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 article begins by describing a class scenario in which a teacher gives her students the L problem (Watanabe 2008), which involves finding the area of a composite figure. Her students inappropriately extend the area formula for rectangles (A = L x W) to composite figures by multiplying all given dimensions. After class, the teacher concluded…

"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…

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…

The vision of mathematics learning advocated by the National Council of Teachers of Mathematics (NCTM) for twenty-five years (1989, 1991, 2000, 2014) positions students as active learners, constructing their knowledge of mathematics through exploration, discussion, and reflection. World-class standards put into place by states and provinces over…

Problem solving is one of the main competences we seek to teach students at school for use in their future lives. However, when dealing with mathematical problems, teachers encounter a wide variety of difficulties. To foster students' problem-solving skills, the authors developed "strategy keys." Strategy keys can serve as material to…

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…

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…

Inquiry-based instruction is a student-centered approach to teaching that focuses on active learning (Barron and Darling-Hammond 2008) in which students engage with "tasks that promote reasoning and problem solving" (NCTM 2014). Specifically, such tasks encourage a variety of solution strategies and stimulate use of the NCTM Process…

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…

This article demonstrates how to consider differentiating instruction for diverse learners while maintaining the cognitive demand of a mathematics task. The authors present scenarios involving hypothetical cases of students in inclusive classrooms who engaged in productive struggle within the differentiated task. The authors specifically focus on…

The Puppy Love problem asked fifth and sixth grade students to use their prior knowledge of measures of central tendency to determine a data set when given the mean, mode, median, and range of the set. The problem discussed in this article is a task with a higher level of cognitive demand because it requires that students (1) explore and…

Teachers across the nation are taking up the call to prepare students for new standards and assessments that require written explanations on a variety of math tasks. But what does it really mean to "explain your answer," and how do educators begin supporting students to write in a genre that is new to both students and teachers? This…

It is difficult but important for mathematics teachers to help students see themselves as capable mathematics learners, that is, to help each student develop a positive mathematics identity. A student's mathematics identity is a powerful influence on his or her engagement and participation in mathematics. Students act in ways that are consistent…

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)…