Getting the right answers in maths is only half the problem. Understanding why what you're doing works is the part that often stumps students and teachers alike. The essential guide for mathematics teachers and those training to teach, "Yes, but Why?" answers all your questions, and sheds light on the hidden connections between…

For students to develop adequate conceptual understanding about fractions, they require experiences that afford them opportunities to think flexibly about multiple interpretations of fractions. This article presents a sequence of lessons designed to offer such experiences for students in Years 3 and Year 4. The lessons adopt a challenging tasks…

In this article, the author describes how to help develop students' conceptual understanding of fractions through the tactical card-based game Nearest to One. Nearest to One promotes number-sense based strategies for comparing fractions, such as benchmarking (e.g., Is the fraction greater or less than one-half?) and building to the next whole,…

The traditional technique for converting repeating decimals to common fractions can be found in nearly every algebra textbook that has been published, as well as in many precalculus texts. However, students generally encounter repeating decimal numerals earlier than high school when they study rational numbers in prealgebra classes. Therefore, how…

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…

By the time they reach middle school, all students have been taught to add fractions. However, not all have "learned" to add fractions. The common mistake in adding fractions is to report that a/b + c/d is equal to (a + c)/(b + d). It is certainly necessary to correct this mistake when a student makes it. However, this occasion also…

Many fraction activities rely on the use of area models for developing partitioning skills. These models, however, are limited in their ability to assist students to visualise a fraction of an object when the whole changes. This article describes a fraction modelling activity that requires the transfer of water from one container to another. The…

Presents an activity on fractions and explains how students obtain different fractions having different patterns when they are represented by their decimal expansions. (ASK)

Finding a fractional number equal to an infinite decimal is solved by two usual methods. Then a third method is discussed that allows students to avoid having to confront the idea of an attained infinity of symbols. (MNS)

An efficient division algorithm is developed, using a computer program, to convert any positive fraction to its decimal representation. The computer program listing is included. (MNS)

Presents three games using calculators, specifically Texas Instruments' Math Explorer, as an aid to teaching fractions and decimals. Briefly discusses the development by the Texas Education Agency of staff development modules for teachers to learn about calculators, mathematics, and the incorporation of calculators into the teaching of…

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)

These materials are designed to be used as a tool to in-service school personnel who may wish to improve achievement levels on the mathematics objectives as measured by the Michigan Education Assessment Program (MEAP). Four areas of mathematics instruction (fractions, decimals, ratio and proportion, and percent) have been addressed in these…

Work with recurring decimals provides pupils with an opportunity for exploration and examination of a wide variety of mathematical ideas and strategies. Examples of work done by one group of pupils who were presented with an opportunity to explore such decimals is featured. (MP)

The use of money to teach mathematical topics such as fractions, percents, decimals, and nondecimal numeration is encouraged. (MP)