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• Author or Editor: Nesrin Cengiz
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Facilitating Productive Discussions

Capitalize on student thinking to create opportunities to further their mathematical reasoning.

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Making Sense of Equivalent Ratios

A framework using contexts, language, and representations can support middle school students' justifications.

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Take a Bite out of Fraction Division

When it comes to fractions, students often understand just part of the story. Assign some meaningful problems to help them see the whole picture.

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Games to Support Decimal Number Reasoning

Activities help students develop an understanding of decimals by using number cards and place-value cards to form decimal amounts, compare these amounts, and justify their decisions by using representations.

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Research, Reflection, Practice: Children Generate their Own Representations

“How many teeth have you lost?” Imagine second graders collecting data from their peers about how many teeth each child is missing and then creating their own data representations that mean something to them. Instead of showing her students how to create a bar graph of the data, this teacher asks them to display the information in some way that helps them make sense of their data. Students work in small groups, discuss their ideas with peers, and create their own data representations. Then they share their data with the entire class, discussing differences in their representations and interpretations.

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Tasks to Develop Language for Ratio Relationships

Tasks that have been developed to build a foundation for ratio meanings and language not only provide valuable information about student thinking but also support proportional reasoning.