Creating and Understanding Similar Figures using Geometer's Sketch Pad
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1 The College at Brockport: State University of New York Digital Lesson Plans CMST Institute Creating and Understanding Similar Figures using Geometer's Sketch Pad Samuel Simpson The College at Brockport Follow this and additional works at: Part of the Physical Sciences and Mathematics Commons, and the Science and Mathematics Education Commons Repository Citation Simpson, Samuel, "Creating and Understanding Similar Figures using Geometer's Sketch Pad" (2006). Lesson Plans This Lesson Plan is brought to you for free and open access by the CMST Institute at Digital It has been accepted for inclusion in Lesson Plans by an authorized administrator of Digital For more information, please contact
2 Challenge Project Similar Figures
3 Similar Figures Lessons based on the CMP Stretching and Shrinking Similarity Mr. Simpson and Ms. Wilson Frederick Douglass Preparatory School
4 Overview The project uses GSP and is based on the CMP text, Stretching and Shrinking Similarity. Three lessons are presented. Lesson 1 Creating Similar Figures Lesson 2 The WUMP Family Lesson 3 Understanding Similar Figures
5 Lesson Overviews Lesson 1: Creating Similar Figures - Students create a similar shape using a coordinate system. Students will begin to form a more precise mathematical definition of similar. Lesson 2 The WUMP Family students graph members of a fractious family, plus other figures that claim to be in the Wump family. Members are similar to one another. The imposters are not similar. Students compare the shapes side lengths and angles of the figure they have drawn. Lesson 3 Understanding Similar Figures Students expand on their understanding of similarity to include the relationship of scale factor, perimeter and area.
6 Lesson 1: Creating Similar Figures
7 Lesson 1: Creating Similar Figures Name Date: Lesson 1 Creating Similar Figures 1.The coordinates of the square below are: A (1,2), B (1,7), C (6,7), D (6,2)8 Problem 1 Creating Similar Figures What are the coordinates of a new square (JKLM) with a scale factor of 2? Plot the new figure on the coordinate grid below. 1. What are the coordinates of a new square (JKLM) with a scale factor of 2? 2. Plot the new figure on the coordinate grid below. 3. What is the perimeter of figure ABCD? 4. What is the area of figure ABCD? 5. What is the perimeter of figure JKLM? 6. What is the area of figure JKLM?
8 Lesson 1: Creating Similar Figures
9 Lesson 2: The WUMP Family Name: Date: Lesson 2 Drawing Wumps Zack and Marta s computer game involves a family called the Wumps. The members of the Wump family are various sizes, but they all have the same shape. Mug Wump is the game s main character. By enlarging or reducing Mug, a player can transform him into other Wump family members. Zack and Marta experimented on paper with enlarging and reducing figures on a coordinate grid. First Zack drew Mug Wump on dot paper. Then, he labeled the key points from A to Z and from AA to FF and listed the coordinates for each point. Marta described the rules that would transform Mug into different sizes to create other members of the Wump family. Problem 2.1 Lurking among the members of the Wump family are some impostors who, at first glance, look like the Wumps but are actually quite different. A. Use the instructions below to draw Mug Wump on the dot paper grid. B. Make Bug, Lug, Thug and Zug. After drawing the character, compare them to Mug. Which characters are the imposters? C. Compare Mug to the other characters. What things are the same about Mug and Zug s? Mug and Bug? Mug and Thug? What things are different? Think about the general shape, the lengths of sides, and the angles of each figure. Instructions for drawing Wumps 1.
10 Lesson 2: The WUMP Family
11 Lesson 2: The WUMP Family
12 Lesson 2: The WUMP Family
13 Lesson 2: The WUMP Family
14 Lesson 3: Understanding Similar Figures Name: Date: Lesson 3 Understanding Similar Figures Examine the two similar figures below and answer the questions below.figure A9 Units9 Units Problem 3 Understanding Similar Figures 1.What is the scale factor? a) From Figure B to Figure A. b) From Figure A to Figure B 2.What is the ratio of the corresponding sides? 3. a) What is the perimeter of figure A? What is the perimeter of figure B? b) What is the ratio of the perimeters? 4. a) What is the area of figure A (Area = ½ base x height)? What is the area of figure B? b) What is the ratio of the areas? 5. How do the ratios of the perimeters relate to the ratios of the areas? 6. How many small triangles will fit into the large triangle?
15 Lesson 3: Understanding Similar Figures
16 References Stretching and Shrinking Similarity Lappan, Fey, Fitzgerald, Friel, and Phillips Prentice Hall 2002 Glenview, Illinois
Notes 1.2. Notes 1.3
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Coordinates of Characters Mug Wump Glum sum Tum Crum Rule (x, y) (1.5x, 1.5y) (3x, 2y) (4x, 4y) (2x, y) Nose (Start Over)
A C E Applications Connections Extensions Applications 1. The table below gives key coordinates for drawing Mug Wump s mouth and nose. It also gives rules for finding the corresponding points for four
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Stretching and Shrinking Understanding Similarity Unit Opener..................................................... 2 Mathematical Highlights.......................................... 4 Enlarging and Reducing
Coordinates of Characters. c. Which of the new characters (Glum, Sum, Tum, and Crum) are members of the Wump family, and which are impostors?
Applications 1. This table gives key coordinates for drawing the mouth and nose of Mug Wump. It also gives rules for finding the corresponding points for four other characters some members of the Wump
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