The purpose of this guide is to provide strategies and materials for developing and implementing lessons for students who need intensive instruction in the area of place value, numeracy, and counting. Resource room teachers, math interventionists, and others working with struggling students may find this guide helpful. Within college- and…

Without a doubt, fractions prove to be a stumbling block for many children. Researchers have suggested a variety of explanations for why this is the case. The introduction of symbolization and operations before the development of conceptual understanding of fractions, a lack of understanding of the role of the numerator and denominator, and an…

Do your students need more opportunities do develop number sense and reasoning? Are you looking to get your students energized and talking about mathematics? Have you wondered how practical, replicable, and engaging activities would complement your mathematics instruction? This guide answers the question "What could I do differently?" by…

This article introduces a fun, hands-on activity for comparing hand water displacements.

Linear algebra students are typically introduced to the problem of how to convert from one coordinate system to another in a very abstract way. Often, two bases for a given vector space are provided, and students are taught how to determine a transition matrix to be used for changing coordinates. If students are successful in memorizing this…

In the author's experience with this activity, students struggle with the idea of representativeness in probability. Therefore, this student misconception is part of the classroom discussion about the activities in this lesson. Representativeness is related to the (incorrect) idea that outcomes that seem more random are more likely to happen. This…

Stephen Tucker presents a fractions game that addresses a range of fraction concepts including equivalence and computation. The REFractions game also improves students' fluency with representing, comparing and adding fractions.

The Common Core State Standards for Mathematics (CCSSI 2010) expect second grade students to "fluently add and subtract within 20 using mental strategies" (2.OA.B.2). Most children begin with number word sequences and counting approximations and then develop greater skill with counting. But do all teachers really understand how this…

Middle school students' mathematical understanding benefits from connecting mathematics to other content areas in the curriculum. This month's activity explores the issue of the scarcity of freshwater, a natural resource (activity sheets are included). This activity concentrates on the critical areas mentioned in the Common Core State…

"Classroom Discussions: Seeing Math Discourse in Action, Grades K-6" provides preservice and inservice instructors, coaches and facilitators with real, classroom-based video examples that illustrate the principles and practices covered in the authors' best-selling book, "Classroom Discussions: Using Math Talk to Help Students Learn, Grade K-6,…

This book identifies and examines two big ideas and related essential understandings for teaching multiplication and division in grades 3-5. Big Idea 1 captures the notion that multiplication is usefully defined as a scalar operation. Problem situations modeled by multiplication have an element that represents the scalar and an element that…

The goal of this practice guide is to offer educators specific, evidence-based recommendations that address the challenge of teaching early math to children ages 3 to 6. The guide provides practical, clear information on critical topics related to teaching early math and is based on the best available evidence as judged by the authors. The guide…

This book focuses on essential knowledge for teachers about rational numbers. It is organized around four big ideas, supported by multiple smaller, interconnected ideas--essential understandings. Taking teachers beyond a simple introduction to rational numbers, the book will broaden and deepen their mathematical understanding of one of the most…

"The Zeroing in on Number and Operations" series, which aligns with the Common Core State Standards and the NCTM Standards on Focal Points, features easy-to-use tools for teaching key concepts in number and operations and for addressing common misconceptions. Sharing the insights they've gained through decades of mathematics teaching and research,…

The new Common Core State Standards for Mathematics have been formulated to provide students with instruction that will help them acquire a thorough knowledge of math at their grade level, which will in turn enable them to move on to higher mathematics with competence and confidence. "Hands-on Activities for Teaching the Common Core Math…