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## Functions and the Volume of Vases

While filling vases with water and observing volume and height relationships, students learn the fundamentals of functions.

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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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## CCSSM Challenge: Graphing Ratio and Proportion

A Cherry Syrup problem can build links between ratio and graphing.

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## Quick Reads: Using Technology to Build a Pen for Browser

### a good idea in a small package

Making mathematics meaningful is a challenge that all math teachers endeavor to meet. As math teachers, we spend countless hours crafting problems that will energize students and help them connect mathematical topics to their everyday lives. Being successful in our efforts requires that we allow students to explore ideas before we provide explanations and demands that we ask questions to promote a depth of thinking and reasoning that would not occur without such probing (Marshall and Horton 2009).

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## High-Impact Solutions for Struggling Mathematics Students

To maximize classroom time spent on practice and concept attainment, a teaching team discarded traditional warm-up activities and homework assignments.

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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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## Informing Practice: Mathematical Practices That Promote Twenty-First Century Skills

Skills that students will need in the twenty-first century, such as financial literacy, are explored in this classroom-centered research article.

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## Visualizing Equations Using Color Tiles

Algebraic reasoning is often promoted through an analysis of and generalizations about patterns that appear in mathematics, in nature, or in everyday situations (Driscoll 1999; Kieran 2006; Lee 1996). In accordance with this tendency, the Common Core (CCSSI 2010) emphasizes finding patterns and expressing such regularity in repeated reasoning as an important mathematical practice. NCTM (2000) also recommends that students participate in patterning activities by asking them to describe numeric and geometric patterns; generalize patterns to predict what comes next while providing a rationale for their predictions; and represent patterns in multiple ways, including drawings, tables, symbols, and graphs.