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## Attending to Precision with Secret Messages

Introduce your students to a fun and innovative game to encourage precise communication

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## Creating Inequalities from Real-World Experiences

Research-based strategies are described for supporting students as they mathematize real-world scenarios and create inequalities to model situations and contexts from their own lives.

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## Riding the RAFT

Writing about mathematics holds a wealth of benefits for students. When students are given opportunities to write in math class, it helps develop mathematical thinking and language (Carter 2009; McCarthy 2008; Yang 2005), encourages self-reflection (Carter 2009; Danielson 2010; O'Kelley 2013), and provides a better way to organize ideas (Linhart 2014; Rogers 2014). Many teachers incorporate journaling and other types of reflective writing into their instruction already (Sjoberg, Slavit, and Coon 2004; Sanders 2009), but what about other forms of writing? NCTM states the importance of writing, in that students in the middle grades should be “more explicit about basing their writing on a sense of audience and purpose” (NCTM 2000, p. 62). How can we help students develop this important skill in math class?.

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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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## Reveal Limitations through Fraction Division Problem Posing

Students notoriously struggle with division of fractions in 5 key areas. Hear what those 5 areas are and how recommendations address the limitations.

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## Algebra Homework: A Sandwich!

Given two slices of bread—a problem and the answer—students fill in the fixings: their own mathematics reasoning.

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## Mysterious Subtraction

Conjecturing is central to the work of reasoning and proving. This task gives fourth and fifth graders a chance to make conjectures and prove (or disprove) them.

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## Strengthening Discussions

Teachers can foster strategy sharing by attending to the cognitive demands that students experience while talking, listening, and making mistakes.

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## Cartoon Corner: Investing in Whose Retirement?

A cartoon highlighting growth of a retirement fund is coupled with a full-page activity sheet.

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## Seeing Spots and Developing Multiplicative Sense Making

Cans on a grocery store shelf and Hirst's Capric Acid Amide can illustrate dot arrays, thus helping students understand the distributive property, partial products, and the standard algorithm for multiplication.