Learning to Think Mathematically With Number Lines

Below are some excerpts from the book Learning to Think Mathematically With Number Lines by Jeff Frykholm

 

"One of the most overlooked tools of the elementary and middle school classroom is the number line. Typically displayed above the chalkboard right above the alphabet, the number line is often visible to children, though rarely used as effectively as it might be. "

 

"Recently, however, there has been a growing body of research to suggest the importance of the number line as a tool for helping children develop greater flexibility in mental arithmetic as they actively construct mathematical meaning, number sense, and understandings of number relationships."      

 

"The number line is an easy model to understand and has great advantages in helping students understand the relative magnitude and position of numbers, as well as to visualize operations. As a result, Dutch mathematicians in the 90ʼs were among the first in the world to return to the “empty number line,” giving this time-tested model a new identity as perhaps the most important construct within the realm of number and operation. Since that time, mathematics educators across the world have similarly turned to this excellent model with great results."  

The EMPTY NUMBER LINE is also often refereed to as the OPEN NUMBER LINE.  An easy and fun way to get started with this type of number line is to play the game "Guess My Number."   Decide on the magnitude of your number depending on your audience.  Write a number on a piece of paper and put it in an envelope with a ? on the front.   Tell students that they can ask YES or NO questions until they think they know the exact number.   At first it is very hard for them to not just want to say "Is your number 88?" Help by modeling questions like "Is your number larger than ___ ? "   "Is your number between ___ and ___?"  But before they start guessing, draw a line on the board and maybe place a beginning and ending number or maybe just an ending number.   Tell students your number is on this number line.  How many questions do they need to ask before they are able to guess your number?



SparkleBox is a UK resource with lots of free printables for all subject areas.   They have an excellent selection of number lines for all ages.   Below  are a few examples.