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## GPS: The Dog Leash Problem

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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## Promoting Equitable Problem Solving with Numberless Math Stories

Use these three strategies to support student perseverance and discourse about context.

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## Recalibrating Beliefs and Teaching Practices

In 2018, NCTM published the first of three books in their Catalyzing Change series. Across the three texts, they call for the dismantling of all forms of inequitable grouping structures from early childhood and elementary school (NCTM 2020a) to middle school (NCTM 2020b) and high school (NCTM 2018). NCTM (2020a) asserted—

Any ability grouping in mathematics education is an inequitable structure that perpetuates privilege for a few and marginality for others. Ability grouping practices often occur with good intentions; we want to understand children’s learning needs and then tailor the content,

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## Sibling Longevity

We explore the statistical likelihood of one, or more, siblings in a family of nine surviving to 100 years of age.

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## Problems to Ponder

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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## Exploring Sequences Related to Medial Triangles

Sequences are an important topic—not only in mathematics but also in the mathematics curriculum. Exploring sequences related to medial triangles offers learners opportunities to solve problems involving sequences within geometric contexts. Sequences related to medial triangles are also a rich source of beautiful and interesting geometric patterns that can be discovered with the use of dynamic geometry software (DGS) such as GeoGebra or Web Sketchpad. In addition, exploring sequences with DGS allows learners to formulate and test conjectures, an important mathematical process. In this article, I describe how my students used GeoGebra and geometric reasoning to visualize, discover, formulate,

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## Take a Seat at the Equation Café

Design projects to encourage your students’ self-efficacy and motivate mathematics learning by helping them apply their prior knowledge from real-world experiences.

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## Challenging Students to Experience Mathematics as Mathematicians

An unsolved problem gets elementary and middle school students thinking and doing mathematics like mathematicians.

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## Problems to Ponder

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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## Teaching Word-Problem Solving through Tape Diagrams

Get familiar with this visual instructional tool to help students make sense of mathematical relationships and select suitable operations for word problems at varied grade levels.