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.

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1 Comment (+add yours?)

  1. sharoncas
    Jul 09, 2012 @ 17:46:13

    I really like how you broke this lesson up. You have also asked questions that require higher order thinking. I also like how they will respond to #4 in a journal. This will give you a good idea of their understanding of the lesson.

    Reply

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