7249
/www/nrich/html/content/id/7249/
1
2011-02-01T00:00:01
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">This activity is a very practical one and it would be good to be
able to work with someone else on it. <br></br>
<br></br>
Here is the question we would like you to work on: <br></br>
<br></br>
<p style="font-weight: bold; font-style: italic;">What can you say
about the car that passes the school gates next Monday morning at
the end of playtime?</p>
<br></br>
What will you have to do in the time leading up to Monday to make a
statement that is very likely to be true?<br></br>
<br></br>
We would love to hear about what you did.<br></br>
<br></br>
What statement/s did you make? <br></br>
<br></br>
What information did you collect in order to make those statements?
<br></br>
<br></br>
How did you find out whether the statements were true? <br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<p><span class="editorial">A class from Culford School in Suffolk
UK all sent in a paragraph or two explaining how they went about
this activity. You can read everything they sent in this</span> <a class="editorial" href="/content/id/7249/Culford.doc">Word
document</a> <span class="editorial">or</span> <a class="editorial" href="/content/id/7249/Culford%20as%20pdf.pdf">this pdf</a><span class="editorial">.</span></p>
<p class="editorial">I was so impressed I contacted the teacher to
congratulate the pupils and to find out about how the work started.
This is what he wrote back;</p>
<br></br>
I used the challenge with the top sets in years 6 and 7,
deliberately choosing an easier (2*) open-ended task to allow them
to take it where they wished. This is something I do quite often
with the puzzles on the website as it allows an accessible start to
be taken as far as possible. It was introduced in the classroom
with the webpage up on the Interactive White Board so that they
could keep referring back to the original challenge whilst
discussing it in their groups and we could scribble on it and
highlight keywords. As you can see from their responses we covered
all sorts of eventualities from what happens if a car doesn't come
at the right time or if loads come on a car-transporter up to what
if the world ends on Sunday and does that make our prediction
invalid! The pupils decided on their strategy, location and time of
testing and the older ones devised the spreadsheets for the
surveying that were then used by both classes, with varying degrees
of success. They then collated the information into bar graphs and
pie charts before making their prediction. <br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><div class="embed">
<h2>The Car That Passes</h2>
This activity is a very practical one and it would be good to be able to work with someone else on it.<br></br>
<br></br>
Here is the question we would like you to work on:<br></br>
<br></br>
<p style="font-weight: bold; font-style: italic;">What can you say about the car that passes the school gates next Monday morning at the end of playtime?</p>
<br></br>
What will you have to do in the time leading up to Monday to make a statement that is very likely to be true?<br></br>
<br></br>
We would love to hear about what you did.<br></br>
<br></br>
What statement/s did you make?<br></br>
<br></br>
What information did you collect in order to make those statements?<br></br>
<br></br>
How did you find out whether the statements were true?</div>
<br></br>
<h3>Why do this problem?</h3>
<div>This <a href="http://nrich.maths.org/7249&part=">activity</a> is very appropriate when starting off the topic of probability, as is <a href="http://nrich.maths.org/7248&part=">In the Playground</a>. They both give the opportunity for pupils to make their own decisions and discover some important issues in this area of mathematics. This investigation will need to take place over a
period of several days.</div>
<br></br>
<h3>Possible approach</h3>
<div>This really needs to be presented as part of a class discussion. Pose the question, adapting it appropriately to suit your setting. Pupils will need to listen to each other's ideas and decide on what action needs to be taken. A 'brainstorming' session may be the result with learners suggesting surveying the traffic, focusing on, for example:</div>
<div style="margin-left: 40px;">The car's colour</div>
<div style="margin-left: 40px;">Who is driving the car</div>
<div style="margin-left: 40px;">The direction the car is traveling in</div>
<div style="margin-left: 40px;">The number of passengers in the car etc. etc.</div>
<div> </div>
<div>The pupils will probably need a few days to gather their information, perhaps in pairs or small groups, and then time to analyse it. They will then need to be given the chance to come up with their statements. Look out for children who use vocabulary associated with probability appropriately (such as 'very likely', 'likely', 'certain' etc.) and justify their statements using the data they
have gathered. This work would make a fantastic wall display.</div>
<div> </div>
<div>Ask the class how they will know if their statements are true. The only way is to test them at the specified time! Children can then reflect on their work. This reflection time is just as important as the previous stages and you can pose several questions, such as:</div>
<ul>
<li>Was the car as we expected?</li>
<li>Can we explain why some of the statements turned out to be true and some false?</li>
<li>What might have happened if we had collected data just for one day? Why?</li>
<li>What might have happened if w'?d collected data for longer? Why?</li>
</ul>
<br></br>
<h3>Key questions</h3>
<div>What things are you going to do to find out information?</div>
<div>Will you decide beforehand what you particularly want to look at when gathering information?</div>
<div>(After the event) What can you now say about the data you collected and what you have seen just now? </div>
<br></br>
<h3>Possible extension</h3>
Ideas for further investigation may well come from the pupils when the event is over and you've had a chance to discuss the appropriateness of the data collected.
<h3>Possible support</h3>
Some pupils may need support in gathering their information in a practical sense. This task is not intended to 'test' particular recording or presentation methods, rather it is intended to focus on the process of data collection and interpretation as a whole.<br></br>
<br></br>
<br></br>
<span style="font-style: italic;">You can read about some of the issues which might arise when teaching probability in</span> <a href="http://nrich.maths.org/7326&part=" style="font-style: italic;">this article</a><span style="font-style: italic;">.</span><br></br></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">What things are you going to do to find out information?<br></br>
How will you decide what statements to make about the car? <br></br>
How will you test whether the statements were true or not? <br></br></mdoxml>
5
3
0
1
0
0
0
The car that passes
What statements can you make about the car that passes the school
gates at 11am on Monday? How will you come up with statements and
test your ideas?
Using, Applying and Reasoning about Mathematics
Investigations
Probability
Experimental probability
Probability
Theoretical probability
Collecting Data
Data collection
Handling, Processing and Representing Data
Handling data
Handling, Processing and Representing Data
Interpreting data
Admin
Upper primary mapping document