Exploring Dilations

If I were to use this activity with my students, I would take all of the questions from the activity sheet and infuse them into various components of my lesson.  For example, I would provide students with a coordinate grid, and have them plot the pre-images and images for the triangle and pentagon. I think this would be a great question to start the class prior to beginning a full lesson on dilations; therefore, I would use this question as the Problem of the Day.

Once the P.O.D is complete, I would have a student re-plot the images on my drop-down coordinate grid so the entire class can see the answer and check their work.  Subsequently, I would engage students in a class discussion about Question #3.  Based on student’s answers to Question #3, I would then ask the folowing questions:

Teacher: What do you notice about the size of the images?

Student Response: One is bigger than the other.

Teacher: Why do you think one is bigger than the other?

Student Respone: Because we had to multiply each coordinate by two.

Teacher:  What do you think would happen if we multiplied each coordinate by .2?

Student Response:  The image would probably get smaller.

Teacher: Why? 

Student Response: Because we’re not multiplying by a whole number.

Teacher:  Take a look at the angles, the distance, and orientation of the figures.  Have they changed?

Student Response: The angles and the orientation are the same, but the distance is not the same.

Student Question: Why does it look like the images have been translated?

Teacher Response: Because with a diliation, the distance is not the same, but the points are enlarged or contracted on the same path of motion.

Student Question: So, is a dilation a transformation?

Teacher Response: Yes, a dilation is a type of transformation, but the dilated image is either smaller or larger than the original.

Post-Discussion Classwork/Reflection

Students will complete Question #5 in class to re-inforce their understanding of the lesson.  Subsequently, they will answer Question#4 in their journals.

Learning Activity 5-B-1

I enjoyed engaging in the refelcti0nal symmetry activity; it was very similar to the reflection activities my students complete in class.  I particularly liked the open-ended question at the bottom of the page.  For example, usually my students complete exercises that require them to reflect over the X and the Y axis.  However, I liked how this activity had students reflect over the Y-Axis first, then engage in higher-order thinking to consider what would happen if they reflected over the  X-axis.

A nice extension of this lesson would require students to identify the new coordinates after completing their reflections.  It would be a nice way to assess student’s understanding of reading coordinates.  Additionally, assuming they write the new coordinates correctly, they could compare and contrast the coordinates to discover the rules for reflecting over the X & Y axis.  This is a lesson I would definitely incorporate into my class.  However, I would modify it even further, and have students write the open-ended response in the journals, prior to reflecting the images over the X-axis.