The fifth-grade curriculum presents many opportunities to use students' prior mathematical knowledge as a way to bridge new and more difficult mathematical ideas. In this article, the authors document an area tiling task given to fifth-grade students to connect aspects of area measurement covered in earlier grades to grade-level standards such as:…

The author wants her students to see any new mathematics--fractions, negative numbers, algebra--as logical extensions of what they already know. This article describes two students' efforts to make sense of their conflicting interpretations of 1/2 × -6, both of which were compelling and logical to them. It describes how discussion, constructing…

In general, units coordination refers to the relationships that students can maintain between various units when working within a numerical situation. It is critical that middle school students learn to coordinate three levels of units not only because of their importance in understanding fractions but also because of their implications for…

Demonstrates how an investigation of measurement and representative numbers can engage all levels of student ability. Asks students to learn about representative numbers in order to answer a question they find intriguing. (YDS)

Presents activities that can be helpful in establishing a conceptual basis for dividing rational numbers. Some activities involve metric units while others are appropriate for small-group work with calculators. (AIM)

Presents an activity that integrates music, dance, and mathematics. (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)

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)

Recommends conducting interviews with students in order to grasp their understanding of fractions and provides interview questions. Presents results of a study using those interview questions and concludes student responses fell into three main categories: (1) described a mental image of an object; (2) drew a model of the fraction using a circle…

Presents a game along with several variations involving three players using three-digit numbers to help students improve their number sense on decimal numbers and fractions. (ASK)

Examines the use of a ratio table for developing students' conceptual understanding of rational number. The ratio table is an alternative to cross-multiplication and can utilize both additive and multiplicative strategies. It organizes numbers and keeps track of operations and results, which aids the teacher in assessment. (MLB)