Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

A robust understanding of place value is essential. Using a problem-based approach set within meaningful contexts, students' attention may be drawn to the multiplicative structure of place value. By using quotitive division problems through a concrete-representational-abstract lesson structure, this study showed a powerful strengthening of Year 3…

With the adoption of the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010), many concepts related to area are covered in third grade: (1) Recognizing area as an attribute of a plane figure; (2) Understanding that a square with a side length of one is a unit square; (3) Measuring area by tiling figures and counting the squares it…

Students with Autism Spectrum Disorders (ASD) have unique educational needs. The concrete representational abstract (CRA) instructional sequence has been shown effective in teaching students with mathematical difficulties. The purpose of this study was to examine the effects of the CRA sequence in teaching students with ASD. A multiple baseline…

When solving mathematical problems, many students know the procedure to get to the answer but cannot explain why they are doing it in that way. According to Skemp (1976) these students have instrumental understanding but not relational understanding of the problem. They have accepted the rules to arriving at the answer without questioning or…

This study is about prospective secondary mathematics teachers' understanding and sense making of representational quantities generated by algebra tiles, the quantitative units (linear vs. areal) inherent in the nature of these quantities, and the quantitative addition and multiplication operations--referent preserving versus referent…

The use of two different colored beans or chips to represent positive and negative charges is discussed as a method of demonstrating operations with integers. (MP)

Described are two methods of calculating developed by the Dutch WISKOBAS Project: addition and subtraction with a loop abacus and multiplication using a grid model. (MP)

A "flipping" clown figure can be used on a number line to help students conceptualize operations using negative numbers. (SJL)

Discusses the use and construction of "fact fans," fun and easy-to-make manipulatives that provide elementary school students with the opportunity to explore mathematics operations being studied in the classroom and to practice addition, subtraction, multiplication, and division facts. (BB)

This research focused on students' learning of mathematical rules with reasoning. A small group of students (age 11-12 yrs) was observed closely by the first author as she taught them fraction rules. The area of focus was fractions and activities were designed pertaining to the four rules of fractions: addition, subtraction, multiplication, and…

This guide contains six sections which offer suggested sequential steps for teaching addition, subtraction, multiplication, division, fraction concepts and algorithms, and decimal fractions. Based on the manipulative approach, the guide offers activities and teaching methods which give students many opportunities to work with models. This approach…

This guide is a collection of ideas for mathematics activities which were assembled and tested by primary teachers. The activities supplement the teaching of basic numeracy and include topics such as algorithms, pyramids, magic squares, multiples, and number values. The guide is organized into four sections: (1) addition and subtraction; (2)…

Activities and games which use dominoes to reinforce basic arithmetic skills are presented. Instructions and materials are provided for the activities and games, most of which involve addition and subtraction. Other skill areas which are covered include recognition and matching of domino patterns, multiplication, and division. A seven-item list of…

This two-volume teacher's guide is to be used with a first-semester, third-grade mathematics program. The program is in large part the outgrowth of involvement with children and was influenced by information gathered in an extended pilot project conducted nationwide during 1975-79. The manner of presentation and the pedagogical ideas and tools are…