Mathematics is a subject that seems to **split the world of learning** into two: the confident and the frightened. Many teachers and tutors discover children who are afraid of maths and who are convinced that the subject is too difficult for them to even have a go. Where did things go wrong for them?

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## Understanding numbers

Understanding why/how numbers work is **key to being able to compute and solve problems**, as is a watertight knowledge of times tables and the use of the four basic Maths operations.

“As a child I struggled with maths and numeracy and my maths teachers, but managed to get along by hard work. Now I love maths. What’s changed? I’ve discovered that numbers are logical, relational and not frightening any more as I’ve discovered, and finally understood, how they all work together. Now I make it my aim in tutoring to instill a love, ability and confidence in maths for all pupils.”– a private tutor.

The 11+/entrance examination in maths is a challenge to most pupils. It is usually set at a standard that is **more difficult than the Key Stage 2 exams** that pupils take towards the end of Year 6 but yet it is normally taken just as the child enters Year 6 – leaving a gap in both knowledge and ability. Some of the 11+ maths topics dip their toes into Key Stage 3 maths, such as the more difficult parts of ratio and algebra. Many pupils are therefore challenged to shift their maths skills up a whole year in order to be at an appropriately confident level for the 11+.

When commencing 11+/entrance exam preparation, plan a course of action with your child/pupil that will **demystify maths** and enable them to participate fully in the subject. This will start with ensuring that they know their times tables fluently, as you cannot rely on every school teaching up to 12 x 12 by the end of Year 5. Ideally children should know them all by the end of Year 4 so that any new maths skills can be taught from that stable platform. Ensure that the child/pupil can confidently use all the four maths operations (+ – x ÷) and choose the correct one(s) for questions in multi-step or problem-solving word format. Then, take a look at the place value of numbers and what each digit is worth up to 100,000,000 before you tackle the more demanding topics of fractions, decimals, percentages etc.

**Maths is a very important subject** and so it is examined at the 11+ stage. Here are some other thoughts about the subject:

*“Nick Gibb (Minister of State for Schools) said that learning times tables by heart should become a fundamental part of primary education for all pupils amid claims that a ‘lack of confidence with numbers’ was having a ‘profound impact’ on the economy.”* – Graeme Paton, Education Editor (The Telegraph, 10/7/12).

*“I’m a great believer in the importance of numeracy – and of children learning it early. Numbers need to be locked into young minds as soon as possible.”* – Joan Bakewell, broadcaster.

*“It is the excitement of maths that we have to convey. I can still remember, as a 17 year-old, how stimulating and rewarding it was to sit up late into the night trying to work out a proof, knowing there must be a solution, and finally getting there.”* – Susan Greenfield, scientist, writer and broadcaster.

**Many children struggle with maths because they don’t fully grasp the basic skills and methods**. This can lead to an inability to apply their knowledge to new mathematical challenges and can leave them feeling out of their depth. Have a plan of action to ensure that you cover all the basic skills required in order to build a solid foundation in maths.

It really is worthwhile checking the basic skills at home or in lessons and then revising or going on to learn all the main skill areas and maths topics that are tested in 11+/entrance exams – don’t take it for granted that your child/pupil can remember to do the simplest tasks. Primary schools differ enormously in what they teach, how well that has been taught and how they stretch the most able pupils.

Below is a suggested list of 30 maths topic areas that are examined at the 11+ stage:

### Maths Topics for 11+

- Place value and rounding
- Writing numbers as words & figures
- Standard addition, subtraction, division and multiplication
- Function/number machines
- Understanding the use of brackets (BODMAS)
- Inverse operations
- Factors: divisibility rules, & prime factors
- Highest common factors and lowest common multiples
- Number sequences & number patterns, ’find the rule’ in diagrams and numbers to the n’th degree
- Money & cost calculations
- Fractions
- Decimals
- Percentages
- Ratio, proportion & scale
- Algebra & equations – to include the use of formulae and expressions
- Special numbers: prime, even, odd, square numbers, square roots, cube numbers, triangular numbers, Roman numerals, negative numbers, consecutive numbers and indices
- Problem-solving, including mixed & several step problems
- Angles and lines: types, intersections, circles, bearings and route diagrams
- 2D shapes: kites, quadrilaterals, triangles, parallelograms, rhombuses etc.
- 3D shapes: cuboids, cylinders, square pyramids, prisms etc.
- Symmetry: line and rotational
- Nets of 3D shapes and open boxes
- Area and perimeter (regular shapes and compound/complex shapes) and the surface area of cuboids
- Measurement: Metric and imperial units of measurement and calculations for length, mass, volume and capacity
- Marking & interpreting scales: decimals, fractions and for mass
- Coordinates into the 4th quadrant; identifying coordinates, translation, rotation and reflection
- Mean, mode, median & range
- Probability
- Tables & data handling, organising and comparing information in diagrams, charts and graphsTo include pie charts, Venn diagrams, Carroll diagrams and speed, time & distance data
- Time: durations, 24hour clock, timetables

The **maths questions in COAsT (Chuckra Online Assessment Tool) are each tagged so that, with the BREAKDOWN tool, you are able to identify any weak areas** in the subject and choose more exercises for your student to practise and improve.

## How do you do that?

Can you remember how to do certain types of sums? It’s all very well working through a page of practice material when it has just been taught you but it can be a challenge to remember how to set out the sum and arrive at the correct answer if you haven’t used that particular method/algorithm for some time.

The LEARN section of this website has a great collection of videos covering each maths topic.

To help you remember quickly, and also as a revision aid, you could create your own set of index cards on postcards with the methods recorded on them and a worked example for each shown. A great alternative to this is a **handy book** called “Mrs J. Rules” which is a self-help book for maths with a warning on the cover that **“May make maths seem easy”**.

This useful little book shows in detail, using uncomplicated illustrations, how to set out a sum and answer it in easily understood steps. The index on the inside of the front and back covers makes it simple to look up any topic areas. The author includes up-to-date teaching methods. For example, there are 3 methods for long multiplication, including partitioning, the grid method and the column method.

The book is **available from the online shop**.

The skills learnt in maths are cumulative and in order to progress it is essential to practise so as to become more accurate and quicker. **Good mental maths skills are vital for building maths confidence**. Useful additional practice can take place out of lesson/tutorial times. How about: rehearshing the times tables at breakfast; telling the time and calculating durations whilst out and about (in a mixture of digital, 24 hour and analogue times); mentally calculating unit costs, totals and change given in the supermarket; play lots of games and puzzles that use maths; make some biscuits or something else yummy to practise measuring and have a daily problem-solving challenge. There are many more occassions when mental maths skills can be practised.

Encourage questions that will help you to explain in simply understood terms how to solve the question and don’t move on to a new concept until you are sure that your child/pupil has completely understood the maths skill you have just taught – the next topic may depend on this. It is always a good idea to check understanding by the use of mini “tests” or the application of any new skills to problem-solving questions.

Be positive about maths, keep it fun and ensure that you offer plenty of praise along the way. It has been identified that the biggest factor in whether a pupil went on to secondary school enjoying maths was whether they had been taught the subject by an enthusiastic primary teacher (source: National Audit Office “Mathematics Performance in Primary Schools: Getting the Best Results”). **You can become that “enthusiastic primary teacher” at home or in tutorials and it could make all the difference in the 11+.**

## More Useful Resources

- Tutorial videos on key maths topics
- Daily maths worksheets
- Key stage 2 maths objectives list – including links to worksheets for each topic
- Fun number games with numCards – part of the 11+ Playing Cards (3 pack)
- COAsT (Chuckra Online Assessement Tool) includes…
- Arithmetic based Educational Games (missingNumber, missingOperator, reArrangeIt)
- Individual Practice Questions by topic in Question Shuffle
- Numerical Reasoning Tests