Article published 9th March 2009

## Preparing your child for 11+ (or 13+) Maths

I was taught things like ‘cross multiply’ and to multiply by 10 put a zero on the end– will these help my child?

We answer your questions and explain why tricks of the trade are not always the best tools...

Find out: what's essential, what's not; what constitutes a hiccup, rather than a hurdle and when to rally rather than retreat!

### My child has maths assessments this year, should I enlist the help of a tutor?

Before you phone the nearest tutoring agency, sign-up for on-line maths or rush to buy the latest self-help guide, it's worth doing a bit of homework. Start by exploring the questions below, that way, even if you do enlist the help of a tutor, you will be better prepared and know the sorts of things to test them on!

- What does my child need to know?

It depends on the age and stage of your child, where in the UK you are based and whether your child is educated in the state or independent sector. - The maths syllabus for common scholarship is based on the maths syllabi's for Common Entrance at 13+ and 11+. They, in turn, are based on the National Curriculum for maths – phew!

The 11+ syllabus falls broadly in line with National Curriculum levels 4 and 5, while 13+ extends to level 7 of the National Curriculum. - What areas of maths will be covered?

The syllabus will differ in the small print but most will cover broadly similar ground.

Maths is divided into four key areas (with problem solving over-arching all four):

1) Number - including fractions, decimals, percentages and integers.

2) Algebra - expressions, equations and formulae

3) Shape and space (geometry) - including area, volume, co-ordinates and nets.

4) Handling data (statistics and probability) - such as the idea of chance, averages and graphical representation of data.

If you’d like more detail about the topics covered see 11+ And 13+ Maths - What Your Child Should Know - Is there a set paper for 11+ maths?

No. There are set papers for Common Entrance at 11+ and 13+ and there is a common academic scholarship exam paper (CASE) which some independent schools use. Aside from these, schools or consortia set their own papers. It is often the way questions are presented, rather than the mathematical requirements, that flummox children so do obtain sample papers from your intended school. - How do I know what MY child will need to cover?

The syllabus is fairly standard but different schools will emphasise different parts of the syllabus and present questions in different ways - some questions will be short and skills-based with considerable guidance/instruction offered, others may be lengthy or of a problem-solving nature with few, if any, mathematical hints. For example, a child may be adept at using Pythagoras in right-angled triangles but not know when, or how, to apply that knowledge – this often differentiates a good, CE, 11+, 13+ or scholarship candidate from a child who is a hard-working but lacks mathematical flair, or who has been taught by rote, rather than from a premise of understanding. Approach either your current school or the school you hope your child will attend. Individual schools and consortia may well issue practice or past papers and have the syllabus to hand; do ask and in good time (years not months before is ideal). Expect your child to sit two papers, one calculator and one non-calculator. - Are any bits of the syllabus key?

Yes - a good working knowledge of:

Multiplication tables - an important pre-requisite to success in 11+ maths; regular reinforcement of tables is essential. Don’t just rely on rote and sequential learning - there is a big difference between counting in 8s and knowing that 7 x 8 = 56.

Fractions are fairly critical (this extends to decimal fractions and percentages). If understanding fractions proves problematic buy some fraction cubes and start working with fractions practically. For example, if your child needs to find ‘a half of a half’ get them to draw a shape, halve it, then ask them to cut each piece in half and discuss the result, linking back to the problem. Do a few more; always start simple, build-up to the complex; let them work out what is going on and how to translate the practical to pen and paper.

Algebra - Children learn basic algebraic skills from a young age but little is taught formally before 11 (save for the most able). At 13+ and beyond sound algebraic ability, including the ability to manipulate equations is fundamental. Good, clear, logical presentation from the outset is essential - if necessary give your child the answer; always stress that the processes are as crucial as the final answer (and often worth more marks!). - My child is fine with a calculator but struggles with mental maths – in this electronic age does it really matter?

Yes, it does! The importance of good mental arithmetic cannot be over-emphasised. As well as being essential for the non-calculator paper, many questions in the calculator paper rely on good mental skills. Skill in using maths is tested at KS2 or 11+ but at KS3 or 13+ a good deal of importance is placed on applying mathematical skills. Moreover, the ability to carry out basic mathematical calculations is important in everyday life and underpins many key areas of mathematics. - English is a struggle. Should I insist on perfection in maths?

English is very important in mathematics, particularly keywords and the ability to decipher problems in words, which can often be quite complex. If your child is struggling with the language aspect of maths try exploring key words together. Start simple, for example: tri always means three eg tripod, tricycle etc so triangle means three angles. Quadrilateral – quad meaning four as in quadrangle, quadruped (girls who ride horses tend to be familiar with this), lateral linked not only to lines but sides. So a quadrilateral is a shape with four straight sides. Extend the English to discuss shapes in general and see if they fit the ‘quadrilateral’ bill. Spelling isn't as crucial in maths as in English but avoiding angels (angles) and spears (spheres) is helpful. Indeed, the importance of being able to use and understand accurate English in approaching mathematical problems cannot be over-emphasised. - What about using a computer?

Great idea – in moderation! There are very many good sites that help and encourage children with their maths – some are great fun, some aimed at revision and reinforcement, others testing. - I was taught things like ‘cross multiply’ and to multiply by 10 add a zero – will these help my child?

No, it’s mathematics not ‘math-magic’! These tricks fail at the first hurdle. If you ask a child to find 13 x 10, your method is quite literally asking 13 + 0 which is 13 not 130. Worse still, 2.3 x 10 does not equal 2.30. Tricks do not help a child to understand the essential reasoning and processes behind calculations and can create added difficulties later. An abacus is a great way to demonstrate place value to young children, with money an excellent, real life tool for older ones. - My child doesn't ever seem to know the answer even to simple questions when asked orally, yet does quite well with pen and paper – why?

Children often don’t answer questions – not because they don’t understand but because they are frightened of giving a wrong answer. It’s easy to get over this hurdle. If a child offers an incorrect answer – don’t jump in with both feet declaring it wrong – or worse still just give them the correct answer and move on - smile and ask how they got the answer (they may even be thinking several steps ahead!). A skilled teacher, learned tutor or adept parent will use this information to establish which bit of the building block isn't quite in place. Often a child will be able to self-correct and so feel doubly pleased. Where this is not the case reassure the child, try to guide them to the correct answer then go back to work on the stumbling blocks (the point where their calculation started to go wrong). - When should we start working through past papers?

Once your child has a reasonable grasp of the syllabus you can start trying out selected exam questions. Working through past papers will help you see the different contexts and ways that maths problems are presented; it will also help your child become familiar with the style of question and the amount of time available to complete the paper. Don’t just rely on papers though – you want your child not just to pass the test but to flourish when they get to their new school. - My child is quite good at maths but never seems to finish a paper – why?

Even if your child is a gifted mathematician, it’s possible s/he has a learning difference or disability that may qualify them for extra time. The idea behind extra time is to enable a child to perform on a level playing field. Reasons for extra time include dyslexia, processing difficulties, slow reading or writing speeds etc. If in doubt speak to school – find out what teaching staff think and if necessary consult an educational psychologist (EP). You will need a report to obtain the extra time even if no additional classroom help is deemed necessary. - My child is pretty good at maths – the syllabus seems rigid – any suggestions?

Yes lots. Don’t be afraid to extend your child’s learning at any given time.I have known youngsters get into the realms of calculus through examining the ‘difference of differences’ in number sequences (triangle numbers is great for this); use factorials (combinations) to work out the probability of a win on the National Lottery and explore the many patterns and links to sequences and series that Pascal’s triangle provides - all well before their 13th birthdays. The list of possibilities is endless - never call a child’s natural curiosity to a halt; try to have open-ended questioning - don’t just ask them how many squares on a chessboard – ask why this is so – and what would happen if the size or shape of the board was changed – you may just find yourself exploring too!. It’s fine to look at things such as trigonometry that aren't examined at 13+ if your child has a genuine thirst and is ready for this important encounter. A child with good algebraic skills will quickly master trig and should be able to use and apply it appropriately.