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A model to derive the volume formula height × base area for prisms to details on making and using the model.

There are two sets of algebraic identities usually taught at the school level - (i) the quadratic ones and (ii) the cubic ones. Both can be modeled in a low-cost way. Nets of solids can be used for the cubic identities. Layouts of both are included along with links to uses.

Algebra tiles are a powerful manipulatives to understand algebraic expressions in single variable up to degree 2. They prevent some misconceptions and can be used all the way till middle-term factorization. They can be easily made from cardboard boxes.

Exponentiation with natural number bases can be model as branching of trees. These branching modules can be easily made by straws by cutting and stapling them. They provide an experiential understanding of exponential growth! They can be used to understand various rules of exponents.

We present in this issue narratives of adult language acquisition. These are of interest in themselves, of course, but of interest also with regard to the teaching of language(s) in schools. Language teaching in school is often bogged down by the weight of scholarly tradition, literary history, and linguistic pride. It suffers, above all, from co-option into a system of syllabus, teaching, and examination, geared to competitive mark-gathering.

Fractions can be modeled in various ways. The model with the square as the whole turned out to be the most useful. It can be used for everything except reducing a fraction to its lowest form.

Process with diagrams and suggested activities are included.


Ten-frames are relatively new to India. They are very useful at the beginning for learning the single-digit numbers. They also facilitate automatization of addition facts with single digit numbers. In addition, they can provide a lot of conceptual clarity wrt odd-even.

Three versions are included:

Ganitmala is a manipulative version of number line. It is a proportional material that has properties of both groupable and pre-grouped models. Jodo Gyan ( introduced them in India.

It can be used for introducing whole numbers and all four operations - addition, subtraction, multiplication and division. It can also be used for the division algorithm to find the HCF!

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!

Nets of solids can be used to make 3D shapes from posters or chart papers. Stage-wise list of solids and how to make them along with diagrams are included.


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