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## Angling for Students' Mathematical Agency

A group of fourth graders went from overreliance on protractors to relying on their own reasoning and understanding of how to measure angles.

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## Reflecting on the Cloud Clock problem

This problem scenario explores the analog clock, a rich source of tasks associated with angles and angle measures. The Cloud Clock problem is an opportunity for students to deepen their understanding of analog clocks, angles, and time and angle measurement. To access the full-size activity sheet, go to http://www.nctm.org/tcm, All Issues. 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.

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## Angle detectives

This problem scenario presents how a fifth-grade class used logical thinking and spatial reasoning to find the angle measurements of certain polygons without using a protractor. To access the full-size activity sheet, go to http://www.nctm.org/tcm, All Issues. 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.

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## Investigations: EEK—a cockroach!

Why would a person who is terrified of cockroaches use them in a math lesson? The idea for this investigation did not occur to me until I read a newspaper article that described Italian scientist Paolo Domenici's research about cockroaches' escape trajectories. In particular, he found that cockroaches have preferred escape trajectories of 90, 120, 150, and 180 degrees from the source of danger (Domenici et al. 2008). Because this real-world information presents a unique problem-solving context for fifth graders to explore angles formed by clockwise and counterclockwise rotations, I overcame my fear of the creatures to develop this investigation.

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## Keep on Rollin'

Here is a simple way to turn an ordinary whiteboard into an interactive tool that allows students to design and build pathways along which a sliding object will flow—within certain constraints—to reach its final destination. Students must reason, conjecture, test, conjecture again, and then retest their design features to determine a solution to the presented investigation.

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## Flipped Learning: Embedding Questions in Videos

Use math videos and different types of inquiries to increase students' intellectual engagement.

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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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## A critical focus on the M in STEAM

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. The authentic STEAM project described here was born of a critical need of one child in the community. Using the Design Thinking framework, a class of fourth graders embarked on what was arguably the most meaningful school project of their lives. We place an explicit focus on the M in STEAM.

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## Weaving Mathematical Concepts through Native American Baskets

The stunning natural beauty of Arizona, New Mexico, southern Colorado, and Utah is indicative of the American Southwest and is reflected in Southwestern baskets. Many Southwestern basket weavers use coiling as their method of construction (see fig. 1). The following problems relate mathematics to the art of basket weaving, with an emphasis on coiling.

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## Clocks: For more than telling time

Postscript items are designed as rich “grab-and-go” resources that any teacher can quickly incorporate into their classroom repertoire with little effort and maximum impact. In this article, classroom clocks are used as an effective tool to support student understanding of basic number, fraction, and geometry concepts.