# The Craft of Word Problems

## CONTENTS OF CURRICULUM UNIT 04.05.05

## The Number Line as a Mathematical Tool

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## Introduction

This unit is designed to be taught to fifth, sixth and seventh grade students. The fifth grade curriculum for mathematics requires students to develop an understanding of fractions, and to interpret percent as part of 100 and as a means of comparing quantities of different sizes or changing sizes (Content Standard 1.4). In sixth grade students continue to develop an understanding of fractions, decimals and percent. Problem solving and mathematical reasoning (Content Standard 5.0) is the central focus and goal of teaching mathematics to children. It is critical that students understand the purpose and reason for the mathematical operations which they learn in the middle school years. To apply the concepts of fractions and percents to word problems is the goal of this unit.

While in a workshop to develop vertical teaming for the mathematics department in the city of New Haven, I had an opportunity to confer with high school teachers. I asked, “What do we need to do in the middle school to prepare students for their math program?” Aside from the obvious of having students memorize their multiplication tables they said, “Students need to place fractions on a number line.” In another conversation with a high school math teacher he shared with me that he felt strongly that we lost students in math because students never quite understand the relationship of fractions to percents. In addition, the professor of this seminar during early discussions, shared with us that the problem faced by many students is that they memorize formulas, and arithmetic operations with little understanding as to why and how to apply in real situations.

The objectives in this unit address the above mentioned concerns; the relationship of fractions and percents by solving word problems with fractions, and placing fractions on a number line. Students will use the number line as a mathematical tool. The intent is for students to see clearly the relationship of fractions to percents, and solve word problems which require answers in fractions and percents. Concepts to be covered will include the alignment of fractions on a number line. A series of number lines will be developed of equal length but divided in different fraction lengths. Lessons will answer why the fraction line separating the numerator form the denominator considered a division line.

Strategy for teaching this unit will be presented in three sections. In the first section students will use a line divided into fourths beginning with from 0 through 2, and another line divided into fifths from 0 through 2, and a third line will be divided into 20 from 0 through 2. A series of word problems will be presented that can be answered using this series of number lines. The objective of this first section is for students to add and subtract fractions using this number line. Word problems will be presented that involve fractions, improper fractions and mixed numbers.

The second section will require students to solve problems using a number line with percents. The third section will combine percents and fractions in a in word problems. The objective is for students to further their understanding of fractions and the relationship of fractions to percents.