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 60
Throughout the Fraction Bars program, students are talking and writing about the concepts of fractions. In the Readiness steps before fraction notation, students are asked to verbalize or write statements describing what happens as they use Fraction Bars to model fraction 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 182
Problem solving occurs in many ways in the Fraction Bars 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 games are followed by specific problem solving questions. Additional problem solving opportunities require the use of such strategies as guessing and checking, making an organized list, and drawing a diagram.
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 Fraction Bars Teacher's Guide Table of Contents shows the many steps that contain instruction in estimation. Opportunities for estimation also are found on the Fraction Bars 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 Fraction Bars program are available on the worksheets in the Teacher Resource Package.
