7522
/www/nrich/html/content/id/7522/
1
2011-08-15T09:52:19
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<br></br>
<p>Here are the lists of first names of the members of Class 5. (They are in alphabetical order of their surnames so they do not seem to be ordered.)<br></br>
</p>
<div style="text-align: center;"><mdo:image width="270" height="306" alt="list of names" src="Alphabet2.png"></mdo:image></div>
<br></br>
<p>One day when $34$ children were in class, Mrs Clifton, their teacher, said they were going to make some block graphs and other things using their first names. She put the class lists onto the white board.<br></br>
<br></br>
First, the class made tally charts of the initial letters of their names. They worked in pairs.<br></br>
The first part of Becky and Selma's tally looked like this:</p>
<p> </p>
<div style="text-align: center;"><mdo:image width="95" height="201" alt="tally" src="Alphabet3.png"></mdo:image></div>
<br></br>
<p>Can you make a full tally chart using the class names?<br></br>
<br></br>
Next they all made frequency tables using this information.<br></br>
This is the first part of Alan and Joe's table:</p>
<p> </p>
<div style="text-align: center;"><mdo:image width="180" height="201" alt="frequency" src="Alphabet4.png"></mdo:image></div>
<br></br>
<p>Can you make a frequency table using all the class's names?<br></br>
<br></br>
Next they decided which letters of the alphabet were needed and which were not needed to make a block graph of their class names. Then the boys took yellow squares and the girls took pale blue squares, drew a picture of themselves and put the initial of their first name on the square and stuck it onto paper to make a pictogram graph.<br></br>
<br></br>
The last part of the class's block graph looked like this:</p>
<div style="text-align: center;"> </div>
<div style="text-align: center;"><mdo:image width="207" height="257" alt="pictogram" src="Alphabet1B.png"></mdo:image></div>
<br></br>
<br></br>
<p>Can you see who was away from school that day from this information?<br></br>
<br></br>
Next they made true block graphs from the class lists to include anyone who was away that day.<br></br>
<br></br>
This is part of the middle of the block graph:</p>
<p> </p>
<div style="text-align: center;"><mdo:image width="162" height="142" alt="block graph" src="Alphabet5.png"></mdo:image></div>
<br></br>
<p>Can you tell what letters these were?<br></br>
Can you make a block graph of all the class?</p>
<br></br>
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<p><span class="editorial">This was a complex challenge to solve with a number of parts to it.</span></p>
<p><span class="editorial">Thank you to everyone who submitted a solution, or part solution.</span></p>
<p><span class="editorial">Here are those that showed solutions to many or all of the parts of the challenge.</span></p>
<p> </p>
<p><span class="editorial">Firstly, Class 2 from Goodleigh School in the UK sent in this contribution:</span></p>
<p><br></br>
First we put all the names into a tally chart by going down the list one by one.<br></br>
Then we put the tally numbers into frequency order.<br></br>
It looked like this:<br></br>
A=$6$ J=$5$ B=$3$ D=$3$ H=$3$ P=$3$ S=$3$ T=$3$ M=$2$ N=$2$ W=$2$<br></br>
Then we looked at the chart and we saw that there was a T missing,So we knew that Tessa was away.In the block graph the letters were: JMNPS<br></br>
</p>
<p style="text-align: center;"><br></br>
<mdo:image src="class2%20chart1.png"></mdo:image></p>
<p style="text-align: center;"> </p>
<p><br></br>
<span class="editorial">Next we have Daisy and Rosie from St Nicolas Junior School, Newbury UK who sent in these two pieces of work:</span></p>
<p style="text-align: center;"><mdo:image src="Oct%202011%20Daisy%202.jpg"></mdo:image></p>
<p style="text-align: center;"><mdo:image src="Oct%202011Rosie%202.jpg"></mdo:image></p>
<p><br></br>
<span class="editorial">Lastly this came from Eliza at Moonee Ponds Central Primary School in Australia.</span></p>
<p><span class="editorial">We can only include a small part on this page, as she sent in a big file. You can look at the whole file</span> <a href="/content/id/7522/Oct%202011%20Eliza.doc">here</a> <span class="editorial">.</span></p>
<p style="text-align: center;"><mdo:image src="Eliza%20Oct%202011.png"></mdo:image></p>
<p> </p>
<p> </p>
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<h2>Class 5's Names</h2>
<br></br>
<p>Here are the lists of first names of the members of Class 5. (They are in alphabetical order of their surnames so they do not seem to be ordered.)<br></br>
</p>
<div style="text-align: center;"><mdo:image alt="list of names" height="306" src="Alphabet2.png" width="270"></mdo:image></div>
<br></br>
<p>One day when $34$ children were in class, Mrs Clifton, their teacher, said they were going to make some block graphs and other things using their first names. She put the class lists onto the white board.<br></br>
<br></br>
First, the class made tally charts of the initial letters of their names. They worked in pairs.<br></br>
The first part of Becky and Selma's tally looked like this:</p>
<p> </p>
<div style="text-align: center;"><mdo:image alt="tally" height="201" src="Alphabet3.png" width="95"></mdo:image></div>
<br></br>
<p>Can you make a full tally chart using the class names?<br></br>
<br></br>
Next they all made frequency tables using this information.<br></br>
This is the first part of Alan and Joe's table:</p>
<p> </p>
<div style="text-align: center;"><mdo:image alt="frequency" height="201" src="Alphabet4.png" width="180"></mdo:image></div>
<br></br>
<p>Can you make a frequency table using all the class's names?<br></br>
<br></br>
Next they decided which letters of the alphabet were needed and which were not needed to make a block graph of their class names. Then the boys took yellow squares and the girls took pale blue squares, drew a picture of themselves and put the initial of their first name on the square and stuck it onto paper to make a pictogram graph.<br></br>
<br></br>
The last part of the class's block graph looked like this:</p>
<div style="text-align: center;"> </div>
<div style="text-align: center;"><mdo:image alt="pictogram" height="257" src="Alphabet1B.png" width="207"></mdo:image></div>
<br></br>
<br></br>
<p>Can you see who was away from school that day from this information?<br></br>
<br></br>
Next they made true block graphs from the class lists to include anyone who was away that day.<br></br>
<br></br>
This is part of the middle of the block graph:</p>
<p> </p>
<div style="text-align: center;"><mdo:image alt="block graph" height="142" src="Alphabet5.png" width="162"></mdo:image></div>
<br></br>
<p>Can you tell what letters these were?<br></br>
Can you make a block graph of all the class?</p>
</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div><a href="http://nrich.maths.org/7522&part=">This problem</a> uses simple and manageable information to illustrate various methods of recording data. The questions require learners to interpret the data presented as well as to re-present the data in different ways themselves. You could also encourage children to look at ways to present data more critically by discussing which
method they think is best and why.</div>
<div> </div>
<h3>Possible approach</h3>
<div>The focus of this particular task is not on data collection itself, but you may wish to tackle this problem once the children have had some experience of creating their own tally charts, frequency tables and bar charts. Alternatively, the activity could be a vehicle for introducing some different ways of representing data which learners may not have come across before. </div>
<div> </div>
<div>Tell the 'story' of the problem and invite pupils to work in pairs. They might find it useful to have a <a href="/content/id/7522/Class5.pdf">copy of the names</a> given at the beginning of the problem and this sheet which contains the tally chart, fequency table and bar chart. Allow pairs to choose the resources they need to create the different representations,
although having squared paper easily available is likely to be helpful.</div>
<div> </div>
<p>In a plenary, initiate discussion about how they knew which member of the class was away that day and encourage them to offer opinions on which of their representations is best for this data. Listen out for those that give clear explanations for their choices.</p>
<div> </div>
<h3>Key questions</h3>
<div>What does this chart/table tell you?</div>
<div>Tell me about the way you're creating your chart/table.</div>
<div>What can you tell from the tally/table/graph you have made?</div>
<div>How do you know who was away from school that day?</div>
<div> </div>
<br></br>
<h3>Possible extension</h3>
<p>The problem <a href="/4938">Real Statistics</a> offers more opportunities for data analysis, and goes on to invite data collection and further analysis.</p>
<p> </p>
<h3>Possible support</h3>
<p><a href="http://nrich.maths.org/247&part=">The Pet Graph</a> is a simpler challenge which focuses just on a block graph.<br></br>
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<p>You might find it helpful to print off <a href="/content/id/7522/Class5.pdf">this list of the class</a> and this sheet which contains the tally, frequency chart and block graph.</p>
<p>It might be a good idea to write out the letters of the alphabet down one side of a sheet of paper in preparation for making the tally.</p>
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<p>Tessa was away.</p>
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5
3
0
1
0
0
0
Class 5's names
Class 5 were looking at the first letter of each of their names. They created different charts to show this information. Can you work out which member of the class was away on that day?
Handling, Processing and Representing Data
Interpreting data
Handling, Processing and Representing Data
Tally charts
Handling, Processing and Representing Data
Frequency tables and diagrams
Handling, Processing and Representing Data
Bar charts
Handling, Processing and Representing Data
Processing and representing data
Admin
Upper primary mapping document