'Multiplication Game' & 'Division Game' - Five Cent, Ten Cent Game is a beautiful game for exploring strategic thinking while practising how to multiplying & divide by 10, 100 & 1 000.
What You Need:
1 Game Board
2 counters of one colour
2 counters of a different colour
Tip - Transparent counters work well in this game but are not crucial.
Game Set Up:
A single counter of one colour is placed on each of the game spaces on the left hand side of the board.
Counters of a different colour are placed on game spaces at the far right end.
How to play:
1. Toss a coin at the beginning of each round to see who goes first. This is important as the random nature of the coin toss adds to the dynamic of the game.
2. The player going first may move their counter on the top row 1, 2 or 3 spaces OR their counter on the bottom row 1 or 2 spaces.
3. Player One reads the number under their counter and multiplies or divides it by number required by that round eg 3rd round means multiply by 1000 and say the answer aloud.
4. Player 2 repeats step 2 and 3 noting there is no jumping on or over the opponent's counters.
Best of Three:
- Round One - multiply by 10
- Round Two - multiply by 100
- Round Three - multiply by 1000
- Round Four - divide by 10
- Round Five - divide by 100
- Round Six - divide by 1000
- Round Seven (if required to break a tie) - the one you feel you need to work on.
How to Win:
Trap your opponent in their starting position so they are unable to make any legal moves.
Before the Game:
- Most children encounter the notion, 'Just adding a zero' when multiplying by 10. Whilst this works for multiplying whole numbers, it comes undone when applied to decimals. The correct way to conceptualise what is happening when multiplying by 10 is to move the decimal point one column to the right. Explore this notion using whole numbers and decimals.
- This concept of, 'moving the decimal point' (as opposed to just adding a zero) transfers to multiplying by 100, 1000, 10000, etc. When multiplying by 100 move the decimal point 2 places to the right. Inversely, when dividing by 10 you move the decimal point one place left. When dividing by 100, move it 2 places left and so on.
Calculator Play - explore existing knowledge around multiplying by multiples of 10. Hand out calculators and ask students to multiply a number by 100 and see how many head straight for the calculator.
Calculators are wonderful tools for many calculations but there are elements of Math where the human mind is more efficient. The calculator is a accurate strategy but in this case it is not efficient. What could this mean?
- Ensure the concept , 'The decimal point is where the whole numbers stop and the parts of numbers start' – Make a poster to help you remember.
- Have the students extrapolate what is happening to the decimal point when multiplying or dividing by 1000, 10 000 and a million.
- Students write their own law for multiplying by 10, 100 and 1000. NB they must include the term 'move the decimal point'
- Explore dividing by 10, 100 and 1000 in the same way. What patterns can you discover?
The ‘‘So What?’ Test
Everything taught in schools should stand up to the ‘So What Test’. ie ‘Why should we learn this stuff?’
- Make a list of situations where this skill will be of use.
- Make a list of occupations that use this skill as a natural part of their daily work.
During the Game:
- A winning strategy seems to have something to do with keeping an even/equal number of spaces between your pieces and you opponents. Investigate this. Is it true? Is it false? Does it lead you to working out another strategy for how to do well at this game?
- Teacher plays the game and models self talk. If I move three spaces, what will they do? What would you do if I were faced with that move? Why?
- It seems to me the person who goes first has a distinct advantage. Monitor you game and work out why this is the case.
- Traditionally this game was played with 10 cent and 5 cent coins. The winner of each round kept the coins. Your students might like to pretend the counters are coins and keep a tally of wins and losses.
- Students design their own game boards to help practice a concept they feel they need to 'work on'.
- Experiment with the amount of spaces on the top row & bottom row to ensure interesting game play.
Included in this Download:
3 x seven space game boards
3x ten space game boards
Teaching Points for before and during the game
Ideas for variations and extensions
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