7820
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<p>Tom's teacher was playing a number game with the class.<br></br>
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She wrote "7" on the white board and asked the class to think of different ways of showing or writing seven.<br></br>
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Ben fetched the dominoes and found these ones:<br></br>
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<mdo:image alt="" height="30" src="Tom1.png" width="184"></mdo:image><br></br>
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Hanna used two dice to make seven which looked much the same as Ben's.<br></br>
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<mdo:image alt="" height="102" src="Tom5.png" width="196"></mdo:image><br></br>
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Annie and Tessa used the Cuisenaire rods and made seven in four different ways. <br></br>
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<mdo:image alt="" height="70" src="Tom2.png" width="421"></mdo:image><br></br>
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William made seven with linking cubes and Thea put seven pegs on a pegboard.<br></br>
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<mdo:image alt="" height="49" src="Tom3.png" width="243"></mdo:image><br></br>
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Nina drew a ladybird with seven spots.<br></br>
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<mdo:image alt="" height="119" src="Tom6.png" width="96"></mdo:image><br></br>
Steven showed seven fingers and Alice put the play-clock to say "7 o'clock".<br></br>
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<mdo:image alt="" height="129" src="Tom4.png" width="129"></mdo:image><br></br>
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Tom's teacher then chose another odd number for the class to make.<br></br>
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Ben said, "There's only one domino this time."<br></br>
"And only one way with the two dice," added Hanna "unless you make it two ways with the different colours, red and blue being different from blue and red."<br></br>
"There isn't a rod that long!" grumbled Annie.<br></br>
"But there's five ways with two rods," Tessa added.<br></br>
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William and Thea had no trouble making the new number with the linking cubes and pegs. "I don't think ladybirds come with that number of spots," mused Nina, "but I could draw one. Just extra spots on both sides."<br></br>
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"I haven't got enough fingers," grumbled Steven, "can I use one from someone else?"<br></br>
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"But I can still make the clock say the right time," said Alice, "But I couldn't have done if the number was much larger."<br></br>
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Tom jumped up and down, "It's my brother's birthday!" he called out, "And that's how old he is today!"<br></br>
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How old was Tom's brother?</p></mdoxml>
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<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<a href="http://nrich.maths.org/7820&part=">This problem</a> is designed to help children see numbers in many different ways. This can help them to abstract out what is sometimes known as "the two-ness of two".<br></br>
<h3>Possible approach</h3>
<div>You could begin by asking the group to tell you, or to draw, as many ways as they of ways of illustrating another number, for example, five or eight. If they do not think or dominoes or clocks or dice you could give hints about these.</div>
<div> </div>
<div>Alternatively, you could start with the problem as it is given. The second number introduced is not meant to be difficult to work out, but should give some opportunity for accurate counting, number recognition and recording by many different means.</div>
<div> </div>
<div>You should have dominoes, dice, play-clocks, pegboards, counters, "Multilink" and coloured rods available, as well as paper and coloured pencils.</div>
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<h3>Key questions</h3>
<div>What is this number?</div>
<div>How many dots are there here?</div>
<div>Can you find a domino with this number of dots?</div>
<div>What time does this clock say?</div>
<div>Can you make a line/stick of that number of cubes?</div>
<div>Can you make the number in a different way with the coloured rods/ Cuisenaire rods?</div>
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<h3>Possible extension</h3>
Learners could choose another number to illustrate or they could try <a href="http://nrich.maths.org/6948&part=">this problem</a>.<br></br>
<h3>Possible support</h3>
Suggest sticking with ways of illustrating seven by using real dominoes etc. or you could use <a href="http://nrich.maths.org/7233&part=">this easier problem</a>.<br></br>
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Think of different ways you can illustrate seven.<br></br>
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Dominoes, dice, play-clocks, pegboards, counters, "Multilink" and coloured rods might help you.<br></br></mdoxml>
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How old is Tom’s brother?
This problem is designed to help children see numbers in many different ways to help them to abstract out the essence of the number.
Using, Applying and Reasoning about Mathematics
Representing
Using, Applying and Reasoning about Mathematics
Selecting and using information
Numbers and the Number System
Reading and writing numbers