9406
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<mdoxml version="1.0"><div>Choose any four numbers from $1$ to $15$ (but no numbers twice!)</div>
<div>Use just those four numbers and addition and subtraction.</div>
<div>Can you make up calculations that make up the numbers from $1$ to your four numbers added together?<br></br>
For Example : suppose you choose $1, 3, 7, 10$<br></br>
If we add all of them together we get $21$.<br></br>
So, trying to make all the answers from $1$ to $21$ out of those $4$ numbers, only using a number once each time we might start off with :-<br></br>
<br></br>
$7 - 3 + 10 = 14$<br></br>
$10 - 1 = 9$<br></br>
$7 = 7$<br></br>
$10 + 7 + 3 - 1 = 20$<br></br>
<br></br>
that gives us four out of the $21$ answers we need to get from my choice of $1, 3, 7, 10.$<br></br>
So we'd have to try and get the remaining seventeen answers.<br></br>
</div>
<h4 style="text-align: center;">Now try a set of four numbers for yourself.<br></br>
</h4></mdoxml>
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<h2>Just Four Numbers</h2>
<div>Choose any four numbers from $1$ to $15$ (but no numbers twice!)</div>
<div>Use just those four numbers and addition and subtraction.</div>
<div>Can you make up calculations that make up the numbers from $1$ to your four numbers added together?<br></br>
For Example : suppose you choose $1, 3, 7, 10$<br></br>
If we add all of them together we get $21$.<br></br>
So, trying to make all the answers from $1$ to $21$ out of those $4$ numbers, only using a number once each time we might start off with :-<br></br>
<br></br>
$7 - 3 + 10 = 14$<br></br>
$10 - 1 = 9$<br></br>
$7 = 7$<br></br>
$10 + 7 + 3 - 1 = 20$<br></br>
<br></br>
that gives us four out of the $21$ answers we need to get from my choice of $1, 3, 7, 10.$<br></br>
So we'd have to try and get the remaining seventeen answers.<br></br>
</div>
<h4 style="text-align: center;">Now try a set of four numbers for yourself.<br></br>
</h4>
</div>
<br></br>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div>This problem gives students the opportunity to make use of their skills in addition and subtraction. By doing so they will probably reinforce many of the number bonds with which they are getting familiar.</div>
<br></br>
<h3>Possible approach</h3>
<div>Working altogether, through the example started on the site can be a good starting point.<br></br>
There may be more than one way of getting an answer and this can be an opportunity for a discussion.<br></br>
Some might simply need to have cards with the number $1$ to $10$ on for them to choose four from. They could doing it in small groups</div>
<br></br>
<h3>Key questions</h3>
<div>How have you tried to et all the answers?<br></br>
Have you used any kind of system?<br></br>
Which were the hardest/easiest answers to find?</div>
<br></br>
<h3>Possible extension</h3>
<div>text</div>
<br></br>
<h3>Possible support</h3>
<div>Some pupils could have cards representing the two operations as well as the four number cards to make number sentences from.</div>
<br></br>
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Just Four Numbers