2859
/www/nrich/html/content/id/2859/
1
2011-02-01T00:00:01
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<mdoxml version="1.0">You can use the computer to see what happens when Tania and Derek are playing a game with a dice. They roll the dice. If the number is odd, Tania wins that round.<br></br>
If the number is a six, Derek wins.<br></br>
(It doesn't matter who throws the die.)<br></br>
Who is more likely to win the game? Why? How could you make the game fair?<br></br>
<br></br>
You might like to use the interactivity below which will roll the dice many times.<br></br>
<a href="/content/id/2859/MusicalChairs.swf">Full Screen Version</a><br></br>
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<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<p class="editorial">Congratulations to all of you who sent in a
correct answer to this problem. There were too many of
you to name all of you here, but well done! The first correct
answer was sent in by Natasha and Nataneil:</p>
<p>Derek's chance is 1 in 6 whereas Tania's chance is 3 in 6 which
gives Tania a bigger chance to win.</p>
<p>This is because there are 6 numbers on a die and Derek has only
chosen 1, and because Tania has chosen 3 she has a bigger
probability to win!!!</p>
<p>To make the game fair one person should have all the odd numbers
and the other person have all the even numbers.</p>
<p class="editorial">I wonder if there are some other ways of
playing a fair game?</p>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><div class="embed">
<h2>Odds or Sixes?</h2>
You can use the computer to see what happens when Tania and Derek are playing a game with a dice. They roll the dice. If the number is odd, Tania wins that round.<br></br>
If the number is a six, Derek wins.<br></br>
(It doesn't matter who throws the die.)<br></br>
Who is more likely to win the game? Why? How could you make the game fair?<br></br>
<br></br>
You might like to use the interactivity below which will roll the dice many times.<br></br>
<a href="/content/id/2859/MusicalChairs.swf">Full Screen Version</a><br></br>
<mdo:flash height="400" id="/content/id/2859/MusicalChairs.swf" width="550"><param name="allowfullscreen" value="true"></param><param name="allowfullscreen" value="true"></param>
<param name="movie" value="/content/id/2859/MusicalChairs.swf"></param>
<param name="flashplayerversion" value="7"></param>
<param name="height" value="400"></param>
<param name="width" value="550"></param>
</mdo:flash></div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div><a href="http://nrich.maths.org/public/viewer.php?obj_id=2859&part=index">This problem</a> gives learners the opportunity to describe and predict outcomes, and consider the meaning of 'fair'. The interactivity simulates the die-throwing which means that data can be collected quickly and easily.</div>
<br></br>
<h3>Possible approach</h3>
<div>You could introduce this problem either by using the interactivity or by having two children come to the front to play it. Whichever way you choose, play the game a few times and if not using the interactivity, record the outcomes on the board. Ask the class to predict what would happen if the game was played many times, for example $100$ times. Take suggestions from the children, looking
out for those who justify their answer based on the few games which have already been played.</div>
<br></br>
<div>Suggest that the group tests out their theories. Again, this could be done using the 'Run x100' button on the interactivity or by pairs throwing dice and then collating class results. Bring pupils together to talk about their findings and ask them whether the game is fair or not and why. Listen out for explanations which compare the number of possible winning throws using appropriate
vocabulary. Some children might quantify the probability of throwing a six, for example, as $1$ out of $6$ or $\frac{1}{6}$ whereas throwing an odd number is $3$ out of $6$, or $\frac{1}{2}$.</div>
<br></br>
<div>It would be useful to encourage children to talk in pairs about what they understand as 'fair' - there will be different, but equally as valid, ideas about how to change the game.</div>
<br></br>
<h3>Key questions</h3>
<div>What numbers are possible to throw on the dice?</div>
<div>Who would win with each number?</div>
<div>Can you use this to decide how to make the game fair?</div>
<br></br>
<h3>Possible extension</h3>
<div>Learners could try <a href="http://nrich.maths.org/public/viewer.php?obj_id=4308&part=index">Odds and Evens</a> which extends the ideas in this problem.</div>
<br></br>
<h3>Possible support</h3>
<div>Having dice available will help those children who are not familiar with them and playing the game for themselves would also be of benefit.</div>
<br></br>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">If you are not using the interactivity, you could try using a real dice and making a note of who wins each time. What happens?<br></br><br></br>What numbers are possible to throw on the dice? Who would win with each number? Can you use this to decide how to make the game fair?<br></br><br></br></mdoxml>
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Odds or Sixes?
Use the interactivity or play this dice game yourself. How could
you make it fair?
Probability
Experimental probability
Information and Communications Technology
Interactivities
Mathematics Tools
Dice