# Special Features

## Special Features of the Decimal Squares Program

The students in this photo are playing the Thousandths Game, one of over 30 decimal games in the Decimal Squares Teacher’s Guide. Each player in turn selects a square and records its decimal in a place value table. This game requires strategy, communication, and reasoning to satisfy the conditions for winning.

Photo courtesy of Herb Moyer
COMMUNICATION AND REASONING

Communication is an essential part of mathematics and mathematics education. It is a way of sharing ideas and clarifying understanding. When students are challenged to think and reason about mathematics and to communicate the results of their thinking to others orally or in writing, they learn to be clear and convincing.
……………………………………………………………………………NCTM Standards 2000, page 60Throughout the Decimal Squares program, students are talking and writing about the concepts of decimals. In the Readiness steps before decimal notation, students are asked to verbalize or write statements describing what happens as they use Decimal Squares to model decimal concepts. In further steps and in the Writing in Mathematics and Problem Solving assignments, students continue to explain their reasoning through written and verbal description.PROBLEM SOLVING

Problem Solving is the cornerstone of school mathematics. … A problem-centered approach to teaching mathematics uses interesting and well-selected problems to launch mathematical lessons and engage students. In this way, new ideas, techniques, and mathematical relationships emerge and become the focus of discussion
…………………………………………………………………………..NCTM Standards 2000, page 182Problem solving occurs in many ways in the Decimal Squares program. Specific Problem Solving questions are contained in EXPANDING THE CONCEPTS in many of the lessons. Student activities with concrete materials provide numerous opportunities for discovery and discussion of concepts and generalizations. The program is designed for students to work in small cooperative groups where they solve problems, look for relationships, and list observations. Many of the lessons have Problem Solving challenges based on questions from the activity mats.

ESTIMATION

Estimation serves as an important companion to computation. It provides a tool for judging the reasonableness of calculator, mental, and paper-and-pencil computations.
…………………………………………………………………………..NCTM Standards 2000, page 155

The Decimal Squares Teacher’s Guide Table of Contents shows the many steps that contain instruction in estimation. Opportunities for estimation also are found on the Decimal Squares worksheets.

APPLICATIONS

Problem solving is central to inquiry and application and should be interwoven throughout the mathematics curriculum to provide a context for learning and applying mathematical ideas.
……………………………………………………………………………NCTM Standards 2000, page 256

Word problem applications for every concept taught in the Decimal Squares program are available on the worksheets in the Teacher Resource Package.