Unit Design for Applying Geometry to the Real World

 

 

Unit Designers:  Stacey Britner     Unit Title: Applying Geometry to the Real World

Content Areas: Mathematics           Time Frame:  4-6 weeks    Grade/Level: 8Th Grade

 

Part 1 - Background

 

Class Profile: Description of the students for whom this unit is designed

8Th grade heterosexual classroom of about 25 students.

The class meets every day for one period, 45 minutes.

 

Specific information on students with special needs:

No special needs for the students.

 

Unit Overview (Goals & Focus) with Rationale for Relevance to Adolescents:

Students will learn the relationships and meanings of angle and shapes of geometry.  They will apply this knowledge to build a bridge.  The students will test to see how much weight it can withstand without collapsing.  Also, they must explain the reasons why the bridge did not withstand more weight without collapsing.  Each student will also provide a drawing, painting, or sculpture that only uses geometric figures to show they understand how geometry relates to art.

 

Part 2 – Unit Focus

 

Integrated Theme:

Geometry is present throughout the world around us. 

Integration Areas:

·         Architecture

·         Art

·         Language Arts

·         Mathematics

Rationale for Integration:

The students will have an introduction to architecture in order to be able to build a bridge.  They will use art to draw something of their liking with only geometric figures.  Their write up of their bridge will incorporate English.

Standards that address integrated areas:

Alignment with National Standards:

Mathematics:

·                     Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

·                     Use coordinate geometry to examine special geometric shapes, such as regular polygons or those with pairs of parallel or perpendicular sides.

·                     Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Language Arts:

·         Use oral language with clarity, voice and fluency to communicate a message.

·         Determine purpose, point of view and audience, and choose an appropriate written, oral or visual format.

·         Demonstrate proficient use of proper mechanics, usage and spelling skills.

Art:

·         Generalize about the effects of visual structures and functions and reflect upon these effects in their own work.

·         Students select media, techniques, and processes; analyze what makes them effective or not effective in communicating ideas; and reflect upon the effectiveness of their choices

·         Students employ organizational structures and analyze what makes them effective or not effective in the communication of ideas

Alignment with Connecticut Frameworks

Mathematics:

·                     6.8-10.2  Develop an understanding of the properties of geometric figures by applying knowledge of coordinate representations.

·                     6.8-10.5  Use manipulatives, models, technology, and real objects to investigate, explore, and describe the geometry in nature and to solve geometric problems.

·                     6.8-10.7  Classify figures in terms of congruence and similarity and apply these relationships.

Language Arts:

·         Make and verify predictions based on prior knowledge and text.

·         Draw verifiable conclusions.

·         Identify the central idea or purpose of a text.

Art:

·         Use different media, techniques and processes ( two dimensional, three dimesional, including media/technology) to communicate ideas, feelings, experiences, and stories.

·         Select and use the elements of art and principles of design to improve communication of their ideas.

·         Compare and contrast purposes for creating works of art.

 

Alignment with Common Core of Learning

Mathematics:

·                     Students will analyze and use spatial relationships and basic concepts of geometry to construct, draw, describe and compare geometric models and their transformations and use geometric relationships and patterns to solve problems.

·                     Communicate numerical, geometric, algebraic, and statistical ideas orally and in written form with models, pictures, graphs and mathematical symbols.

·                     Identify and use connections within mathematics to identify interrelationships and equivalent representations, to construct mathematical models, and to investigate and appreciate mathematical structure.

v      Taken from the Town of Manchester’s Curriculum for 8th grade mathematics.

Language Arts:

1.Students will produce written, oral, and visual texts to express, develop and substantiate ideas and experiences.

Art:

2.Students will reflect upon, describe, analyze, interpret and evaluate their own and others’ work.

3.Create art works that express concepts, ideas and feeling in each art form.

4.Students will understand, select and apply media, techniques, and processes.

 

Big Ideas/Enduring Understandings:

  • Students will understand how certain angles support or do not support a bridge.
  • Students will understand how shapes and symmetry can create art.
  • Students will understand what characteristics create a shape.

Essential Questions:

  • What are the properties of each polygon?
  • What are the different kinds of angles and what are their differences?
  • What is coordinate geometry and how is it used in the working world?
  • What is symmetry?

Critical Content Knowledge:

·         Students will know how to create shapes and angles.

·         Students will know what symmetry is and how to apply it to geometric shapes.

·         Students will know how to communicate geometry through writing, models, and art.

Key Skills:

·         Students will be able to have an understanding of geometric figures.

·         Students will be able to explain why mathematics contributes to why a piece of work is considered artwork.

·         Students will be able to see how geometry is incorporated in more areas of their lives than just in the classroom.

Part 2 – Planning for Performance

Part 2A: The Plan for the End-of-Unit Final Performance Assessment

The Performance Tasks:

  • Build a bridge.
  • Write a report explaining the amount of weight the bridge can support and how you arrived at that weight.
  • Explain why the bridge cannot support more weight.
  • Quizzes will be taken on each section.
  • Present a piece of artwork only using geometric figures.

 

 

 

 

 

Part 3 – Unit Topic/Lesson/Sequence Map

This is VERY brief: use key words only.  Its purpose is to see congruence with standards, increasing complexity in thinking (Bloom’s Taxonomy), preparation towards performance, and variation in assessments.  Insert and delete number of days as needed.  Write-up details in your lessons. 

Monday

 

Tuesday

Wednesday

Thursday

Friday

Unit Introduction

Vocabulary associated with geometry in general.

Use website of basic geometry terms.

 

Polygon Section

Vocabulary and definitions of polygons.(chart)

Use The Geometer’s Sketchpad in computer lab.

Use a Venn Diagram to show the differences between shapes.

 

Angle Section

Explain different types of angles and their characteristics in a chart form.

 

Show how to draw, create, and measure various angles.

 

Quiz on Geometric Vocabulary

Triangle Section

Explain all different types of triangles and their defining characteristics.

Use The Geometer’s Sketchpad in computer lab.

Introduce rotation, reflection, and translation of triangles and other polygons.

Tangram problems

 

Quiz on Triangles and Polygons

Coordinate Plane Section

Using graph paper show how to read and use a coordinate plane.

 

 

Use coordinate planes to better explain reflection, rotation, and translation of figures.

Quiz on Coordinate Plane Section

 

Introduce final two projects, bridge and artwork.

Symmetry Section

Explain what symmetry is and the different types.

Have students bring in a picture of their favorite emblem.

Use the emblems to have the students find out what type of symmetry is being used.

Look at different drawings/pictures of buildings to see the symmetry.

Quiz on Symmetry

 

3-D Shapes

Show how polygons, triangles combined can form 3-D objects.

Use Geometer’s Sketchpad to form different 3-D shapes.

Break students into groups of 4 for bridge project.

Explain assignment details before go to New York City.

Leave on Saturday morning.

New York City Section (3 Days)

Go to Metropolitan Museum to receive a tour of their artwork that involves geometry.

Look at 3 bridges.  Students will take pictures of the bridges to refer back to for their project.

Students will also get to talk to an architect.

 

Have ready for class: pictures of bridges, pictures of artwork from museum.

Go down to the art room to start on artwork project and continue this for the rest of the week. 

Art class

Work on art project.

Art Class

Students have one more week to finalize artwork.

Bridge Project

Break students into their 4 person groups to begin bridge construction.

Bridge project and write up due in 2 weeks.

Students will present bridge projects to class when finished.

Part 4 – Materials for use with Students

 

Print

Worksheets

Audio-Visual

Video showing different bridges around the country/world

Technology

·         Equipment

·         Software

·         Peripherals

Computer, tangram, coordinate plane, coordinate peg board, CD Rom of The Geometer’s Sketchpad, art tools for artwork project

Internet URLs

·          http://library.thinkquest.org/2647/geometry/measure/measure.htm ; explains measurement formulas for the different parts of geometry.

·          http://www.mathleague.com/help/geometry/geometry.htm; basic geometry terms and help.

·          http://math.rice.edu/~lanius/Geom/; questions for quizzes for students.

·          http://www.cs.berkeley.edu/~sequin/ART/; shows artwork incorporating geometry.

·          http://mathforum.org/~sarah/shapiro/; good for ideas on how to teach students to incorporate geometry into their artwork.

People

Architect, Museum tour guide

Supplies

Blue print paper, pencils, colored pencils, rubber bands

Other

Any art materials they need to make their artwork: clay, paint, markers, etc.

CAPT Links & Activities

 

 

Part 5 – Unit Closure

 

Students will present their artwork and bridges to each other for 1-2 class periods.  Presenting these assignments will let the students know that geometry exists outside the classroom.

 

Part 6 – Resources and References

(Those not cited in Materials section above.)

  • Navigating through Geometry in Grades 6-8; Authors: Pugalee, Frykholm, Johnson, Slovin, Malloy, Preston; copyright 2002 by NCTM in Reston, VA

 

 

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