4763
/www/nrich/html/content/id/4763/
1
2011-02-01T00:00:01
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You may like to look at <a href="http://nrich.maths.org/public/viewer.php?obj_id=4734&part=index">Are you well Balanced?</a>
before trying this problem.<br></br>
<a href="/content/id/4763/balancer.swf">Full Screen Version</a>
<br></br>
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<br></br>
I hang three weights on the 8 hook on the left-hand side of the equaliser. <br></br>
<div style="clear: both;">If I have a maximum of four weights left, where could I hang them on the right-hand side of the equaliser so that it balances?</div>
<div style="clear: both;">Are there any other ways of doing it? (I don't need to use all four weights.)</div>
<div style="clear: both;"><hr></hr>
</div>
<div style="clear: both;"></div>
<div style="clear: both;"><a href="/content/id/4763/balancer2.swf">Full Screen Version</a>
</div>
<div style="clear: both;"></div>
<div style="clear: both;"><mdo:flash height="400" width="550"><param name="movie" value="/content/id/4763/balancer2.swf" ></param><param name="flashplayerversion" value="7" ></param><param name="height" value="400" ></param><param name="width" value="550" ></param></mdo:flash><br></br><br></br>
Now I hang three weights on the 10 hook and one on the 6 hook on one side of the equaliser. <br></br>
If I have six weights, where could I hang them on the other side to make it balance?
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<p class="editorial">Well done to those of you who had a good attempt at this problem.</p>
<p><span class="editorial">George of Ardingly College says</span>
:</p>
You just have to make the numbers on the right hand-side add up to the same total as the left hand side.<br></br>
<p><span class="editorial">
Congratulations to Jessica and Emily of Aldermaston CE primary School who found many different solutions to the problem.</span>
</p>
<p>In order to work out this problem we decided we should do a chart, so we
could track how many answers we could come up with. We both did our tally
chart, Emily did one using 4 weights and Jessica did one using less than 4
weights.</p>
<p>At the end we both helped each other. Emily's chart had more
answers than Jessica's chart.
One of the ways that Emily worked some out was splitting one of Jessica's
numbers to 2 numbers and then she would get more solutions.</p>
<p>Tally chart for making 24 with 4 weights:</p>
<p><mdo:image width="453" height="399" src="table1.gif" alt="table1"></mdo:image></p>
<p>Tally Chart for ways to make 24 with less than 4 weights:</p>
<p><mdo:image width="431" height="134" alt="table2" src="table2.gif"></mdo:image></p>
<p></p>
<div>
It is impossible to do it with only 2 weights because there is no 12 hook and 2 12s would make 24.</div>
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<h2>Add the Weights</h2>
<br></br>
You may like to look at <a href="http://nrich.maths.org/public/viewer.php?obj_id=4734&part=index">Are you well Balanced?</a> before trying this problem.<br></br>
<a href="/content/id/4763/balancer.swf">Full Screen Version</a><br></br>
<mdo:flash height="400" id="/content/id/4763/balancer.swf" width="550"><param name="allowfullscreen" value="true"></param><param name="movie" value="/content/id/4763/balancer.swf"></param>
<param name="flashplayerversion" value="7"></param>
<param name="height" value="400"></param>
<param name="width" value="550"></param>
</mdo:flash><br></br>
I hang three weights on the 8 hook on the left-hand side of the equaliser.<br></br>
<div style="clear: both;">If I have a maximum of four weights left, where could I hang them on the right-hand side of the equaliser so that it balances?</div>
<div style="clear: both;">Are there any other ways of doing it? (I don't need to use all four weights.)</div>
<div style="clear: both;">
<hr></hr></div>
<div style="clear: both;"> </div>
<div style="clear: both;"><a href="/content/id/4763/balancer2.swf">Full Screen Version</a></div>
<div style="clear: both;"> </div>
<div style="clear: both;"><mdo:flash height="400" id="/content/id/4763/balancer2.swf" width="550"><param name="allowfullscreen" value="true"></param><param name="movie" value="/content/id/4763/balancer2.swf"></param>
<param name="flashplayerversion" value="7"></param>
<param name="height" value="400"></param>
<param name="width" value="550"></param>
</mdo:flash><br></br>
<br></br>
Now I hang three weights on the 10 hook and one on the 6 hook on one side of the equaliser.<br></br>
If I have six weights, where could I hang them on the other side to make it balance?</div>
</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
In a similar way to <a href="http://nrich.maths.org/4734&part=">Are you well Balanced?</a> , factors and multiples are at the heart of <a href="http://nrich.maths.org/4763&part=">this problem</a> as well as addition and subtraction, even though this may not be the route through which children solve it. It is important, therefore, to discuss ideas of multiplication with the class, perhaps
after children have first thought about the problem on their own for a few minutes and then talked to a partner about possible ways to the solutions.<br></br>
<h3>Key questions</h3>
<div>Where have you tried hanging weights so far?</div>
<div>How will you know that you have got all the ways of making the equaliser balanced?</div>
<div>Is it possible to balance the equaliser with just one weight? With two weights ... three ...?</div>
<br></br>
<h3>Possible extension</h3>
Learners could experiment with the equaliser by trying other numbers and trying to find all the ways of balancing it.<br></br>
<h3>Possible support</h3>
Chldren could try <a href="http://nrich.maths.org/4734&part=">Are you Well Balanced?</a> and <a href="http://nrich.maths.org/4735&part=">Number Balance</a> before trying this problem.<br></br>
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Have you tried out some of your ideas using the interactivity?<br></br>
How many weights would you need just on the 1 hook in order to balance the equaliser? How does this help you?<br></br></mdoxml>
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24 = 10 + 10 + 4<br></br>
24 = 10 + 10 + 1 + 3<br></br>
24 = 10 + 10 + 2 + 2<br></br>
24 = 10 + 9 + 1 + 5<br></br>
24 = 10 + 9 + 2 + 3<br></br>
24 = etc. etc.<br></br>
<br></br>
In a similar way to Are you well Balanced? , factors and multiples
are at the heart of this problem as well as addition and
subtraction, even though this may not be the route through which
children solve it. It is important, therefore, to discuss ideas of
multiplication with the class, perhaps after children have first
thought about the problem on their own for a few minutes and then
talked to a partner about possible ways to the
solutions. <br></br></mdoxml>
2
3
0
1
0
0
0
Add the Weights
If you have only four weights, where could you place them in order
to balance this equaliser?
Measures and Mensuration
Mass and weight
Numbers and the Number System
Factors and multiples
Information and Communications Technology
Interactivities
Calculations and Numerical Methods
Addition & subtraction