There have been calls for at least 30 years in American education for a return to basics in mathematics instruction. The problem lies in defining what is basic. Mathematics is more than arithmetic. It is a fabric of ideas, relationships, principles and procedures. But all too often the emphasis in classroom instruction is on static facts and procedures. The most basic thing in mathematics education is to make sense of such concepts as number, distance, angle, quantity, proportion, part-whole, rotation, location, speed, time, size, area, volume, what must be, what might be, and what cannot be. These concepts are all basic to making sense of the world by explaining, justifying, predicting, comparing, conjecturing, representing, inventing, classifying, ordering and inferring. In this article, the authors offer some activities in-service providers can encourage their teachers to try in group problem-solving situations with one another, and then use with children. They challenge the problem-solver to make sense. When teachers challenge children with problems such as these, they cause them to construct, extend or revise their mental networks. And that is what should be basic in mathematics instruction. (Contains 6 online resources.)