Some ideas for sentence frames/starters that could be incorporated into your lesson are listed below.  If you think a sentence frame/starter will be helpful, consider how will it support students’ mathematical learning and/or development of academic language, and decide which sentence frame/starter (from the list below or that you create) would best support students’ learning. You may find that the starters and frames vary in level of difficulty, and plan to provide them to students accordingly.

Starters

When I dilate a triangle, I notice that:

The angles of the original triangle and of the dilated image of that triangle _______________________________________________

The lengths of the sides of the original triangle and of the dilated image of that triangle ____________________________________________________________________________________________________________

The distance from the center of dilation (the point P) to the vertices of the original triangle and from the center of dilation (the point P) to the dilated image of that triangle________________________________________________________________________________________________________________

(Part 3 prediction)

I predict that if I move the center of dilation (the point P) four grid spaces down, then the dilated image of triangle ABC will

____________________________________________________________________________________________________________

Frames

The ______________ of the original triangle and of the dilated image of that triangle remain the same.

The _____________ of the ______________ of the original triangle and of the dilated image of that triangle are proportional.

 

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Academic Language

Students should have opportunities to see, hear, and write key mathematical ideas during this activity. There are some specific terms that students need to understand in order to engage in this task, and there are some additional terms and phrases that may surface as the students engage with the task. You may think of additional words or phrases that are key to this activity.  As the task is introduced, solved by the students, and discussed, ensure that students have opportunities to experience (i.e., through discussion, pictures, and the use of gestures) and to build understanding for key words and phrases. Examples of words and phrases that may be involved in work on this problem include:

• Stretcher, knot
• dilation of the original triangle; dilated triangle; dilated version of the triangle; dilate
• center of dilation
• the side lengths double
• the distances double
• scale factor
• similar triangles; similarity; similar figures
• predict, reconstruct, locate
• orientation of the triangle
• angles
• side length; line segment
• spaces

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