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Math and The Mind’s Eye
Common Core State Standards Correlation Charts
Unit 10 Seeing Symmetry
Math and The Mind’s Eye
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Unit 10 Seeing Symmetry
Activity 7
Polyominoes and
Polyamonds
Activity 6
Symmetries of Polygons
Activity 5
Combining Shapes
Activity 4
Strip Patterns
Activity 3
Shapes and Symmetries
Activity 2
Mirrors and Shapes
Standard
Activity 1
Paperfolding
This Math and the Mind’s Eye unit uses paper folding to develop geometric ideas and allows for multiple entry points. The activities could be used to teach vocabulary, geometric
properties, symmetry, both folding and rotational, and transformational geometry to middle grades students. They could also be extended to high school Geometry, including
informal proofs.
Comments
4.G.1 Draw points, lines, line segments, rays, angles
(right, acute, obtuse), and perpendicular and parallel
lines. Identify these in two-dimensional figures.
Activity 1 is an excellent introduction, or review, of
vocabulary and geometric properties, including central
angles. The shapes examined go from simple rectangles to
convex quadrilaterals. Students would need to be able to
follow directions for folding and cutting paper squares.
4.G.2 Classify two-dimensional figures based on the
presence or absence of parallel or perpendicular lines, or the
presence or absence of angles of a specified size. Recognize
right triangles as a category, and identify right triangles.
Activity 2 requires mirrors.
4.G.3 Recognize a line of symmetry for a two-dimensional
figure as a line across the figure such that the figure can
be folded along the line into matching parts. Identify linesymmetric figures and draw lines of symmetry.
5.G.3 Understand that attributes belonging to a
category of two-dimensional figures also belong to
all subcategories of that category. For example, all
rectangles have four right angles and squares are
rectangles, so all squares have four right angles.
5.G.4 Classify two-dimensional figures in a hierarchy
based on properties.
7.G.2 Draw (freehand, with ruler and protractor, and with
technology) geometric shapes with given conditions.
Focus on constructing triangles from three measures of
angles or sides, noticing when the conditions determine
a unique triangle, more than one triangle, or no triangle.
8.G.1 Verify experimentally the properties of rotations,
reflections, and translations:
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Activity 7
Polyominoes and
Polyamonds
Activity 6
Symmetries of Polygons
Activity 5
Combining Shapes
Activity 4
Strip Patterns
Activity 3
Shapes and Symmetries
Activity 2
Mirrors and Shapes
Standard
Activity 1
Paperfolding
Unit 10 Seeing Symmetry continued
Comments
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.
Activities 3-7 provide opportunities for learning visual
congruency proofs for a variety of objects.
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.
Activities 6-7 provide opportunities for learning visual
similarity proofs for a variety of objects.
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