Mobile puzzles are pictorial representations of systems of equations; each beam that balances two sets of objects (representing variables as unknown “weights”) represents an equation. Children […]

The number line is not just a school object. It is as much a mathematical idea as functions. Unlike the Number Line Hotel, hundreds charts, Cuisenaire rods, and base ten blocks, the number line is not just a pedagogical aid used only to help children learn; mathematicians refer to it, too.

This page describes one silent teaching activity that serves, at the superficial level, to give students useful practice with multiplication facts, but that also builds deeper […]

Addition and subtraction of whole numbers can be developed together, systematically, starting with recognition of quantities and combinations of quantities, the 10-based structure of the language […]

KenKen(R) puzzles were not built into Think Math! but are a wonderful material to make regularly available to children. These puzzles give excellent arithmetic practice while […]

Area formulas Students who have the informal notion that area is the “amount of 2-D ‘stuff'” contained inside a region can invent for themselves most of […]

Number tricks are fun for children. The fun, all by itself, is valuable, but is not mathematics. But understanding how the trick works is good mathematical, often algebraic, learning.

Informally: When you multiply an integer (a “whole” number, positive, negative or zero) times itself, the resulting product is called a square number, or a perfect […]