The Number Line in the Common Core

Introduction

A long integer number line extends across my classroom wall.  Each student also has a number line of positive and negative numbers taped to his or her desk.  Visual representations are an important tool for students to make connections and relate mathematical concepts.  Despite having number line posters everywhere in the classroom, it has been one of the tools least used by my students.  One of the rare times where students actively utilize the number line is when they add integers.  Students have been taught to move to the right when adding a positive number and to the left when adding a negative number.  During the course of adding integers on the number line, students often count units out loud as they physically move their pencil to mark each moving unit on the number line.  When students are asked to find fractions or percent, however, they prefer using area models rather than the number line, but fractions and decimals exist on the number line, too!  I would like my students to see each number as representing a length, specifically a distance from zero, and to appreciate the number line in terms of measurement, rather than as a counting tool.

According to “Progressions for the Common Core State Standards in Mathematics,” written by the Common Core Standard Writing Team in 2013, decimals are a special sort of measurement on the number line, namely one that you get by starting with unit intervals, and partitioning into the equal subintervals, then partitioning each of these units in equal intervals and so on.  Each unit interval between two whole numbers is marked off into tenths, each of which is marked off into 10 hundredths, each of which is marked off into 10 thousandths, and so on, and over.  These finer and finer partitions constitute a sort of address system for numbers on the number line.¹  For example, 8.26 is, first, between whole numbers 8 and 9, then in the subinterval between 8.2 and 8.3, then exactly at 8.26, six tenths of the way between 8.2 and 8.3.²  Teaching decimal expansions in depth will allow students to make connections among different representations and to see how they are interconnected on the number line.  Decimals should not be treated as an isolated mathematical concept, but understood as a precise system to locate a number on the number line with its unique address.