6074
/www/nrich/html/content/id/6074/
1
2011-02-01T00:00:01
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<mdoxml version="1.0"><br></br>
Here is a game that uses two dice and cards with the numbers $1$ to $12$ on them. The aim of the game is to turn over all the cards. You can turn over the cards that match the numbers on the dice.
<div style="text-align: center;"><mdo:image src="Picture%201.jpg" style="width: 598px; height: 383px;"></mdo:image></div>
<div class="framework"><strong>Notes for adults</strong><br></br>
<br></br>
To play the game, start with the numbers showing on all the cards.<br></br>
<br></br>
The first player rolls the two dice.<br></br>
They can turn over the cards which are the same as the numbers rolled.<br></br>
For example, if a $4$ and a $5$ is rolled, they would turn over the $4$ and $5$ cards. If a double is thrown, the player's turn ends. They can roll the dice again until they can't turn over any more cards. The cards that are left showing are then added and that is their score.<br></br>
The dice are then passed to the next player who turns the cards the right way up again and then rolls the dice in the same way as player one. They now can keep on rolling dice as long as each time they can turn over some new cards. Remember that if a double is thrown, the player's turn ends. When the player can't turn over any more cards, those that are left are added together and that is the
player's score.<br></br>
The winner is the person with the lower score.<br></br>
It can be played with just one turn each or each player can have a number of turns that you decide at the beginning of the game.<br></br>
Here <a class="doclink" href="/content/id/6074/digitcardsnew.doc">.doc</a> <a class="pdflink" href="/content/id/6074/digitcards.pdf">.pdf</a> are some cards which you could print out and cut up to play the game.</div>
<br></br>
You can also play it on the computer using this interactivity.<br></br>
<br></br>
<br></br>
<a href="/content/id/6074/ShutTheBox.swf">Full screen version</a><br></br>
<mdo:flash height="400" id="/content/id/6074/ShutTheBox.swf" width="650"><param name="allowfullscreen" value="true"></param><param name="allowfullscreen" value="true"></param>
<param name="movie" value="/content/id/6074/ShutTheBox.swf"></param>
<param name="flashplayerversion" value="9"></param>
</mdo:flash><br></br>
<br></br>
<h4 style="text-align: center;"> </h4>
<br></br>
<br></br>
<div class="framework"><strong>Notes for adults</strong><br></br>
<br></br>
Additional information about the interactive resource:<br></br>
<br></br>
In variation $1$, you turn over the number shown on one or both dice.<br></br>
In variation $2$, you turn over the value of both dice, their sum, or their difference.<br></br>
In variation $3$, you turn over a combination of numbers that add up to the sum of the dice.<br></br>
In variation $4$, you turn over a combination of numbers that add up to the product of the dice.<br></br>
The "SCORE - SUM" uses scoring by adding the cards that are left.<br></br>
The "SCORE - CONCATENATE" uses scoring by reading the dice scores as digits in a two digit number.</div>
<br></br></mdoxml>
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<mdoxml version="1.0"><br></br>
There is no particular solution to this game.<br></br>
Some people have tried other rules;<br></br>
$1$. You can choose to turn over the numbers you've rolled, or add them together, or subtract one from the other. For example, if you were to roll a $5$ and $4$ you could choose to turn the $4$ and the $5$ over OR you could choose to add or subtract so that you could turn either the $9$ or the $1$ over.<br></br>
$2$. When you came to a stop because you were unable to turn over new numbers, then those two dice numbers pass to the next player who can use them rather than rolling the dice again.<br></br>
$3$. You can choose to turn over any set of cards that has the same total as the dice numbers you have thrown. For example, if you throw a 4 and 5, you could choose to turn over:<br></br>
$4 & 5$ or $9$ or $1 & 8$ or $2 & 7$ or $3 & 6$ or $1 & 2 & 6$ or $1 & 3 & 5$ or $2 & 3 & 4$<br></br>
$4$. You could multiply the two numbers on the dice together and then turn over any set of numbers which has that total. For example, if you throw 4 and 5, as well as the above, you could also choose to turn over:<br></br>
$8 & 12$ or $9 & 11$ or $4 & 6 & 10$ or $1 & 2 & 3 & 4 & 10$, etc.<br></br>
So, try these different versions of the game and different ways of scoring, and tell us what you think works best and why.</mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><div class="embed">
<h2>Shut the Box</h2>
<br></br>
Here is a game that uses two dice and cards with the numbers 1 to 12 on them. The aim of the game is to turn over all the cards. You can turn over the cards that match the numbers on the dice.
<div style="text-align: center;"><mdo:image src="Picture%201.jpg" style="width: 598px; height: 383px;"></mdo:image></div>
<div class="framework"><strong>Notes for adults</strong><br></br>
<br></br>
To play the game, start with the numbers showing on all the cards.<br></br>
<br></br>
The first player rolls the two dice.<br></br>
They can turn over the cards which are the same as the numbers rolled.<br></br>
For example, if a $4$ and a $5$ is rolled, they would turn over the $4$ and $5$ cards. If a double is thrown, the player's turn ends. They can roll the dice again until they can't turn over any more cards. The cards that are left showing are then added and that is their score.<br></br>
The dice are then passed to the next player who turns the cards the right way up again and then rolls the dice in the same way as player one. They now can keep on rolling dice as long as each time they can turn over some new cards. Remember that if a double is thrown, the player's turn ends. When the player can't turn over any more cards, those that are left are added together and that is the
player's score.<br></br>
The winner is the person with the lower score.<br></br>
It can be played with just one turn each or each player can have a number of turns that you decide at the beginning of the game.<br></br>
Here <a class="doclink" href="/content/id/6074/digitcardsnew.doc">.doc</a> <a class="pdflink" href="/content/id/6074/digitcards.pdf">.pdf</a> are some cards which you could print out and cut up to play the game.<br></br>
</div>
<br></br>
You can also play it on the computer using this interactivity.<br></br>
<br></br>
<a href="/content/id/6074/ShutTheBox.swf">Full screen version</a><br></br>
<mdo:flash height="400" id="/content/id/6074/ShutTheBox.swf" width="650"><param name="allowfullscreen" value="true"></param><param name="allowfullscreen" value="true"></param>
<param name="movie" value="/content/id/6074/ShutTheBox.swf"></param>
<param name="flashplayerversion" value="9"></param>
</mdo:flash><br></br>
<br></br>
<h4 style="text-align: center;"> </h4>
<br></br>
<br></br>
<div class="framework"><strong>Notes for adults</strong><br></br>
<br></br>
Additional information about the interactive resource:<br></br>
<br></br>
In variation $1$, you turn over the number shown on one or both dice.<br></br>
In variation $2$, you turn over the value of both dice, their sum, or their difference.<br></br>
In variation $3$, you turn over a combination of numbers that add up to the sum of the dice.<br></br>
In variation $4$, you turn over a combination of numbers that add up to the product of the dice.<br></br>
The "SCORE - SUM" uses scoring by adding the cards that are left.<br></br>
The "SCORE - COCATENATE" uses scoring by reading the dice scores as digits in a two digit number.</div>
</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this game?</span></h3>
<div><a href="http://nrich.maths.org/public/viewer.php?obj_id=6074&part=index">This game</a> can give pupils the opportunity to use their number knowledge and it can be adapted to stretch even the highest attainers. In its simplest form it can be accessed by anyone in the class who is able to connect the number of spots on a die to the numeral that represents it. Altering the rules will give
the children opportunities to explore ideas about what makes a "good" game and to develop winning strategies to play their games.</div>
<br></br>
<h3>Possible approach</h3>
<div>Start with the basic rules and play the game as a class, or perhaps one half of the class against the other, perhaps using large dice. You could use an interactive whiteboard with digits to erase, use "real " <a class="doclink" href="/content/id/6074/digitcardsnew.doc">.doc</a> <a class="pdflink" href="/content/id/6074/digitcards.pdf">.pdf</a> larger cards fixed to an ordinary board with Blu
Tack, or you could simply have the numbers written on the board and cross them out. You could also use the <a href="/content/id/6074/ShutTheBox.swf">interactive version</a> of the game. After playing a few times, encourage the children to be critical of the game. The game offers opportunities for the teacher to identify the children's understanding the meanings of numbers to $6$ and linking their
iconic representation on dice with their numeral.</div>
<br></br>
<div>Pairs of children could then test out the different versions of the game with the aim of explaining why they thought it was good or not so good. This could then lead into a whole-class discussion about features of "good" mathematical games in general. Invite the learners to suggest what else could be changed in the game. Identifying the variables in this way (for example, number of players,
type of dice, number of cards etc) is a useful skill which children can apply again and again. Pairs could test their own version to see whether they have made a good game.</div>
<br></br>
<h3>Key questions</h3>
These questions have been phrased in ways that will help the teacher to identify the children's prior knowledge about both the number concepts involved in playing the game and the strategies and mathematical thinking needed to win.<br></br>
<br></br>
<h4>Number concepts</h4>
How many spots can you see on the two dice?<br></br>
Which cards will you turn over?<br></br>
<div>Can you tell me about why you chose to turn those numbers over?<br></br>
</div>
<h4>Strategies, problem solving and reasoning</h4>
What is good about the game? What is not so good? Why? How could you alter the rules to make it better?<br></br>
<div>Which cards <span style="font-style: italic;">could</span> you turn over? Which would be best? Why?</div>
What else could we change about the game?<br></br>
<br></br>
<h3>Possible extension</h3>
By giving learners the chance to invent their own rules, children can take responsibility for their own mathematics and demonstrate their potential. You can use $12$ numbered cards instead of $6$ and add, subtract or multiply the scores on the two dice together to find the number to turn over. It may be worth considering changing the rule which ends the turn when double is thrown.<br></br>
<h3><br></br>
Possible support</h3>
<div>Most children will find it manageable to use numbers $1$- $6$ to start with. Do let them go on to explore their own games, they may well surprise you!</div>
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<mdoxml version="1.0">Which cards <span style="font-style: italic;">could</span> you turn
down using the numbers you've rolled?<br></br>
If you've got several choices, how will you decide what to
do?<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">There is no particular solution to this game.<br></br>
Some people have tried other rules;<br></br>
$1$. You can choose to turn over the numbers you've rolled, or add them together, or subtract one from the other. For example, if you were to roll a $5$ and $4$ you could choose to turn the $4$ and the $5$ over OR you could choose to add or subtract so that you could turn either the $9$ or the $1$ over.<br></br>
$2$. When you came to a stop because you were unable to turn over new numbers, then those two dice numbers pass to the next player who can use them rather than rolling the dice again.<br></br>
$3$. You can choose to turn over any set of cards that has the same total as the dice numbers you have thrown. For example, if you throw a 4 and 5, you could choose to turn over:<br></br>
$4 & 5$ or $9$ or $1 & 8$ or $2 & 7$ or $3 & 6$ or $1 & 2 & 6$ or $1 & 3 & 5$ or $2 & 3 & 4$<br></br>
$4$. You could multiply the two numbers on the dice together and then turn over any set of numbers which has that total. For example, if you throw 4 and 5, as well as the above, you could also choose to turn over:<br></br>
$8 & 12$ or $9 & 11$ or $4 & 6 & 10$ or $1 & 2 & 3 & 4 & 10$, etc.<br></br>
So, try these different versions of the game and different ways of scoring, and tell us what you think works best and why.</mdoxml>
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Shut the box
An old game but lots of arithmetic!
Calculations and Numerical Methods
Addition & subtraction
Calculations and Numerical Methods
Multiplication & division
Using, Applying and Reasoning about Mathematics
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Lower primary mapping document