Exploring Dilations 1
Lesson 1 of 16
Objective: SWBAT describe dilations using the center of dilation and scale factor on a coordinate plane.
To begin the lesson I project the Eye Opener Launch Problem on the whiteboard and ask each student to read it silently and answer the questions. The task is a simple yet a good opener for the lesson. I allow considerable time for students to figure out the answers to the questions, then call on volunteers to share and explain their answers to the class.
It is important that students understand that a dilation may mean a reduction in size of a figure as well as an enlargement of it. Since dilations produce similar figures, it is also critical to make sure that students are clear that the shape will remain the same.
I now pair students at random and hand each a copy of the resource Cat Dilations. A ruler will also be needed so I ask students to take them out. I tell students that they need to be very precise and neat when using their ruler for this task. Good sharpened pencils are also good to have.
Before starting, I ask students if what they see is like the eye doctor/pupil example discussed previously and to explain how. Then I instruct students to read the directions and write what they observe about the lines drawn. Students usually speak with other groups about their findings, which I stimulate. They should see that in each case, the lines intersect at the same point.
I indicate that the intersection point is called the Center of Dilation. Then, I ask students to recall the eye dilation problem and find how many times smaller the small cat is compared to the big one. (Most students will easily see, by counting the lines to find the length of sides that the small cat is ½ the size of the large one). I try always to let them figure it out and ask quicker students not to yell out anything so as to allow others more time. Then I ask….”if the small cat is ½ the larger one, then the larger one would be how many times larger than the smaller? I find that students are quick to say twice. I finish by stating that these values, just like the values in the eye doctor/pupil problem are called Scale Factors.
I then write the following questions on the board and give learners about 10 minutes to answer.
- How does the scale factor relate to the distance between the center of dilation, little cat, and big cat? Use your ruler to determine this.
- If we begin with the large cat, what happens if we draw a cat with a scale factor of 1?
- How do we determine which scale factor, 1/2 or 2, is correct for these pictures?
- In general, what can you say about scale factors smaller or larger than 1?
At this point I tell the learners that the original figure is always called the pre-image and its vertices are labeled with capital letters, say A, B, C……while the final figure is called the image and its corresponding vertices have the same letters, but prime, (A’, B’, C’, etc.)
To end the lesson I project the resource Closure Dilations 1 on the board. The task is for students to describe each of the three images when a pre-image, a scale factor, and a center of dilation are given.
What I like to do is show the first pre-image, ask everyone to read the question to themselves and think of an answers, and then I call on someone to go up to the board and briefly explain his/her answer. I encourage the chosen student to using his/her hands to show where the image will fall and the direction of the images that stem from the center of dilation.
This video clip includes some of the ideas in this lesson for review.