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Counting using positive and negative numbers

Counting using positive and negative numbers

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Counting using positive and negative numbers

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Tutor: Alice

Summary

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 −3-3−3.


Find your starting point: −3-3−3.


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 2‾\underline{2} 2​.


+1+1+1+1+1↷↷↷↷↷−5−4−3‾−2−1012‾345∣∣∣∣∣∣∣∣∣∣∣\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}−5∣​​−4∣​​−3​∣​+1↷​−2∣​+1↷​−1∣​+1↷​0∣​+1↷​1∣​+1↷​2​∣​​3∣​​4∣​​5∣​​​​​


Example 2

Count backwards in threes from 666​.


Find your starting point: 666.


Count down in threes until you reach zero. 


Continue through zero, counting backwards three each time. 


The numbers 6,3,0,−36, 3, 0, -36,3,0,−3 and −6-6−6 form a sequence that is decreasing by three.


−3−3−3−3↶↶↶↶−6‾−3036‾∣∣∣∣∣\begin{array}{cccccccccccccc}&-3&&-3&&-3&&-3&& \\& \curvearrowleft&&\curvearrowleft &&\curvearrowleft &&\curvearrowleft &&\\\underline{-6}&&-3&&\bold0&&3&&\underline6& \\|&&|&&|&&|&&|& \\ \hline\end{array}−6​∣​−3↶​−3∣​−3↶​0∣​−3↶​3∣​−3↶​6​∣​​​​​​


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


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Negative numbers

Unit 1

Negative numbers

Counting backwards through zero: Negative numbers

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Counting backwards through zero: Negative numbers

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Counting using positive and negative numbers

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Counting using positive and negative numbers

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FAQs - Frequently Asked Questions

How do I count forwards and backwards using positive and negative numbers?

Counting forwards and backwards through zero with negative numbers using a number line is exactly the same as just using positive numbers. - To count forwards, move up the number line in the increasing direction. - To count backwards, move down the number line in the decreasing direction.

What do I use to count forwards and backwards?

To count forwards and backwards using both positive and negative numbers, use a number line.

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