District Unit Plans

Collection Contents


An introduction to flow proofs.
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A demonstration activity on the importance of precision in writing proofs.
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Students measure the angles and side lengths of a parallelogram in order to discover the basic properties.
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Students identify angle types (corresponding, alternate interior, alt exterior, etc.) and measure them to discover which pairs are congruent or supplementary.
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An extension exercise to solidify the perpendicular bisector theorem
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Circles in Triangles

by Sameen Shoenhair

This task challenges a student to use geometric properties of circles and triangles to prove that two triangles are congruent. A student must be able to use congruency and corresponding parts to reason about lengths of sides. A student must be able to construct lines to make sense of a diagram. A student needs to use geometric properties to find the radius of a circle inscribed in a right triangle.
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Students construct a parallelogram, measure the side lengths and angles, and observe that opposite sides are congruent, opposite angles are congruent, and consecutive angles are supplementary. Then they construct the diagonals, measure the distances from the vertices to the point of intersection, and discover that the diagonals bisect each other.
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Midsegment

by Sameen Shoenhair

Geometer's Sketchpad sketch that investigates midsegments of triangles.
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Online questions about Isosceles Triangles, their angles, and their sides.
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Proving Triangle Theorems

by Sameen Shoenhair

Show theorems about triangles are true, such as "measures of interior angles of a triangle sum to 180 degrees", "base angles of isosceles triangles are equal", and more.
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This lesson unit is intended to help you assess how well students are able to produce and evaluate geometrical proofs. In particular, this unit is intended to help you identify and assist students who have difficulties in: Interpreting diagrams. Identifying mathematical knowledge relevant to an argument. Linking visual and algebraic representations. Producing and evaluating mathematical arguments.
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This lesson unit is intended to help you assess how well students can: Understand the concepts of length and area. Use the concept of area in proving why two areas are or are not equal. Construct their own examples and counterexamples to help justify or refute conjectures.
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Medians in a Triangle

by Sameen Shoenhair

Geometer's Sketchpad activity, complete with worksheets, on medians in a triangle.
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Circumcenter

by Sameen Shoenhair

Geometer's Sketchpad sketch on circumcenters.
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Triangle Centers

by Sameen Shoenhair

Website that explores centers of a triangle. It also has links to Geometer's Sketchpad sketches to help explore the concepts further.
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Quadrilaterals

by Sameen Shoenhair

This task challenges a student to use geometric properties to find and prove relationships about an inscribed quadrilateral. A student must analyze characteristics and properties of 2?dimensional figures and develop mathematical arguments of the relationships within the figures.
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