# 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.*