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José Manuel Martínez and Laura Ramírez

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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Walter Stark

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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Laurie St. Julien

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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Amanda Sibley and Terri L. Kurz

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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Sarah B. Bush, Richard Cox, and Kristin Leigh Cook

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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Jody Guarino

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.

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A cartoon exploring a problem about cutting up pizza is coupled with a full-page activity sheet.

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Rebecca R. Robichaux and Paulette R. Rodrigue

Sorting shapes and solving riddles develop and advance children's geometric thinking and understanding while promoting mathematical communication, cooperative learning, and numerous representations.

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Sarah Ferguson

Explore the creation of a unique problem-based learning (PBL) experience.

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Finding regular polygons, such as equilateral triangles, squares, hexagons, and even octagons, in art or architecture is not unusual, but seeing a nonagon, or nine-sided regular polygon, such as the Mongolian drum (see photograph 1) is less common. Perhaps 9 is a special number in Mongolia: Shamans have 99 tengri, or spirits, (55 benevolent ones and 44 “dark” ones) on their drums, although the drums are more often circular.