Math 8 Unit 6

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Section 6.1 begins with a technology tool investigation to challenge students to use rigid transformations (translation, rotation, and reflection) to get a key into a lock. While students solve puzzles, they will begin to predict the result of each of the transformations, as well as notice how transformations can sometimes be interchanged and undone. Students then begin to perform basic transformations on a coordinate plane that they create on graph paper. The focus on naming points using coordinates is important as students examine how the coordinates change as shapes are translated about the plane.

At the beginning of Section 6.2, students investigate what happens when the coordinates of vertices of a shape are multiplied, which introduces the idea of dilation and the focusturns to geometric comparisons. Students will look at ways to do and to “undo” dilations. They will investigate characteristics of similar and congruent shapes. They will identify the relationships between the lengths of corresponding sides of similar figures, and use scale factors to find the lengths of missing sides. Students will see that dividing by a scale factor has the same effect on a shape as multiplying by its reciprocal.

Section 6.1 introduces students to the vocabulary of rigid transformations. This is a good time to remind students to attend to precision as they describe the movement of shapes on a coordinate graph. In Section 6.2 students make sense of and persevere in solving problems with similar figures. They reason abstractly and quantitatively when determining similarity and finding missing side lengths of similar figures.

8.G.1 Verify experimentally the properties of rotations, reflections, and translations:

a. Lines are taken to lines, and line segments to line segments of the same length.

b. Angles are taken to angles of the same measure.

c. Parallel lines are taken to parallel lines.

8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.

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