2400
/www/nrich/html/content/id/2400/
1
2011-02-01T00:00:01
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<p>It was raining and Tom, Vincent, Charlie and Edward had been playing a game with dice during break.</p>
<p>"You never get a six when you want one," grumbled Charlie, "I'm sure sixes come less than the other numbers!"</p>
<p style="text-align: center;"><mdo:image alt="a die" height="68" src="2400.png" width="75"></mdo:image></p>
<p>Miss Brown heard him.</p>
<p>"You can all try throwing dice and noting what you get," she said, "It fits in quite well with the work we are going to do next. Throw the dice and make a list of what you get. See if you get less sixes then."</p>
<p>"It's only when it matters if you get a six," grumbled Charlie.</p>
<p>Miss Brown thought for a moment.</p>
<p>"I'll give a Team Point to the one who gets the most sixes," she said, "Mind you, no cheating!"</p>
<p>"Wow!" exclaimed Vincent.</p>
<p>The boys worked in pairs and made lists of their throws. They all threw the dice the same number of times. Here is the list that Tom made for Edward's throws:</p>
<p align="center"><mdo:image align="top" alt="tally chart to show throws of die" bgcolor="" height="226" src="dice2.gif" width="108"></mdo:image></p>
<p>They decided to make each of the numbers on the dice a different colour when they recorded the work so they could compare them easily.<br></br>
<br></br>
Here is the graph Edward made from his figures:</p>
<p align="center"><mdo:image align="top" alt="bar chart to show throws of die" bgcolor="" height="256" src="dice3.gif" width="241"></mdo:image></p>
<p><br></br>
Here is Charlie's unfinished graph (he hasn't labelled anything yet):</p>
<p align="center"><mdo:image alt="" height="223" src="NewDice.png" width="251"></mdo:image></p>
<p><br></br>
Here is Tom's unfinished graph:</p>
<p align="center"><mdo:image align="top" alt="scatter graph to show throws of die" bgcolor="" height="181" src="dice5.gif" width="178"></mdo:image></p>
<p><br></br>
Here is Vincent's unfinished pie-chart:</p>
<p align="center"><mdo:image align="top" alt="pie chart to show throws of die" bgcolor="" height="172" src="dice6.gif" width="172"></mdo:image></p>
<p><br></br>
Who won the Team Point for the most sixes?</p>
<p>How many $1$s, $2$s, $3$s, $4$s, $5$s and $6$s were thrown altogether?</p>
<p>What percentage (or: How many out of $100$) of the throws were sixes?</p>
<br></br>
<div><a href="http://nrich.maths.org/public/viewer.php?obj_id=6839&part=">Click here for a poster of this problem</a>.</div>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<p class="editorial">Lisa from Haberdashers Askes School for Girls answered the questions:</p>
<br></br>
Charlie threw the most 6's.<br></br>
<br></br>
15 6's were rolled,<br></br>
15 5's were rolled,<br></br>
21 4's were rolled,<br></br>
11 3's were rolled,<br></br>
21 2's were rolled,<br></br>
17 1's were rolled.<br></br>
15% of the100 throws were 6's<br></br>
<br></br>
<p class="editorial">Thank you also to Akalya, Vanessa and Kirsty from Devonshire Primary School who sent in a clear solution to this problem.</p>
<br></br>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><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=2400&part=index">
This problem</a> challenges learners to interpret data carefully
and to search for all the information that there is implicit in any
graphical representation. The question encourages them to contrast
different ways of representing similar data and helps to make
explicit their interpretation of what the data represents in order
to solve the problem.</div>
<br></br>
<div>Later on in secondary school children often leave out the
labels on axes so rendering the representation meaningless. This
question will help children to realise the significance of the
labels.</div>
<br></br>
<h3>Possible approach</h3>
<div>You could get the group to make about sixteen throws of a die
and make a rough bar chart of the results of the throws on the
board. Then give a brief introduction to the problem as given
'?? just reading will probably be
sufficient.</div>
<br></br>
<div>After this learners could work in pairs on the actual problem
from a computer or a printed sheet so that they are able to talk
through their ideas with a partner.</div>
<br></br>
<div>At the end of the lesson you should discuss not only the
answers to the problem itself, and how these were reached, but also
to stress why it is important not to leave out the labels on axes
of a graph.</div>
<br></br>
<h3>Key questions</h3>
<div>What number does green (etc) represent?</div>
<div>What colour is six (etc)?</div>
<div>How can you label this axis?</div>
<div>How many times did they all throw the dice?</div>
<br></br>
<h3>Possible extension</h3>
Learners could make graphical representations of their own dice
throws or do <a href="http://nrich.maths.org/public/viewer.php?obj_id=2399&part=index">
How Big Are Classes 5, 6 and 7?</a> <br></br>
<h3>Possible support</h3>
Suggest trying <a href="http://nrich.maths.org/public/viewer.php?obj_id=247&part=index">
The Pet Graph</a> first which is simpler and easier to
understand.<br></br>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<p>Remember that all the boys threw the dice $25$ times and that the colours of the numbers remain the same for all diagrams.<br></br>
<br></br>
The 25 throws are represented by 360 degrees on the pie chart. How many degrees will be needed to represent each throw?</p>
<br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
Tom won the team point<br></br>
1-17 throws, 2-21, 3-11, 4-20, 5-15, 6-16<br></br>
16%<br></br>
<br></br>
<br></br>
<br></br>
<br></br></mdoxml>
2
3
0
1
0
0
0
You Never Get a Six
Charlie thinks that a six comes up less often than the other
numbers on the dice. Have a look at the results of the test his
class did to see if he was right.
Fractions, Decimals, Percentages, Ratio and Proportion
Calculating with percentages
Handling, Processing and Representing Data
Bar charts
Probability
Experimental probability
Handling, Processing and Representing Data
Pie charts