Mathematical modeling is an important and accessible process for elementary school students because it allows them to use mathematics to engage with the world and consider if and when to use it to help them reason about a situation. It fosters productive struggle and twenty-first-century skills that will aid them throughout their lifetime.

The goal in this article is to support teachers in better understanding what it means to model with mathematics by focusing on three key decision-making processes: Simplification, Relationship Mapping, and Situation Analysis. The authors use the Theme Park task to help teachers develop a vision of how students engage in these three decision-making…

Tape diagrams, also known as strip diagrams, bar models, fraction strips, or length models, are linear representations that can be used to effectively model quantitative relationships during problem solving. Tape diagrams are a powerful model recommended by the Common Core, but they are relatively new to teachers and students in the United States.…

The goals of problem-solving activities in the elementary grades often include making sense of story problems, developing a range of strategies, and reaching accurate solutions. These are important mathematical aims, but they do not fully address the demands of modeling with mathematics as described in the fourth of the Common Core's eight…

Engaging students in studies about conservation and sustainability can support their understanding of making environmental conscious decisions to conserve Earth. This article aims to contribute these efforts and direct students' attention to how they can use mathematics to make environmental decisions. Contributors to iSTEM: Integrating…

To develop second-grade students' confidence and ease, this author presents examples of learning tasks (Number of the Day, Word Problem Solving, and Modeling New Mathematical Ideas) that align with Common Core State Standards for Mathematics and that build mathematical fluency to promote students' creative expression of mathematical…

Early elementary school students are expected to solve twelve distinct types of word problems. A math researcher and two teachers pose a structure for thinking about one problem type that has not been studied as closely as the other eleven. In this article, the authors share some of their discoveries with regard to the variety of…

In 2000, the "National Council of Teachers of Mathematics" recommended that Algebra Standards, "instructional programs from prekindergarten through grade 12 should enable all students to use mathematical models to represent and understand quantitative relationships." In this article, the authors suggest the "Balance"…

In this article, the author shares how his fourth-grade students' creative thinking concerning a long-standing research problem stimulated changes in his instructional strategies. He begins by providing an example which illustrates that the standard tool of democracy, the plurality vote, suffers serious deficiencies: "The winner can be the…

A new mathematical tool, known as Engage, Explore, Explain (EEE) model, was developed that was simple for teachers to use, could guide them as they planned exploratory experiences, and was useful to teach mathematics for understanding. The EEE model provides a lesson structure for teachers to use with almost any mathematics topic and can easily be…

Children live in a highly sophisticated world composed of interlocking complex systems. An appreciation and understanding of such systems is critical for making effective decisions about everyone's lives as individuals and as community members. This article addresses one approach to introducing children of all achievement levels to introductory…

Discusses the concept of three-dimensional perspective. Presents some assessment tasks to help develop perspective and describes student responses. (Author/NB)

Presents a variety of activities in which 4th grade students investigate prisms and pyramids by building models from folded paper and drinking straws. (Author/NB)

Proposes a system to help at-risk students develop problem solving skills. Provides some teaching methods and evaluation ideas. (KHR)

Mathematical modeling is explored as both problem posing and problem solving from two perspectives, that of the child and the teacher. Mathematical modeling provides rich learning experiences for elementary school children and their teachers.