# Representing Minus

Henri Picciotto

• In designing manipulatives for algebra, the most challenging decisions revolve around the representation of minus.
• Does it reinforce the misconception that -xis negative?
• Does it preserve the geometric integrity of the area model?
• Does it support integer arithmetic? equation solving?
• The Lab Gear design for minus is a way to give the best possible answer to those questions, at the cost of a slightly tricky model involving two representations. See: Algebra Manipulatives: Comparison and History.
• Note that work with the 3D blocks is not compatible with the representations of minus. At any one time, you should be doing one or the other — not both.