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## Paint bucket polygons

Use photo editing software as a teaching tool to bring inaccessible polygon definitions within reach of your students' understanding.

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## Who Is the Squarest of Them All?

Students are asked to solve a problem that involves viewing the characteristics of a square.

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## Writing Code to Assess Geometric Reasoning

Engage students and promote thinking in a student-centered environment that is rich with technology.

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## Solutions: Mirror, mirror

Each month, this section of the problem solvers department showcases students' in-depth thinking and discusses the classroom results of using problems presented in previous issues of Teaching Children Mathematics. In the problem from the December 2015/January 2016 issue, the task that integrates students' understanding of shapes and their properties and reflections. Students must determine which shapes can be reflected over a line so that the original shape and its reflection form specified figures.

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## Mathematics Concepts Using STEM Connections

Introduce two topics in math, volume and triangle types, by using connections to STEM. Contributors to the iSTEM (Integrating Science, Technology, Engineering, and Mathematics) department share ideas and activities that stimulate student interest in the integrated fields of science, technology, engineering, and mathematics (STEM) in K–grade 6 classrooms.

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## Problem: Build me—if you can

In this month's problem scenario, students engage in productive struggle to explore the part-whole fraction relationship by building triangles represented with pattern blocks. Each month, elementary school teachers receive a problem along with suggested instructional notes. Teachers are asked to use the problem in their own classrooms and report solutions, strategies, reflections, and misconceptions to the journal audience.

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## Untangling Geometric Ideas

This geometry lesson uses the work of abstract artist Wassily Kandinsky as a springboard and is intended to promote the conceptual understanding of mathematics through problem solving, group cooperation, mathematical negotiations, and dialogue.

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## A smorgasbord of assessment options

Presented with a variety of palatable, inquiry-based, creative learning choices in geometry, this teacher and her fifth graders found tremendous satisfaction in meeting target goals for reasoning skills and taking important “next steps” in learning.

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## Changing the whole

Students benefit from hands-on tasks exploring number, area, and fractional relationships when the value of a whole changes. This activity uses pattern blocks to explore different designs with different constraints (e.g., a target value, a set number of blocks, or a final shape) while changing the value of the whole. For example, if the trapezoid is worth 1 1/2, create different sizes of triangles and find their value.

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## Exploring the Woolly Properties of Quadrilaterals

To explore properties of quadrilaterals in a creative setting that focuses on discovery over memorization, assign your students the Wolves and Sheep problem.