The Number Line

Look at a ruler. Along its edge are numbers - 0, 1, 2, 3 - with exactly the same space between each one and the next. You have used this idea all your life without giving it a name. What happens if we take the ruler away and keep only the numbers in their places?

Numbers in a row

Draw a straight line. Put a mark near the left end and call it 0. Then put more marks to the right, all the same distance apart, and number them 1, 2, 3, 4, and so on. This is a number line.

The arrow at the end means the line goes on. In the One More, Forever lesson we saw that the counting numbers never run out; on the number line, that means the marks never stop. We just can't draw all of them.

Notice where the line starts: at 0, not at 1, like a ruler. Zero, from the Zero lesson, gets its own place, one step to the left of 1.

Every number has a place

On the number line:

• each number sits in one place, and each place has one number;
• the steps between neighbours are always the same size: 3 to 4 is as long as 9 to 10;
• the further right you go, the bigger the numbers get.

That last rule is the most useful. A number line turns "how big" into "how far along". Seven is further along than four, so seven is bigger.

Counting is hopping

Counting can be seen on the number line too. Start at 0. Each time you count one more, hop one step to the right. After five hops you land on 5.

Where you land is the number you counted to. In the next module we will use these hops for adding and taking away.

Room between the marks

There is space between the marks: between 2 and 3, for example. Is anything there? With the counting numbers alone, no. But a ruler has smaller marks between its numbers, and in the module on parts of a whole we will find numbers to put in those gaps too.

Try it at home

1. Draw a number line from 0 to 10 on a sheet of paper. Use a ruler to make every step 1 centimetre.
2. Put a button on 0. Hop it 3 steps, then 4 more. Where does it land? Answer below.
3. Find a number line in your home: on a ruler, a tape measure, a thermometer, the dial of an oven.

Answer: 7.

Words to know

• number line - a straight line with the numbers marked on it in order, at equal steps, with bigger numbers further to the right

Big idea

A number line gives every number its own place, in order, at equal steps. Bigger numbers are further to the right, and counting is hopping along it one step at a time.