ALEX Resources

   View Standards     Standard(s): [MA2019] ACC-7 (7) 42 :

42. Verify experimentally the properties of rigid motions (rotations, reflections, and translations): lines are taken to lines, and line segments are taken to line segments of the same length; angles are taken to angles of the same measure; and parallel lines are taken to parallel lines.

a. Given a pair of two-dimensional figures, determine if a series of rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are congruent; describe the transformation sequence that verifies a congruence relationship. [Grade 8, 22]

[MA2019] ACC-7 (7) 43 :

43. Use coordinates to describe the effect of transformations (dilations, translations, rotations, and reflections) on two-dimensional figures. [Grade 8, 23]

[MA2019] ACC-7 (7) 44 :

44. Given a pair of two-dimensional figures, determine if a series of dilations and rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are similar; describe the transformation sequence that exhibits the similarity between them. [Grade 8, 24]

[MA2019] REG-8 (8) 22 :

22. Verify experimentally the properties of rigid motions (rotations, reflections, and translations): lines are taken to lines, and line segments are taken to line segments of the same length; angles are taken to angles of the same measure; and parallel lines are taken to parallel lines.

a. Given a pair of two-dimensional figures, determine if a series of rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are congruent; describe the transformation sequence that verifies a congruence relationship.

[MA2019] REG-8 (8) 23 :

23. Use coordinates to describe the effect of transformations (dilations, translations, rotations, and reflections) on two-dimensional figures.

[MA2019] REG-8 (8) 24 :

24. Given a pair of two-dimensional figures, determine if a series of dilations and rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are similar; describe the transformation sequence that exhibits the similarity between them.

Watch an animated demonstration of translating and reflecting a triangle on the coordinate plane in this video from KCPT. In the accompanying classroom activity, students watch the video and then consider the effect of translating and reflecting on the coordinates of the vertices of the triangle. Next, they draw translations and reflections of a triangle and identify the number of units and direction of translation as well as the lines of reflection in classmates drawings. To get the most from the lesson, students should be comfortable graphing points on the coordinate plane. Prior exposure to reflection is helpful.

   View Standards     Standard(s): [MA2019] ACC-7 (7) 43 :

43. Use coordinates to describe the effect of transformations (dilations, translations, rotations, and reflections) on two-dimensional figures. [Grade 8, 23]

[MA2019] REG-8 (8) 23 :

23. Use coordinates to describe the effect of transformations (dilations, translations, rotations, and reflections) on two-dimensional figures.

[MA2019] GEO-19 (9-12) 26 :

26. Verify experimentally the properties of dilations given by a center and a scale factor.

a. Verify that a dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

b. Verify that the dilation of a line segment is longer or shorter in the ratio given by the scale factor.

In this animated Math Shorts video from the Utah Education Network, learn about rotation, which describes how a geometric shape turns around a point, called the center of rotation. When a geometric shape rotates on a coordinate plane, it stays exactly the same distance from the center of rotation. In the accompanying classroom activity, students are given two rotations from a handout and work in pairs to try to determine whether one figure is a rotation of the other figure around the given point. If the figure is a rotation, the student pair must add one more rotation to the grid. If the figure is not a rotation, the student pair must add one accurate rotation to the grid. This resource is part of the Math at the Core: Middle School Collection.

   View Standards     Standard(s): [MA2019] ACC-7 (7) 43 :

43. Use coordinates to describe the effect of transformations (dilations, translations, rotations, and reflections) on two-dimensional figures. [Grade 8, 23]

[MA2019] ACC-7 (7) 44 :

44. Given a pair of two-dimensional figures, determine if a series of dilations and rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are similar; describe the transformation sequence that exhibits the similarity between them. [Grade 8, 24]

[MA2019] REG-8 (8) 23 :

23. Use coordinates to describe the effect of transformations (dilations, translations, rotations, and reflections) on two-dimensional figures.

[MA2019] REG-8 (8) 24 :

24. Given a pair of two-dimensional figures, determine if a series of dilations and rigid motions maps one figure onto the other, recognizing that if such a sequence exists the figures are similar; describe the transformation sequence that exhibits the similarity between them.

[MA2019] GEO-19 (9-12) 26 :

26. Verify experimentally the properties of dilations given by a center and a scale factor.

a. Verify that a dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.

b. Verify that the dilation of a line segment is longer or shorter in the ratio given by the scale factor.

Watch as the National Museum of Mathematics uses an image of a visitor to create a "Human Tree" using dilations. This video focuses on how similar figures can create dilations and how exponents can be used in an equation to express the proportional relationship in fractals. This video was submitted through the Innovation Math Challenge, a contest open to professional and nonprofessional producers.

   View Standards     Standard(s): [MA2019] REG-8 (8) 23 :

23. Use coordinates to describe the effect of transformations (dilations, translations, rotations, and reflections) on two-dimensional figures.

Module 3, Topic A begins by demonstrating the need for a precise definition of dilation instead of “same shape, different size” because dilation will be applied to geometric shapes that are not polygons. Students begin their work with dilations off the coordinate plane by experimenting with dilations using a compass and straightedge in order to develop conceptual understanding. It is vital that students have access to these tools in order to develop an intuitive sense of dilation and to prepare for further work in Geometry.