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/www/nrich/html/content/03/03/cupboardlove4/
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2011-02-01T00:00:01
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<td>In this problem, we're going to make some squares out of Cuisenaire rods.</td>
<td rowspan="3" style="padding:5px;"><mdo:image alt="unit rod, unit rod surrounded by square of four 2 rods, two 2 rods surrounded by square of four 3 rods, three 3 rods surrounded by square of four 4 rods, four 4 rods surrounded by square of four 5 rods" height="490" src="cuisenaire.gif" width="161"></mdo:image></td>
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<td>How would you describe what is happening as the pattern develops?<br></br>
What will the next square look like?<br></br>
What colour rod will be in the centre?<br></br>
How many dark green (next colour) ones will be needed?</td>
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<td>The next four colours are black, brown, blue, orange.<br></br>
Can you describe this pattern in full?<br></br>
Can you generalise the situation?</td>
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If you don't have any Cuisenaire rods, you might like to use our <a href="http://nrich.maths.org/4348&part=">Cuisenaire environment</a> to have a go at this problem.<br></br></mdoxml>
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<p><span class="editorial">Maja (Eastwood Primary School) noticed
that:</span></p>
The pattern is, the colour of the border is the colour of the
centre on the next square underneath and the square gets longer by
$1$ line.<br></br>
<br></br>
<p class="editorial">Maja is right, and because the square gets
wider by $1$ unit each time, it also has to get taller by $1$ line
so an extra rod is added to the centre each time. Continuing the
pattern then, the next square will have $5$ yellow rods in the
centre, surrounded by green rods. After that we will need $6$ green
rods in the centre, surrounded by black rods. And so on.</p>
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<h2>Cuisenaire Rods</h2>
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<table style="border:none;">
<tbody>
<tr>
<td>In this problem, we're going to make some squares out of Cuisenaire rods.</td>
<td rowspan="3" style="padding:5px;"><mdo:image alt="unit rod, unit rod surrounded by square of four 2 rods, two 2 rods surrounded by square of four 3 rods, three 3 rods surrounded by square of four 4 rods, four 4 rods surrounded by square of four 5 rods" height="490" src="cuisenaire.gif" width="161"></mdo:image></td>
</tr>
<tr>
<td>How would you describe what is happening as the pattern develops?<br></br>
What will the next square look like?<br></br>
What colour rod will be in the centre?<br></br>
How many dark green (next colour) ones will be needed?</td>
</tr>
<tr>
<td>The next four colours are black, brown, blue, orange.<br></br>
Can you describe this pattern in full?<br></br>
Can you generalise the situation?</td>
</tr>
</tbody>
</table>
If you don't have any Cuisenaire rods, you might like to use our <a href="http://nrich.maths.org/4348&part=">Cuisenaire environment</a> to have a go at this problem.</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div><a href="http://nrich.maths.org/13&part=">This problem</a> encourages children to make conjuctures and generalisations, and it may lead into discussions about square numbers.</div>
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<h3>Possible extension</h3>
<div>Children could create their own pattern, perhaps based on rectangles, and then make similar conjectures and generalisations.</div>
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<h3>Possible support</h3>
<div>Learners could use some Cuisenaire rods to have a go at this problem or the <a href="http://nrich.maths.org/4348&part=">Cuisenaire environment</a>. Alternatively, drawing rods on squared paper might help. </div>
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<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">You could use some Cuisenaire rods to have a go at this problem or
you could use the <a href="http://nrich.maths.org/4348&part=">Cuisenaire
environment</a>.<br></br>
Alternatively, drawing rods on squared paper might help.<br></br></mdoxml>
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Cuisenaire Rods
These squares have been made from Cuisenaire rods. Can you describe
the pattern? What would the next square look like?
Using, Applying and Reasoning about Mathematics
Generalising
Using, Applying and Reasoning about Mathematics
Practical Activity
Numbers and the Number System
Square numbers
Mathematics Tools
Cuisenaire rods