Home

Maths

Number and place value

Counting using positive and negative numbers

Counting using positive and negative numbers

Videos

Summary

Exercises

Select Lesson

Algebra

Simple formulae

Linear number sequences

Missing number problems

Solving equations with two unknowns

Ratio and proportion

Solving ratio problems

Calculating percentages of amounts

Scale factor problems

Unequal sharing

Statistics

Pie charts

Line graphs

Discrete and continuous data

Mean, median, mode and range

Geometry - position and direction

Coordinate polygons

Drawing and reflecting shapes on the coordinate grid

Drawing and translating shapes on the coordinate grid

Describing positions in the four quadrants

Geometry - properties of shapes

2D shapes: Types and properties

3D shapes: Types and properties

Comparing and classifying shapes

3D shape nets

Geometric shapes: Types and properties

Parts of a circle

Drawing and measuring angles with a protractor

Angles around a point and on a straight line

Finding missing angles

Measurement

Calculate and convert between units of measure

Perimeter of composite rectilinear shapes

Area of irregular shapes

Area of parallelograms and triangles

Formulae for the area and volume of shapes

Calculating the volume of cubes and cuboids

Fractions

Finding fractions of amounts

Mixed numbers and improper fractions

Comparing and ordering fractions greater than 1

Simplifying fractions

Add and subtract fractions: Different denominators

Multiplying pairs of proper fractions

Dividing fractions by whole numbers

Equivalent fractions, decimals and percentages

Multiplying decimals by whole numbers

Dividing and expressing the answer as a decimal

Multiplication and division

Times tables up to 12 x 12

Multiplying a 4-digit number by a 1 or 2-digit number

Dividing numbers up to 4 digits by a 2-digit number

Mental maths strategies

Common factors and multiples

Order of operations: BIDMAS

Using estimation to check answers

Addition and subtraction

Adding numbers using mental maths

Using column addition to add numbers

Subtracting numbers using mental maths

Using column subtraction to subtract numbers

Multi-step problems with addition and subtraction

Inverse operations to check calculations

Number and place value

Numbers to 10,000,000

Place value: Four-digit numbers

Representing numbers in different ways

Rounding any number up to 1,000,000

Counting using positive and negative numbers

Counting in powers of 10

Negative numbers

Explainer Video

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.


Read more

Learn with Basics

Learn the basics with theory units and practise what you learned with exercise sets!
Length:
Negative numbers

Unit 1

Negative numbers

Counting backwards through zero: Negative numbers

Unit 2

Counting backwards through zero: Negative numbers

Jump Ahead

Score 80% to jump directly to the final unit.

Optional

This is the current lesson and goal (target) of the path

Counting using positive and negative numbers

Unit 3

Counting using positive and negative numbers

Final Test

Test reviewing all units to claim a reward planet.

Create an account to complete the exercises

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.

©2020 - 2024 evulpo AG

Beta