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GPS: Composing and Decomposing Shapes Across the Grades

Kyle Carpenter and Sarah Roller Dyess

Growing Problem Solvers provides four original, related, classroom-ready mathematical tasks, one for each grade band. Together, these tasks illustrate the trajectory of learners' growth as problem solvers across their years of school mathematics.

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Broken Ceiling Lights: Circular Area Without the Radius

Nicholas J. Gilbertson

A customer walks in to a lighting store with a broken ceiling light, and the solution to finding a replacement glass illuminates an alternative approach to finding the circumference and area of a circle without knowing the circle’s center, radius, or diameter.

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Exploring Young Children’s Math Thinking in Sandcastle Building

Hannah Tan and Cynthia Lim

Children explore concepts of capacity and height measurement through sand play in nursery class.

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Problems to Ponder

Chris Harrow and Justin Johns

Problems to Ponder provides 28 varying, classroom-ready mathematics problems that collectively span PK–12, arranged in the order of the grade level. Answers to the problems are available online. Individuals are encouraged to submit a problem or a collection of problems directly to mtlt@nctm.org. If published, the authors of problems will be acknowledged.

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Using Public Records to Scaffold Joint Sense Making

Keith R. Leatham, Blake E. Peterson, Ben Freeburn, Sini W. Graff, Laura R. Van Zoest, Shari L. Stockero, and Nitchada Kamlue

Teachers can more productively use board work to scaffold joint sense making.

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Construct It! Progressively Precise: Three Levels of Geometric Constructions

Carmen Petrick Smith

This article shares an activity scaffolding the construction of the circumcenter of a triangle, culminating with a Triangle-Ball Championship game.

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Prove It! Graph Theory and Induction: The Next Big Thing

Jeffrey P. Smith

Eighth-grade students participated in a two-day lab exploring graph theory. In addition to learning about a completely new topic, they experienced a subtle introduction to proof by induction.

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Let’s Be Flexible

Clayton Edwards and Rebecca Robichaux-Davis

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Problems to Ponder

Chris Harrow and Justin Gregory Johns

Problems to Ponder provides 28 varying, classroom-ready mathematics problems that collectively span PK–12, arranged in the order of the grade level. Answers to the problems are available online. Individuals are encouraged to submit a problem or a collection of problems directly to mtlt@nctm.org. If published, the authors of problems will be acknowledged.

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Advancing Agency Through Conjecturing

Kristin Doherty

Support students in conjecturing in ways that can promote their agency in the learning process.