CCSS.Math.Content.HSG-CO.A.3
The standard
Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself.
Common Core State Standards for Mathematics
What this standard means
Students need to identify a shape’s symmetries. They should name rotations by angle and center, and name reflection lines that make the figure land exactly on itself. They must work with rectangles, parallelograms, trapezoids, and regular polygons, not just squares and triangles.
Mastery looks like clear, complete lists. For example, a non-square rectangle has 180 degree rotational symmetry and two lines of reflection. Common errors include assuming every quadrilateral has line symmetry, mixing up regular and non-regular polygons, and forgetting that a full 360 degree turn always maps a figure onto itself.
Ways to teach it
- Give students paper cutouts of each shape, a pin for the center, and mirrors to test rotations and reflection lines.
- Ask students to explain why a parallelogram usually has rotational symmetry but no reflection symmetry.
- Show one shape and ask students to list all rotations and reflection lines on a half sheet in three minutes.
- Have students find logos, tiles, or road signs that match each symmetry type and label the rotations and reflection lines.
Plan a lesson for CCSS.Math.Content.HSG-CO.A.3
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