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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

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How to Study Smart: 20 Scientific Ways to Learn Faster – Daniel Wong

Most of us have to learn something new at some point in our lives. Thankfully my GCSE, A level and BA days are behind me, but I still like to do short courses and if ever a fairy godmother dropped a fortune in my lap I’d love to do a Masters in the future.

These tips, which I found on the Open2Study Facebook page are for everyone who still has exams to pass. I especially like the one about taking notes with pen and paper, because I always feel more creative with a pen in my hand than a keyboard at my fingertips.

How to Study Smart: 20 Scientific Ways to Learn Faster – Daniel Wong.

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How I passed the QTS maths test – part 3

The second part is the more traditional pen and paper sort of maths. I found this section less intimidating than the first part, because although there was an overall time limit, it wasn’t a limit per question. I still had to work hard to get through it though.

I owe my success in this part to two men: Derek Haylock and my dad! I bought a copy of Derek Haylock’s Mathematics Explained for Primary Teachers and worked my way through it. It’s on the reading list for a lot of primary PGCE courses, but I’d also recommend it to secondary teachers worried about the skills test. You can often pick up second-hand copies on Amazon fairly cheaply.

I worked through the book cover to cover and almost everything fell into place. All those equations and theories and rules and numbers and letters that had seemed completely meaningless while I was at school, suddenly made sense. The writer has a really easy to read, easy to understand style, and he makes maths seem a lot less scary.

As I worked through the book, I made a note of anything I still wasn’t sure of. It was actually surprisingly little as the book was so good, but there were one or two things – box and whisker diagrams for a start! Then I gave my dad a copy of the book and my list, and he tutored me for one hour a week for about three weeks, by which time I was feeling confident.

Now not everyone is lucky enough to have my dad, but if you have family or friends who are good at maths you could ask them for the same help. The advantage of working through the book the way I did, means that you are able to ask for very specific, targeted help rather than having to say. “I just don’t get it. Teach me the whole of maths.” Obviously this means a financial advantage to you if you are considering a tutor because you won’t need to pay for as many sessions.

I know a lot of people hate the skills tests and question their necessity when you already have to prove you have a grade C or above at GCSE to get a place on a teacher training course. However I’m really grateful that I had to take it. It’s made me relearn my maths and I feel so much more confident than I ever used to. I also feel that it’s made me a better teacher. Having struggled for years, I can understand why people find it so hard, but having finally made sense of it I know there is a way.

If you feel you need one-to-one help to pass your skills tests, and you live in north Birmingham, get in touch to see how I can help you.

Related posts: Passing the QTS maths skills test – Part 1       Passing the QTS maths skills test – Part 2

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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