades 0607: Circumference of a Circle
Math Explanation
Grade 0708: Circumference and Area of a Circle: Finding Radius and Diameter Given Area or Circumference
6. Solve realworld and mathematical problems involving area, volume and surface area of two and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
Video:
What Is Threedimensional?
Building a Threedimensional Figure from a Twodimensional Drawing
Drawing Twodimensional Views of a Threedimensional Object
Matching Twodimensional Views to the Threedimensional Object
Perspective Drawing: Illusion of Threedimensions
Perspective: Drawing a Cube
Drawing in Perspective
Defining Area & Volume
The Area of Rectangles
Practice Problems: Finding the Area of Rectangles
The Area of Squares
The Area of Parallelograms & Triangles
The Area of Irregular Polygons
Section E: Surface Area
Section F: Volume
Introduction (3D Figures)
Example 1: Properties of Cubes and Spheres
Example 2: Properties of Rectangular Prisms and Cylinders
Example 3: Properties of Pyramids and Cones
Math Explanation
Grades 0708: Areas of Polygons: Finding Combined Area
Grades 0607: Area of a Parallelogram: Finding Area of Parallelogram from a Diagram
Grades 0607: Surface Area of a Prism: Finding Area of Faces of a Triangular Prism and Adding to Find Surface Area
Grades 0607: Surface Area of a Prism: Finding Surface Area in Real Life Situations
Grade 0708: Volume of a Prism: Finding Base Area and Base Perimeter of a Right Prism
Open Resources
* See also Grade 7, Math, Volume
Resource 1: Surface Area of a Box, Surface Area of a Pyramid, Surface Area of a Pyramid with a Triangular Base, Surface Area of a Cylinder, Surface Area Review, Surface Area Word Problems
Media type: video, interactive Description: Short, easytounderstand videos and interactive problems and quizzes on calculating the surface area of various solids Level: Intermediate
Credit: Systems Impact Inc. dba MathMastery.com License: CC BY
Notes/activity suggestions:
Tags: grade7, math, geometry, rectangular solid, prism, pyramid, cylinder, surface area 
Resource 2: Surface Area and Volume
Media type: text Description: This unit contains lesson plans, quizzes, and an assessment project. Students will investigate nets, which are 2D representations of 3D objects, surface areas and volumes of various prisms, and more. The project has students designing their own packaging, calculating the surface area, volume, and cost of materials, for a product of their choice. Level: Intermediate
Credit: Devin Byrka License: CC BY NC
Notes/activity suggestions:
Tags: grade7, math, geometry, surface area, volume

Resource 3: Nets Media type: interactive Description: A SMART Board notebook for drawing nets of 3D shapes. Level: Intermediate
Credit: SMART Technologies License: CC BY
Notes/activity suggestions:
Tags: grade7, math, geometry, nets, solids, 3dimensional shapes, SMART

Resource 4: Nets Media type: text Description: A lesson and related activities for nets to introduce students to 3dimensional objects and ideas related to surface area. Level: Beginning, Intermediate
Credit: Siyavula Uploaders, Connexions License: CC BY
Notes/activity suggestions:
Tags: grade7, math, geometry, surface area, nets 
Resource 5: Teaching Surface Area Media type: text Description: A set of ideas about teaching surface area. Student materials include Surface Area Worksheets and this activity to Design a Toblerone Box Level: Intermediate
Credit: Simon Job License: CC BY NC SA
Notes/activity suggestions:
Tags: grade7, math, geometry, surface area, nets

Resource: Media type: Description: Level:
Credit: License:
Notes/activity suggestions:
Tags:
Thinkfinity Resources
Cube NetsIn this applet, from Illuminations, students explore nets, twodimensional figures that can be folded into threedimensional objects. Grade:3  8 Resources: Interactive  Activity Subject: Mathematics  Geometry Keywords: Geometry  Cubes  nets
Last modified at 6/17/2011 1:35 PM by SEAFORD\mkidder



