Here’s the first of a series of Key Stage Two maths workbooks with which I was involved.

There are 630 long addition questions in this book which start easy and get progressively more difficult.

The workbook is A4, 56 pages containing questions and answers.

Research has shown that practice and repetition are key to securing numeracy (see website for details regarding repetition as a key step in learning and recall).

In this book the maths starts with two digit numbers and ends with numbers in the thousands. Suitable for ages 8 to 12 – from Primary School to the first year of Secondary School if further help is required with long addition:

Page 1 Example: 65 + 7

Page 15 Example: 164 + 187

Page 27 Example: 942 + 726

Page 42 Example: 8,916 + 6,945

I highly recommend a child doing two pages of this book every day especially during Easter, Summer and Christmas breaks to help secure numeracy while on long breaks from school.

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.

## 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.

Maths tutorials are not cheap so you have to make the most of every session. Do this by planning ahead based on your child’s current school work.

It is tempting to “hand over” control of tutorial sessions entirely to a tutor. This is a mistake. Ideally the tutorial sessions should be in-sync or just ahead of what your child is learning at school.

If the tutorials are a week or so ahead of the curriculum schedule then when your child is taught a subject, say fractions, your tutor should already have covered the basics. This means the child has a much better chance of understanding everything in class and being able to do their homework exhibiting a good level of understanding.

The advantage of this approach is that the child is always “primed” for the lessons at school.

As I have mentioned in other posts, it is also useful to use tutorial time to review any topics or specific homework questions which the child found difficult. This helps secure the understanding which in turn better prepares the child for SAT’s and entrance exams.

## What is a good length of time for a maths tutorial?

Most tutorials are an hour, but we should question why this is, considering most group lessons in a school environment are 50 minutes.

A tutorial session should not be taken up with the tutor sitting there marking work while the child attempts new questions from a workbook – all of that should be done between sessions. Beware of tutors who do this.

When a tutorial session is one-to-one less than 50 minutes should be enough to address a topic and for the child to have learned something, understood it and applied it to a question or two which they haven’t seen before.

We find that 30 minutes is a good amount of time to address a specific issue – for example a child not understanding how to multiply and divide fractions and then simplify the answer.

For more general tutorial sessions such as reviewing percentage in general, forty five minutes works well.

Remember that it’s up to you and your child to bring to the tutorial session what you want to get out of it. Specifically, email your tutor ahead of time saying “Tomorrow we’d like to focus on angles and types of triangles because John doesn’t understand how to do his homework”. The more specific you can be, the more your child will get out of their tutorial sessions.

## Fractions (including decimals and percentages) online tuition

Fractions (including decimals and percentages) can be difficult subjects to secure in the Maths Curriculum. A child should be able to:

Use common factors to simplify fractions (including when fractions are greater than one, e.g. 11/5)

Add, subtract, multiply and divide fractions with different denominators and mixed numbers

Associate a fraction with division and calculate decimal equivalents (years 5 & 6)

Identify the value of each digit up to three decimal places and divide numbers by 10, 100 and 1000 (years 5 & 6)

Decode fractions, decimals and percentages from plain English text to solve multi-step problems (years 5 & 6)

## Addition and Subtraction Online Maths Tuition

Addition and Subtraction is a fundamental subject in the Maths Curriculum. A child should be able to:

Add and subtract who numbers (with more than 4 digits in years 5 & 6)

Use columnar methods for long addition & subtraction

Sole addition & subtraction problems with multiple steps working out which operators to use

Addition & subtraction including negative numbers (in years 5 & 6)

Decoding numbers and operators from plain English and whether to add or subtract the numbers

Perform mental calculations with mixed operators and large numbers (years 5 & 6)