Unit Overview

Content Area: Mathematics-Geometry
Unit Title: Similar Polygons (Rep-Tile Quadrilaterals–Connected Math Stretching & Shrinking)
Name:  Charlotte Richardson
School: Lakeside Middle
Date: July, 2010

Unit Summary
Students deepen their understanding of what it means for two figures to be similar.  Through experiments with rep-tiles (shapes where copies are put together to make larger, similar figures), students explore the relationship between the scale factor of two similar figures.  They also discover how triangles are special.  These experiences help them build mental images to support their evolving ideas about the relationship between scale factor and area.

In previous grades, students have investigated area, perimeter, and congruency.

21st century themes
Global Awareness / Health Literacy

Unit Rationale
Students may use these skills in a career path of future academic endeavors.  Students may need these skills in careers such as construction, masonry, engineering, etc.  Furthermore, students will need these skills in order to continue through middle, high school, and possibly college.

Learning Targets

Standards Key Ideas and Details
7.G Geometry

Content Statements
Draw, construct, and describe geometrical figures and describe the relationships between them.

7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

Unit Essential Questions

• How can you conclude that two or more figures are similar?
• How does scale factor influence similarity between figures?

Unit Enduring Understandings

• Two figures are similar if they are the same shape and have congruent corresponding angles.
• Scale Factor influences similarity between figures in that if their corresponding sides are not proportional, they cannot be similar.

Unit Learning Targets
Students will...

• Construct similar quadrilaterals from smaller, congruent (identical) figures
• Identify corresponding angles to show whether or not two figures are proportional.

Evidence of Learning

Summative Assessment (1-2 days)
Students will complete a written test in order to demonstrate understanding of similar figures and scale factors.  Test may be distributed in multiple forms in order to meet needs of individual students.

Equipment Needed:
Pencil, Tests (multiple forms if necessary)

Teacher Resources:
Teacher’s Guide

Formative Assessments:

• Construct similar figures
• Complete various worksheets related to similar figures
• Brain Breaks
• Homework

Lesson Plans
Lesson 1
Stretching and Shrinking:  Investigation 3 – 3.1 Rep-Tile Quadrilaterals
Teachers’ Guide pgs. 54-60
Student Workbooks pgs. 38-39
80 minutes/ 4-5 days

Lesson 2
Stretching and Shrinking:  Investigation 3 – 3.2 Rep-Tile Triangles
Teachers’ Guide pgs. 61-64
Student Workbooks pgs. 40-41
80 minutes/ 4-5 days

Lesson 3
Stretching and Shrinking:  Investigation 3 – 3.3 Scale Factors and Similar Shapes
Teachers’ Guide pgs. 65-68
Student Workbooks pgs. 42-43
80 minutes/ 4-5 days

Teacher Notes
Possible Brain Breaks:

• Use images that are similar / not similar, have students stand if they think images are similar.
• Stand up and do finger stretches before doing posters
• Work with a partner to create similar figures using their arms, legs, and bodies (i.e. form arrows with arms, make an x by standing in jumping jack form)
• Work with a partner to create non-similar figures using their arms, legs, and bodies

***May use extension activity boxes to allow children who are not understanding completely, or finish early.

• Place the following items in a closed storage container.  Small marshmallows or gumdrops separated into small storage bags, a few boxes of toothpicks, and directions to create figures that are similar.  More of a challenge – set specific scale factors and have students build similar figures to satisfy the scale factor.  Include paper to sketch answers.

Curriculum Development Resources
Click the links below to access additional resources used to design this unit:

***Use with smart board to check understanding after finishing the connected math.  Could be used as an extension if students do not grasp ideas.

http://nlvm.usu.edu/en/nav/topic_t_3.html
***Use with SMARTBoard to have students manipulate various shapes and relate to scale factor. (Online manipulatives)

http://www.beaconlearningcenter.com/WebLessons/SamsSimilarShapes/default.htm#page1
***Use with students on the SMARTBoard or in the computer lab.

Lesson Plan 1
Content Area: Mathematics
Lesson Title: Similar Polygons
Timeframe: X hours/days

Lesson Components

21st Century Themes
X Global Awareness-(Connect to Job Practicality)
Financial, Economic, Business, and Entrepreneurial Literacy
Civic Literacy
Health Literacy

21st Century Skills
x   Creativity and Innovation-(Creating File Folder Posters)
x   Media Literacy-(Using internet/video clips to support learning)
x    Critical Thinking and Problem Solving-(Exploring similar shapes and coming to individual conclusions)
ICT Literacy
x   Communication and Collaboration
Life and Career Skills
Information Literacy
Interdisciplinary Connections:
Integration of Technology: SMARTBoard, Document Camera, Student Computers/Computer Lab
Equipment & materials needed:
SMART Board / Projector
Document Camera
Laptop / Internet Access
Student Computers
It’s All Similar to Me worksheet
Connected Math Teacher’s Manual / Student Workbooks
Interactive Student Notebooks (ISN)
Pencil
Calculator (Optional)

Goals/Objectives/CPIs
Students:

• will be able to identify similar figures with at least 80% accuracy
• will be able to calculate scale factor with at least 80% accuracy

Learning Activities/Instructional Strategies
Engagement –

• Review vocabulary from other units that will apply to this lesson (quadrilateral, similar, congruent, corresponding, angles) by placing file folders on the board with the words written in different colors.  Teacher will ask students to volunteer what each term means to engage their background knowledge.  As students respond then they will be asked to draw an example on the file folder using the corresponding color.  Take a few volunteers to draw different examples in order to allow students to connect to the lesson.
• Work from the Connected Math Stretching and Shrinking: Understanding Similarity Book – 3.1 Rep-Tile Quadrilaterals.

Launch:

• Create a file folder poster for rep-tile.
• Explain that they will investigate different shapes that will be rep-tiles.
• Use shape sets (hexagon, square) and document camera to provide an example as well as non-example.
• Discuss the examples and allow students to make inferences about other quadrilaterals

** demonstrate how to take notes using the table handout and document camera.

• Distribute Investigation 3 (pg. 38) to the students to glue into their interactive notebooks.  Read and review, highlight key information.

Exploration –
Explore:

• Hold up various shapes as a warm up with working with tiles

***“Hold up a quadrilateral.”;  “Find a tile that is not a quadrilateral.” , “Hold up a tile that has 4 sides…what is the mathematical term for a 4 sided figure?”

• Small groups of 3 or 4 in order to explore different quadrilaterals that are rep-tiles.

***record their findings on a table provided (same as for notes)
***glue into their interactive notebooks

• pg. 39 - small groups.
• Create a larger poster of quadrilateral retile – share out
• Intro. scale factor fusing posters
• online geoboard to construct original ideas, and then sketch into interactive notebooks below worksheet problems.

*** (http://nlvm.usu.edu/en/nav/topic_t_3.html)
Explanation –

• Similar Figures and Corresponding Angles packet – small group activity.

***Discuss activity / share findings

Elaboration –

*** draw similar figures on the SMART Board (4 or 5 pairs of figures).
-mark corresponding sides.
-discuss how they can find out if two figures are actually similar

***May use computer lab/student computers in class
***Discuss findings and realizations.
***Challenges / Extra Credit:  Do the last 2 parts on the worksheet (Not required at this point).

Evaluation –
Day 1:

• Teacher will use constant questioning throughout lesson to build comprehension of topic.
• Students will complete the “Quick Slip” form to close and assess students’ understanding.
• Homework: Student Book pg. 44 # 1

Day 2:

• Students will hold up specific tiles as specified by teacher to assess understanding of quadrilaterals prior to starting the Explore section of Rep-Tiles Explore section.
• Conferencing with students during exploration
• Homework: Student Book pg. #22-23

Day 3:

• Teacher will ask questions to assess understanding of concepts throughout lesson.
• Use student explanations of solutions to problems with document camera
• Homework: Student Book pg. #33

• Answer questions throughout lesson (see evaluation)
• Construct similar figures (see exploration)
• Complete various worksheets related to similar figures (see elaboration & exploration)
• Brain Breaks
• Homework (see evaluation)

Universal Design for Learning Options

 Multiple Means of Representation Perception – projection onto SMART Board, in addition to student handouts, using various colors to organize information. (see elaboration) Language & symbols – pre-teaching vocabulary by using file folder posters and student examples (see engagement) Comprehension – using concrete examples of similar figures, using manipulatives, summarizing on worksheets and tables (see engagement, exploration, explanation, elaboration)

 Multiple Means of Action and Expression Physical activity – can manipulate online keyboard, switch opportunities for people with limited gross motor capabilities using SMART Board, and other assistive technologies (see exploration & elaboration) Expressive skills and fluency – students may use the computers to complete certain assignments or stay with the group for guided practice, use of tangible manipulatives, creation of posters to summarize their learning (see engagement, exploration, explanation, elaboration) Executive functions – provide practice with organizational skills via tables and interactive student notebook (see engagement)

 Multiple Means of Engagement Recruiting interest – provided optional challenge questions on worksheets that involve use of the internet, extension activity boxes (see elaboration) Sustaining effort and persistence – using small groups where students work together to develop a conclusive answer to problems, strategic grouping of higher functioning students with lower functioning to support peer tutoring opportunities (see exploration) Self-regulation – providing brain breaks and opportunities to refocus on problem, monitoring by walking so that asking for help is less intimidating

Resources