Operations & Algebraic Thinking

January 9, 2020

Puzzles: Mobile Puzzles

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 […]
December 3, 2019

The Number Line – subtraction, and measurement

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.
December 3, 2019

Difference of Squares

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 […]
December 3, 2019

Addition and Subtraction

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 […]
November 21, 2019

Hundreds Chart and the Number Line Hotel

Hundreds chart A hundreds chart in which “higher numbers” are higher, and “the 30s” are all on the same row. Unlike the number line, which is […]
November 21, 2019


This article deals with the meaning of multiplication, how it is introduced in Think Math!, and the early acquisition of facts.
November 21, 2019

Puzzles: KenKen Puzzles

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 […]
November 21, 2019

Guess My Rule

How to Play Guess My Rule games are games in which one person thinks up and gives examples of some “rule,” and the player(s) try to […]
November 21, 2019

Puzzles: Who Am I Puzzles

Who-Am-I? puzzles give clues about some mathematical object — usually a number or a shape — and you are to figure out what the object is. […]
November 21, 2019

Measurement: Discovering formulas for area

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 […]
November 20, 2019

Algebraic Thinking

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.
November 20, 2019

Puzzles: Introducing KenKen Puzzles

This page focuses on a way to introduce KenKen puzzles so that students see, focus on, and learn the logic, not just guessing. These puzzles give […]
November 4, 2019

Square Number

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 […]