The activities in Communicating About Mathematics build on the strands begun in The Importance of Patterns, while focusing on the written and oral communication of students’ mathematical ideas.
One of the underlying principles of IMP is that doing mathematics involves offering ideas for analysis and critique as well as analyzing and critiquing the ideas offered by others. The process of convincing others of the validity of solutions and strategies, and of understanding and analyzing the solutions and strategies of others, is what mathematicians do when they present and publish proofs of theorems, solutions to problems, and new techniques for solving problems.
In Communicating About Mathematics, students will present their solutions to the first POW and begin work on the second one. They will explore a model for integer arithmetic and then write a primer on this model for others. This work will extend their understanding of arithmetic with integers and order of operations, building blocks of algebraic thinking. Students will also solve several problems that require careful reading of a mathematical situation and the creation and communication of solutions to an open-ended task. They will use a powerful problem-solving strategy called working backward.