Is anything more refreshing than going for a nice, long swim? The math scenarios presented in this article will take the reader back to hot summer days and remind the reader what a cool dip in the water feels like. Solving these problems is enjoyable and encourages the solver to think of the many ways that math is all around--even in the middle of…

In a classroom teaching experiment, we explored fifth graders' ability to identify relationships in and between two patterns--what we may refer to as functional relationships. Conventional functions curricula are dominated by defining relationships between two patterns via a rule, describing how to find y or f(x) given a particular value for x…

How do cross-bracing, geometry, and base isolation help buildings withstand earthquakes? These important structural design features involve fundamental geometry that elementary school students can readily model and understand. The problem activity, Designing an Earthquake-Resistant Building, was undertaken by several classes of sixth- grade…

After teaching the concept of division with remainders for many years, Vanessa Battreal, Vanessa Brewster, and Juli Dixon noticed that interpreting remainders in contextualized problems is particularly challenging for elementary school students. To effectively interpret remainders, students must attend to problem context and consider carefully…

Teachers who participated in a recent summer institute focused on implementing the Common Core State Standards for Mathematics (CCSSM). Throughout the summer institute, teachers had many in-depth discussions about the meanings they attributed to the Standards for Mathematical Practice (SMPs). In this article, the authors share some of the…

Project-based learning (PBL) is an effective approach to STEM education because it allows students to experience scientific inquiry by using their knowledge and skills in science, technology, engineering, and mathematics (STEM) to solve realistic problems. PBL consists of four components: (1) posing and comprehending a driving question; (2)…

In this article, the authors discuss a special type of multiplication-and-division-of-fractions problem that elementary school teachers can use to promote children's understanding of fractional quantities and their relationships. These problems are accessible to students working at different levels of fraction understanding, and they can be solved…

The National Council of Teachers of Mathematics' (NCTM's) "Principles and Standards for School Mathematics" (2000) outlines fi ve Process Standards that are essential for developing deep understanding of mathematics: (1) Problem Solving; (2) Reasoning and Proof; (3) Communication; (4) Connections; and (5) Representation. The Common Core…

In this article, Sarah Currier, a math specialist at Elizabeth Hall International School in Minnesota, describes how she used origami in a deliberate manner to teach content. She shares how she uses paper folding to teach mathematical concepts, reinforce vocabulary, and as a problem-solving model. She also offers ideas for using origami in other…

Statistical literacy is essential in everyone's personal lives as consumers, citizens, and professionals. To make informed life and professional decisions, students are required to read, understand, and interpret vast amounts of information, much of which is quantitative. To develop statistical literacy so students are able to make sense of…

In this article, the authors illustrates techniques for integrating diverse learners in shared mathematical contexts while providing differentiated support or challenge, as necessary. The techniques described were developed for a curriculum project entitled Learning Mathematics through Representations (LMR). A premise of LMR is that students'…

In this article, authors Jordan T. Hede and Jonathan D. Bostic present a classroom activity that challenges upper elementary students' understanding of area beyond a memorized formula and explores the meaning behind students using A = l × w to solve rectangular area problems. This activity will deepen students' understanding of the area…

This is a story about teachers engaging in mathematics teacher leadership. The focus is on the teachers' learning, and the purpose is to illuminate the process. The setting is a semester-long graduate class called Teacher Leadership in Mathematics Education, and the characters are elementary and middle school teachers. Those in this group…

As partners in a professional development project, the authors jumped at the opportunity to use a real-life problem to engage elementary and middle school teachers in a one-day exploration of the concept of area. "Length times width"--a common response to the question, "What is area?"--is a rote formulaic expression that applies only to certain…