2419
/www/nrich/html/content/id/2419/
1
2011-02-01T00:00:01
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<mdo:image alt="view from greenhouse" height="200" src="treegreenhouse.jpg" width="200"></mdo:image>
<p>Mum, Dad and their two children, Emily and Isabel, moved into a new house. At the end of the lawn was a big tree which had a disease and was dying.</p>
<p align="center"><mdo:image align="top" alt="tree, greenhouse and house" bgcolor="" height="293" src="tree.gif" width="489"></mdo:image></p>
<p align="center"> </p>
<p>Mum said she wanted to cut the tree down before it fell down.</p>
<p>Dad said, "How do we know we won't hit the greenhouse?"</p>
<p>Mum answered," We'll measure the lawn and find out how tall the tree is!"</p>
<p>"How?!!" Dad, Emily and Isabel all exclaimed.</p>
<p>Mum said,"I'll show you!"</p>
<p>Emily measured the distance from the tree to the greenhouse with her metre ruler.</p>
<p>"Thirty-one and fourteen centimetres," Emily said.</p>
<p>"Now measure the shadow of the tree, you two, and make it fairly accurate!"</p>
<p>Emily and Dad measured the tree's shadow. Mum and Isabel pushed the end of the bamboo cane into the ground so that exactly a metre stuck out.</p>
<p>"Now," said Mum, "we'll measure the shadow of this cane and then we will be able to work out the height of the tree."</p>
<p>The shadow of the tree was $36.3$ metres long and the shadow of the cane was $123$ centimetres.</p>
<p>"It's OK," Mum announced, "it won't reach the greenhouse!"</p>
<p align="center"><mdo:image align="top" alt="fallen tree, greenhouse and house" bgcolor="" height="169" src="tree2.gif" width="259"></mdo:image></p>
<p> </p>
<p>How tall was the tree?</p>
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<p class="editorial">Conor from Sticklepath School decided to
estimate the height of the tree:</p>
If the bamboo cane was exactly 1m (100cm) and the length of the
shadow was 123cm then that means that the shadow is 23cm longer
than the bamboo cane is.<br></br>
<div style="clear: both;">23cm is about 1/5 more than 100cm (the
length of the bamboo cane).<br></br>
<div style="clear: both;">1/5 of 36.3m (the length of the trees
shadow) is about 7cm. 36.3m -7cm is 29.3m. 29.3m is about the
height of the tree.<br></br>
<div style="clear: both;">It will also cut down without hitting the
greenhouse because the lawn was 31m and 14cm enough room for the
tree to be cut down without trashing the greenhouse!</div>
</div>
</div>
<br></br>
<p class="editorial">This is a good idea, Conor. Alexis from St
Thomas Moore Roman Catholic School wrote:</p>
<br></br>
The tree was 29.51 metres. <br></br>
<div style="clear: both;">I worked this out because of the vital
clue that when the bamboo stick stood at exactly one metre tall the
shadow was 1.23 metres. Therefore, the shadow is 1.23 times as tall
as the real height.<br></br>
<div style="clear: both;">Taking this into account we can divide
the height of the shadow of the tree by 1.23 to get the real
height.</div>
<div style="clear: both;"></div>
<p class="editorial" style="clear: both;">Maria who goes to IES in
Spain, used this method too. She said:</p>
<div style="clear: both;">As 1 m of cane produce a shadow of 1,23
m, X m of tree must produce a shadow of 36,3 m.<br></br>
<div style="clear: both;">X= 363000 x 100/123=2951.2 cm is the
height of the tree.<br></br>
<div style="clear: both;">So the tree won´t reach the
greenhouse!</div>
</div>
</div>
</div>
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<h3><span style="font-weight: bold;">Why do this
problem?</span></h3>
<a href="http://nrich.maths.org/public/viewer.php?obj_id=2419&part=index">
This problem</a> will encourage children to draw diagrams and mark
measurements on them in the process of solving the problem.<br></br>
<h3>Key questions</h3>
<div>Would it be a good idea to draw a diagram of the tree and its
shadow, and the stick and its shadow?</div>
<div>Would using a calculator help you?</div>
<br></br>
<h3>Possible extension</h3>
Learners could try <a href="http://nrich.maths.org/public/viewer.php?obj_id=1975&part=index">
Hello Again</a> which is a Stage 3 problem.<br></br>
<h3>Possible support</h3>
Suggest starting by drawing a diagram of the tree and its shadow,
and the stick and its shadow. Alternatively, learners could try <a href="http://nrich.maths.org/public/viewer.php?obj_id=4783&part=index">
Once upon a time</a> which is a similar, but easier, problem.
<br></br>
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Draw a diagram of the tree and its shadow, and the stick and its shadow.
</p>
<p>
You can use a calculator to help you.
</p>
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The tree and the greenhouse
Mum, Dad, Tim and Jill moved into a new house. If they cut down the
big tree, will it miss the greenhouse?
Fractions, Decimals, Percentages, Ratio and Proportion
Calculating with ratio & proportion