7544
/www/nrich/html/content/id/7544/
1
2011-09-07T10:50:32
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<p>This is a view, from above, of my friend's garden. You see a black path and a square patch in the middle.</p>
<p style="text-align: center;"> <mdo:image alt="empty" height="327" src="empty%20frame.jpg" width="327"></mdo:image></p>
<p style="text-align: left;">He wants to tile the square in the middle with tiles going straight across and down. He would also like to have the corner of a tile at each of the corners of the square.</p>
<p>Then it'll look like this;</p>
<p style="text-align: center;"> <mdo:image alt="frame 3" height="327" src="frame%203.jpg" width="327"></mdo:image></p>
<p style="text-align: center;"> </p>
<p style="text-align: left;">So, we are off to help him. He has a good tile cutter to get the "part-tiles", so he'll be able to cut a tile into two or more pieces and use them all. But I said that we would fetch the tiles for him. How many do we need for the example above?</p>
<p>How many would we need for these two other garden square shapes that someone might like to have? How are you working it out?</p>
<p style="text-align: center;"> <mdo:image alt="frame 1" height="327" src="frame%201.jpg" width="327"></mdo:image></p>
<p style="text-align: center;"> <mdo:image alt="newFrame2" height="327" src="newFrame2.jpg" width="327"></mdo:image></p>
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<h2>Tiles in the Garden</h2>
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<p>This is a view, from above, of my friend's garden. You see a black path and a square patch in the middle.</p>
<p style="text-align: center;"> <mdo:image alt="empty" height="327" src="empty%20frame.jpg" width="327"></mdo:image></p>
<p style="text-align: left;">He wants to tile the square in the middle with tiles going straight across and down. He would also like to have the corner of a tile at each of the corners of the square.</p>
<p>Then it'll look like this;</p>
<p style="text-align: center;"> <mdo:image alt="frame 3" height="327" src="frame%203.jpg" width="327"></mdo:image></p>
<p style="text-align: center;"> </p>
<p style="text-align: left;">So, we are off to help him. He has a good tile cutter to get the "part-tiles", so he'll be able to cut a tile into two or more pieces and use them all. But I said that we would fetch the tiles for him. How many do we need for the example above?</p>
<p>How many would we need for these two other garden square shapes that someone might like to have? How are you working it out?</p>
<p style="text-align: center;"> <mdo:image alt="frame 1" height="327" src="frame%201.jpg" width="327"></mdo:image></p>
<p style="text-align: center;"> <mdo:image alt="newFrame2" height="327" src="newFrame2.jpg" width="327"></mdo:image></p>
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</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/7544"><font class="Apple-style-span" color="#0044AA">activity</font></a><a href="http://nrich.maths.org/7544"> </a>is designed to create a challenge that pupils will not have been taught or leant how to do straight away. they therefore have to use their individual problem solving skills. When different approaches have been used by different
groups or individuals then the discussion about different appraoches can take place.</div>
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<h3>Possible approach</h3>
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<div style="margin: 0px; padding: 0px;">Explain that you're not expecting them to necessarily know straight away how to do it. Encourage them to devise a way, through problem solving to find the answers. The pupils may be ecouraged to validate their suggestions. Then a discussion can be had around the class as to the advantages and disadvantages of the different approaches.</div>
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<h3>Key questions</h3>
<div>Tell me about what you are doing?</div>
<div>Are you happy with your answers?</div>
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<h3>Possible extension</h3>
<div>Create other rectangles that could fit over a framework of smaller squares, here are two examples.</div>
<div style="text-align: center;"><mdo:image src="further%20grids%201%2B2pics.jpg"></mdo:image></div>
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<h3>Possible support</h3>
<div>You may need for some pupils to use some large-squared paper and a pair of scissors to cut out the shapes required.</div>
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Tiles in the Garden
Using, Applying and Reasoning about Mathematics
Investigations
Measures and Mensuration
Area
Measures and Mensuration
Surface and surface area