# manipulatives

## Book Review : Arrow Cards

Arrow cards are a simple manipulative to grasp place value or more generally the base-ten number-writing system that we use. Dr. Maria Montessori invented the static cards shown in Figure 1. These cards are used along with proportional material like static beads (unit = single bead, ten = 10 beads strung together forming a line, hundred = 10 tens strung together to form a square and thousand = 10 hundreds strung to form a cube) to gain a sense of numbers – the quantities they indicate and the numerals that represent them and how they are linked.

## Making Multiple Versions of Flats-Longs-Units to Teach Numbers and their Operations

2D base 10 blocks, popularly known as Flats-Longs-Units (FLU) are the most useful of all manipulatives for numbers. They can be extended to decimals through fractions as well as to algebra tiles.

These pre-grouped proportional manipulatives can be used to introduce numbers up to 999 and the four operations - addition, subtraction, multiplication and division. In fact, they can be used to understand the division algorithm to find the square root!

## Introduction to Algebra II - At Right Angles Pullout

This article is Part II of the series ‘Algebra – a language of patterns and designs.’ The approach is based on the perception of algebra as a generalisation of relationships.

In Part I, we introduced the ideas of variable, constant, term and expression via numerical patterns. Various operations (addition, subtraction, multiplication) involving terms and expressions were also studied.

## Introduction to Algebra I - At Right Angles Pullout

The late Shri P. K. Srinivasan had developed an approach to the teaching of algebra titled ‘Algebra – a language of patterns and designs’. I have used it for several years at the Class 6 level and found it to be very useful in making a smooth introduction to algebra, to the idea and usage of concepts such as variable and constant, to performing operations involving terms and expressions. This approach steadily progresses from studying numerical patterns to line and 2-D designs, finally leading to indices and identities.

## Pullout Section March 2014 - Teaching Multiplication

Here are some questions which arise while teaching Multiplication: Should children memorize the multiplication tables? Is it enough if one only teaches the procedure of multiplication? Perhaps answers to these questions can be found if we reflect on the importance given to the construction of knowledge. If we see that children must understand how facts and procedures are derived, and how concepts can be visualized, then our approach will be dictated by that understanding.

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