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## Cartoon Corner: Presidential Puzzlers

A cartoon involving presidential birth dates is coupled with a full-page activity sheet.

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## Mathematical Explorations: A New Twist on Collaborative Learning

Research on students' learning has made it clear that learning happens through an interaction with others and through communication. In the classroom, the more students talk and discuss their ideas, the more they learn. However, within a one-hour period, it is hard to give everyone an equal opportunity to talk and share their ideas. Organizing students in groups distributes classroom talk more widely and equitably (Cohen and Lotan 1997).

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## Palette of Problems

A monthly set of problems is aimed at a variety of ability levels.

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## Palette of Problems – May 2014

A monthly set of problems is aimed at a variety of ability levels.

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## Differentiated Instruction in Shared Mathematical Contexts

Try these methods for integrating diverse learners.

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## The Mathematics of Tiling

People who lay tile for a living use mathematics every day to decide how much tile, grout, and other supplies are required to complete each job. Measurement and geometry are an integral part of designing tile patterns. Collections of short activities focus on a monthly theme that includes four activities each for grade bands K–2, 3–4, and 5–6 and aims for an inquiry or problem-solving orientation.

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## Revisit Pattern Blocks to Develop Rational Number Sense

A classic manipulative, used since the 1960s, continues to offer opportunities for intriguing problem solving involving proportions.

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## Sizing Up the Grinch's Heart

How do middle school students interpret the phrase “two sizes too small”? Examining students' responses will re-form your thinking about teaching similarity and using nonstandard shapes.

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## Virtual manipulatives to assess understanding

Three preservice teachers used virtual manipulatives during clinical interviews with students of elementary school age. The technology exposed students' problem-solving strategies and mathematical understanding, promoting just-in-time teaching about the target content. The process of completing and reflecting on the interviews contributed to growth of the preservice teachers' technological pedagogical content knowledge.

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## Investigations: My bar graph tells a story

Connecting stories to qualitative coordinate graphs has been suggested as an effective instructional strategy (Blubaugh and Emmons 1999; Maus 2005; NCTM 2000). Even students who are able to create bar graphs may struggle to correctly interpret them. Giving children opportunities to work with qualitative graphs can help them develop the skills to interpret, describe, and compare information from a graph even without the availability of numeric labels. This investigation addresses the Data Analysis and Probability Standard (NCTM 2000) and explores the value of connecting stories with qualitative bar graph instruction, which too often focuses on only counting, tallying, and creating bar graphs.