Unit Overview

Content Area: Geometry
Unit Title: Stretching and Shrinking
Name: Michelle Kean
School: Lindenwold Middle
Date: July, 2010

Unit Summary

• This unit explores the idea of similar and congruent figures. It also ties scale factor to similarity and how it is used in everyday life.
• Inclusion students in this setting need some minor to moderate accommodations, mostly in the form of scaffolding, to be successful. They are given the choice to go to a different room, with the Special Ed teacher, for tests and quizzes.

Primary interdisciplinary connections
Geography Map Scale

21st century themes
Global Awareness (Map Skills)

Unit Rationale
Students need to understand rules for similar figures and how scale factor is related to similarity. The graphing of the figures helps the students see how scale factor is related to similarity and its many practical uses in everyday life.

Learning Targets

Standards Key Ideas and Details
7G and 8G

Content Statements

• Draw, Construct, and describe geometrical figures and describe the relationships between them.
• Understand congruence and similarity using physical models, transparencies, or geometry software.

7G  1 Solve problems involving scale drawings of geometric figures. Include computing actual lengths and areas from a scale drawing and reproducing a scale drawing at t different scale.
7G  2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions.
8G  1 Verify experimentally the properties of rotations, reflections, and translations.

1. Lines are taken to lines, and line segments to line segments of same length.
2. Angles are taken to angles of the same measure.
3. Parallel lines are taken to parallel lines.

8G  2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
8G  3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
8G  4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

Unit Essential Questions

• What real world situations can be analyzed using similar figures?
• How can geometric relationships be described using geometric language?
• How can geometric/algebraic relationships best be represented and verified?

Unit Enduring Understandings

• Similar figures are proportional and using ratios can solve problems.
• Understanding the equivalence of ratios of sides to examine similar figures and find unknown lengths.
• Similarity is used to solve everyday problems.
• Shape and area can be conserved during mathematical translations.
• Coordinate geometry can be used to represent and verify geometric/algebraic relationships.

Unit Learning Targets
Students will...

• Identify similar figures visually and by comparing sides and angles.
• Recognize that side lengths between similar figures change by a constant scale factor.
• Build larger, similar shapes from copies of a basic shape.
• Divide shapes into smaller, similar shapes.
• Determine and use scale factor to find unknown side lengths.

Evidence of Learning

Summative Assessment (Approx. 4 weeks)
Pre-Assessment
Mid-unit test
Unit test
Scale Factor Project

Equipment Needed:
Senteo Response System
Smart Board presentation of pre-assessment
Pencil/Paper Test for mid and unit test
Blank coordinate grid paper for project
Rulers/colored pencils for project

Teacher Resources:
CMP teacher resource disk.

Formative Assessments:

• Completing activities in each investigation
• Teacher Questioning during activities
• Ace questions following each investigation
• Mathematical reflections following each investigation
• Formal and informal quizzes

Lesson Plans
Lesson 1: Investigation 1
Enlarging and Reducing Shapes
1 hour (1 period)

Lesson 2: Investigation 2/Problem 2.1
Drawing Wumps/Making Similar Figures
2 hours (2 periods)

Lesson 3: Investigation 2/Problem 2.2
Hats Off to the Wumps/Changing a Figure’s Size and Location
1 hour (1period)

Lesson 4: Investigation 2/ Problem 2.3
Mouthing Off and Nosing Around/Scale Factor
1 hour (1 period)

Lesson 5: Investigation 2 /Selected Ace Questions, Mathematical Reflections as Review for Quiz
1 hour (1 period)

Lesson 6: Investigation 1 and 2 Quiz
1 hour (1 period)

Lesson 7: Investigation 3
Similar Polygons
2 hours (2 periods)

Lesson 8: Investigation 3/ Selected Ace Questions, Mathematical Reflections
1 hour (1 period)

Lesson 9: Investigation 1-3 review for Mid-Unit Test
1 hour (1 period)

Lesson 10: Mid-Unit Test
1 hour (1 period)

Lesson 11: Investigation 4
Similarity and Ratios Within Polygons
1 hour (1 period)

Lesson 12: Investigation 4/ Selected Ace Questions, Mathematical Reflections
1 hour (1 period)

Lesson 13: Investigation 5
Using Similar Triangles and Rectangles
1 hour (1 period)

Lesson 14: Investigation 5/ Selected Ace Questions, Mathematical Reflections
1 hour (1 period)

Lesson 15: Investigation 4-5 review for Unit Test
1 hour (1 period)

Lesson 16: Unit Test
1 hour (1 period)

Lesson 17: Scale Factor Project
2 hours (2 periods)

Teacher Notes
Some students will require numbered grid paper and/or enlarged grid paper. Some students may also need some assistance in plotting coordinate points and/or understanding the concept of connecting points to create an image and will need copies of final product to compare their work to. Some students will need to have all scale factor scenarios set up in pictures, not just word problems.

Curriculum Development Resources
CMP Teacher’s Guide and Student Book, CMP Teacher Disk, Brain pop, You Tube/Teacher Tube, Geometer Sketchpad, Smart Notebook

Lesson Plan 1
Content Area: Mathematics
Lesson Title: Drawing Wumps/Making Similar Figures
Timeframe: 2 hours/2 days

Lesson Components

21st Century Themes
X Global Awareness-(Map skills/map scale)
Financial, Economic, Business, and Entrepreneurial Literacy
Civic Literacy
Health Literacy

21st Century Skills
x   Creativity and Innovation
Media Literacy
x    Critical Thinking and Problem Solving
ICT Literacy
x   Communication and Collaboration
x   Life and Career Skills
x   Information Literacy
Interdisciplinary Connections: Geography, Art
Integration of Technology: Calculator, Document Camera, SMART Board, Geometer Sketchpad, Student                 Laptops
Equipment & materials needed: Lab sheets 2.1 A, B and C (from teachers’ manual or CMP disk)
Calculator, Document Camera, SMART Board, Teacher Computer, Student Laptops, Geometer Sketchpad,

Goals/Objectives/CPIs
Students:

 Make a list of coordinates using scale factor with 80% accuracy. Complete drawing using coordinates and grid paper or Geometer Sketchpad with 80% accuracy.
• Decide which figures are similar according to similarity rules with 80% accuracy.

Learning Activities/Instructional Strategies

 Engagement- Show video of similarity and congruence (http://www.youtube.com/watch?v=bbYuCj_eM_w) Show examples of similar and congruent on smart board. (http://www.mathleague.com/help/geometry/coordinates.htm)  See what examples the students can come up with, possibly reference fun house mirrors from amusement parks or carnivals. Exploration-The students will be given a table with coordinates of an original cartoon character and columns for them to create coordinates for images of the original character.  (Lab sheet 2.1 A) The students will use the rules given and complete the coordinates for the images. The students then actually draw the figures by plotting the coordinate points, either on grid paper (Lab sheet 2.1 B or C) or on Geometer Sketchpad. From these drawing they will determine which are similar and which are not. After similarity is determined they will then explore the rules for creating the similar characters and what is the same or similar about the rules that create similar figures versus those that are not similar.  Play quick congruent/similar game. www.harcourtschool.com/activity/similar-congruent Explanation- Teacher leads as students share and discuss drawings and theories about which characters are similar and which are not. Elaboration-As students complete the activity they are to get a laptop and go to Brainpop. (A subscription is required for this website) They are to watch video on similar figures and take quiz. Print out quiz as they complete. Evaluation- Accuracy of similarity determinations.

• Complete table of coordinates using scale factor
• Complete drawings of figures using coordinates
• Decide which figures are similar
• Brainpop quiz results (informal quiz)

Universal Design for Learning Options

 Multiple Means of Representation Perception: Use pictures on smartboard, use cutout shapes for the students to compare, use real life examples of figures, have students use geometer sketchpad to create figures, use different websites for reinforcement. (See engagement and exploration) Language & symbols: Scaffold worksheets with labeled axis and/or partially filled out lab sheet 2.1A. (See Teacher notes) Comprehension: Use variety of real world and geometric examples in the form of pictures and hands on models. Play internet game and take internet tutorial and quiz to reinforce comprehension. (See engagement, exploration, and Teacher Notes)

 Multiple Means of Action and Expression Physical activity: The students will be playing a game at the smartboard. The students will be drawing shapes from set of coordinates. They will also be getting computers to complete internet activities. (See engagement and exploration) Expressive skills and fluency: The students will show examples of similarity in their drawings. They will relate similarity to the given rules. They will also express understanding in the results of their internet activities. (See exploration) Executive functions: Videos, games, real world examples, hands on drawing activity. (see engagement, explorations and elaborations)

 Multiple Means of Engagement Recruiting interest: Show video. Use smartboard examples, real world example, student examples, text book examples, and internet games.  (See engagement) Sustaining effort and persistence: Drawing pictures using pencil/paper or computer program. Playing computer games. Find real world examples. (See exploration) Self-regulation: Choice to work alone or in small groups but must complete all activities including drawings, internet games and quiz. (See exploration and elaboration)

Resources