This article explores teaching practices described in NCTM's Principles to Actions: Ensuring Mathematical Success for All. Student thinking, a learning cycle, and procedural fluency are discussed in this article, which is the second installment in the series. [For the first installment in this series see "Promoting a Conceptual Understanding…

This article explores three processes involved in attending to evidence of students' thinking, one of the Mathematics Teaching Practices found in "Principles to Actions: Ensuring Mathematical Success for All." These processes, explored during a classroom activity on proportional relationships, are discussed in this article, another…

Ever try to captivate students with real-world applications only to discover that they live in a very different world? Assigning an Extreme Word Problem activity to students alleviates this dilemma by placing the authorship of a problem squarely into the hands of learners. Rather than trying to be hip and finding word problems that resonate with…

"Principles to Actions: Ensuring Mathematical Success for All" (NCTM 2014) emphasizes eight teaching practices for effective mathematics teaching, one of which is to "use and connect multiple representations" (NCTM 2014, p. 24). An action that describes how teachers might promote this practice is to "allocate substantial…

Minecraft is an open world survival computer game that was originally created in Sweden in 2011 and later purchased by Microsoft® in 2014. It is among the most popular computer games with students of all ages because it gives players a sense of ownership and opportunities for creative exploration. The game has three unique features: (1) no clear…

This article describes a project in which students investigate the question: What dihedral angles between pairs of mirrors in a kaleidoscope result in perfectly symmetric images? The unit culminates with students building their own kaleidoscopes. This content aligns with parts of the Common Core's standards for fifth grade (classify…

If teachers have a deeper comprehension of their students' reading ability, it may lead to students' improved literacy and understanding of the subject. The account presented in this article of the author's growing interest in mathematical literacy specifically involves mathematical reading. This shift in interest began with a six-week…

Every day, 27,000 trees are used to make bathroom tissue. Americans use an average of 23.6 rolls per person per year, and more than 7 billion rolls of toilet paper are sold yearly in the United States alone. Perhaps the amount of bathroom tissue used can be reduced by changing the dimensions of the paper or the core. This brief article presents…

Long before the release of the Common Core State Standards (CCSSI 2010), the Mathematical Tug-of-War was engaging students in the type of reasoning and problem solving described by the Standards for Mathematical Practice (SMP). In this updated version of a Marilyn Burns task, students use algebraic reasoning to determine the outcome of a contest…

The lottery has rich potential for mathematical explorations. It serves as a real-world context to explore concepts of permutations, combinations, sample space, and probability in terms of making sense of the lottery games. The lottery offers additional possibilities in terms of scaling, data analysis, and spatial analysis. Finally, by readily…

In "Principles to Actions: Ensuring Mathematical Success for All," NCTM (2014) defines productive struggle as students delving "more deeply into understanding the mathematical structure of problems and relationships among mathematical ideas, instead of simply seeking correct solutions" (p. 48). Hiebert and Grouws (2007, p. 387)…

Making math more engaging for students is a challenge that every teacher faces on a daily basis. These authors write that they are constantly searching for rich problem-solving tasks that cover the necessary content, develop critical-thinking skills, and engage student interest. The Mystery Fraction activity provided here focuses on a key number…

Open-ended mathematical tasks provide great opportunities for students to engage in authentic mathematical practices, such as conjecturing, generalizing, and justifying. Supporting students in open-ended tasks can be challenging. Appropriate scaffolding of a task has been linked to more opportunities for student learning and better student…

This article discusses how teaching via problem solving helps enact the Mathematics Teaching Practices and supports students' learning and development of the Standards for Mathematical Practice. This approach involves selecting and implementing mathematical tasks that serve as vehicles for meeting the learning goals for the lesson. For the lesson…

Geometric transformations have long been topics of middle school mathematics. Generations of middle school students have learned to reflect, rotate, and translate geometric objects. Historically, though, the mathematics of "movement" might have been considered a departure from other more central middle-grades geometric content areas,…