This guide contains six sections which offer suggested sequential steps for teaching addition, subtraction, multiplication, division, fraction concepts and algorithms, and decimal fractions. Based on the manipulative approach, the guide offers activities and teaching methods which give students many opportunities to work with models. This approach gives the students, who are in the concrete stage of development as defined by Piaget, help with the discovery and understanding of the mathematical concepts. To help the teacher guide the students through the lessons, a two-column format is used in which sample questions and teaching suggestions are listed to the right of the activities. An introductory page for each section describes the approach used and presents background information on children's learning and on the mathematical operation or concept involved. Des Moines (Iowa) Mathematics Performance Objective numbers are listed to the left of appropriate lessons. (DC)