Proportional Relationships & Geometry

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Objective

SWBAT solve problems involving scale factor using the concept of ratio relationships

Big Idea

Scaling Up & Scaling Down: Using the concept of proportional relationships to find the measurements of similar shapes and object.

Curriculum Reinforcer

5 minutes

The Curriculum Reinforcer is basically a quick three to five question quiz containing information from previously taught standards that will allow you to determine areas in which your students may need to review. When I create my Curriculum Reinforcers, I make sure to mix up the types of problems. I use multiple choice, open-ended questions, as well as questions that require constructed responses. I may provide a mixture all in one day or, I may have all multiple choice one day and a mixture the next. It all depends on what I am looking for my students to be able to do. Often times, I also mix the standards however, there are times when I don't. I mix them so that I can see how well my students are fairing in more than one standard. In those instances when I don't mix up the standards, I am trying to see if the students are able to understand the standard when it is presented in a variety of ways.

Engagement

5 minutes

To engage my students in this lesson, I will bring in several items; a model car, a model plane, a globe, and a map of The City of Atlanta. I will show my students a large picture of each of these items on the digital projector and as a class, we will discuss the actual size of each item. As we go through each picture projected on the screen, I will present the object that matches that picture. In each instance we will discuss the similarities and differences between the "real thing" represented by the projected image and the objects that I brought into the classroom. I will also point out to them that the projected image is different in size from the actual object, as well.  

Instruction & Teacher Modeling

10 minutes

To start off today's instruction, I will have some pre-cut similar shapes that I will use to demonstrate the concept of proportionality as it pertains to regular polygons. In my demonstration, I will show my students how the angles of similar polygons are congruent while the sides are not congruent, but proportional. MP4 (Please see the attached video to see my demonstration)

After demonstrating the characteristics of similar figures, I will then model how to find the length of a missing side when given two similar shapes, one with two side lengths provided and one that provides only on side length and asks that you find a missing side length. To model this, I will work through the three real world situations presented in the attached PowerPoint.

The three problems will allow me to demonstrate the following to my students:

  1. How to find the side length of a larger similar figure.
  2. How to find the side length of a smaller similar figure.
  3. How to find the scale factor between two similar figures.

 

 

Try It Out

10 minutes

To determine whether or not my students understand the concepts taught during today's lesson, I will have them complete three problems that are similar to those that I demonstrated during the instructional portion of this lesson. The three problems that I will have the complete are in the PowerPoint attached to this section of this lesson. (MP1)

Independent Exploration

20 minutes

For the independent exploration piece of this lesson, my students will complete a worksheet that requires them to recognize when two triangles are similar. These triangles are presented to the students on a grid. And, based upon what they have learned, the students will have to determine which of the triangles on the grid are similar. There could be only a pair that are similar or more than just a pair. (MP1 and MP2)

They will have to not only determine which triangles are similar but, they will also have to explain in words and mathematically how they made their determination. (MP3 and MP6)

The students will be given approximately 15 minutes to complete the assignment. They will then be given another 5 minutes to confer with a partner about their solutions. During their time with a partner, the students will need to compare and contrast their solutions as well as their methods to arriving to their solutions. (MP3 and MP6)

Closing Summary

20 minutes

To close out this lesson, each pair of students will present an overview of their discussion. They will need to ensure that they cover the following topics:

  1. The method in which each of them solved their problem. Did their methods differ? If so, in what way?
  2. Did they both arrive to the same solution? If not, did they discuss why their solutions were different and come to a consensus about which solution is correct?
  3. They need to tell something that they learned during the discussion

 

During this time, it is important to let the students know that it is okay if different sets of partners have similar answers because it is important to know commonalities as well as differences in their understanding and approach to solution processes. (MP1, MP2, MP3, and MP6)