Place value underpins much of what people do in number. In this article, the author describes some simple tasks that may be used to assess students' understanding of place value. This set of tasks, the Six Tasks of Place Value (SToPV), takes five minutes to administer and can give direct insight into a student's understanding of the number system…

In the September 2010 issue of "Mathematics Teaching," Tom O'Brien offered practical advice about how to teach addition, subtraction, multiplication, and division and contrasted his point of view with that of H.H. Wu. In this article, the author revisits Tom's examples, drawing on his methodology while, hopefully, simplifying it and giving it…

How do composing and decomposing numbers connect with the properties of addition? Focus on the ideas that you need to thoroughly understand in order to teach with confidence. The mathematical content of this book focuses on essential knowledge for teachers about numbers and number systems. It is organized around one big idea and supported by…

This is the first volume of a series produced by the State Education Department of the University of the State of New York. Mathematics objectives and sample items included were originally developed by four local school districts and are not intended to be official or comprehensive, but an aid to teachers in constructing curricula and making…

Modular arithmetic is used to find the frequency of Friday 13th's in any year. (MM)

Developed by a committee of the National Council of Teachers of Mathematics, this publication is designed to help teachers provide interesting and worthwhile learning opportunities for slow learners in grades five through eight. It employs a variety of teaching strategies, many not commonly known or practiced, which are particularly helpful with…

Describes number strips, arrow diagrams, and grids for number operations. Provides diagrams for the activity materials. (YP)

Describes a pattern which emerged from an examination of the digits of the squares of numbers. Provides eight examples having the pattern at the units or tens digit of the number. (YP)

Discusses a number series made from the multiplication of numbers to digits. Presents a number series for diverse multiplication numbers. (YP)

Discusses mental computation and how and when it should be taught. Describes seven properties of mental algorithms. (YP)

This volume was prepared by the School Mathematics Study Group (SMSG) to help elementary teachers develop a sufficient subject matter competence in the mathematics of the elementary school program. Background material for related SMSG materials for grades four through eight are included. Chapters in the book are: (1) What is Mathematics; (2)…

This workbook for elementary teachers presents basic definitions and examples in the areas of set theory, numeration systems, fundamental operations and geometry. Text organization does not use programming frames. Answers to examples are included in a separate section. (DT)

Beginning with peg manipulation the author sets up a different multiplication system and set of primes. (JM)

Discusses a counting system and number operations. Suggests six distinct areas in a "number" subject: one-to-one correspondences; simple counting process; complicated counting process; addition and multiplication; algorithms for the operations; and the decimal system. (YP)