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…

In this article, the authors engage middle-grades students in a series of tasks to develop the mathematical idea of equal versus equivalent, culminating in a gerrymandering task with social, political, economic, and educational implications. The primary mathematical goals of this exploration were to involve students in solving real-world problems…

Building sets, video games, and scatterplots may seem unrelated, but when they are combined into a problem-based learning (PBL) lesson, these elements join to create a unique learning experience. PBL lessons drive instruction by focusing learning and activities around a central challenge or question while providing a relevant, captivating, and…

This article explores teaching practices described in NCTM's Principles to Actions: Ensuring Mathematical Success for All. Common factors, common multiples, strip diagrams, and double number lines are discussed in this, the third installment in the series. [For the second installment in this series see "Connecting the Dots: Building…

This brief "Math for Real" article introduces Ohanna, a seventh grader who lives in New York City and regularly takes the bus to get around the city. Ohanna pays $2.50 per bus ride when using her MetroCard. She earns a 5% bonus when she refills the card with a minimum of $5.00. For example, if she adds $10.00 on her MetroCard, her…

Mr. Perez and Mrs. Peterson co-teach a ninth-grade algebra class. Perez and Peterson's class includes four students with individualized education programs (IEPs). In response to legislation, such as the No Child Left Behind (NCLB) Act (2001) and the Individuals with Disabilities Education Improvement Act (2006), an increasing number of students…

Teachers put a great deal of energy into searching for ways to engage each and every student. Some of these efforts fail. Others look promising one day, only to become less effective as the novelty wears off. Teachers want their students to feel ownership of their learning. They also believes that students engage more when learning mathematics…

Reasoning and problem solving are both critical acts in mathematics learning. The author has met many teachers who tell her they would love to highlight them more but feel they cannot because of the pressures of content coverage, pacing guides, and district tests. In this article, she describes a teaching intervention that highlighted problem…

With the adoption of the Common Core State Standards for Mathematics (CCSSM), many teachers are changing their classroom structure from teacher-directed to student-centered. When the author began designing and using problem-based tasks she saw a drastic improvement in student engagement and problem-solving skills. The author describes the Cake…

In education, "dialogue protocols," or "protocols," are structured guidelines that were developed to promote meaningful and efficient communication and learning. They are "vehicles for building the skills--and culture-- necessary for collaborative work. The authors share protocols that were found to transform practices…

Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…

Many teachers have designed lessons for students who will be working in groups to discuss and solve a problem. After investing time in constructing an interesting problem, creating strategically designed groups, and introducing the problem carefully, teachers may be left wondering how to help students collaborate to make sense of mathematical…

Many current and future teachers have little experience with modeling and how to integrate it into their teaching. However, with the introduction of the Common Core State Standards for Mathematics (CCSSM) and its emphasis on mathematical modeling in all grades (CCSSI 2010), this integration has become paramount. Therefore, middle-grades teachers…

The article uses vignettes to illustrate a small group of of grade 5 students who worked on different types of temperature problems (Wessman-Enzinger and Tobias 2015). The Common Core State Standards for Mathematics (CCSSM) recommends including contexts, such as temperature, paired with the introduction to integers in grade 6 and integer…

Statistics standards found in the Common Core (CCSSI 2010) and other state standards require considerable instructional time and focus for students to develop the depth and breadth of understanding necessary. In this article, the authors offer an approach to teaching a statistics unit that combines student choice with authentic and sustained…