On the surface, the number line may seem like a basic tool with obvious applications. However, using a number line is not always intuitive for students. Students may not recognize significant features such as the size of the unit, how units are represented by iterated equal lengths, or that the accumulation of iterated units is a magnitude of…

In this article, we direct attention to what becomes critical in teaching activities for toddlers (1-3-year-olds) to learn the meaning of numbers. One activity we thoroughly explore is interactive book reading, based on previous research indicating positive learning outcomes from this type of mathematical activity, as it has shown to…

This article describes how teachers address issues and tensions that students meet in learning division of fractions. First, students must make sense of division of fractions on their own by working individually and in small groups, using concrete or pictorial representations, inventing their own processes, and presenting and justifying their…

Fluency with basic number facts is vital for students' progress in mathematics. Not only does it contribute to students' facility with mental computation and algorithms, but an understanding of numbers and their properties builds a foundation for future mathematical work including algebra. There are many activities that can help students…

Prime numbers are often described as the "building blocks" of natural numbers. This article shows how the author and his students took this idea literally by using prime factorizations to build numbers with blocks. In this activity, students explore many concepts of number theory, including the relationship between greatest common factors and…

Students around the world have difficulties in learning about fractions. In many countries, the average student never gains a conceptual knowledge of fractions. This research guide provides suggestions for teachers and administrators looking to improve fraction instruction in their classrooms or schools. The recommendations are based on a…

Number sense has been recognised as central to young children's development of mathematics for a number of decades. A student with a "good" sense of number normally has a thorough understanding of relationships among numbers and operations--being able flexibly to partition and combine numbers in convenient ways to allow appropriate…

Problems are discussed in which addition facts are presented using words instead of numbers. The letters are then replaced by numbers that will make the addition problems correct. (MP)

The author cites research from students' misconceptions of decimal notation that indicates that many students treat decimals as another whole number to the right of the decimal point. This "whole number thinking" leads some students to believe, in the context of comparing decimals, that "longer is larger" (for example, 0.45 is…

Mathematics activities and materials for teaching and reinforcing number concepts are presented. The activities, which rely primarily on number cards, are divided into the following sections: (1) sets less than ten; (2) the teen numbers; (3) sets and numerals to 100; (4) numeration; and (5) words that represent numbers (e.g., "one=1").…

An ancient Chinese method of calculating ages indirectly can provide interesting practice with number concepts. (SD)

Three worksheets explore perfect, deficient, abundant, and amicable numbers by attaching mystical connotations to numbers and their divisors. (JT)

These worksheets will provide students with experiences in identifying largest and smallest single-digit numbers, in writing names for single-digit numbers, in tests of divisibility, and in writing number sentences. (MP)

Provides instructions for 23 mathematics learning activities for young children in early childhood settings. Includes activities for ordering, numeral recognition, counting, number sense and numeration, and a list of suggested music, movement, and book ideas for each area. (KB)

A method of identification of pigs used by farmers is described as an application of a base three numeration system. (MP)