# Exploring Dilations

Posted February 21, 2010

on:**Describe in detail how you would present this activity to your students.**

I would start this lesson by displaying graph paper background on the Smartboard. I would then have the students create a triangle. Three different students would determine the vertices. I would then create a copy of the triangle and paste it on the page. With the copy I would enlarge it using the corner and dragging it (a feature in Smartboad). We would talk about what I did and how it is the same and different from the original. I would place the new enlarged triangle in such a way that the coordinates can be determined. I would have the students write the new coordinates for each vertex. We would do this with a couple different shapes.

After I am sure the students understand the coordinate system I would give them the coordinates for two shapes and have them plot it on their own graph paper. We would then look for similarities and difference. The next problem would be for me to give them coordinates for a shape and provide them with some of the coordinates and ask them to determine which ones are missing. The final problem we would work together would be to provide the coordinates for the shape and ask them to create the new shape with only one coordinate provided. I would then provide some coordinates for them to graph and ask them to create the new shape based on the property provided. (I would only use whole and half numbers so that graphing would be easier, I have inclusion students in all of my classes and this would allow them to do the activity without getting lost in the conversions.) If students finished this I would then ask them to create two objects (different than what we had already used in class) so that someone else could determine what multiplier was used.

**Anticipate the questions you might ask students during this activity. What type of prompting questions would you ask during this activity?**

What do you notice about the two shapes I had you graph?

What similarities and differences do you notice?

What coordinates are missing? Explain

How do you know what coordinates are missing?

What did you do to determine the missing coordinates?

Can you add or subtract and create a similar shape?

**Anticipate your students’ questions. What types of questions might they ask and how would you answer them?**

*Does it matter where the shape is located on the graph paper?*

No because the paper is just for you to use as a reference, it has nothing to do with the shape.

*Is multiplication the only way to do this?*

No. Can anyone tell me another operation that could be used to make a dilation? Division. (Some of my students understand that division is the same as multiplying by a fraction but most do not.)

*Does the length of each side change?*

Yes the do. Can you tell me by how much they change? How do you know?

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