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Ledyard Mathematics Department

Integrated Mathematics II

Unit 7: Surface Area and Volume

Abstract

This unit focuses on three-dimensional geometry. It begins with an introduction to common solids using two-dimensional nets. Basic vocabulary and properties are developed. Students must then utilize the nets to develop formulas for surface area and volume of common solids for the purpose of application. Lastly, students investigate how a change in measurement of one or more parts of similar solids affects its surface area and volume. Algebraic concepts and properties are integrated throughout this unit.

Essential Question: How do geometric relationships and measurements help us to solve problems and make sense of our world?

Focus Questions

  1. How are solids constructed from plane figures? (GMCore:3.1a)

  1. How are surface areas of solids calculated and how do these values help to solve real world problems? (GMCore:3.3a)

  1. How are volumes of solids calculated and how do these values help to solve real world problems? (GMCore:3.3a)

  1. How does a proportional change in measurement affect the surface area and volume of solids? (GMCore:3.2a)

Benchmarks

The student will be able to:

  1. Given a net, name the solid and identify the plane figures from which it is constructed. (F1, GMCore:3.1a.1)

  1. Connect the derivation of surface area formulas for solids to their nets. (F1, GMCore:3.1a.1 and F2, GMCore:3.3a.4)

  1. Solve surface area problems by using formulas for prisms, cylinders, spheres, pyramids and cones to calculate their surface areas. (F2, GMCore:3.3a.4)

  1. Apply the concept of surface area to solve real world problems. (F2, GMCore:3.3a.4)

  1. Use formulas for prisms, cylinders, spheres, cones and pyramids to calculate their volumes. (F3, GMCore:3.3a.4)

  1. Apply the concept of volume to solve real world problems. (F3, GMCore:3.3a.4)

  1. Use the similarity ratio of two similar solids to find the ratios of their surface areas and volumes. (F4, GMCore:3.2a.2)

  1. Use the ratio of the surface areas or the ratio of the volumes of two similar solids to find the similarity ratio. (F4, GMCore:3.2a.2)

Technology Education Framework Connection
Content Standards 1, 5, 6
Computer Use:  on-line text and tutorial
Calculators

Required Activities (Common Experiences)

  1. Students use nets to derive surface area formulas. (GMCore:3.1a.1)

  1. Given a diagram and dimensions of a pyramid, students relate perimeter of the base to the circumference of a circle in order to find missing measures.  (e.g. 2005 CAPT release item, “Great Pyramid”, #15)  (GMCore:3.3a.4)

  1. Students determine the amount of wrapping paper needed to cover boxes of various sizes and shapes by choosing the correct formula and explaining in writing how to solve the problem. (F2, GMCore:3.3a.4)

  1. Students investigate how changing the dimensions of a solid, proportionally changes its surface area and volume. (F4, GMCore:3.2a.2)

  1. Students justify an appropriate container choice by calculating each volume and comparing the results.  Students choose the necessary formulas, calculate, compare, and justify their decision in writing. (CAPT release item- Ice Chests) (F3, GMCore:3.3a.4)

 Suggested Activities

  1. Use the solid models to derive the volume formulas for cones and cylinders with congruent bases. (F3, GMCore:3.3a.4

Assessment Tasks

  1. Required activities above

  1. Teacher generated quizzes and tests

Instructional Resources and Materials

Measurement tools
Calculator(TI-30XIIS)
Isometric dot paper and graph paper
Photocopies of nets/solids with their appropriate nets
See through solid models
CAPT formula sheet
“Click-it” Blocks/Unit Cubes
Prentice Hall Mathematics Course 3

Connections

Marketing - Economics of packaging

English - Prefixes of regular polyhedrons, Gulliver’s Travels by Jonathan Swift – Can giants exist?  Why or why not?

Art - The study of perspective drawing to make 3-dimensional drawings

Pacing

This unit is expected to take ten class periods under the block schedule.

Notes to Teacher

 

Approved by Instructional Council 6/05/06.