III. Unit 3-Geometry and Measurement

Abstract

In this unit, students will fully develop and apply formulas for perimeter and area of polygons as well as circumference and area of circles.  Student investigation of right triangles will include the Pythagorean Theorem. Students will recognize how to apply this information to solve real world problems.  This unit also covers three-dimensional geometry.  Basic vocabulary and properties are discussed. Students must utilize the formulas for surface area and volume of common solids for the purpose of application. Lastly, students investigate transformations and reflections using scaled figures on a grid.

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

Focus Questions:

  1. How do perimeter and area formulas for plane figures help us to solve real world problems? (GMCore: 3.3.1)

  2. How is the Pythagorean Theorem useful to find missing lengths of right triangles? (GMCore: 3.3.2)

  3. How is the surface area of a solid determined and how does the surface area help us to solve real world problems? (GMCore: 3.3.4)

  4. How are volumes of solids determined and when do we use volume in our every day lives? (GMCore: 3.3.4)

  5. Why is it important to know how to transform and reflect figures with accuracy and precision? (GMCore: 3.2.3)

Benchmarks:

The student will be able to

  1. Perform unit conversions (GM6: 3.3b.1)

  2. Use established formulas for area and perimeter for real world application (F1, GMCore: 3.3.1)

  3. Solve problems involving perimeter and area including how a change in one or more parts of the geometric figures may affect its perimeter and area (F1, GMCore: 3.2.2).

  4. Calculate area/circumference of circles using appropriate formulas and units.  Using estimation techniques, judge the reasonableness of solutions (F1, GMCore: 3.3.1, 3.3.3).

  5. Use Pythagorean Theorem to find missing lengths of right triangles (F2, GMCore: 3.3.2).

  6. Appropriately apply the concept of surface area to real world problems (F3, GMCore: 3.3.4).

  7. Appropriately apply the concept of volume to real world problems (F4, GMCore: 3.3.4).

  8. Use transformations and reflections to accurately relocate figures on a grid (F5, GMCore: 3.2.3)

Required Activities (Common Experiences):

  1. Reinforce concepts of area and perimeter. For example: roofing a house and its material and labor costs (F1, GMCore: 3.3.1).

  2. Reinforce concepts of measurement/estimation of irregular regions using a scale drawing:  Distance and land area calculations using an Atlas. (F1, GM6: 3.3b.1, GMCore: 3.2.2)

  3. Reinforce the concept of how a change in dimension can affect area and perimeter. “Painting Enlargement”, 2004 CAPT released item (F1, GMCore: 3.2.2).

  4. Reinforce the concepts of area and perimeter of polygons as well as area and circumference of circles using reality-based applications.  “Skateboard Park”, CAPT released item (F1, GMCore: 3.3.1).

  5. Surface area and volume problem.  “Storage Container”, CAPT Coach, Grade 10, p.246, #10, #13. (Edit to include area) (F3, F4, GMCore: 3.3.4)

  6. Translate and Reflect figures on a coordinate plane. “Library Table”, CAPT Coach, Grade 10, p.242, #27. (Edit to omit rotation and include reflection)
         (F5, GMCore: 3.2.3)

Suggested Activities:

  1. Investigate the maximum area of a rectangle given a perimeter. For example: reference Prentice Hall p. 59 (F2, GMCore: 3.2.2, 3.3.1).

  2. Determine through numerical means a method and pattern to find the least surface area for a given volume for packaging.  Reference NCTM Connections Book (GMCore: 3.3.4).

  3. Investigate rotations in conjunction with translations and reflections.  “Library Desk”, CAPT Coach, Grade 10, p.60-61 (F5, GMCore: 3.2.3)

Student Portfolio Unit Assessments:

  1. Reinforce the concepts of area estimation of irregular regions to include correct units with scale factor.   “Tolland County”, 9th grade CAPT Practice (F1, GM7: 3.3.1, GMCore: 3.3.1, 3.3.3).

  1. Reinforce the concepts of area and perimeter of polygons as well as area and circumference of circles using reality-based applications.  “Hugo’s Pizza”, CAPT released item (F1, GMCore: 3.3.1, 3.3.3).

  1. Surface area and Volume problem.  “Storage Containers”, CAPT Coach 10, p.172-173, #9, #10. (Edit to include area) (F3, F4, GMCore: 3.3.4)

  1. Translation and Reflection. ”Quilt Design”, Math 10 CAPTest, p. 178. (F5, GMCore: 3.2.3)    

Instructional Resources and Materials:

Exploring Geometry Activity Book, copyright 1999
CAPT release items

Math 10 CAPTest

CAPT Coach grade 10

Measurement Tools-Ruler and Protractor
Scientific Calculator
Dot Paper
Graph Paper
Art supplies As Needed
Geometry Textbook

Connections:  Models real-world decision making situations.

Pacing:  10 block class meetings

Notes to Teacher:

 

Approved by Instructional Council on 12/5/05
BOE 1/18/06