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## Why Is the Midpoint an Average?

The relationship between a midpoint and an average showcases the interplay between procedural knowledge and conceptual knowledge in learning mathematics for teaching.

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## Core Conversations with Educative Dragging

The Measure-Trace-Algebratize (MTA) approach allows students to uncover algebraic relationships within familiar geometric objects.

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## Flying High with the Bird Tetrahedron

An origami activity can lead to rich tasks in several branches of mathematics.

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## Mathematical Lens: Mathematics and the Art of Sol LeWitt

Students analyze a photograph to solve mathematical questions related to the images captured in the photograph. This month, the art of sculptor and painter Sol LeWitt is analyzed. Counting, combinatorics, and spatial visualization are among the mathematical themes evinced.

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## Don't Fence Me In!

This method for counting lattice octagons strengthens students' counting skills and geometrical thinking.

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## Activities for Students: Filling Bottles with Water

In this activity, students gradually fill bottles of different shapes and graph the water level (height) versus the volume of water inside the bottles. Then they explore the relationship between the shape of a bottle and the resulting graph.

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## Ponderings on Pocket-sized Polyhedra

Pop-up polyhedra–three-dimensional models that can be stored for future reference–are easily constructed using The Geometer's Sketchpad and give students experience in using transformations in the plane.

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## Geometry and the Design of Product Packaging

Simulating a real-world marketing situation, students examine the mathematical calculations that play an integral part in product design.