Colouring-in shapes to understand fractions is a powerful way of learning

By far the best way for a child to learn fractions (and then decimals and percentages) is to actually draw then by colouring in shapes

Once a child has spent some DRAWING fractions they will have the confidence and ability to make the leap into numbers without the need to see shapes.

In an online tutorial I start with simple shapes and fractions – for example to colour in a half or a quarter of a rectangle broken down into four squares.

Once a child is used to this, they can SEE how to add 1/4 and 3/8.

Once a child has moved on from drawing fractions visually they can always go back to this method if they need to for more advanced geometry.

In an online tutorial a child has time to solve ten or more fractions by drawing them out, with which I will be assisting.

It can take as little as one or two sessions for the child to “click” how fractions work. You can almost hear it!

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Building confidence during online tutorials

A fantastic by-product of the online tutorial is the child gaining confidence to ask valuable questions as they learn

I have noticed over the years that when a child first starts being tutored, they are very reserved and often hesitant about either saying they don’t understand, or asking any further questions.

This is understandable and is a challenge for the online tutor.

This generally improves over time, but one excellent way to bring this forward asap is to get a child to ask ME a questions.

For example, I might ask a child to work out a percentage or a fraction division relating to money. After I think they’ve got the hang of it I ask them to ask me a question.

On the iPad they might write something like 1/4 divided by 3/7. I tell them in advance that I might get it wrong (on purpose hopefully) and they have to check my working out and let me know how many marks I deserve.

This is a great way to up the dialog and to make sure they can answer their own question. It is often a bit of fun and very engaging for the child.

Sometimes I like to make an obvious error to make sure they’re fully engaged.

The by-product of this is increased questioning from the child which anecdotally also transfers into the classroom which I see as a huge win for the child.

Bespoke Online Maths Tuition

Bespoke online maths tuition can significantly improve your child’s ability by focusing on the topics he or she needs to focus on the most

At school a maths teacher has to work with a lot of children across a broad range of abilities. This works in general, but if a child is struggling with one particular topic – e.g. fractions and percentages, the teacher may not be able to give the child all the help they need to master the topic.

This is were online maths tuition is so valuable.

The Tutor Dragon can focus on the one topic your child has been struggling with to make sure they master that topic.

The outcome is three-fold;

Firstly, your child will be much more confident in the classroom. It cannot be overstated how important this psychological aspect of learning is.

Secondly, by overcoming one topic, it raises your child’s numeracy in general. Learning how to work out percentages involves a lot of multiplication, division, addition and subtraction as well as relating maths to the real world.

Thirdly, higher scores in the exams. A high or low score in a few questions relating to fractions for example can make the difference between an A and a B, or a B and a C for example.

A Free Introductory Session with the Tutor Dragon

For a free introductory session please contact us using the form below.

Reminder: You’ll need an iPad or touch-screen and a stylus – free Tutor Dragon notepad and Dragon stylus when you sign up for your first paid tutorial.

Children learn more by doing than listening

During a tutorial a child learns a lot because they’re listening, learning and most importantly DOING…

In a classroom a child will listen, hopefully learn and then during homework recall.

In the classroom it is not possible to each each child to come up to the front and show whether or not they’ve understood how to work out perimeter and area of an irregular shape. Only when the teacher marks their homework will any lack of understanding become apparent.

In an online tutorial however, a child will be called upon continually to show they’ve understood and to recall this by solving a similar but different problem.

The aim of every online tutorial is for the child to be able to understand a topic more deeply and to use recall and experience to solve similar but different problems.

Fractions Tutorial Work Best Online

Learning fractions addition and subtraction visually is a great way to secure fractions numeracy

Fractions lend themselves to be taught online very well, enabling both tutor and tutee to colour in boxes, rub them out, add them up and simplify the answers.

Below is a screenshot from a recent tutorial I had with a Y3 child who has just begun to learn about fractions.

It is great to see a child suddenly understand that four eighths is the same as a half.

Often a couple of fractions tutorials BEFORE a child starts to learn fractions at school gives them a HUGE advantage in understanding the basics which will enable them to not only keep up with the class, but often to lead the class and the homework.

Online maths tutorials for children moving to an English Speaking country

If your family is moving to an English speaking country we can help with online maths tutorials which will help with numeracy and English fluency.


The Tutor Dragon has experience tutoring children where English is not their first language.

The maths tutorials are mostly numerical using a shared whiteboard with the tutor and the child talking via WhatsApp (or similar application such as Skype of KakaoTalk).

Before or After Moving to an English Speaking Country

Whether you are about to, or have already moved to an English speaking country, the Tutor Dragon can help your child with mathematical numeracy and English fluency using the vocabulary your child will be using at school and with their homework.

The sessions are all online and you will ideally need an iPad or device with a touch-screen and a stylus.


Please contact the Tutor Dragon for a free introductory session.

Year 3 Multiplication Wheels

Click here for some simple Multiplication Wheels for Year 3 with answer sheet

Why are Multiplication Wheels useful?

Multiplication Wheels are useful because they help relate multiplying numbers with progressively adding numbers – e.g. 5, 10, 15, 20 – meaning 4×5=20.

They are also useful because they look more interesting than simply writing out tables of multiplications.

Tutor Dragon Addition A4 Poster to Print at Home

Click on the image for a PDF of the Tutor Dragon Addition A4 sheet to print and stick up on your child’s wall

Why is this addition PDF useful?

This simple A4 PDF does not follow the normal pattern of 1×1=1, 2×1=2 etc.

Instead it uses a randomised approach which is a significantly better way for a child to improve numeracy.

Going from 3×8=24 to 9×6=54 works better than 5×6=30 and 6×6=36.

A child should be able to recite the times table in their heads faster and faster as they approach the age of 11 in preparedness to go to Secondary School.

Online maths tutorials start in Hong Kong

Very pleased to announce we’re starting online maths tutorials with clients in Hong Kong.

Sessions are run out of London starting at 6AM London time which is currently 1PM in Hong Kong.

We accept payment in HKD via a PayPal link.

Please get in contact if you are interested in booking a free introductory session, which will help check the technology works for you.

As a reminder, you need a touch-screen device like an iPad or laptop with a touch screen, and a stylus which is easier to use than trying to do maths with your finger.

What should a child do between each tutorial?

Between each tutorial a child should practice what has been taught in the tutorial and try working on a new topic to be covered in the next tutorial.

A tutor should give two types of homework for a child to do between tutorial sessions. The first is a series of questions to make sure the child has secured what has been taught in the last tutorial session. This gives the tutor a good idea if that topic (e.g. percentages) needs any further work.

Secondly, the tutor can cover new work in the tutorial and give an example say on how to convert a percentage to a fraction, then give the child some questions covering that new work.

This gives the chid an opportunity to try out a little bit of learning over some new questions and prepares them for the next tutorial.

Only a few questions are required – I suggest a maximum of 5 to tests the previous subject has been secured, and 5 to test new territory.

Please contact me if you have any questions or are interested in an initial free session.