1176
/www/nrich/html/content/03/06/penta3/
1
2011-02-01T00:00:01
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">
<link href="../../../liz_Style_Sheets/acknowledgement.css" rel="stylesheet" type="text/css"></link>
<style type="text/css">
/**/
p.c1 {text-align: center}
/**/
</style>
<p>Anna and Becky were playing a game. They put one purple cube and
two yellow cubes into a bag.</p>
<p class="c1"><mdo:image src="cubes.gif" alt="one purple and two yellow cubes" width="146" height="134"></mdo:image></p>
<p>First Anna picked a cube out of the bag without looking, then
Becky picked one out.<br></br>
If the two cubes the girls picked out were the same colour, Anna
won the game. If they picked out two differently coloured cubes,
then Becky was the the winner.</p>
<p>Is this a fair game?<br></br>
Explain your answer.</p>
<p class="acknowledgement">Thank you to Doug Williams from the
<a href="http://www.blackdouglas.com.au/taskcentre">Mathematics
Task Centre Project</a> for this problem. If you'd like to take
this idea a bit further, look at <a href="../public/viewer.php?obj_id=919">In a Box</a>.</p>
</mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<p><span class="editorial">Simone sent us her work on this
problem:</span></p>
<div>I tried playing this game with my partner at school, and he
won much more often than me. He won if the colours were different,
and I won if the colours were the same.</div>
<div>I think this is because there are three different pairs that
could come out when we take the cubes out: it could be purple
yellow, or yellow yellow, or yellow purple. Each one is just as
likely. But Becky wins on two of these, and Anna only wins on one.
So the game isn't fair.</div>
<div> </div>
<p class="editorial">Well done, Simone. I wonder how you know
that all three of the possibilities are equally likely? </p>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><div class="embed">
<h2>Same or Different?</h2>
<p>Anna and Becky were playing a game. They put one purple cube and two yellow cubes into a bag.</p>
<p class="c1"><mdo:image alt="one purple and two yellow cubes" height="134" src="cubes.gif" width="146"></mdo:image></p>
<p>First Anna picked a cube out of the bag without looking, then Becky picked one out.<br></br>
If the two cubes the girls picked out were the same colour, Anna won the game. If they picked out two differently coloured cubes, then Becky was the the winner.</p>
<p>Is this a fair game?<br></br>
Explain your answer.</p>
<p class="acknowledgement">Thank you to Doug Williams from the <a href="http://www.blackdouglas.com.au/taskcentre">Mathematics Task Centre Project</a> for this problem. If you'd like to take this idea a bit further, look at <a href="../public/viewer.php?obj_id=919">In a Box</a>.</p>
</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=1176&part=index">This problem</a> provides a context in which pupils can explore the likelihood of events and therefore gain experience in using appropriate vocabulary.</div>
<br></br>
<h3>Possible approach</h3>
<div>You could set this problem up by acting it out with two children. Put three cubes, two of one colour and one of a different colour, in a bag and explain how the game works. Play a few times and ask the whole group to consider whether they think it is a fair game or not. Their answers may well depend on the outcomes of the games they have seen, for example someone may suggest that it is fair
because each child happened to win twice each. In other circumstances, someone may suggest it isn't fair because one child won more games than the other.</div>
<br></br>
<div>Ask learners what they would expect to happen if you played many, many more games. Give them time to think about this in pairs and have cubes available for them to work with should they want them. As the children discuss the problem, listen out for those who are looking at all the possibilities and analysing each in turn.</div>
<br></br>
<div>In the plenary, invite some pairs to share their methods and explanations for their solution. It would be helpful for them to write on the whiteboard as they talk so that the processes are recorded. Some may justify their answer in terms of numbers of possible ways that Anna/Becky can win. Some may have given probabilities in terms of fractions for each girl winning, but this is not
necessary for a full and convincing solution.</div>
<br></br>
<h3>Key questions</h3>
<div>What colour cube <span style="font-style: italic;">could</span> Anna pick from the bag? What are Becky's options then?</div>
<div>What are all the different ways that two cubes could be taken from the bag?</div>
<br></br>
<h3>Possible extension</h3>
<div>Children could try <a href="http://nrich.maths.org/public/viewer.php?obj_id=919&part=index">In aBox</a> which takes these ideas a bit further.</div>
<br></br>
<h3>Possible support</h3>
<div>Encouraging children to list all the different ways to pick out two cubes will help them access this problem.</div>
<br></br>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<p>Try playing the game a large number of times (e.g. $30$ or more)
with a friend and record who wins each time. You could do this at
school and ask members of your class to play five games in pairs,
then gather all the results together. Did someone seem to win more
often?</p>
<p>If the first cube drawn out of the bag is purple, what is the
chance that the next one is the same? Or different?<br></br>
What about if the first cube is yellow?</p>
<br></br></mdoxml>
2
4
0
1
0
0
0
Same or Different?
Anna and Becky put one purple cube and two yellow cubes into a bag
to play a game. Is the game fair? Explain your answer.
Probability
Theoretical probability
Admin
Upper primary mapping document