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## All the Way Around a Circle: An Angle Lesson

In this lesson, third graders were asked how many degrees is a full rotation around a circle. After we gave students time and space to disagree, to make and test conjectures, and to explore, they reasoned about angle as turn and determined a full rotation is 360 degrees.

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## Virtual Place Value

Compare how third graders think mathematically when using virtual versus concrete base-ten blocks to learn place-value concepts.

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## Back-to-school shopping

This department showcases students' in-depth thinking and work on previously published problems. The August 2012 problem scenario leverages back-to-school shopping advertisements for this real-life scenario about making purchases using discount coupons. To access the full-size activity sheet, go to http://www.nctm.org/tcm, Back Issues.

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## Singing and gaming to math literacy

Games and videos lend themselves to student engagement and learning, but how do teachers determine what is most beneficial to student learning? How can we effectively incorporate technology into our teaching of mathematics?

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## Using Technology to Balance Algebraic Explorations

Free, Web-based balance tools can help students visualize the concept of the equal sign as the pivot point of an equation.

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## Using voice recorders to capture their thinking

Teachers share success stories and ideas that stimulate thinking about the effective use of technology in K–grade 6 classrooms. This article describes how students can use available technology to communicate and share their thinking in popular media formats.

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## Abby and the number line

Students say some amazing things. Back Talk highlights the learning of one or two students and their approach to solving a math problem or prompt. Each article includes the prompt used to initiate the discussion, a portion of dialogue, student work samples (when applicable) and teacher insights into the mathematical thinking of the students. In this month's episode, a six-year-old rising first grader uses a computer simulation to understand addition and subtraction on the number line.

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## A picture is worth 100 math ideas

Teachers share success stories and ideas that stimulate thinking about the effective use of technology in K—grade 6 classrooms. One way to keep young students engaged and interested in practicing counting is to involve them in using cameras. This article explains how first graders capture 100 images, use Windows MovieMaker or PhotoStory to turn the still images into a video, and then narrate a story using precise math vocabulary to explain their mathematical thinking.

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## Teaching and Learning with Real-World Tools

To better prepare students for their future careers, a fifth-grade teacher designs and implements a lesson that uses spreadsheet software to graph functions.

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## Using Technology to Teach Equivalence

Professional development equips practitioners with skills to enhance student learning.