# ALEX Lesson Plan

## Falling Down a Rabbit Hole Can Lead to a King Sized Experience - Exploring Similar Figures Using Proportions

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This lesson provided by:
 Author: Lillie Coleman System: Fairfield City School: Fairfield High Preparatory School
General Lesson Information
 Lesson Plan ID: 30067 Title: Falling Down a Rabbit Hole Can Lead to a King Sized Experience - Exploring Similar Figures Using Proportions Overview/Annotation: In this lesson, students will explore the concept of similarity.  Students will first simplify ratios, solve proportions using the cross product property, and use properties of proportions to solve real-world problems.  Similar polygons will then be introduced and their properties used to solve real-world problems.
Associated Standards and Objectives
Content Standard(s):
 MA2015 (7) 2. Recognize and represent proportional relationships between quantities. [7-RP2] a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. [7-RP2a] b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. [7-RP2b] c. Represent proportional relationships by equations. [7-RP2c] Example: If total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. d. Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate. [7-RP2d] MA2015 (9-12) Geometry 15. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. [G-SRT2] Example 1: MA220100912GEO1503.jpg Given the two triangles above, show that they are similar. 4/8 = 6/12 They are similar by SSS. The scale factor is equivalent. Example 2: MA220100912GEO1507.jpg Show that the two triangles are similar. Two corresponding sides are proportional and the included angle is congruent. (SAS similarity)

Local/National Standards:

Numbers and Operations

Understand meanings of operations and how they relate to one another

Compute fluently and make reasonable estimates

Algebra

Understand patterns, relations, and functions

Use mathematical models to represent and understand quantitative relationships

Geometry

Analyze characteristics and properties of two- and three- dimensional geometric shapes and develop mathematical arguments about geometric relationships

Measurement

Apply appropriate techniques, tools, and formulas to determine measurements

Primary Learning Objective(s):

Students will be able to:

Apply proportional reasoning to solving problems.

Find measures of corresponding parts of similar figures.

Deduce the measure of an angle in a polygon from given assumptions.

Deduce the length of a side of a polygon from given assumptions.

Identify geometric models that represent problem situations.

Preparation Information
 Total Duration: 61 to 90 Minutes Materials and Resources: Students will complete all activities in groups of 4.Group members will be determined by student performance during the background review.Each student will need a measuring tool, pencil, paper, and four function calculator.Teacher should request maps from the local motor club.  Maps can also be obtained from social studies colleagues or printed from the Internet.  Please note that all maps must contain a scale.Teacher and students should be familiar with the Internet. Technology Resources Needed: One Internet capable laptop per group of 4 students.Document camera, Internet capable laptop, projector and whiteboard combination for demonstrations and presentations by teacher and students. Background/Preparation: Teacher will review the problem-solving skill of translating words to algebra symbols by setting up and solving proportions.The Multiplication Property of Equality and cross product recognition should be retaught.Students will also be reminded that when expressing a ratio a/b; b cannot be zero because you cannot divide by zero. (the denominator)Teacher will use the web link below to facilitate the proportion review:http://www.phschool.com/webcodes10/index.cfm?fuseaction=home.gotoWebCode&wcprefix=aue&wcsuffix=0701Then click on 'Solving Proportions'.
Procedures/Activities: