2003
/www/nrich/html/content/04/01/letme2/
1
2011-02-01T00:00:01
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<p><mdo:image width="100" height="100" align="left" alt="Picture of a girl" src="girl.gif"></mdo:image>Sally
Brown has an equal number of brothers and sisters.</p>
<p>Mark Brown, her older brother, has twice as many sisters as
brothers.</p>
<p>How many children are there in the Brown family?</p>
<p></p>
<mdo:flash height="350" width="350"><param value="/content/04/01/letme2/brown_family.swf" name="movie" ></param><param value="6" name="flashplayerversion" ></param></mdo:flash><br></br>
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<p>Class M7 from Alexandra School sent in this solution which they
worked on together:</p>
<blockquote>
<p>First we added one brother and checked whether the statements
for Sally and Mark were true. Then we added one brother ... another
sister ... another brother ... until we found an arrangement that
worked. These are our results:</p>
<p> </p>
</blockquote>
<table width="40%" border="1" align="center" cellpadding="5">
<caption>Table of results for Brown family</caption>
<tr>
<td>Boys</td>
<td>Girls</td>
<td>True for Sally</td>
<td>True for Mark</td>
</tr>
<tr>
<td>1</td>
<td>2</td>
<td>Yes</td>
<td>No</td>
</tr>
<tr>
<td>2</td>
<td>2</td>
<td>No</td>
<td>No</td>
</tr>
<tr>
<td>2</td>
<td>3</td>
<td>Yes</td>
<td>No</td>
</tr>
<tr>
<td>3</td>
<td>3</td>
<td>No</td>
<td>No</td>
</tr>
<tr>
<td>3</td>
<td>4</td>
<td>Yes</td>
<td>Yes</td>
</tr>
</table>
<blockquote>
<p>So there are three boys and four girls in the Brown family.</p>
</blockquote>
<p>They added:</p>
<blockquote>
<p>We really enjoyed being able to click to add another brother or
sister appear. It helped us to work systematically through the
puzzle and find the solution.</p>
</blockquote>
<p>This is very clearly presented, well done. We had many other
solutions which used the interactivity too, and some from people
who drew pictures themselves, which is just as good.</p>
</mdoxml>
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<h2>The Brown Family</h2>
<br></br>
<p><mdo:image align="left" alt="Picture of a girl" height="100" src="girl.gif" width="100"></mdo:image>Sally Brown has an equal number of brothers and sisters.</p>
<p>Mark Brown, her older brother, has twice as many sisters as brothers.</p>
<p>How many children are there in the Brown family?</p>
<p> </p>
<mdo:flash height="350" id="/content/04/01/letme2/brown_family.swf" width="350"><param name="allowfullscreen" value="true"></param><param name="movie" value="/content/04/01/letme2/brown_family.swf"></param>
<param name="flashplayerversion" value="6"></param>
</mdo:flash><br></br>
</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<a href="http://nrich.maths.org/public/viewer.php?obj_id=2003&part=index">This problem</a> requires logical thinking and could be a good way to introduce a trial and improvement approach. Children need to understand the difference between having a certain number of brothers and the number of boys in a family.<br></br>
<h3>Possible approach</h3>
<div>You could start with a discussion on how many brothers and sisters the members of the class have and relate this to the number of boys and girls in their families.</div>
<br></br>
<div>Alternatively, you could use the interactivity on an interactive whiteboard to introduce, but not to solve, the problem. After this, children could work in pairs on the problem either using the interactivity or using paper/miniwhiteboards to make jottings. It would be worth stopping them after a few minutes to see how they are going about tackling the problem and to share some ideas. You
could also draw attention to different ways of representing the problem that you have noticed.</div>
<br></br>
<div>You may wish to introduce the idea of recording in a table. Some children could be challenged to design their own table while you could give others <a href="/content/04/01/letme2/2003.pdf">this sheet</a> to complete. Filling in the first line or two of the table together as a class would give them a good start.</div>
<br></br>
<h3>Key questions</h3>
<div>How many brothers has Sally got now?</div>
How many brothers has Mark got now?
<div>How many boys are there in the family now?</div>
<br></br>
<h3>Possible extension</h3>
Children could make up different problems for each other such as "What would the answer be if Mark had three times as many sisters as brothers?" Alternatively, they could make up similar problems about their own, or invented, families.<br></br>
<h3>Possible support</h3>
Some learners would benefit from using the interactivity if possible, or counters in two colours to represent boys and girls.<br></br></mdoxml>
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<div>Start by imagining that Sally has one sister and one
brother.</div>
<div>How many brothers and sisters does this mean Mark has?</div>
<div>Try other numbers of brothers and sisters for Sally.</div>
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The Brown Family
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Calculations and Numerical Methods
Multiplication & division
Calculations and Numerical Methods
Addition & subtraction
Using, Applying and Reasoning about Mathematics
Trial and improvement
Algebra
Introducing algebra
Information and Communications Technology
Interactivities
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