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### Number and algebra

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### Advanced mathematics

# Up and Down Donkey

## Up and Down Donkey

This game used to be sold commercially so some families may have a box hiding in a cupboard!

**Version 2**

You can play the same game as above using sets of the following cards instead:

Cards with the numbers 1-10 written in words: 1-10WordNumberCards.pdf

Cards with the numbers 1-10 arranged in dot patterns - 1-10DotNumberCards.pdf or 1-10DotNumberCards2.pdf

Cards with the digits 1-10: 1-20NumberCards.pdf

**Version 3**

Using any of the sets of cards above, you can play a similar game but this time you build up twelve stacks in the centre. Six of the centre stacks must be the odd numbers in numerical order from 1 at the bottom to 9 at the top. The other six stacks must be the even numbers from 2 at the bottom to 10 at the top.

**Version 4**

In this version, as well as being able to place a card on one of the centre stacks, a player can also place a card on top of any other player's face-up stack. This can be done with the next higher or lower number e.g. a 7 or a 9 can be placed on an 8.

**Over to you ...**

Can you devise your own rules to make a more thought-provoking game? For example, you could build the centre stacks in the same way but allow players to put cards on their opponent's stacks which were multiples or factors of the top card. In this version the numbers 11, 13, 17 and 19 are the safest to have face up on top but 6 is much more risky. Why?
**Why play this game?**

Up and Down Donkey gives children the chance to become more fluent in counting, in a motivating context. The game is easily adaptable:

- you can offer variations which require some strategic (and therefore higher-order) thinking

and/or

- you can introduce higher-level content (e.g. odds/evens; factors/multiples), so the game supports children's understanding of the structure of our number system.

**Possible approach**

This may be most easily introduced to a small group of children. If possible, begin to play the game against another adult completely in silence, using six sets of the most appropriate cards (1-10DotNumberCards.pdf or 1-10DotNumberCards2.pdf or 1-10DigitNumberCards.pdf or 1-10WordNumberCards.pdf or 1-20NumberCards.pdf). Explain to the group that you'd like them to watch carefully to see whether they can work out how to play. Stop after a suitable number of turns
and suggest that the children talk in pairs about the possible rules of the game.

Carry on playing to give learners chance to reflect on their discussions, and then bring everyone together to clarify how they think they play the game.

Once the group has decided upon the rules and how to win, give pairs of children copies of the cards. Give them time to play several times so that they become immersed in the game. You may like to leave sets of the cards available for the children to use during their own free time or play times.

Set aside some time to talk to the whole group about the game. This might be better done a week or so after first introducing the game when they have had chance to play many times. Invite comments about whether they think it is a good game and why/why not. How could they make it better? At this point you could introduce one of the suggested variations or suggest the children make up their own versions. It might be helpful for some children to have guidance as to how to vary the game. For example, you could specifically ask them to create some different cards. Or you could ask them to suggest a different rule for the centre stacks. It's important that pairs try out their new versions, to check that the game works!

#### Key questions

Which number/s do we need next for the centre stack/s?

Where could you put that card?

#### Possible extension

Having the opportunity to create their own version of the game gives learners the chance to show you what they can do, without you setting a 'ceiling' of possible achievement.

#### Possible support

Play with a group of children and deliberately talk out loud as you do so, explicitly voicing the decisions you are making. Not only will this reinforce the rules, but it will model the thinking processes too.

Or search by topic

Age 5 to 11

Challenge Level

- Game
- Teachers' Resources

This game used to be sold commercially so some families may have a box hiding in a cupboard!

Here we will describe several versions of the game but you will also be able to invent your own games by creatively varying the rules.

**Version 1**

All you need are six sets of these cards which feature the numbers 1 to 10.

*Objective*

The object of the game is to build up six stacks in the middle of the table, face up, in order from 1 at the bottom to 10 on the top. The first player to get rid of all his cards is the winner. If the game has to stop at a pre-arranged time the player with the fewest cards wins.

*Rules*

- The cards are shuffled well and all the cards are dealt face down to the players. (Note that 120 can be divided exactly by 2, 3, 4, 5 and 6 - the number of players that can take part.) Without looking at them, the players pile up their cards into a stack, face down in front of them.
- The first player on the left of the dealer starts by turning over the top card of her personal stack. If it is a 1 she can start a stack in the centre and she can go on playing as long as she can put her cards onto the centre stacks (for example if her second card is a 1 or a 2). With the first card she is unable to build onto one of the centre stacks, she starts her own face-up stack in front of herself. This ends her turn.
- From now on play is a little different, each player can:
- Look to see if he can place the top card of his face-up stack on a centre stack. He can then either place the next card(s) from his face-up stack on the centre stacks, according to the rules given.
- When this is impossible he turns over the next card of his face-down stack and places it on a centre stack. If he can't do that, it goes on top of his own face-up stack.

- Whenever a player disposes of a card on a centre stack she has another turn. The turn ends when the player has to place a card on her own face-up stack.
- If a player makes a mistake the other players call out WRONG and each hands him one of his own cards which the wrongdoer puts on his face-down stack.
- When a player has used up her face-down stack she turns over her face-up stack and carries on.

You can play the same game as above using sets of the following cards instead:

Cards with the numbers 1-10 written in words: 1-10WordNumberCards.pdf

Cards with the numbers 1-10 arranged in dot patterns - 1-10DotNumberCards.pdf or 1-10DotNumberCards2.pdf

Cards with the digits 1-10: 1-20NumberCards.pdf

Using any of the sets of cards above, you can play a similar game but this time you build up twelve stacks in the centre. Six of the centre stacks must be the odd numbers in numerical order from 1 at the bottom to 9 at the top. The other six stacks must be the even numbers from 2 at the bottom to 10 at the top.

In this version, as well as being able to place a card on one of the centre stacks, a player can also place a card on top of any other player's face-up stack. This can be done with the next higher or lower number e.g. a 7 or a 9 can be placed on an 8.

Can you devise your own rules to make a more thought-provoking game? For example, you could build the centre stacks in the same way but allow players to put cards on their opponent's stacks which were multiples or factors of the top card. In this version the numbers 11, 13, 17 and 19 are the safest to have face up on top but 6 is much more risky. Why?

Up and Down Donkey gives children the chance to become more fluent in counting, in a motivating context. The game is easily adaptable:

- you can offer variations which require some strategic (and therefore higher-order) thinking

and/or

- you can introduce higher-level content (e.g. odds/evens; factors/multiples), so the game supports children's understanding of the structure of our number system.

Carry on playing to give learners chance to reflect on their discussions, and then bring everyone together to clarify how they think they play the game.

Once the group has decided upon the rules and how to win, give pairs of children copies of the cards. Give them time to play several times so that they become immersed in the game. You may like to leave sets of the cards available for the children to use during their own free time or play times.

Set aside some time to talk to the whole group about the game. This might be better done a week or so after first introducing the game when they have had chance to play many times. Invite comments about whether they think it is a good game and why/why not. How could they make it better? At this point you could introduce one of the suggested variations or suggest the children make up their own versions. It might be helpful for some children to have guidance as to how to vary the game. For example, you could specifically ask them to create some different cards. Or you could ask them to suggest a different rule for the centre stacks. It's important that pairs try out their new versions, to check that the game works!

Where could you put that card?