In this lesson, students will learn the key concepts of dilations. Students are already familiar with scaling and scale factor, so we’ll start by using a scale factor to draw a similar shape. Then we’ll use similar strategies to apply dilations to coordinate points, both on and off the coordinate grid! You can expect this lesson with independent practice to take one `45`-minute class period.
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Students will be able to apply dilations to coordinate points.
Start students off with a review of how to use scale factor to create a similar shape. The wording of the warm up allows students to use reasoning to answer the questions, rather than bringing in the vocabulary of “scale factor” just yet.
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The key is for students to recognize that in order to double the size of the rectangle they need to multiply both the length and width by `2`, making the new dimensions `6` feet by `16` feet.
Next, you’ll want to more formally talk about scale factor. Explain that a scale factor allows us to create similar shapes, because all the side lengths will be in the same ratio.
Point out that these are similar triangles because their side lengths create a ratio. Each side length on the right is `3` times its corresponding side length on the left.
Reviewing scale factor with similar polygons allows students to transfer their thinking to coordinate points. After emphasizing that the scale factor is applied to each side length, it will be easy for students to understand that the scale factor is applied to both coordinates in an ordered pair.
Giving this first example without a coordinate grid allows students to focus on the fact that each coordinate gets multiplied by the scale factor. The transitions on this slide will help in taking this example one step at a time. You may want to also let students know that we will only be focusing on dilations where the origin is the center of dilation. We’ll expand on this in the next example.
For this next example we’re giving a point on the coordinate grid. You can ask students what they think we should do first. Ultimately, you should identify the ordered pair for Point `X` first. Then the problem becomes similar to the previous example. Apply the scale factor to both coordinates, then write the new coordinate point. Lastly, students should plot the new point. You can have a student come to the board to draw the new point, or use the transitions on the slide to show it.
With this example, you’ll also want to bring up how the new coordinate point is closer to the origin than the original point. Explain to students that since the origin is the center of dilation, the scale factor tells us if the new point will be closer to the origin or further away from the origin. Relate this to using a scale factor to create a larger figure or a smaller figure.
Allow students to work in partners on the matching activity. Students will match questions with answers as they dilate points on and off the coordinate grid. The activity contains an answer key which you can use to check students’ answers before they move onto the ByteLearn practice.
*Teacher tip: Make sure you don’t print these double-sided!
Now it’s time for some independent practice! You can assign a ByteLearn online practice to your class using the link below. Students will get immediate feedback and step-by-step help if they need it. Set a due date and allow students to finish the assignment for homework. Once complete, you’ll see detailed reports of students who may need additional support, students who are ready for a challenge, and other interesting insights!
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