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## Exploring Slope with Stairs & Steps

Two activities help develop students' understandings of rate of change and slope within STEM contexts.

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## A Vehicle for Bivariate Data Analysis

Top-selling cars in America can be the catalyst that drives an analysis of data.

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## Dilations and the Equation of a Line

Track students' understanding of proportional reasoning by combining transformational geometry, similar-triangle reasoning, and linear relationships.

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## Connecting Representations: Using Predict, Check, Explain

Although educators agree that making connections with the real world, as advocated by Principles to Actions: Ensuring Mathematical Success for All (NCTM 2014), is important, making such connections while addressing important mathematics is elusive. We have found, however, that math content coupled with the instructional strategy of predict, check, explain can bridge such real-world contexts. In so doing, this procedure supports the research-informed teaching practices of using evidence of student thinking and aiding meaningful mathematical discussion.

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## All Talk and More Action

Students' understanding of proportional relationships become apparent during an algebra project that focuses on constructing mathematical arguments.

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Consider four important elements of setting up challenging mathematics problems to support all students' learning.

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## Math for Real: Comfortable Construction

### “when will I ever use this?”

Finding the best step and tread for stairs provides the real-life tie in to this activity on slope and graphing.

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## Math for Real: Canine Care

### “when will I ever use this?”

Ages and weights of various dogs provide the real-life tie in to this activity on linear relationships.

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## Secondary Mathematics Inclusion: Merging with Special Education

A conceptual framework can show a general education and a special education teacher how to team teach so that a range of students can learn together in today's classroom.

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## It's a Bird, It's a Plane, It's a Dilated Superhero

The more connections that students can make between mathematical content and the real world, the better they will become at developing critical thinking and understanding mathematics. This lesson on exploring geometric dilations encourages small cooperative-group critiques and connections to an abundance of middle school math concepts. Graphing proportional relationships and finding the constant of proportionality are big ideas in middle school mathematics. This two-part lesson connects these ideas and many more Common Core State Standards (CCSSI 2010) through fun, student-driven activities.