Counting using positive and negative numbers

In a nutshell

Counting forwards and backwards using both positive and negative numbers is easy when you use a number line. Doing so creates a sequence. 

Counting using positive and negative numbers

To count forwards and backwards through zero with negative numbers, using a number line, use the following steps:

• To count forwards, move up the number line in the increasing direction.
  
• To count backwards, move down the number line in the decreasing direction.

Example 1

Count forwards five from $$-3$$.

Find your starting point: $$-3$$.

Count up three in ones until you reach zero. 

Then, continue up a further two, taking you through zero into the positive numbers until you reach $$\underline{2}$$.

$$\begin{array}{cccccccccccccc}&&&&&+1&&+1&&+1&&+1&&+1 \\& &&&&\curvearrowright&&\curvearrowright &&\curvearrowright &&\curvearrowright &&\curvearrowright&&\\-5&&-4&&\underline{-3}&&-2&&-1&&\bold0&&1&&\underline2 &&3&&4&&5\\|&&|&&|&&|&&|&&|&&|&&|&&|&&|&&| \\ \hline\end{array}$$​​​

Example 2

Count backwards in threes from $$6$$​.

Find your starting point: $$6$$.

Count down in threes until you reach zero. 

Continue through zero, counting backwards three each time. 

The numbers $$6, 3, 0, -3$$ and $$-6$$ form a sequence that is decreasing by three.

$$\begin{array}{cccccccccccccc}&-3&&-3&&-3&&-3&& \\& \curvearrowleft&&\curvearrowleft &&\curvearrowleft &&\curvearrowleft &&\\\underline{-6}&&-3&&\bold0&&3&&\underline6& \\|&&|&&|&&|&&|& \\ \hline\end{array}$$​​​

There is no end to this counting. The negative numbers, just like the positive numbers, continue on forever.