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/www/nrich/html/content/02/09/penta5/
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2011-02-01T00:00:01
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<p>Here are the prices for 1st and 2nd class mail within the UK [in 2002].</p>
<table style="width: 327px; height: 490px;" border="">
<tbody>
<tr>
<th scope="cols">Weight up to</th>
<th scope="cols">First Class</th>
<th scope="cols">Second Class</th>
</tr>
<tr>
<td>$60g$</td>
<td>$27p$</td>
<td>$19p$</td>
</tr>
<tr>
<td>$100g$</td>
<td>$41p$</td>
<td>$33p$</td>
</tr>
<tr>
<td>$150g$</td>
<td>$57p$</td>
<td>$44p$</td>
</tr>
<tr>
<td>$200g$</td>
<td>$72p$</td>
<td>$54p$</td>
</tr>
<tr>
<td>$250g$</td>
<td>$84p$</td>
<td>$66p$</td>
</tr>
<tr>
<td>$300g$</td>
<td>$96p$</td>
<td>$76p$</td>
</tr>
<tr>
<td>$350g$</td>
<td>$£1.09$</td>
<td>$87p$</td>
</tr>
<tr>
<td>$400g$</td>
<td>$£1.30$</td>
<td>$£1.05$</td>
</tr>
<tr>
<td>$450g$</td>
<td>$£1.48$</td>
<td>$£1.19$</td>
</tr>
<tr>
<td>$500g$</td>
<td>$£1.66$</td>
<td>$£1.35$</td>
</tr>
<tr>
<td>$600g$</td>
<td>$£2.00$</td>
<td>$£1.60$</td>
</tr>
<tr>
<td>$700g$</td>
<td>$£2.51$</td>
<td>$£1.83$</td>
</tr>
<tr>
<td>$750g$</td>
<td>$£2.69$</td>
<td>$£1.94$*</td>
</tr>
<tr>
<td>$800g$</td>
<td>$£2.91$</td>
<td> </td>
</tr>
<tr>
<td>$900g$</td>
<td>$£3.20$</td>
<td> </td>
</tr>
<tr>
<td>$1kg$</td>
<td>$£3.49$</td>
<td> </td>
</tr>
</tbody>
</table>
<p>Costs for First Class items over $1kg$ are $£3.49$ and then $85p$ for each extra $250g$.<br></br>
*Items over $750g$ cannot be sent second class.</p>
<p>You have an unlimited number of each of these stamps:</p>
<table style="" border="">
<tbody>
<tr>
<td><mdo:image alt="4p stamp" src="stamp1.gif"></mdo:image></td>
<td><mdo:image alt="10p stamp" src="stamp2.gif"></mdo:image></td>
<td><mdo:image alt="19p stamp" src="stamp3.gif"></mdo:image></td>
<td><mdo:image alt="27p stamp" src="stamp4.gif"></mdo:image></td>
<td><mdo:image alt="37p stamp" src="stamp5.gif"></mdo:image></td>
<td><mdo:image alt="£1.00 stamp" src="stamp6.gif"></mdo:image></td>
</tr>
<tr>
<td>
<div class="c1">$4p$</div>
</td>
<td>
<div class="c1">$10p$</div>
</td>
<td>
<div class="c1">$19p$</div>
</td>
<td>
<div class="c1">$27p$</div>
</td>
<td>
<div class="c1">$37p$</div>
</td>
<td>
<div class="c1">$£1.00$</div>
</td>
</tr>
</tbody>
</table>
<p style="font-style: italic;">Reproduced by kind permission of Consignia plc. All rights reserved.</p>
<p style="margin-left: 40px;">1/ Which stamps would you need to post a parcel weighing $825g$?</p>
<p style="margin-left: 40px;">2/ I want to send a package 1st class which weighs $235g$. It is very small so I want to use as few stamps as possible. Which ones would I use?</p>
<p style="margin-left: 40px;">3/ If I only had $3$ of each kind of stamp, which $2$nd class price could I not make?</p>
<p style="margin-left: 40px;">4/ How many different combinations of stamps could be stuck on a letter weighing $140g$ if it goes 1st class?</p>
<p style="margin-left: 40px;">5/ I use the following stamps to send two items, one 1st class and the other 2nd class:</p>
<table style="" border="">
<tbody>
<tr>
<td><mdo:image alt="E stamp" src="stamp5.gif"></mdo:image></td>
<td><mdo:image alt="1st class stamp" src="stamp4.gif"></mdo:image></td>
<td><mdo:image alt="2nd class stamp" src="stamp3.gif"></mdo:image></td>
<td><mdo:image alt="10p stamp" src="stamp2.gif"></mdo:image></td>
<td><mdo:image alt="10p stamp" src="stamp2.gif"></mdo:image></td>
<td><mdo:image alt="4p stamp" src="stamp1.gif"></mdo:image></td>
<td><mdo:image alt="4p stamp" src="stamp1.gif"></mdo:image></td>
</tr>
</tbody>
</table>
<p style="margin-left: 40px;">What could their weights be?</p>
<p>Further extension to this activity can be carried out by considering the value of the stamps alone, as numbers $4$, $10$, $19$, $27$, $37$ & $100$. For example taking the $5$ lowest numbers [missing out the $100$] challenging the pupils to come up with the smallest number of ways you can get totals between $4$ and $50$. This could lead to questions about what totals can NOT be had, and
checking to see if you've really got the smallest number of ways, each time.</p>
<p style="font-style: italic;">All tables reproduced by kind permission of Consignia plc. All rights reserved.</p>
<p style="font-style: italic;">UK folk need to be aware that all this has changed since 2009 ! <a href="http://www.royalmail.com/portal/rm/content1?mediaId=50800722&catId=400029">(See Royal Mail)</a></p>
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<p class="editorial">Martha from Tattingstone School sent us a very
clearly answer to the first part:</p>
<mdo:image height="291" width="700" alt="parcel would cost £3.20 so need three £1 stamps and two 10p stamps" src="pentapostpart1.gif"></mdo:image>
<p><span class="editorial">Martha goes on to give the solution for
the second part too:</span> <mdo:image height="374" width="700" alt="package costs 84p so for as few stamps as possible need two 37p and one 10p" src="pentapost%20part2.gif"></mdo:image></p>
<p><span class="editorial">Caroline, also from Tattingstone, has
answered the third part of the problem:</span> <mdo:image height="454" width="767" alt="44p can't be made" src="pentapostpart3.gif"></mdo:image></p>
<p><span class="editorial">Well done Caroline - although perhaps it
would have been better to write 3 x 4, not 4 x 3. Back to Martha
for part four:</span> <mdo:image height="294" width="700" alt="3 combinations: three 19p stamps; two 10p and a 37p or three 10p and a 27p" src="pentapostpart4.gif"></mdo:image></p>
<p><span class="editorial">Finally, Caroline has answered the last
part for us:</span> <mdo:image height="197" width="706" alt="up to 150g first class (costing 57p) and up to 200g second class (costing 54p)" src="pentapostpart5.gif"></mdo:image></p>
<p class="editorial">Excellent answers both of you! Very well
done.</p>
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<h3><span style="font-weight: bold;">Why do this
problem?</span></h3>
<div>This <a href="http://nrich.maths.org/public/viewer.php?obj_id=1133&part=">
activity</a> is a good everyday example of the use of addition and
multiplication. It also helps pupils see the use of arithmetic in
practical situations.</div>
<br></br>
<h3>Possible approach</h3>
<div>Start off a general discuss about posting to see what they
know about posting letters and cards. When they are happy to talk
about stamps present them with the challenge. You may
prefer to update the charges and adapt the challenge to suit the
current pricing system.</div>
<br></br>
<h3>Key questions</h3>
<div>Tell me how you have worked this out.</div>
<br></br>
<h3>Possible extension</h3>
<div>Pupils could invent their own question based upon the
present-day costs of postage.</div>
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<p>It may be helpful to write out the different combinations of
stamps that could be used for each price.</p>
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The cost will be $£3.20$ so there are many ways of
making this from the available stamps. 4, 10, 19, 27, 37,
100. <br></br>
The smallest number of stamps would be 100, 100, 100, 10, 10.<br></br>
The largest number of stamps would be 80 of the 4's.<br></br></mdoxml>
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Penta Post
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
Measures and Mensuration
Money
Calculations and Numerical Methods
Multiplication & division
Calculations and Numerical Methods
Addition & subtraction
Decision Mathematics and Combinatorics
Combinations