Picture the scene, you’re helping your child with maths homework and you come across a calculation which you have worked out in your head in seconds, or even worse, a younger sibling has blurted out the answer. However, your child is still sitting there, crunching up their face, trying to think hard about the answer. Maybe your child thinks that the answer should appear by magic in their head? So you wait, and encourage and try not to rush your child as that is when the panic sets in. You’re putting pressure on your child to hurry up, when clearly there’s nothing to hurry up about because that answer is not materialising. In the end your child guesses the answer.
As a teacher I have seen this many times. The child doesn’t actually have the skills and strategies to work out the answer. So they try to think if they have done something like this before and then remember that answer. It doesn’t work of course, as maths is all about application of skills to new situations. Once you teach the methods, the child should be able to use them in any situation.
So this article will try to address the problems that are caused by poor mental maths. How can you help? Does it really matter in this high tech world where we have calculators on our mobile phones?
Children who are weak in maths will also struggle with mental arithmetic. They work things out too slowly, often get the answer wrong and fail to retain important number facts. Weak mental maths skills means that a child will make silly mistakes in their calculations and will struggle to finish the work set. In older children, they rely on the calculator and when you ask them to work it out on paper, they have forgotten how to. So practicing mental maths will help your child in all areas of maths and boost their grades.
Encourage your child to work things out in their head. One of my students was doing the question “7+3”. I know that he can put a number in his head and count on, but when I saw him working it out, he counted 7 fingers, then counted 3 fingers and then added them up. This took him twice as long as it should have. If you want to know more about the “counting on” method, which is used in schools, Topnotchteaching explains it really well.
He was doing this because he lacked confidence and counting out the numbers gave him a sense of security, it was buying him time to get the answer right. Children don’t like mental maths because they have a greater chance of making mistakes, and have nothing to “fall back on”. The only way of getting over this is form a habit of working things out in their head.
Don’t expect a child to learn number facts for the sake of learning them. Times tables, number bonds and knowing the number of grams in a kilogram are all examples of this. These can be learnt, or even crammed for tests, and just as easily forgotten. Maths is like a language. Unless it is used regularly and in different contexts, it will not be remembered. For example, times tables need to be learnt and then used in word problems, applied to fractions, used in division questions and used in everyday life. We use maths in our daily routines, more than we realise. Find the maths in your child’s life and help them realise that maths isn’t just something to be used in the classroom, it is all around us.
Here are some simple strategies to help strengthen mental arithmetic.
The most important skill is to learn times tables. This article gives you some practical ways to teach times tables.
Practice mental maths as a daily routine.
Have a set of questions saved on your phone or your computer or even printed out and fire these at your child. Make it look like a game so that it’s not too overwhelming.
Practice loads! do loads of past papers and if you run out of past papers to do, do them again, especially the questions you didn’t do so well on.
After revising a topic, go through past papers but only do the questions on that topic. For example if you’ve just revised circle theorem, do past paper questions on circle theorem only.
Your textbook is full of explanations and worked examples you can follow, study and use to improve your understanding. It’s generally a good idea to find a topic you need help with, read through the explanation (looking up anything you don’t understand), before following along with the examples.
After every exam paper, make a list of what you did poorly on and revise it.
Revise with a friend or work in a small group.
You can explain maths to your friends.
Your friends can explain things to you.
You can work together on problems.
You can test each other.
One of the most effective ways to learn a new skill is to write down the steps you have to take – either as a list or as a flowchart.
Make flash cards, but double sided ones, the reverse side having questions on it or page numbers from your text book where you can find these questions. You could have a set for each of the following:
FORMULAS. The formulas you need to memorise for the exam
METHODS. How to work out a problem, for example the method for working out Pythagoras.
DEFINITIONS. Write down the meanings of maths words you need to know.
NEED TO KNOW. In maths there are quantities and number you must know off by heart. Such as grams in a kilogram or square numbers. One side has the question, the other side has the answer.
Make a cheat sheet. This is one sheet of A4 paper with a summary of everything you need to know.
Go online and revise topics by watching videos or practicing questions online.
Create mind maps. There should be a word/question or something in the middle of the page, with questions, facts or methods coming out.
Create posters. Make them colourful and big so that they catch your eye. Display these posters on your walls so that you see them all the time.
Use highlighters and shade/colour in important facts from text books and workbooks.
If you have a really good set of notes or still have your maths workbooks from school, then you can write questions in the margins to jog your memory as you read.
Use sticky notes to write down formulas and facts, they are quick and easy to do, as you learn each fact, just throw the sticky note away.
LOOK at a worked example of a question. COVER it. WRITE it yourself and work it out from memory. CHECK to see if you’ve done it right. If you’ve missed something out or done it wrong, TRY AGAIN.
If after all this you are still not getting anywhere, let us do the work for you. Book a free assessment and let us take care of things.
Magnetix are construction toys, but they are also very useful for teaching about space and shape. I get children to make different shapes with them, including 3D shapes. But in this article I am focussing on quadrilaterals, because they can be the most confusing ones to learn about.
Here is how not to do it……..
For each shape children need to know:
number of sides
length of sides – whether equal or not
sides parallel or not
all sides equal length
opposite sides parallel
all interior angles 90 degrees
2 long sides, 2 short
opposite sides equal length
opposite sides parallel
all angles 90 degrees
To make a rhombus, just make a square and tilt the sides.
all sides equal length
opposite sides parallel
none of the angles are 90 degrees, 2 acute angles, 2 obtuse
To Make a parallelogram, make a rectangle and tilt the sides.
There are some things that I can’t do without, whether it’s at home or at work in the classroom. These objects have either made my life much easier or have provided fun and inspirational ways of approaching learning. All the items on my list have been tried and tested over the years.
A Decent Dictionary
For many years I used to have a tiny pocket dictionary in the house which was actually a free gift when I opened my first bank account. It was well used and handy as it was small enough to carry around. However, it was just a dictionary and not dictionary/thesaurus, the writing was too small and even after looking up the meaning of a word, I often found it difficult to comprehend.
Things have changed a bit since then. I would definitely recommend getting a dictionary which is also a thesaurus. The ones we use at our centre are by Collins and are available to buy here.
We use these daily to help children who need help with number work. What I love about this one is that you can draw all over it with a dry wipe pen and wipe off again. Every home should have one if they have young children and every primary school should have one too. There are hundreds of ways of using this as a teaching and learning tool. Click here for ideas.
A World Atlas
With the development of “Google Earth”, atlases seem to be going into extinction. But I think that nothing beats turning the pages in an atlas, and looking for places of interest. At our centre, we have a map of the world on the wall, and both children and parents never tire of looking at it. I have this one at home, and its simple and easy to use.
Pictionary is a board game where you have to draw a picture of a word shown on a card. the other players have to guess what it is. But I use it in a different way. I use it to develop vocabulary and thinking skills. Children have to tell me things about the object without saying what it is. It’s not as easy as it sounds, but excellent for getting kids to think. Try this word: engine.
I use playing cards as a visual and kinesthetic stimulus for children doing maths. Here are some great ideas on how to use playing cards to help your child with maths.
Schools used to pick the brightest pupils in the year and allow them to take their GCSE maths exam early. This was called early entry and the pass rate was very good. These students could then take on an additional maths GCSE like statistics. Nowadays, the majority of pupils are sitting early entry GCSE maths whether they have a good chance of passing or not.
This article by the BBC and this paper by the department for education summarise the consequences of this practice. But I want to tell you my story….
Last week, all the students who sat their GCSE Maths in November 2010, got their results. Last week, I had many calls from panicking parents whose year 11’s failed to get that grade C. These now have to re-take their exam in March or in May this year. They will have to revise everything again but this time they will have other subjects to revise as well so the pressure will be much greater.
Having assessed these students, I’ve come to 2 conclusions:
that they should never have been entered for the exam in November in the first place. I assessed a student who got a “U” (ungraded) in the higher paper suggesting that at best he was a low “D” grade at the time of the exam and that he could have done worse because of exam day nerves. The grades possible in the higher paper are “A*” to “D”. If a student gets lower than the pass mark for a “D” then they fail.
that the students have already forgotten some of the maths they studied for the exam. In the majority of cases, the students who told me they got a “D” in the exam for example, got an “E” in my assessment. The student who got a “C” in the exam got a “D” in my assessment.
These students are cramming for exams and are being taught to pass exams and not to learn skills which can be applied to real life or in further education. A good friend of mine who teaches A level Maths at College says that the students who pass the early entry exam, struggle with A level Maths because they have forgotten everything they learnt by the time they start college. He has to spend the first 2 weeks of the A level course going through basic maths skills to make sure that the children are able to cope with A level standard work. I teach A level Chemistry which needs a good foundation in maths. I find that I have to teach skills like being able to work out ratios, re-arranging an algebraic formula and using a calculator. And the same goes for english skills, like comprehension and being able to answer a question so that it makes sense.
It’s an old argument and one that will always exist as long as exams exist. Students take pride in getting their GCSE’s early and they pride themselves in getting more GCSE’s. Schools have a reputation to keep, and league to tables to worry about. Many teachers view pass rates as a reflection of their own teaching. We all have our own agenda. I just wish that parents didn’t have to get dragged into all this!
Before teaching a child to halve a number, make sure that they can halve a shape. Most children find it easy to halve a shape and don’t realise that halving means the same as splitting into 2 equal parts. So before teaching your child how to halve a number, please make sure that they have understood the following common misconceptions:
1. When you half a shape, you must make sure that it is split in the middle. This teaches the child that halving must be fair and that both halves must look the same.
2. There is more than one way to half a shape. Ask your child to halve a rectangle or square in as many ways as possible. This should include diagonally as well.
3. Draw and inaccurately half some shapes so that some are split unequally, some are split into three or more pieces. then ask your child to find out if they have been halved.
There are many ways to explain the term of “half of”; sharing equally between 2 people, counting in 2’s, dividing by 2, opposite of doubling and splitting down the middle.
Therefore, there are a variety of ways of teaching halving. Choose a method that your child finds easy, and stick to it. Once they are confident with that method, try to teach a different way of halving.
I always start off teaching a child how to share equally. I usually use counters and draw 2 smiley faces on a whiteboard or piece of paper representing me and the child. The child has to share the counters between the smiley faces. Sometimes you have to teach a child “one for you, one for me” and once they have learnt this they find it quite easy. Make sure that once all the counters have been shared between the 2 smiley faces, that they have been shared equally. the child needs to check every time. “How many do you have and how many do I have” seems to work well. What if the counters have not been shared equally? The child can repeat again or if they have caught on, they will be able to move some counters around to make the distribution fair. I use this method for up to 24 counters.
For numbers larger than 24, using counters can be time-consuming and often ends up with the child miscounting. By now the child should know half of 2, 4, 6, 8, and 10 without working them out. So I break down larger numbers into manageable chunks, and then ask the child to share equally between 2 smiley faces.
Example 1: Draw 2 smiley faces. Half of 30 = 10+10+10 Draw three 10’s in circles at the side as in diagram below.
How to half 30
Then share as in the diagram below, the smiley faces will get 10 each and then, there will be 10 left which will have to be split into 5’s. So each person gets 15.
How to halve 30
The same method can be used for bigger numbers and it’s easy and simple.
half of 34 = 10+10+10+4
half of 50 = 10+10+10+10+10
Do try this with your children and let me know if it works.
This game is great for teaching young children to count in 10’s and units. I have used this game in teaching and the children love it. I have kept it simple by sticking to 10’s and 1’s, but you can use larger coins if you want and adapt according to the ability of the child.
Suitable for age 5 and above. You will need:
2 players – 2 children, or one adult, one child
At least 10, 10p coins, real or plastic
At least 10, 1p coins
Pencil and paper
A small bag or container to place the coins
How To Play
Put all the coins in the bag and take turns to take out a random number of coins. Count the coins and write down the amount. Replace the coins in the bag. Let the other player have a go and compare the amounts. The player with the most money wins the round. Continue for as many rounds as you like, but I recommend 10 at least.