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LFS DIGITAL > Instructional Unit Topics > Math Unit Topics > Three dimensional object  

Three dimensional object

 

Content Area

Grade Level

Mathematics

7

Unit Topic

Three-Dimensional 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 three-dimensional objects from two-dimensional 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 two-dimensional figures that result from slicing three dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

 

Solve real-life 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 real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional 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 (Cross-Dimensional Representations)

Example 1: Scale Drawings--Maps

Example 2: Blueprints--Museum

Recognizing Scale

Example 1: Proportion and Scale--Capitol Model

Example 2: Congruence and Similarity--Flags

Example 3: Proportionate Growth--Sharks and Nautilus

Math Overview

Grades 06-07: Scale Drawings

Grade 07-08: Scale Drawings and Models

Math Explanation

Grades 06-07: Scale Drawings: Using Scales to Find Area

Grades 06-07: Scale Drawings: Matching a Scale Factor with Measurements

Grades 06-07: Scale Drawings: Using Scales to Make a Diagram of a Real Object

Grades 06-07: Ratios: Finding Ratios for Area in a Diagram

Grade 07-08: Similar Solids: Using Ratio of Surface Area of Solids to Find Ratio of Volumes

Grade 07-08: Ratios and Rates: Relating Ratio of Length to Ratio of Perimeter and Area

Grades 06-07: Similar Polygons: Finding the Ratio of the Perimeter and Area of Similar Polygons

 

 

3. Describe the two-dimensional figures that result from slicing three dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Video:

Example 3: Planar Cross-Sections--Earth and MRI

Instructional Image

Hailstone; cross section

Math Explanation

Grade 07-08: Volume of a Cylinder: Finding Area of Cross Section of Cylinder and Finding Volume

 

Solve real-life 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 06-07: Circumference of a Circle

Math Explanation

Grade 07-08: Circumference and Area of a Circle: Finding Radius and Diameter Given Area or Circumference

 

6. Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Video:

What Is Three-dimensional?

Building a Three-dimensional Figure from a Two-dimensional Drawing

Drawing Two-dimensional Views of a Three-dimensional Object

Matching Two-dimensional Views to the Three-dimensional Object

Perspective Drawing: Illusion of Three-dimensions

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 (3-D 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 07-08: Areas of Polygons: Finding Combined Area

Grades 06-07: Area of a Parallelogram: Finding Area of Parallelogram from a Diagram

Grades 06-07: Surface Area of a Prism: Finding Area of Faces of a Triangular Prism and Adding to Find Surface Area

Grades 06-07: Surface Area of a Prism: Finding Surface Area in Real Life Situations

Grade 07-08: 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, easy-to-understand 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

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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 3-D shapes.
Level: Intermediate

Credit: SMART Technologies
License: CC BY

Notes/activity suggestions:

Tags: grade7, math, geometry, nets, solids, 3-dimensional shapes, SMART

--------------------------------------------------------------------------------------------------------------------

 

Resource 4:  Nets
Media type: text
Description: A lesson and related activities for nets to introduce students to 3-dimensional 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

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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

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Thinkfinity Resources 


Cube Nets-In this applet, from Illuminations, students explore nets, two-dimensional figures that can be folded into three-dimensional 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