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2011-02-01T00:00:01
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<p>If you put three beads onto a tens/units abacus you could make
the numbers $3$, $30$, $12$ or $21$.</p>
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<div>Explore the numbers you can make using six beads.</div>
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<p class="editorial">We had over 60 correct answers to this
challenge. Here are just some of them that also say a bit about
what they did.</p>
<br></br>
<p class="editorial">Nicholas from Congleton wrote:</p>
<div>I used six lego bricks to pretend they were beads on an
abacus. I started with six bricks on one side (the units) to make
$6$ then swapped it to the tens side to make $60$.</div>
<div>I then took one brick and moved it over to the units side to
make $51$, then swapped them over (making $15$).</div>
<div>I moved another from the $5$ to the $1$.</div>
<div>Then I repeated the process until I got to three on each
side.</div>
<br></br>
<div>Answers: $6, 60, 15, 51, 42, 24$ and $33$.</div>
<br></br>
P.S.: I wrote down the answers on a jotter as I went along.<br></br>
<br></br>
<p class="editorial">Emily from Mount School wrote:</p>
<div>With six beads I made $6, 15, 24, 33, 42, 51, 60$.</div>
<div>I started with all the beads on the units and then just kept
moving one across.</div>
I noticed that with three beads you made four numbers and with six
beads I made seven numbers so I tried it with four beads and made
five numbers, always one more number than beads.<br></br>
<br></br>
<p class="editorial">Sam from Comberton wrote:</p>
<div>First I drew some abacus on a piece of paper.</div>
<div>Next I drew the beads and wrote the number it made
underneath.</div>
<div>I started with no beads on the Tens column and then increased
it by one each time and at the same take taking one bead off the
units column each time.</div>
<div>I got seven numbers. They were $6, 15, 24, 33, 42, 51$ and
$60$.</div>
<br></br>
<p class="editorial">We had the following splendid picture and
notes from a key Stage 2 teacher at Ysgol Aberdyfi in Wales.</p>
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<h2>6 Beads</h2>
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<p>If you put three beads onto a tens/units abacus you could make the numbers $3$, $30$, $12$ or $21$.</p>
<p style="text-align: center;"><mdo:image alt="abacus" height="124" src="abacus.jpg" width="491"></mdo:image></p>
<p style="text-align: center;"> </p>
<div>Explore the numbers you can make using six beads.</div>
<div style="text-align: center;"><mdo:image alt="pic4" height="138" src="Picture%204.jpg" width="238"></mdo:image></div>
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<h3> </h3>
<h3><span style="font-weight: bold;">Why do this problem?</span></h3>
<div><a href="http://nrich.maths.org/public/viewer.php?obj_id=152&part=index">This problem</a> is a good, yet simple, activity that can get pupils thinking hard about numerals, numbers and place value.</div>
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<h3>Possible approach</h3>
<div>You could start the children off by showing them one of the examples for three beads and then asking for other ways the beads could be arranged, reading the numbers together. You may want to use a basic drawing of the abacus on an interactive whiteboard and have 'beads' to drag into place. At this stage, you could encourage learners to try and explain how we know we have all the different
ways.</div>
<br></br>
<div>After this the children could work in pairs with six beads so that they are able to talk through their ideas with a partner. They could use a real abacus or counters on a sheet of paper divided into two, to separate the tens from the units. Invite them to find a way to record what they have done. The could use digit cards to make the number which is represented on the abacus.</div>
<br></br>
In the plenary, children could compare the ways in which they have recorded their findings and you could discuss the advantages of each. You could then talk about which recording methods would be best if we wanted to be sure that we had all the ways of using six beads. At this point, you could share any that have used such a system, or you could demonstrate your own way.
<h3>Key questions</h3>
<div>What can you tell me about the numbers you've found?</div>
<div>Are there any other ways you can arrange those beads?</div>
<div>How can you tell if you have them all?</div>
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<h3>Possible extension</h3>
<div>Learners could increase the number of beads or they could be asked to investigate what would happen if there were three columns: units, tens and hundreds.</div>
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<h3>Possible support</h3>
Some children may find it easier to use four beads, rather than going straight on to six. Using practical apparatus, such as counters, is essential for those having difficulties in understanding the problem.<br></br>
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It might help to use six counters on a piece of paper divided into
two columns, one labelled tens and the other units. <br></br>
How will you know you have found all the different ways?<br></br></mdoxml>
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<strong style="font-weight: 400;">Deniz from</strong> Irmak Primary
School, Istanbul, Turkey sent in a solution for this problem.
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6 Beads
If you put three beads onto a tens/ones abacus you could make the
numbers 3, 30, 12 or 21. What numbers can be made with six beads?
Numbers and the Number System
Place value
Using, Applying and Reasoning about Mathematics
Working systematically
Mathematics Tools
Digit cards
Mathematics Tools
Counters