The five keys for All Kids Can Learn Arithmetic are taught in ways that communicate to children and are inseparable from the lessons used to teach them.
• “Equals” as “balanced” or “is the same as” is taught with a math balance where students acquire a literal feel for both sides of a number sentence or algebraic equation being equal or “balanced.”
• The operations of addition, subtraction, multiplication, and division are taught as actions using four characters who depict the actions in everyday activities: Motley Crab Adder who “just” combines, like puts groceries in a shopping basket; Tractor subtracter who “just” separates, like sweeps the floor; Sir Crab Multiplier who combines “neatly” (by 2s, 3s, 4s, ...), like makes a beaded belt; and Collider Divider who separates “neatly” (into 2s, 3s, 4s, ...), like picks teams.
• The number facts are taught as problems to be figured out: “If you know it, write it down. If you don’t, or aren’t sure, figure it out. NO GUESSING!” The counting skills for figuring them out are taught with songs, stories, and games.
• Making fair trades is taught with base 2, base 3, and base 10 blocks called “lands” where, in Two Land (base 2), for example, two identical blocks make the next bigger block and may be traded for it or vice versa. Trading with blocks is then extended to trading with colored counters. The goal is to learn when and how to make an exchange in any land as required in daily living with time, money, and measurement as well as in base 10 arithmetic.
• Fractions are taught with real fractions: fraction “pies” or “cakes”—large circular regions cut into halves, thirds, fourths, fifths, sixths, eighths, ninths, tenths, twelfths, fifteenths, and sixteenths.