Math 7-9

Geometric Reasoning

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How Geometric Reasoning connects to...

Geometric Reasoning involves using abstract thinking to define, analyze, and make arguments about shapes and spatial relationships. Students must also be able to formalize these arguments in written proofs. Students' geometric knowledge provides concrete representations and models for abstract math concepts, which can serve as an entry point to higher-order math thinking skills.

Main Ideas

Children begin with intuitive geometric knowledge (e.g., about shape and symmetry) which builds through exposure to events in the world. In school, this informal knowledge is built upon and expanded into more formal understanding of geometric concepts including:

Symmetry: Reflection across a line (e.g., folding) within a shape;

Congruence: The relationship between shapes through rotation, reflection, or translations; and

Similarity: The relationship between shapes whose sides are proportional and angles are equal.

Geometric Reasoning is scaffolded by Spatial Skills, which allow students to understand two and three-dimensional shapes and space, and by communicating and making arguments about these concepts through different channels, including sensorimotor and embodied activity.

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