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## “Reflections on High-Quality Math Instruction”

From the Archives highlights articles from NCTM’s legacy journals, previously discussed by the MTLT Journal Club.

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## Same Task but Different Learning Goals

This article models how to plan and facilitate implementing the same task in two sixth-grade classrooms with two different learning goals using the Five Practices structure.

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## Using Number Talks to Compare Fractions

Using this strategy, a teacher facilitates a short conversation during which students verbally explain and justify reasoning. We have found that a coordinated series of number talks supports students’ reasoning when comparing fractions.

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## Tackling Tangential Student Contributions

Do your students ever share ideas that are only peripherally related to the discussion you are having? We discuss ways to minimize and deal with such contributions.

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## Learning Trajectories for Vertical Coherence

Three learning trajectories and their connections show how to promote vertical coherence in PK–12 mathematics education.

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## Partial Pies

A series of tasks encourage students to reflect on the reasonableness of their number sense and use benchmarks to refine their estimations.

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## Global Connections through Mathematical Problem Solving

Teachers from two countries designed a model-eliciting activity about the global issue of wind energy. They share teaching and student outcomes from a cross-border engagement in the task with students from Indonesia and the United States through synchronous video conference.

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## One Task, Multiple Proportional Reasoning Strategies

Tasks and materials that allow for different approaches can help teachers incorporate student reasoning and can promote connections across different mathematical ideas.

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## Extending Choral Counting

This instructional activity gives teachers access to student thinking that can be leveraged to extend and connect their ideas.

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## Unit Fractions as Superheroes for Instruction

The complexity of understanding unit fractions is often underappreciated in instruction. We introduce a continuum of children's understanding of unit fractions to explore this complexity and to help teachers make sense of children's strategies and recognize milestones in the development of unit-fraction understanding. Suggestions for developing this understanding are provided.