Tag: mental maths

Posted on

Subtraction by Adding On

This is also sometimes called “subtraction using a blank numberline” and I’ve even heard it called “that nonsensical modern method”. This latter is a real misnomer since it is neither nonsensical nor modern. In fact it’s a method that dates back to before I was born, in days before we had calculators and electronic tills. It’s also a really useful method involving counting forwards, which is always easier than counting backwards – even for maths geniuses!

Let’s return to those old-fashioned little shops. I buy some sweets for 24p and hand over a £5. To work out my change, the shopkeeper needs to calculate £5 – 24p. Now she could count £4.99, £4.98, £4.97 until she had subtracted 24p, but what you actually would have heard is this:

24 and 6 makes 30, and 20 makes 50 and another 50 makes £1. 2, 3, 4, £5. And while doing this they counted the change (£4.76) into your hand.

This is the method that schools have returned to. To begin with, Children use a “blank numberline” – that is, a line that they can write the numbers on themselves. They then write the lower number at one end, and see what they need to add to make the higher number. Here’s an example:

96-38

numberline

The children first of all use their knowledge of number bonds to add to the next 10 (38 + 2 = 40).
They then use their ability to add multiples of 10. In the example above the child has done 40+10 = 50 and then 50 + 40 = 90. They may have been able to see straight away 40 + 50 = 90 and done this as one step, or they may have needed to do 40 + 10 = 50, 50 + 10 = 60, 60 + 10 = 70 and so on up to 90. The method isn’t about having to complete it in a certain number of steps, it’s about each child breaking it down into the smallest number of steps that they can manage.
When they reach the multiple of 10 before the higher number, they add on whatever units are needed to make the higher number, in this case it was +6 to make 96.
Finally, they add up all the numbers they added on to find the answer: 2+10+40+6 = 58 so 96 – 38 = 58.

When they are confident with this, they move on to jotting down only the numbers they are adding on, and they keep the tally in their head, until eventually they develop their working memory enough to hold all of the numbers in their head and write down just the answer.

Related posts: Teaching the Times Tables, Teaching Sequencing and Column Addition

Posted on

How I passed the QTS maths test – part 2

The first part of the QTS skills test is the mental maths section. To pass this, it helps to have a good grasp of times tables. I was lucky that I already knew these really well because my school had insisted we knew up to 12 x 12 by the end of year 4.

If you who don’t know your times tables, my first piece of advice would be – learn them. Get to know them inside out and back to front. If you’re a visual learner, pin flashcards on your bathroom mirror, inside your fridge, above your desk and anywhere else you are likely to spot them as you go about your day. If you’re an auditory learner, record yourself saying them and listen to them instead of the radio when you’re out in the car, watch times tables songs on YouTube and sing along. If you’re a kinaesthetic learner, try turn tables cards.

Learn some times tables tricks. If there are any in particular that you struggle with, give yourself an incentive to remember them. If 7 x 8, 7 x 9 and 9 x 6 are the ones really holding you back, change the PIN on your bank card to 7856, the PIN on your phone to 7963 and your house alarm to 9654!

When you are confident that you know them, make sure you know them backwards. It helps to know that 2 x 9 and 3 x 6 both equal 18, but it helps even more if you can look at 18 and know that it’s divisible by 2, 3, 6 and 9.Finally, practice spotting relations between numbers. If you know 4 x 8 = 32, then you also know 320 is divisible by 4 and 8 as well as by 10, 40 and 80.

Then enlist a friend who is good at maths to give you some problems to solve. I got my husband to set me 3 problems a day, along the lines of: If I can buy two tins of soup for 70p, how many can I buy for £4.20? Here I had to spot the relationship between 42÷7 = 6 and 420 ÷ 70 = 6 . Once you know what sort of thing you’re looking for, it doesn’t take that long to spot it.

Ok after tables make sure you are confident with number bonds eg 6 + 4 =10 and 3+7 = 10 so 16 + 4 = 20 and 13 + 7 = 20. If you’re anything like I was, even though you know 3 + 7 = 10 you still feel obliged to count on your fingers – you know, just in case it’s changed since last time! The key is practice, practice, practice until you can override that desire. Then make sure you are equally confident at splitting single digit numbers into smaller ones. Eg 7 = 6 + 1 and 5 + 2 and 4 + 3. This means you can now quickly turn 18 + 7 into 18 + 2 (= 20) + 5 = 25, without needing to slow yourself down by counting on fingers.

Last of all it was time to get to grips with fractions and percentages. The first thing to remember is that fractions and percentages are the same. I wasn’t convinced either, but remember that per cent means out of 100 so 70% = 70/100 and doesn’t that look just like a fraction. The second thing to remember is that fractions are easy when you know your times tables and have practiced looking for relationships between numbers. 1/7 of 42 = …oh look it’s that relationship between 7 and 42 again and by now we all know that’s six.

For the mental maths part of the test I practiced for 10 minutes every day for 6 weeks and that was plenty. If I hadn’t already known my times tables I may have needed double that time, but still not as long as you might think for a mathsphobic. And if I can do it you can too.

If you feel you need a little tuition to get you through the skills tests, and you live in north Birmingham, get in touch to see how I can help you.

Related posts: Passing the QTS maths test – Part 1,  Passing the QTS maths test – Part 3

Posted on

Free Maths Worksheets

One of the challenges of supply teaching is knowing where to find worksheets on a range of topics that can be accessed quickly, printed free of charge, and adapted easily to suit the need of a class you barely know.

Here are some of my favourite sites for maths worksheets, all of which were free to use at the time of writing this post. Some of them are American, so this needs to be considered when teaching about money – although some of them allow you to change the currency.

www.dadsworksheets.com

www.education.com

www.helpingwithmath.com

www.math-aids.com

www.mental-arithmetic.co.uk

www.primaryresources.co.uk

www.senteacher.org

www.tes.co.uk

www.worksheetplace.com

www.worksheetworks.com

Many thanks to Erin Edwards for the following suggestions:

http://www.midkent.ac.uk/resource/english-maths/

http://www.bbc.co.uk/skillswise/0/

http://www.skillsworkshop.org/numeracy

What other sites do you use for maths worksheets?  Why not leave your suggestions in the comments below?

Posted on

What’s the best order to learn times tables in?

Sometimes, something seems so obvious to you that you can’t imagine that other people don’t already do it.

This is how I feel about times tables. I’ve always encouraged children to learn them in a particular order and have always just assumed that everyone else does too. However, the more different schools I work in, and the more I come into contact with children who are being asked to learn their times tables in numerical order, the more I have come to realise that this is not necessarily the case.

I always get my pupils to start with the 10x tables. These are easy. There’s a pattern to 1×10=10, 2×10=20, 3×10=30 that makes them easy to remember. Once the child has spotted the pattern they can easily recall them in any order. I follow x10 with x11. There’s another pattern here 1×11=11, 2×11=22, 3×11=33 that takes them all the way through to 9×11=99. They already know 10×11 from their 10x tables, and if they struggle with 11×11 and 12×11 there is a little 11x tables trick they can use to work them out.

After that we look at 2x tables. There isn’t a pattern to these, but the answers are all even numbers, they are all doubles of the question, and the highest answer is 24, so they are fairly easy to learn.

When they are confident with x2, it’s time to move on to x4. All the answers here are double the 2x tables, so while they are learning 4x they are still practising 2x. This is important as I have seen so many children forget the x table they have just learnt when they start learning a new one.

After x4 comes x8 because – you guessed it – it’s double x4. If necessary the children can look at the number in the question and do double (x2), double (x4) and double again – eg 3 x 8 –> double 3 is 6, double 6 is 12 and double 12 is 24 so 3 x 8 = 24. This means that while learning their 8x tables, children are continuing to practice x2 and x4.

By now the children are feeling confident because they know their 8x tables, and everybody knows that’s a hard one, so it’s time to drop back a notch to a couple of easier ones to get two more under their belts in quick succession. In the 5x tables, all the answers end in 5 or 0, which is a big clue to the answer, the answers are all half of the 10x tables, and most children can count really quickly in 5s so even if they struggle with recall they can work them out quickly. Then we look at the x9 finger trick so that even if they never manage to learn their 9x tables off by heart, they can work then out so quickly on their fingers that it doesn’t matter.

Then we take stock of where we are. They know their x1 x2 x4 x5 x8 x9 x10 and x11 so they can see that we are 2/3 of the way through them, and two of the so-called tricky ones (x8 and x9) are out of the way.

And so we move onto the threes. Now in my opinion, x3 really is a tricky one. There are no patterns, it’s not as easy to count in 3s as it is on 2s, 5s or 10s and there are no tricks. After x7 I think it’s the trickiest one there is. However, now it’s not so bad because they have learnt most of their tables already, so there’s only 3×3, 6×3, 7×3 and 12×3 left to learn which doesn’t seem too daunting at all.

And then of course x6 is double x3, so they can learn x6 and practise x3 at the same time.

By the time they have finished their 6x tables, the only ones left are 7×7, 7×12 (and 12×7) and 12×12, and buoyed up by the confidence of having learnt all the others it doesn’t take long to finish these last few.

If you need some idea for how to learn the times tables, rather than just this suggestion of which order to learn them in, have a look at Teaching the Times Tables.