Rotational symmetry and reflection symmetry are key. What is the same and what is different in similar figures?
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See the standards throughout the grades: http://www.corestandards.org/Math/Content/G/
G1.e. Identify and draw lines of symmetry and identify rotational symmetry in various shapes and designs (e.g. rectangles have two lines of symmetry, parallelograms have 180-degree rotational symmetry).
G3.a. Define, find, and be able to use a scale factor.
G3.b. Determine if two shapes are similar. If a pair of shapes is known to be similar, find missing lengths and angles. Focus especially on triangles.
G3.c. Identify congruent and similar shapes. Explain why, referring to specific properties of side lengths and angles. Identify congruent as a subset of similar.
As students explore symmetry, similarity, and congruence, ensure that students have opportunities to construct examples and non examples.
Slides for Chapter 14 in Mathematics for Elementary Teachers with Activities, 5th edition by Sybilla Beckmann.
G1.e Which One Doesn't Belong. Students identify reasons why shapes do or do not belong in a group.
G1.e Manipulatives for students to make designs with specific types of symmetry physical Pattern Blocks or virtual Pattern Blocks
G3.b Offline activity on Identifying Similar Triangles by Shell Center
G3.c. Online Activity allowing students to explore congruent triangles of various sizes Triangle Congruence by MathOpenRef.com
G3.c Manipulatives to explore congruency AngLegs