The activities in this section are not meant to be a complete teaching method for these topics, rather they are examples of the kinds of activities instructors can make up to go with whatever text they are using, or whatever other lessons they are teaching. They are arranged here according to the subject matter of the activities. In each content area, there are group activities and activities using manipulatives or visual representations of some kind. Each section has an introduction with suggestions for using the activities in the section.
There are two kinds of activities here: in the first, students use manipulatives to model or demonstrate for themselves some of the ideas inherent in the place value system, and in the second, students work in groups at the board. The ideas in one set practice and reinforce the ideas in the other set; there is a lot of practice and review involved in each, and a measured but quite quick movement towards more complex mathematical ideas.
I have used both these sets of activities successfully for many years, but would refer the reader to the discussions of student resistance and of group work in Chapters 2 and 5 to ensure a secure underpinning for these activities.
The activities on the following pages require students to use math tools (manipulatives) to demonstrate their understanding of the place value system. Either commercial or home-made tools may be used. Each page might take about half an hour, and the same kinds of questions appear on every page, although they are more complex in later pages than in the earlier ones. Students may use the math tools for help with any of the questions, but the checkmark symbol
next to a question means that the answer must be demonstrated with the tools. As students work on the activities, the instructor can circulate and sign off demonstrations as students get them ready, and mark the answers to questions not requiring demonstrations. Encourage students to compare answers with one another, and, in the case of a disagreement, to use the tools to figure out who is right.