Jumping the Line

Of the four models shown below, which one doesn’t belong?

Number Line

So far in our number journey we have been counting and identifying numbers in terms of the objects they represent—4 counters, 4 beads, 4 tile, or 4 pennies. We’ve used dots, counters, number racks, and number frames to visualize a specific number of objects. In this chapter, we look at another tool to explore numbers—the number line. 

The number line is a flexible tool for counting and visualizing numbers in terms of amounts and distance. The uniform space (the interval) between two successive tick marks represents 1 unit. This unit can represent 1 tile, 1 centimeter, 1 mile, or even 1 potato.

We use the number line to count and visualize numbers of units in various ways. For instance we can represent the number 3 using three single-unit jumps,

1 three-unit jump,

or a 1-unit jump next to a 2-unit jump.

Use the number line below to show two jumps that together show the number 7. Select the 1-unit jumps, and then move and stretch them to show your solution.

Here’s a couple possibilities: 3 and 4 , 5 and 2. Can you think of any other two-jump combinations?

Open and Closed Number Lines

Because number lines use units of length between tick marks to represent numbers, we can change the size of the unit to deepen our understanding of quantity. The position of just two tick marks determines the size of the unit and where other tick marks and numbers will fall on the number line. Try placing your own number marks on the number line below.

With fewer than two numbers on a number line, the unit remains undetermined; the number line at that point is considered to be “open.” What number could the question mark be?

With two or more numbers on the line, the unit is defined and the number line is now considered “closed.” Now what number do you think the question mark should be?

Number lines help us see numbers in sequence beginning with zero, but what about larger numbers? One can see that 184 is 4 more than 180 and 6 less than 190. But does this portion of the number line give you a sense of how large 184 is?  

To see the full representation of 184, we may want to see all the units of space from 0 to 184. It’s possible to do, but with single units, displaying that distance would require a very long number line or very small units. In our next chapter, we revisit groupings of 10 as a more efficient way to represent larger numbers.