# Cancelling Fractions. A game for 2-4 players.

You will need:

Slow Rounds:

• Play like this while they get used to the game.
• Give out a card, read the fraction, ask them if they have it on their board? (Probably they will say no)
• Ask which table both those numbers are found in? For example, if the card says 15/20, those two numbers are both in the 5 times table. Ask what position the 15 is in (answer, 3). What position is the 20 in (answer, 4). So, 15/20 is WORTH 3/4.
• The pupil covers 3/4 with the card.
• Take in turns until someone has 4 covered (or all covered, depending what pace you want).

Fast Rounds:

• Play like this once they are really confident and getting bored with the pace…
• Hand out one card each, fast, they grab it and place it on their board. Commiserate if it is a duplicate that they don’t need “Oh no, not another one EQUIVALENT to 3/4!”. If they are pleased, celebrate “Great, you needed 2/9”. This gets the correct terminology bedded in, and also they see that fractions that are equivalent to each other generally LOOK really different.
• If 2 pupils draw (covering 4 fractions) have a tie break round with another card. At this pace, it works well to aim to cover all the factions up.
• If someone goes “bingo” check their board to make sure all the cards are in the right place.

Super Fast Round:

• Give each pupil 5 cards and see if anyone can go bingo.

Bonus level thinking:

• “You need one more card. What do you want to get?” Suppose it is 2/5. Point out they need a fraction made up of a “position 2, position 5” pair. Placing one finger in each position explains this nicely. It’s very gratifying if they get what they want straight away!
• Get the pupils to highlight the odd numbers before they start. Think about whether a fraction’s numbers are odd or even, or one of each, and which tables they should be looking in. Being hazy about the importance of odds and evens is common amongst struggling mathematicians.

# Isometric Drawing

One of my Year 6 groups tried some Isometric Drawing for the first time today. It’s perfectly possible for people to get hopelessly confused the first time they try this, but they all listened carefully, started simple (drawing one cube, then two) but it didn’t take long before they were digging into the box of Cuisinnaire Rode and setting themselves some really tough challenges. The most extreme one was this, six “ten” rods, piled up. Groans ensued and most of them decided it was impossible. However, some of them stuck at it and their drawings were brilliant!

I noticed a couple of them had abandoned their pre-printed paper and were busy drawing soomething of their own on the class whiteboard:

# Recommended calculator CASIO fx-83GT PLUS

I have a huge weakness for calculators, so if I see a new one that looks interesting, I usually buy it and see if it could replace my current favourite as my “Top Calculator”.

Since the launch of the CASIO fx-83GT PLUS, the calculator market has been, for GCSE at least, a bit of a one-horse race. Several strong features are common across the whole market, they all basically do the job. What sets the 83GT apart is some unique features:

• The ability to factorise whole numbers (The FACT function). This is not only useful, but fun. What can be a dry subject to teach, suddenly becomes an area for experiemntation and competition, which happen to be my two favourite ways to spend time when I’m teaching Maths. The answers are expressed in Index Form so the pupil is taken straight to the gold standard of factorising numbers. So, I use it to teach index notation too. Factorising is crucial for a number of Mathematical areas, so it’s really nice that CASIO think it’s worthwhile to devote a function to it.
• Recurring decimals – well hidden above the “x squared” key, (it looks like a box with a dot on top), this function enables the pupil to type in recurring decimals. Answers can also be converted from recurring decimal, to fraction, to rounded decimal. Again, this encourages experimentation.

It will probably set you back between £9 and £12 depending on where you get it.

Update – June 2015 – still think this is the best.

Click to see recommended compass

# Why do children give 10p too much change?

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.

# Lesson Idea

## Starter

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.

## Main

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…)