2642 /www/nrich/html/content/id/2642/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <br></br> How many different ways can you post this triangle into the black hole?<br></br> A dot has been drawn on the triangle to help you keep track.<br></br> <br></br> The triangle is yellow on the other side.<br></br> If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?<br></br>  <br></br> <a href="/content/id/2642/Triangle.swf">Full Size Version</a> <mdo:flash height="290" width="550"><param value="/content/id/2642/Triangle.swf" name="movie" ></param><param value="6" name="flashplayerversion" ></param><param value="290" name="height" ></param><param value="550" name="width" ></param></mdo:flash><br></br> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p class="editorial">Thank you for all your correct solutions. Three were particularly well explained.</p> <p class="editorial">Zeenat from St Margaret's Preparatory School wrote:</p> <div>If the triangle is on the blue side then I found three ways to post it into the black hole. I used the dot to help me. I moved the dot to the three different corners of the triangle by turning the triangle and that is how I found three ways of posting the triangle into the black hole.</div> <div>If I had to post it on both sides (blue and yellow) then there would be $6$ ways of doing it because I know that $3$ ways plus $3$ ways is equal to $6$ ways of doing it.</div> <br></br> <p class="editorial">Mia from St Teresa's said:</p> I found six ways, three blue and three  yellow. The dot was at the top, then on the left and then on the right.<br></br> <br></br> <p class="editorial">Amy from St Alban's Roman Catholic Primary School told us:</p> <div>There are six ways.</div> <div>The first you can just put the triangle in - $1$ way.</div> <div>Then flip over the triangle to yellow - $2$ ways.</div> <div>Then you turn the triangle so that the point is at the other corner - $3$ ways.</div> <div>Turn the triangle as in number $3$ and flip the triangle yellow - $4$ ways.</div> <div>Keep turning until the point is at the last corner - $5$ ways.</div> <div>For the last time, turn it as in number $5$ and flip it yellow - $6$ ways.</div> <div>That is all of the ways.</div> <br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Posting Triangles</h2> <br></br> <br></br> How many different ways can you post this triangle into the black hole?<br></br> A dot has been drawn on the triangle to help you keep track.<br></br> <br></br> The triangle is yellow on the other side.<br></br> If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?<br></br>  <br></br> <a href="/content/id/2642/Triangle.swf">Full Size Version</a><mdo:flash height="290" id="/content/id/2642/Triangle.swf" width="550"><param name="allowfullscreen" value="true"></param><param name="allowfullscreen" value="true"></param> <param name="movie" value="/content/id/2642/Triangle.swf"></param> <param name="flashplayerversion" value="6"></param> <param name="height" value="290"></param> <param name="width" value="550"></param> </mdo:flash><br></br>  </div> <br></br> <h3><span style="font-weight: bold;">Why do this problem?</span></h3> Tackling <a href="http://nrich.maths.org/2642&amp;part=">this problem</a> will give a context in which children can explore transformations and begin to get an idea of working systematically. It introduces ideas of symmetry without introducing the word itself but builds on notions of posting shapes into a shape sorter that are part of essential pre-school mathematical experience for all children.<br></br> <br></br> <h3>Possible approach</h3> The activity can be introduced by using the interactive version or a real shape sorter that you might borrow from the EYFS department. Mark one corner of the shape and look at ways of posting it into the slot. Keeping track of the options you have tried is tricky and introduces the children to the importance of recording in geometric problems. They may decide to use drawings to help them.<br></br> The children could go on to try the task for themselves either working with a shape sorter or on computers.<br></br> <br></br> <h3>Key questions</h3> <div>How many different positions can you find for the black dot to be in when the blue side is facing up?</div> <div>How about when the yellow side is facing up?</div> <br></br> <h3>Possible extension</h3> Children could use other shapes from a selection to create their own &#39;slot&#39; and ask their own questions.<br></br> <br></br> <h3>Possible support</h3> Using a triangle from a selection of shapes and a shape sorter might help children picture this more easily. It might also be helpful to create laminated shapes like the triangle which are blue on one side and yellow on the other and which have one corner marked with a dot. A template sheet with black shapes which they have to match would also help. This will enable the children to make a series of pictures showing the different way of posting the shapes and save them the task of recording their results.<br></br> <a href="/content/id/2642/EquilateralTris.pdf">This sheet</a> of equilateral triangles could be printed off on different colours of paper/card and laminated as necessary. </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> How many different positions can you find for the black dot to be in when the blue side is facing up?<br></br> How about when the yellow side is facing up?<br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Six ways in total:<br></br>Blue side up - black dot at top, black dot on right, black dot on left<br></br> Green side up - black dot at top, black dot on right, black dot on left<br></br><br></br></mdoxml> 2 3 1 0 0 0 0 If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether? Using, Applying and Reasoning about Mathematics Visualising Transformations and their Properties Rotations 2D Geometry, Shape and Space Equilateral triangles Information and Communications Technology Interactivities