The overarching goal of Butterflies, Pinwheels, and Wallpaper is to develop student understanding of congruence and similarity of geometric figures, and the mathematical techniques for finding and applying those relationships of shapes. The basic idea of congruence is that two figures have the same shape and size if it is possible to perform one or more transformations that “move” one figure onto the other. The basic idea of similarity is that two figures have the same shape if it is possible to perform a dilation, and perhaps one or more rigid motions, to transform one figure onto the other.
The two main topics of this Unit that highlight congruence and similarity are rigid motions and dilation. Investigations 1–3 develop and apply properties of line reflections, rotations, and translations. These rigid motions are used to transform figures for creating symmetric designs and to compare the size and shape of congruent figures. Investigation 4 extends the transformation concept to include dilations of similar figures.
Butterflies, Pinwheels, and Wallpaper builds on important prior work in the Grade 7 Units Shapes and Designs and Stretching and Shrinking . It also makes significant connections to two prior Units on measurement, Grade 6 Covering and Surroundingand Grade 7 Filling and Wrapping .
The two main topics of this Unit that highlight congruence and similarity are rigid motions and dilation. Investigations 1–3 develop and apply properties of line reflections, rotations, and translations. These rigid motions are used to transform figures for creating symmetric designs and to compare the size and shape of congruent figures. Investigation 4 extends the transformation concept to include dilations of similar figures.
Butterflies, Pinwheels, and Wallpaper builds on important prior work in the Grade 7 Units Shapes and Designs and Stretching and Shrinking . It also makes significant connections to two prior Units on measurement, Grade 6 Covering and Surroundingand Grade 7 Filling and Wrapping .
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3 -Transforming Coordinates
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4 -Dilations and Similar Figures
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