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TG Grade 5 Symmetry and Congruence

Page history last edited by jr1743@txstate.edu 10 years, 3 months ago

 

Submitted by:

Jennifer Lickert

Date:

4-1-10

Edited by:

Sarah Juarez-Farias

Date:

4-1-10

 

Unit Name: Team Geometry: Symmetry and Congruence

Unit Length: 5 class periods  

Overview: The students will determine how the geometric concepts of symmetry and congruence affect the outcomes of many of their favorite sports.

DESIRED RESULTS

TEKS and SEs

The student is expected to generates geometric definitions using critical attributes

 

5.7A Identify critical attributes including parallel, perpendicular, and congruent parts of geometric shapes and solids

5.7B Use critical attributes to define geometric shapes or solids

5.8A Sketch the results of translations, rotations, and reflections

5.11A Measure to solve problems involving length (including perimeter), weight, capacity, time, temperature, and area

Critical Vocabulary

Congruent/Congruency/Non-congruent

Equal/ Unequal

Fair/Unfair

Parallel/Parallelism

Perimeter

Perpendicular/Perpendicularity

Reflection

Rotation

Symmetry/Symmetrical/Asymmetrical

Translation

 

Enduring Understandings (Big Ideas)

Geometry affects boundaries, rules, and scoring of many of the students’ favorite sports; the students will be able to explain how geometry affects the outcome of many of their favorite sports. The symmetrical and congruent aspects of the outline of a playing area allow every player to have an equal opportunity to win the game.  

Essential Questions

How many lines of symmetry does a particular playing area have?

Can you use tools to measure and prove the fields’ symmetry?

How do you think not having symmetry on a playing area would affect the outcome of the game?

What are the congruent aspects of the playing area?

Is there a relationship between the symmetry of the area and the congruency of the shapes on the area?

Learning Goals and Objectives

The student will learn about congruence and symmetry during the lesson, but will also practice their measurement skills as they prove relationships between shapes on the playing area and sketch reflections of playing areas. Students will also begin to develop the relationship between symmetry, congruence, and fairness of the game by designing an area that is symmetrical and an area that is asymmetrical and comparing them to one another.  

Materials Needed

Compass

Computer with geometric software (GeoGebra/Sketchpad)

Mira’s or Mirrors for reflective sketches

Patty paper

Protractors

Rulers

Scale drawings of playing areas (football, baseball, basketball, soccer, and volleyball)

ASSESSMENT PLAN

Performance Tasks

Given the description and the dimensions of a playing area, and using a Mira, the students will create a model drawing of a sports’ court or field. Using that model, they will describe how the geometric concepts of congruency and symmetry affect the outcome of the game. The students will also create an asymmetrical non-congruent version of the playing area and will describe how the asymmetry and non-congruence affect the outcome of the game.

 

Other Evidence

The student will use tools to sketch an accurate scale model of each court showing the symmetry and congruence of the different shapes that make up the court. Students will be able to describe each shape that makes up the court and the symmetry and congruence of the individual shapes.

 

 

LEARNING PLAN

Engage: TSW examine scale drawings of a volleyball court, which the teacher will project for the class to generate discussion and record class observations. Students will note the dimensions of the playing area and will describe and label the different shapes they see. The teacher will question the students about placement of the shapes on the playing area and will make note of vocabulary the students introduce to the discussion.

 

Explore: TSW use tools, such as patty paper, rulers, compasses and Mira to measure and observe the different areas of a diagram of the playing area. They will observe the relationships between the dimensions and the different “sides” of the court. They will determine if the playing area is “fair” for both teams and explain why this is.  They will determine the dimensions of the different shapes they see in the model-and what their relation is to other shapes on the playing area (transformations).

 

Explain: TSW discuss the symmetry and congruency of the playing area applying vocabulary to the observations they made during their exploration. TTW create the outline of a volleyball court using the program GeoGebra to allow the students to demonstrate how changing the symmetry of the court would affect the game.

 

file:///C:/Documents%20and%20Settings/Owner/Desktop/Masters%20Work/CI%205304/volleyball_court.html

 

 

 

Elaborate: TSW apply their knowledge of symmetry and congruency to a different sports’ court or field. TSW work in groups to write a summary of the different examples of symmetry, congruency, and translations they see on the court.

 

Evaluate: Given the description and the dimensions of a playing area, and using a Mira, the students will create a model drawing of a sports’ court or field. Using that model, they will describe how the geometric concepts of congruency and symmetry affect the outcome of the game. The students will also create an asymmetrical non-congruent version of the playing area and will describe how the asymmetry and non-congruence affect the outcome of the game.

 

 Time 

5 class periods

 

½ class period

 

 

 

 

 

½ class period

 

 

 

 

 

 

 

1 class period

 

 

 

 

 

 

 

1 class period

 

 

 

 

 

1 class period

 

 

Extension:

Design a playing area for a game you create. What geometric principles will you use and how will they affect how you play your game?

Modifications:

To differentiate for students’ levels and abilities, vary the playing field for observation for different levels of students, or modify the dimensions of the playing field to allow easier measurements to work with. For students with spatial/visual issues, allow students to glue pre cut shapes onto a teacher created playing area or allow the student to trace the shapes onto the playing area with a stencil.

       

 

 

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