Ready to play?

If the road to mathematical fluency is wearing down children’s enthusiasm for the subject, it’s time to bring out the games, says Mike Askew...

I’m a fan of games in the mathematics classroom: pupils enjoy them and, once they know how to play, can return to the same formats time and again – which is more than can be said for a page of calculations.

There are many advantages to including games in pupils’ diet of mathematical tasks, and these include:

Practising skills

The repetitive nature of play in most games and, if the game is good, the motivation to keep on playing, means pupils get to practise skills many times over, until they become embedded.

Before starting a game it is important to share with children the skills they will be practising and, when finished, to check if pupils’ fluency has improved. If, for example, a game is intended to improve children’s recall of addition bonds, but children play by counting on in ones – rather than recalling what they know – it is not serving its purpose.

Deepening learning

There is research evidence that pupils do not always need to bring what they already know to a game, but can develop mathematical understanding through play. The researcher Robert Siegler, for example, has explored the impact of playing simple number track games for only a few minutes a day over a four-week period. His findings show that children entering school with limited mathematical understanding catch up with their peers by playing such games, and that the effect is sustained over time.

Developing strategic mathematical thinking

Many games providing practice are based largely in chance – rolling a die or selecting a card – and that’s fine, but a good game will also involve an element of strategy.

Strategy games are a great way of addressing the approach advocated in the new curriculum of enabling confident pupils to go deeper into the mathematics, rather than moving them on to further content; including an element of chance ensures that everyone can expect to win. Thus pupils can play chance and strategy games at different levels of sophistication and all get something out of them.

Assessment opportunities

Once pupils know how a game is played it requires little teacher input and so provides an opportunity to observe pupils, to note how fluent they are in the skill(s) involved and to identify any strategic thinking being used.

School home links

Many games require little equipment other than paper and pencil and so can be sent home for pupils to teach their families.

Encouraging learner independence

I often introduce games with some ambiguity in the rules. For example, in ‘Multiplication connect four’ (explained below) I would not mention that both paperclips can be placed on the same factor. An element of imprecision means questions will arise as a game is played and, in response to pupils asking if certain moves are allowed, the question can be turned back on them. What do they think? Will that rule make it a better game? Try it and see.

But of course, the best reason for playing a game is that it can be a great pleasure.

Reflecting on playing

Time needs to be spent reflecting on every game once it has been played. Questions to ask on every occasion include:

• How did it feel?
• What did you learn?
• What could you change?

It is important to discuss children’s emotional response, too – not everyone likes the competition that can be provoked by games, and that needs to be an OK response. How could the experience be made more pleasurable for all?

It is also helpful to ask pupils to change the game – they could change the rules, but they can also be challenged to change the mathematics. Having created a new version of the game, they can teach it to others and get feedback on whether or not it has worked.

Choosing games

There are a tremendous number of games to download from the internet, so how to choose between them? As well as looking to see whether or not a game addresses particular curriculum content, I ask myself two questions:

• Is the game just about practice or does it contain an element of strategy? Practice games are fine, but have a shorter shelf life.
• Can this be a frame-game? A frame-game is one in which the basic structure can be used repeatedly, while the content is changed to incorporate different mathematical skills. Games like Bingo and Connect Four (see below) are great frame-games: the basic forms can be used to create a multitude of games with different content. I came across the idea of ‘frame-game’ from the games developer Thiagi (whose website thiagi.com has many great examples). His games are mostly for corporative training but many can be adapted for the classroom.

Although not essential, I also look for games that do not require a lot of equipment beyond cards, dice, spinners or counters and are easy to set up.

Below is a selection of games that embody these principles. I make no claims to originality in creating these, so the sources are included – visiting these will open the door to a host of other possibilities.

1. Practice games

Fingers

Players: Three
Purpose: To practise fluency in addition bonds
Preparation: None

This game plays a little like ‘rock, paper, scissors’. Each player starts with one hand behind her back, then players take it in turns to chant “one, two, show”. On the word ‘show’, everyone brings forward their hand, holding up between 0 and five fingers. The first person to correctly call out the total number of fingers scores a point.

Variations: Hide both hands and show a number to 10. Play in pairs and call out the product of the two numbers.

Salute

Players: Three
Purpose: Practise fluency in addition and subtraction bonds.
Preparation: Each group needs a pack of playing cards with the picture cards removed (or half such a pack).

In each round, one player is The Captain who deals a card to each of the other players. When The Captain says “salute”, the other two players put their cards, number side out, up to their foreheads, without looking at them. They can, however, see the number on the other player’s card.

The Captain adds the two numbers on the cards and announces the total – for example, if The Captain can see 5 and 7, she says “Twelve”. The other two players each have to figure out what number is on their card. A point is awarded to the person who first correctly identifies her card.

Variation: The Captain calls out the product of the two numbers.

Twenty-five

Players: Three
Purpose: Practise fluency in addition and subtraction bonds.
Preparation: Each pair needs a pack of playing cards with the picture cards removed (or half such a pack)

Players mix the cards and place them face down between them. They take it in turns to flip over the top card, placing it in a face-up pile.

As each card is turned over, a running total is created. For example, if the first card turned over is 7 and the next player turns over 8, he calls out “Fifteen”.

If a card turned over will take the running total over 25, that player must subtract the value. So, if the running total is 23 and a 4 is turned over, the player says “Nineteen”. If the next card is, say, a 2, the player reverts to adding, announcing “Twenty one”; but if it was, say, a 9, he must again subtract. The winner is the player to say “Twenty five”. (Players shuffle the face up cards and turn them face down if they run out before reaching 25).

Variation: Changing the numbers on the cards and the target number opens up many possibilities.

2. Chance and strategy games

Multiplication bingo

Players: Class or group
Purpose: Practise fluency in multiplication bonds. Reasoning about which numbers are possible products.
Preparation: Each player needs a three-by-three grid. The ‘bingo caller’ (teacher if whole class, or one of the group members) needs a set of 36 cards with all the multiplication bonds from 1 x 1 to 6 x 6.

Everyone writes nine numbers from 1 – 36 on their grid, one number in each cell. The bingo caller then shuffles the cards and reads out one of the multiplication bonds. If the product is on a player’s board, he or she crosses it out. Play continues in this way, with the winner being the first to cross out three numbers in row – vertical, horizontal, or diagonal.

In this version of the game, players set up their boards before they know how the game will be played. That is deliberate as it means pupils are likely to put numbers on their board that are never going to get crossed out. The strategic challenge, before playing the game again, is to design a better bingo board, i.e. one that increases the chances of winning.

Variation:  An obvious variation of the game is to play with bonds to 10 x 10, or 12 x 12.

Multiplication connect four
Players: Pairs
Purpose: Practise fluency in multiplication bonds. Reasoning about strategies for winning.
Preparation: Each pair needs a copy of the playing board and a list of factors as illustrated (see Fig. 1). They need two paperclips and counters in two colours.

Player one puts a paperclip on one of the factors. Player two puts a paperclip on another factor, then multiplies together the two factors and covers the product on the board using a counter. For example, if the first paperclip is placed on the number 4 and the second player chooses to place his paperclip on the number six, he would then cover up 24 with his counter.

The first player then moves one paperclip to another factor and, if she can, covers the product on the board with a counter. (Both paperclips can be on the same factor.) The winner is the first player to get four counters in a row – vertical, horizontal or diagonal.

Pick a pair

Whatever the skill to be practised, there’s a maths game to match…

1. washmath.org

Games and resources written by teachers and lecturers from across Washington in the US. (Fingers, Salute and 25 can be found here).

2. nctm.org

The National Council of Teachers of Mathematics (NCTM) has members across the UK and Canada and although resources are written for ‘elementary’ schools, many can be applied to the UK curriculum.

3. Classroom gems

John Dabell’s book, Games, ideas and activities for primary mathematics (published by Longman, 2009) includes many suggestions, including Multiplication bingo.

4. nrich.maths.org

As the name of the website suggests, NRICH looks to share rich mathematics in meaningful contexts. Plenty of strategy games are available.

About the author

Mike Askew is adjunct professor at Monash University. Now working freelance, Mike teaches, researches and writes about primary mathematics (mikeaskew.net).