This article discusses how teaching via problem solving helps enact the Mathematics Teaching Practices and supports students' learning and development of the Standards for Mathematical Practice. This approach involves selecting and implementing mathematical tasks that serve as vehicles for meeting the learning goals for the lesson. For the lesson…

Rational number interpretations can include part-whole, measure, ratio, quotient, and operator. These are all subconstructs of partitioning (Barnett-Clarke et al. 2010; Behr et al. 1980; Clarke, Roche, and Mitchell 2008; Flores, Samson, and Yanik 2006). Each of these subconstructs uses different cognitive skills (Driscoll 1984), so it is important…

The authors introduce an educational video game (application, or "app"), "CandyFactory Educational Game," designed to promote students' development of partitive understanding of fractions while demonstrating the critical need to promote that development. The app includes essential game features of immediate feedback,…

This article describes the instructional process of helping students visualize irrational numbers. Students learn to create a spiral, called "the wheel of Theodorus," which demonstrates irrational and rational lengths. Examples of student work help the reader appreciate the delightful possibilities of this project. (Contains 4 figures.)

Presents an historical lesson on the development of numbers and the special characteristics of zero. Includes activity sheets designed to help students focus their attention on the value of numerals including zero, place value, and operation with zero. (KHR)

Features a question that focuses on the use of cryptology to teach modes. (ASK)

Describes a game in which students strengthen their number sense by using mental mathematics to find and check factors and multiples of numbers up to 100. (ASK)

Explores the study of ordered pairs to allow students to demonstrate their own creativity, apply previously learned computer skills, evaluate their own work, and draw connections to other mathematical strands. Using a spreadsheet, students construct a drawing composed of connected ordered pairs, the inverse, and the negative of the drawing. (ASK)

Presents mathematics questions to analyze what advertisements are saying mathematically. (ASK)

Describes a number line activity based on students' individual timelines to help students understand the concepts of integers and rational numbers. Middle school students and their parents construct a number line using positive and negative rational numbers to represent dates of events before and after the student's birth. (KHR)

Describes an activity in which students investigate the symmetry of factor sets of composite numbers using the TI-83 graphing calculator. This activity allows students to observe patterns, make predictions, and verify their accuracy. (ASK)

Presents an activity in which students must arrange five fractions represented by dominoes in ascending order and justify their reasons for the ordering. Representing common fractions with dominoes helps identify students' misconceptions about fractions. (ASK)

Presents two problems with multiple approaches concerning the one hundredth of something. Describes student attempts at solving these nonroutine problems using a variety of strategies. (ASK)

Describes a mathematics activity using square pads of notepaper and sticky notes to do simple paper folding in order to increase students' understanding of fractions. (ASK)

Discusses problems related to teaching decimals and fractions and converting between these two representations. Provides problems and activities that teachers can use in their classrooms to overcome student difficulties related to these subjects. (ASK)