ALEX Lesson Plan

     

You can die now or "dilate R to R'"

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  This lesson provided by:  
Author:Caleb Salamone
System: Blount County
School: Cleveland High School
  General Lesson Information  
Lesson Plan ID: 32230

Title:

You can die now or "dilate R to R'"

Overview/Annotation:

This lesson will teach students to not only create a dilation, but also assist them in understanding the relationship of similarity between a figure and its image through a dilation.  Students will use an online math tool to adjust the location of the point of dilation, and they will find the scale factor changes when the point of dilation moves.  Students will also find that parallel lines can be used to create a dilation.

 Associated Standards and Objectives 
Content Standard(s):
Mathematics
MA2015 (2015)
Grade: 9-12
Geometry
14 ) Verify experimentally the properties of dilations given by a center and a scale factor. [G-SRT1]

a. A dilation takes a line not passing through the center of the dilation to a parallel line and leaves a line passing through the center unchanged. [G-SRT1a]

b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. [G-SRT1b]

Local/National Standards:

 

Primary Learning Objective(s):

Students will be able to construct a dilation from a given figure on the coordinate plane, a given point of dilation, and a scale factor of 2 using parallel lines.  They will also find the lengths from the point of dilation to points and their image follow the scale factor too.

Additional Learning Objective(s):

 
 Preparation Information 

Total Duration:

31 to 60 Minutes

Materials and Resources:

Students will need graph paper, rulers, and possibly tape if they have to extend their graph paper to fit their dilation.

Technology Resources Needed:

Each student, or group will need a laptop, or computer to experiment with the math tool provided here.

Digital projector and computer for modeling the use of the math tool.  Document camera for students to present their graph to the class.

Background/Preparation:

The students need to be familiar with the distance formula and or the Pythagorean theorem.  Students will need to be able to navigate a webpage.

  Procedures/Activities: 

Students should be grouped strategically into groups of 2-4 people with each group or person having a laptop or computer.

Let the students experiment with moving the center of dilation and the pre-image, and how these effect the image resulted in the dilation.

Have them not move their shape for a second and ask them what they think their scale factor is, and ask them to prove it to you with the distance formula or Pythagorean Theorem.

Have them discuss in their group what the relationship between the corresponding sides is. You are hoping for them to determine that one is half the length of the other, but you also want them to discover that they are parallel to each other.

Have them find the slope of corresponding sides and determine if they are the same.

Give them the coordinates of their own shape like A(2,3) B(5,8) C(4,0) and D(2,-2) and have them find the slope of each side. Have them draw a guide line from the center of dilation through one of the points out at least twice the length from the center to the point to find the image point of A which would be A'(4,6) if the scale factor is 2.

Have them use the slopes of the corresponding sides of the pre-image to draw parallel lines from the point A' to extend 2 times as long as AB and AD to find B' and D'.

Continue this process until the entire image is found.

Have students verify that the pre-image is in fact a similar figure using the distance formula.

I recommend that each group be given a different set of points to promote individuality and fidelity of assessment.

Students can also present their graph to the whole class by the use of a document camera.


  Assessment  

Assessment Strategies

-The student will accurately graph a dilation with the center at the origin, and a scale factor of 2.  They will also show all measures of sides and how they relate to the scale factor using the distance formula.

-10th grade Geometry students should be given more than 3 points in more than one quadrant.

-They will graph the dilation using Parallel lines, and they will use the distance formula to verify that the scale factor is consistent for each of the sides of the dilation.

Acceleration:

Students who need more of a challenge will need to be given more points, and also a different center of dilation.  I also recommend that you give them a dilation of 3 or greater.

Intervention:

Students who struggle should be given a dilation factor of 1/2 and they should also have points whose coordinates are even, so they can find the image with less difficulty.  Here is also another math tool that will help students understand how to use parallel lines to draw dilations more visually.

Each area below is a direct link to general teaching strategies/classroom accommodations for students with identified learning and/or behavior problems such as: reading or math performance below grade level; test or classroom assignments/quizzes at a failing level; failure to complete assignments independently; difficulty with short-term memory, abstract concepts, staying on task, or following directions; poor peer interaction or temper tantrums, and other learning or behavior problems.

Presentation of Material Environment
Time Demands Materials
Attention Using Groups and Peers
Assisting the Reluctant Starter Dealing with Inappropriate Behavior
Be sure to check the student's IEP for specific accommodations.