Category Archives: non-calculator

Methods to use when a calculator is not available

IGCSE or GCSE Maths for Home Schooled Students?

Choices of Qualification….

You have a choice between GCSE (the standard qualification, just like the one taken in schools) and IGCSE (the international GCSE, designed to be taken in more remote locations.). Both are suitable for a home schooled course, both can lead to a Higher grade (up to A*) or a Foundation grade (up to C). But the two exams are different in a couple of important respects, that may not be immediately obvious if you try to wade through the different syllabus documents.

Some schools have adopted IGCSE in place of GCSE and the qualification is recognised by UCAS as equivalent.

GCSE Maths

You will take 2 papers, one is calculator and one non-calculator. The exam is offered by EDEXCEL and AQA, and the content of the exam is the same, so you can use both board’s past papers in your practice period. Also, because this is the market leading GCSE, there are oodles of other materials published online and in paper form, for you to choose from.


Offered by EDEXCEL only, and appealing to a narrower market so there are fewer past papers and additional materials available. But the biggest difference is you can use a calculator for both papers. In order to make sure the value of an IGCSE is not diminished by this, the syllabus contains a few extra topics that do not appear on the GCSE syllabus. For example, at Foundation you will do some Set Theory, and at Higher you would do some Calculus.

Would IGCSE be better for me?

If you are quite comfortable with mental arithmetic and written “sums”, and you are pretty good with your tables, then you shouldn’t struggle too much with the non-calculator paper, and it isn’t worth venturing into the slightly more unusual qualification. If, however, you really struggle with arithmetic and really only feel confident with Maths if you can have a calculator to hand, then IGCSE is worth serious consideration.

Does it lead on OK to A level?

To prepare for A level you must do the Higher IGCSE exam. I did wonder, when I first met the syllabus, whether it was a good idea to let people “off the hook” by using a calculator all the time…. would it not mean that, for the one non-calculator paper you would take in Year 12, you had forgotten how to do arithmetic? The answer seems to be “no”, from my experience. If you repeatedly ask your calculator what 6×7 is, and it tells you 42, then eventually it seems to “stick”. Far from being a cheat, the constant sight of the correct answer seems to be quite helpful in learning those elusive tables facts! The Year 12 non-calculator module is not particluarly arithmetic-heavy in any case so, even if you need some revision of techniques, it’s not a heavyweight problem.

Where would I take the exam?

Either way, you will need to take the exam at a local approved examination centre.

Will I need a Maths Tutor?

You may want to just learn at home.  You and/or one of your family members needs to be pretty confident with Maths in order to manage on your own.  You may find yourself looking for a tutor if:

  • Learning Maths together turns out to be really stressful – experience (as a tutor and teacher myself) has taught me that even in the most cheerful of families, trying to do Maths together can be a minefield. Some adults struggle with Maths themselves so they bring to the table some sympathy with the learner, but also some fear of the subject and a sense that they have “blocks”.
  • Doing past papers and then wading through marking them is OK if you are persistent – it isn’t rocket science but you do need confidence to be able to say “yes, you really ARE hitting your personal target grade now”. You may find yourself wanting that reassurance from an experienced tutor, closer to the exam.
  • Maths just might turn out to be too hard for the student/parent team after all (this can happen with other subjects too but Maths is notorious). In these circumstances you may need to enlist the help of a tutor.
  • You KNOW that Maths is a subject you struggle with. It always has been…. you just don’t seem to “get it”…. it really upsets you sometimes. In this circumstance, you will find an experienced tutor a really valuable support.

I can help you if you are in or near Bournemouth UK

If you live in or near Bournemouth and are home schooled then I may be able to help you. the good news for you is, because most people need tuition after school hours, but you would probably prefer it during the day, most tutors will find it relatively easy to fit you in. The best tutors are fully booked for their evening slots for most of the time, but many have availablity during the daytimes, even close to exams.

For tutors all over the country try


Measuring Angles

Dear M,

There are a lot of quite nice resources online that help to build the skills of estimating and measuring angles. Using a protractor is about 3 times more confusing than using a ruler, so it’s something that needs a whole lot of practice. If I was Prime Minister, then angles on exam papers would always be TRUE angles so you could use REAL estimation skills to work them out, but they aren’t. Oh, and I’m not Prime Minister…. As we discussed today in our lesson, it doesn’t matter if you photocopy an angle larger or smaller, it stays the same size (which is pretty weird when you put it like that….. most things DO get bigger when they get bigger, don’t they!)

I have ordered the builders’ angle measurer that we looked at online  and chatted to the plumbers who are in my house today who don’t use one of those but thought it sounded incredibly useful!

Link to the online game of measuring angles on screen….

Screen Shot 2014-05-14 at 12.18.46Brilliant “make an angle game” that we played, and you were so good at! The link takes you to the start screen – we skipped the intro then chose “make the angles game”. To practice full-on measuring, where you have to place the protractor without any help from the computer, the option to pick is “up to 180 degrees in ones”.

Build your own printable worksheet (to use with a real protractor) – gave you one to do, here is a link to it just in case, feel free to make some more worksheets if you want more practice.

I wonder how you will get on, measuring angles over 180 degrees, when your own protractor only goes up to 180…. It’s a genuine mathematical problem, and I think that if you give it 5 minutes of careful thought, you may come up with something. It isn’t impossible, but it isn’t obvious either. As always, if you can figure out your own solution, you are MUCH more likely to remember it!

If your mind goes a blank when you try to use your 180 degree protractor, I would recommend this video because the teacher is making an effort to not be boring, is quite funny, but rather quiet, so you’ll have to listen carefully!


Getting used to negative numbers Part I – a simple game

IMG_0328The Philosophy of the Game

The learner will be more confident with negative numbers once they can sketch a number line like this in their heads. Helping to make one by numbering the chips is a great way to get to know how the line works. During play, the colour of the card will tell you whether to move towards the losers’ end (boo, red, negative) or the winners’ end (hooray, black, positive). This emotional response to the DIFFERENCE between plus and minus is really important later, especially in algebra when kids may not see the minus signs. Confidence subtracting EVEN WHEN THE ANSWER IS NEGATIVE takes time to learn, but this game is ideal, treating the minus numbers as just more places on the number line after you count 5,4,3,2,1,0….

You will need:

  • A pack of playing cards, use just the Ace,2,3,4,5 of all 4 suits.
  • A piece of A4 paper, scissors, a ruler, sellotape and a pen
  • 2 different small counters. A 1p coin and a 5p coin would do fine.

To prepare the game board

  • Cut the paper in half legthways and sellotape the two peices together to make a long thin shape. Rule a line across it and mark on it a number line with 0 in the centre, the negative numbers on the left, and the positive numbers going right. The scale must be regular (use the ruler to mark out 2cm-apart chips). It should look like this:negative number game
  • Place both the counters on the 0 (one below and one above, will avoid collsisions!

To Play:

  • The BLACK cards are positive values 1 to 5, and the reds are negative 1 to 5.
  • Shuffle the cards and take turns to choose one, moving either right (black) or left (red) the right number of chips.
  • The winner is the first one to go over the 11 (ie score 12), OR the loser is the one who falls off the left hand end by scoring -12.
  • If noone falls of the end, declare the winner after a timed period, say 5 minutes.
  • To make it more challenging, pick 1,2 or 3 cards each. The player decides how many cards to take and then takes them.

Next Time you play:

  • Can the child make the board? With a bit of help, perhaps?
  • Can they total their 2 or 3 cards before they move, or do they prefer to make the moves for each of their cards in turn?

Next Time:

  • Once the number line is a simple concept for them, you can play with all the cards from Ace to 10, and just keep a score on paper without counting any counters up and down the number line. Winner is the one with the highest (or maybe the least negative) score after say 15 rounds. Players can choose up to 10 cards in one round, and some interesting strategies develop for totalling their hands. More in the next post.

Subtraction Confusion – a very simple solution

Do any of your students get in a mess with “double borrowing”? There’s a very simple solution which builds on their existing knowledge of subtraction with borrowing….

Easy subtraction - one "layer" of borrowing
Easy subtraction – one “layer” of borrowing

Much harder subtraction - the borrowing cascades from left to right
Much harder subtraction – the borrowing cascades from left to right and is very likely to go wrong.

There is a very simple solution to this, encourage the student to look at the number differently. Borrow ONCE from the “200” on the top, which becomes 199.

Borrow ONCE from the "200" in the top number
Borrow ONCE from the “200” in the top number – now this sum is ready to do, and there’s far less that can go wrong.

Try it on a student near you, and use the reply box to tell readers what happened next!