So it's 28

6778 /www/nrich/html/content/id/6778/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <div style="text-align: center;"><mdo:image width="212" height="114" src="just%2028.jpg" alt="just 28"></mdo:image></div> <div style="text-align: left;">I've just found that I keep coming across the number $28$.</div> <div style="text-align: left;">Next Year's calendar for February:</div> <div style="text-align: center;"><mdo:image width="272" height="208" src="Screen%20shot%202009-09-12%20at%2009.40.29.jpg" alt="Screen 09/12"></mdo:image></div> <br></br> then there's my set of $28$ dominoes:<br></br> <div style="text-align: center;"><mdo:image width="192" height="179" alt="S Dominoes" src="small%20dominoes.jpg"></mdo:image></div> <br></br> So, why don't you explore this number? Find $28$ flat shapes the same and put them together in some way.<br></br> <br></br> Here are some I found using circular discs, octagons, hexagons, triangles and pentagons.<br></br> <div style="text-align: center;"><mdo:image width="125" height="169" src="28%20disc%20small.jpg" alt="discs"></mdo:image><mdo:image width="184" height="176" alt="new oct" src="new%2028%20Oct.jpg"></mdo:image><mdo:image width="155" height="138" src="28%20Hex%20Small.jpg" alt="hex"></mdo:image></div> <br></br> <div style="text-align: center;"><mdo:image width="151" height="193" src="28%20Tri%20small.jpg" alt="tri"></mdo:image><mdo:image width="159" height="206" src="28%20Pent%20Small.jpg" alt="pent"></mdo:image></div> <div style="text-align: left;">You may like to try $28$ cubes and get something like this:</div> <div style="text-align: center;"><mdo:image width="208" height="149" src="28%20new%20cubes.jpg" alt="28 new"></mdo:image></div> <div style="text-align: left;">or put together to make a caterpillar with changes at the ends.</div> <div style="text-align: center;"><mdo:image width="459" height="102" alt="cateerpillar" src="Caterpillar%20small.jpg"></mdo:image></div> <div style="text-align: left;">Let us know what you come up with and what you notice.</div> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p class="editorial">We had very few ideas sent in but it seems that most pupils went on to the other challenge focussed on $28$: <a href="http://nrich.maths.org/6779&part=">$28$ and It's Onwards and Upwards</a>.</p> <p class="editorial">Matthew wrote the following and sent in the picture to go with it:</p> <br></br> I used $28$ tessellating crosses, which are on the file. Looks quite cool. The scary thing is, after copying and pasting $28$ crosses (having just made them a random size), I, co-incidentally, couldn't fit any more than $28$ on the page ...<br></br> <div style="text-align: center;"><mdo:image height="239" width="182" alt="Kanumilli" src="So%20Its%2028%20Matthew%20Kanumilli%20onJkiG.jpg"></mdo:image></div> <p class="editorial" style="text-align: left;">and Emma wrote:</p> <br></br> I got grid paper and drew $14$ squares that were touching and drew a line diagonally through every square. I got $28$ triangles because I had $14$ squares and split them in $2$ which made $28$ because $14+14=28$. That is how I got $28$ triangles.<br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>So It's 28</h2> <br></br> <div style="text-align: center;"><mdo:image alt="just 28" height="114" src="just%2028.jpg" width="212"></mdo:image></div> <div style="text-align: left;">I've just found that I keep coming across the number $28$.</div> <div style="text-align: left;">Next Year's calendar for February:</div> <div style="text-align: center;"><mdo:image alt="Screen 09/12" height="208" src="Screen%20shot%202009-09-12%20at%2009.40.29.jpg" width="272"></mdo:image></div> <br></br> then there's my set of $28$ dominoes:<br></br> <div style="text-align: center;"><mdo:image alt="S Dominoes" height="179" src="small%20dominoes.jpg" width="192"></mdo:image></div> <br></br> So, why don't you explore this number? Find $28$ flat shapes the same and put them together in some way.<br></br> <br></br> Here are some I found using circular discs, octagons, hexagons, triangles and pentagons.<br></br> <div style="text-align: center;"><mdo:image alt="discs" height="169" src="28%20disc%20small.jpg" width="125"></mdo:image><mdo:image alt="new oct" height="176" src="new%2028%20Oct.jpg" width="184"></mdo:image><mdo:image alt="hex" height="138" src="28%20Hex%20Small.jpg" width="155"></mdo:image></div> <br></br> <div style="text-align: center;"><mdo:image alt="tri" height="193" src="28%20Tri%20small.jpg" width="151"></mdo:image><mdo:image alt="pent" height="206" src="28%20Pent%20Small.jpg" width="159"></mdo:image></div> <div style="text-align: left;">You may like to try $28$ cubes and get something like this:</div> <div style="text-align: center;"><mdo:image alt="28 new" height="149" src="28%20new%20cubes.jpg" width="208"></mdo:image></div> <div style="text-align: left;">or put together to make a caterpillar with changes at the ends.</div> <div style="text-align: center;"><mdo:image alt="cateerpillar" height="102" src="Caterpillar%20small.jpg" width="459"></mdo:image></div> <div style="text-align: left;">Let us know what you come up with and what you notice.</div> </div> <br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> <div><a href="http://nrich.maths.org/public/viewer.php?obj_id=6778&part=">This activity</a> is good for allowing pupils to explore both shapes and number, or to choose a particular aspect to focus on. There is a lot of freedom involved and there are exciting things to find out. Learners will be able to take control of their own learning and choose their own direction in this task.</div> <br></br> <h3>Possible approach</h3> <div>You could begin by showing some of the pictures in the problem on the screen for the pupils to see and talk about. What similarities do they notice? What differences? They may pick up on the fact that the common link is the number $28$ straight away, but if not you can ask questions to probe them further. If some would like more examples they can be found <a href="/content/id/6778/28.pdf">here</a>.</div> <br></br> <div>You can then set the group off on their own ideas using the number $28$. Pupils should be encouraged to ask themselves questions like " I wonder what would happen if I ...?", making a small change and exploring further.</div> <br></br> <h3>Key questions</h3> <div>Tell me about what you've got here.</div> <div>Is there anything special about this shape you have made?</div> <div>Can you find another arrangement?</div> <br></br> <h3>Possible extension</h3> <div>Talk about symmetry and look for final shapes that are symmetrical and those that are asymmetric.</div> <div>Children who are used to investigating and have done well with this may like to move on to <a href="http://nrich.maths.org/public/viewer.php?obj_id=6779&part=">28! and It's Upward and Onward.</a></div> <br></br> <h3>Possible support</h3> <div>There may be a need for help with those with less developed fine motor skills for moving the shapes and fitting them together. Magnetic shapes can sometimes help.</div> <br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Perhaps you can find $28$ things to investigate. How about counters or cubes or sticks or ...?<br></br></mdoxml> 2 3 1 0 0 0 0 So it's 28 Here is your chance to investigate the number 28 using shapes, cubes ... in fact anything at all. Using, Applying and Reasoning about Mathematics Investigations Numbers and the Number System Properties of numbers