7228 /www/nrich/html/content/id/7228/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <div style="text-align: center;">So, you are at the party and sitting round the table with seven friends.</div> <br></br> <div style="text-align: center;"> <mdo:image alt="8 roundSq" height="170" src="8%20round%20a%20Sq.jpg" width="170"></mdo:image></div> <div style="text-align: left;">At the top left hand corner is the friend who is giving the party. S/he has a bag of sweets and starts giving them out in a clockwise direction: one for her/himself, two for the next person and three for the next and so on.</div> <div style="text-align: center;"><mdo:image alt="8 sweets" height="153" src="8%20sweets%20round%20Sq.jpg" width="156"></mdo:image></div> <div>There are other similar parties going on at the same time. They have bigger square tables with more children sitting round on each side.</div> <div> </div> <div>Explore and compare all the tables:  $2$ on each side, $3$ on each side, $4$ on each side and $5$ on each side.</div> <div> </div> <div>You could look at:</div> <div>the total number of sweets that children sitting opposite each other have;</div> <div>the total number of sweets needed for each size of table;</div> <div>the total number of sweets belonging to children who are diagonally opposite.</div> <div> </div> <div>Then, what about  five- and six-sided tables?</div> <div style="text-align: center;"><mdo:image alt="5 sides" height="99" src="5%20sides.jpg" width="99"></mdo:image><mdo:image alt="6 sides" height="117" src="6%20sides.jpg" width="117"></mdo:image></div> <div> </div> <br></br>  <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p class="editorial">We had some really good ideas sent in, some that were illustrated well using the computer. From Kent College we had Primrose and Charlotte, Sophie and Nia, Stephanie, Nandini and Hazel.</p> <p class="editorial">Well here we have a superb piece of work, sent in by Abi and Charlotte from the same school, that I would advise people to look at for working investigatively on this activity.</p> <div>When we first looked at the problem we decided to test the difference between the amount of sweets each table needed, and we came up with these results.  </div> <div> </div> <div> <mdo:image width="480" height="106" alt="" src="Sol1.png"></mdo:image></div> <div> </div> <div>We looked at the results to see if there was a pattern in the difference between the amounts of sweets. Despite the fact there wasn't a pattern there we were determined to find a pattern. So we looked further into the problem and saw a pattern between the differences. </div> <div> </div> <div> <mdo:image width="483" height="225" alt="" src="Sol2.png"></mdo:image></div> <div> </div> <div>From that we could guess the next two amount of sweets needed. </div> <div> </div> <div> <mdo:image width="580" height="254" src="Sol3.png" alt=""></mdo:image></div> <div> </div> <div>When we saw this we thought of why it could have happened. Then we realised that a square has four sides and four squared is $16$ so to get proof we checked with a triangle. </div> <div> </div> <div> <mdo:image width="487" height="183" alt="" src="Sol4.png"></mdo:image></div> <div> </div> <div>There is a pattern. So the difference between the difference between the difference is always nought. </div> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Sitting Round the Party Tables</h2> <br></br> <div style="text-align: center;">So, you are at the party and sitting round the table with seven friends.</div> <br></br> <div style="text-align: center;"> <mdo:image alt="8 roundSq" height="170" src="8%20round%20a%20Sq.jpg" width="170"></mdo:image></div> <div style="text-align: left;">At the top left hand corner is the friend who is giving the party. S/he has a bag of sweets and starts giving them out in a clockwise direction: one for her/himself, two for the next person and three for the next and so on.</div> <div style="text-align: center;"><mdo:image alt="8 sweets" height="153" src="8%20sweets%20round%20Sq.jpg" width="156"></mdo:image></div> <div>There are other similar parties going on at the same time. They have bigger square tables with more children sitting round on each side.</div> <div> </div> <div>Explore and compare all the tables:  $2$ on each side, $3$ on each side, $4$ on each side and $5$ on each side.</div> <div> </div> <div>You could look at:</div> <div>the total number of sweets that children sitting opposite each other have;</div> <div>the total number of sweets needed for each size of table;</div> <div>the total number of sweets belonging to children who are diagonally opposite.</div> <div> </div> <div>Then, what about  five- and six-sided tables?</div> <div style="text-align: center;"><mdo:image alt="5 sides" height="99" src="5%20sides.jpg" width="99"></mdo:image><mdo:image alt="6 sides" height="117" src="6%20sides.jpg" width="117"></mdo:image></div> <div> </div> <br></br>  </div> <br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <div>This <a href="http://nrich.maths.org/7228&amp;part=">activity</a> gives pupils the opportunity to explore some simple number relationships, from which they can be encouraged to make some generalisations. It may also be a good context in which to help pupils ask their own questions - "I wonder what would happen if we ...?".</div> <br></br> <h3>Possible approach</h3> <div>With younger pupils, or those with little experience of exploring in mathematics and talking about their mathematical thoughts, it would be good to act out the problem as first described.</div> <div> </div> <div>With more experienced pupils you could just present the challenge orally and ask them to explore further.  Encourage learners to write down all the things they notice.  It might also be appropriate for you to bring everyone together after some time to discuss how they are recording their work.  </div> <div> </div> <div>Invite pupils to ask and begin to answer their own questions: "I wonder what would happen if I ...?".  You could use some of the suggestions in the problem itself to prompt those who may not be used to doing this.</div> <br></br> <h3>Key questions</h3> <div>Tell me about what you have noticed about the numbers of sweets.</div> <div>What else are you going to explore?</div> <div>Tell me about what&#39;s going on at the other party tables.</div> <div>Are there any special things you notice about the seats in particular places?</div> <br></br> <h3>Possible extension</h3> <div>Some pupils might look at generalisations that they can say about tables of ANY size or of ANY shape.</div> <br></br> <h3>Possible support</h3> <div>Some pupils may find it helpful to approach the problem using practical equipment, for example using counters to represent the sweets and having &#39;tables&#39; made out of paper or card.</div> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> You could use some practical equipment to help you work on this problem, such as counters.<br></br> Are there any special things you notice about the seats in particular places? <br></br>  <br></br></mdoxml> 5 3 1 1 0 0 0 In this challenge, party goers are sitting around a table and sweets are given out in a particular way. Investigate the total number of sweets that people sitting in different positions have. Numbers and the Number System Counting Using, Applying and Reasoning about Mathematics Generalising Calculations and Numerical Methods Addition & subtraction Admin Lower primary mapping document Admin Upper primary mapping document