Callum buys a packet of crisps for 62p. He pays with a £2 coin. How much change will he get?
The correct answer is £1.38 but a proportion of children will answer £1.48. The logic goes like this:
- Count up from 8p to 10p, that’s 2p
- Count up from 60p to 100p (or £1) that’s 40p
- Count up from £1 to £2, that’s £1.
The tiny error that has crept in is not noticing that, the counting up from 8p to 10p actually means we start from 70p… and if you’re still following this, then you are clearly good at understanding abstract verbal ways of looking at Maths. My hunch is most people who see themselves as “good at Maths” may be Auditory learners. Most of the people I end up teaching 1-1 don’t favour this learning style. They prefer visual approaches, or Kinaesthetic.
Auditory/Visual learners may confidently get the right answer to this question of giving change, using the standard Numeracy Strategy approach of “counting along the number line”. They may sketch the line and, in due course, be able to “see it in their head”, or just recite the “jumps” up to £2 (That’s visual and Auditory respectively.)
Kinaesthetic learners may struggle to jot down the number line with enough confidence to be able to get the right answer. They may not be clear what “lies between” 62p and £2. (or, worse, between £3.27 and £10.00).
The best standard resource in the classroom for these learners is a 100-square but you will need 2 squares for this problem. Click the picture for a black and white printable pdf (Two Pounds Square) of the £2 hundred-squares. Or, if you want a coloured one, print this one (Two Pound Square colour version)
To use this printable to work out the change, ask the student to find the square containing 62p. Then count to the end of the row, that’s 8p. Now count up to £1. That’s 30p. Now jump to £2. That’s £1. So the “jumps” total £1.38.
You will need the printable cards Click for the printable pdf
Have some cards marked 10p, 20p, 30p, 12p, 11p, 31p. Take turns to draw a card, and move your counter up, by that amount of money. First person to go over £2 wins (and it’s a nice touch to ask “where would you be now, if the next card was printed?”. That will tell you if they are able to extrapolate the ideas on beyond £2). This game will get the players used to “counting up” on the board, and difference between a move of 1p and a move of 10p.
You will need the rest of the cards from the set you just printed (the ones in normal type). Place face down on the table and shuffle. Take turns to look at a card, and calculate the change from £2. If you can turn over the correct card as your second one, keep them both. Otherwise, turn them back face down again. The winner is the one who has the most cards. (Note, Kinaesthetic learners seem to be really good at “pairs”, because they can remember where the cards are. Since I don’t have this strength, I lose, pretty well every time…)