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…

Young children spend a much greater amount of time on practicing multiplication facts compared to understanding the concept of multiplication. When students have long-term, foundational concepts rather than a series of fragmented algorithms or facts, they are more likely to understand and generalize the mathematics. Using generalized models that…

Many teachers are using the Five Practices model to guide them in orchestrating whole-class mathematics discussions that focus on understanding: (1) anticipate an array of possible student-generated solution strategies to a mathematical task before implementing the lesson; (2) monitor students' work as they grapple with the task; (3) select a…

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…

Modeling requires that people develop representations or procedures to address particular problem situations (Lesh et al. 2000). Mathematical modeling is used to describe essential characteristics of a phenomenon or a situation that one intends to study in the real world through building mathematical objects. This article describes how fifth-grade…

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…

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…

Describes several activities of the Data and Chance program involving third and fourth graders. Students use real-life situations to investigate probability. (MKR)

Presents examples of direct modeling and invented strategies of students for problem solving. Teachers are encouraged to capitalize on children's abilities to use these invented strategies and in time guide the student toward a standard, more efficient strategy. (AIM)

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)

Describes the development of mathematical thinking as children construct a mini mall. Students learn the importance of cooperation with their peers as they explore mathematical concepts such as one-to-one correspondence, classification, intersection of sets, coin identification and values, addition, subtraction, and problem solving. (Author/NB)

Suggests an elementary school activity and questions to promote five types of mathematical thinking including modeling, logical analysis, inference, optimization, and abstraction. Discusses evaluating activities for mathematical reasoning opportunities. (ASK)