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• Author or Editor: Kling Gina
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Applying known facts to derive unknown facts results in efficiency, flexibility, and an understanding of number combinations for young students.

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## Graphing Calculators as Tools

The many uses of handheld technology for learning mathematics inherently involve specialized knowledge that is framed as TPACK: technology, pedagogy, and content knowledge.

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## Assessing Basic Facts Fluency

Have you had it with timed tests, which present a number of concerns and limitations? Try a variety of alternative assessments from this sampling that allows teachers to accurately and appropriately measure childre's fact fluency.

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## Enriching Addition and Subtraction Fact Mastery through Games

Becoming fluent with basic facts is developmental. Use games infused with a focus on acquisition of strategies to help students in the early grades progress to computational fluency.

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## Three Steps to Mastering Multiplication Facts

First understand what fluency is, then use these games and a sequence of strategies to help your students develop facility and confidence.

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## Eight Unproductive Practices in Developing Fact Fluency

Basic fact fluency has always been of interest to elementary school teachers and is particularly relevant because a wide variety of supplementary materials of varying quality exist for this topic. This article unpacks eight common unproductive practices with basic facts instruction and assessment.

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## What's Your Angle on Angles?

The word angle may conjure up several thoughts—a corner, two rays and a vertex, or a degree measure. But what about the idea of a turn (a rotation around a fixed point) or of the space between two rays, and what exactly is a degree? Many upper-elementary students have such limited notions of angle that they struggle to provide an appropriate mathematical definition for the term and, instead, describe what we are measuring when we measure an angle. Yet, according to NCTM (2000), students in grades 6–8 must be able to “carefully examine the features of shapes in order to precisely define and describe fundamental shapes” (p. 233). Angle is certainly a prominent feature of shape, so, beginning in the elementary grades, providing students with opportunities to carefully explore the idea of angle is critical for the development of their understanding of geometry. Doing so, however, requires us as teachers to first realize the complexity of the concept of angle. As one sixth-grade student put it, “An angle is a lot more than just degrees.”

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## The Best of TCM, MTMS, and MT on Fluency, Understanding, and Productive Struggle

Revisit this collection of articles through the lens of Mathematics Teaching Practice 6: Build procedural fluency from conceptual understanding and Practice 7: Support productive struggle in learning mathematics.