Factorising Race

A game for 2 players. The winner is the player with most points at the end.

Starter (optional)

  • Play a game with the 13x table. This is almost completely unfamiliar and the kids will be intrigued. The KEY fact is that 7×13=91 because 91 is a terribly prime-looking number but it isn’t. Pupils who are confident with their other tables will, by learning this factorisation, have completed the full set of skills in factorising numbers under 100. 

Screen Shot 2014-05-13 at 16.50.05Introduction:

  • Make sure the players can factorise a number using their calculator. On the CASIO fx-83gt PLUS this is done by entering the number, pressing equals, SHIFT and ., ,,, (this has “FACT” written above it in yellow). The Prime Factor Form is displayed as the answer.

Each turn:

  • Roll 2 (or 3) dice, and choose which number to build. For example, a 5 and a 1 could be 15, 51 or 6. Factorise your chosen number. The score is the number of prime factors. eg 15 would score 2 for 3×5. 8 would score 3 because it is 2 cubed. 24 scores 4 because it is 2x2x2x3. 71 scores 1 because it is prime. ** You may need to explain the “Index Form” that the calculator displays. This is a very important notation anyway, which a lot of students misunderstand.

What Maths is learned:

  • To choose the best number, ideally the players have to mentally factorise both numbers. They will make repeated use of the standard divisibility tests (for 2, 3, 5 and 9) and probably invent a few more (this evening my pupil realised 357 and 217 must both be in the 7x table, just by looking at them.)
  • Once they know a number will divide, they have to actually DO it mentally. Practice makes perfect here!
  • A printed tables sheet may be a help.
  • In their enthusiasm to win they are stretching their own mental maths to the limit. If they don’t fully factorise both numbers, they may miss a high score!
  • A younger pupil may want to try all the possible numbers with the calculator – this is good practice anyway and reinforces the correct factorisations.
  • An enthusiastic player will start to memorise some of the factorisations – this is really helpful knowledge.

Cancelling Fractions. A game for 2-4 players.

cancelling-fractions-game

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.