8123
/www/nrich/html/content/id/8123/
1
2012-05-01T00:00:00
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<mdoxml version="1.0"><p class="chalkboard" style="text-align: center;">How many dots?</p>
<p style="text-align: center;"><mdo:image src="Starter%20dots.jpg"></mdo:image></p>
<p style="text-align: center;"> How did you count them?</p>
<p> </p>
<p> What about your friends, how did each of them count the dots?</p>
<p> </p>
<p>Ask your teacher for some other pictures of dots for you to count and share ideas about how you counted them.</p></mdoxml>
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<span class="editorial">Thank you for the many contributions you sent in. Many pupils also wrote about how they did the counting and others just sent in the total number, which was $23$. Charlotte also S Anselm's Prep School, sent a rather different way, together with a picture to illustrate it.</span><br></br>
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I put little rings around the dots like you would in a wordsearch. Then I counted up how many dots were in each ring remembering not to count the ones we've already counted! I did the sums by the side to add up all the dots in the rings (which I called carniverous worms) and it came to ... $23$.
<div style="text-align: center;"><mdo:image src="how%20we%27d%20count%20pic.jpg"></mdo:image></div>
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<span class="editorial">Thank you all of you and for the splendid solutions from S. Anselm's. Keep the solutions coming in.</span><br></br></mdoxml>
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<h2>How We'd Count</h2>
<p class="chalkboard" style="text-align: center;">How many dots?</p>
<p style="text-align: center;"><mdo:image src="Starter%20dots.jpg"></mdo:image></p>
<p style="text-align: center;"> How did you count them?</p>
<p> </p>
<p> What about your friends, how did each of them count the dots?</p>
<p> </p>
<p>Ask your teacher for some other pictures of dots for you to count and share ideas about how you counted them.</p>
</div>
<h3> <span style="font-weight: bold;">Why do this problem?</span></h3>
<div>This <a href="http://www.nrich.maths.org.uk/8123">activity</a> enables the adult to learn something of how children visualise numbers when counting and/or adding. The activity is also a good catalyst for children having a discussion together and sharing their ideas, as it is easy to see that there is no "right" way of going about it. A key element of this is the adult creating an
encouraging environment where children feel comfortable to share their thinking. </div>
<div> </div>
<h3>Possible approach</h3>
<p>Display the 'blue' image so that everyone can see it - it may be helpful to use a whiteboard, if one is available. The aim is to encourage the children to 'say' what is in their heads about the counting such as, </p>
<p><em>'I can see three lines. One is a line of six and one is a line of five and there's a line of four and then there is these other ones in between.'</em></p>
<p>They may well see something different to what you see. Be prepared for surprises! </p>
<p>A valuable discussion can then follow with the children saying what they think about others' 'say' about their counting.</p>
<p>Here are some further examples that can be used in a similar way <a class="doclink" href="/content/id/8123/different%20ones%20to%20see.doc">doc </a> <a class="pdflink" href="/content/id/8123/different%20ones%20to%20see.pdf">pdf</a></p>
<p> </p>
<h3>Key questions</h3>
<p>How many?</p>
<div>How do you know?</div>
<div>What did you do?</div>
<div>How would you check?</div>
<div>What made you decide to change your way of counting this time? </div>
<div> </div>
<h3>Possible extension</h3>
<p>A handful of pebbles scattered on to a tray can lead to similar questions and discussions.</p>
<p>The children could then go on to try counting other things that they come across in the real world such as seeds on a sunflower, patterns on clothing, flowers in a flower-bed or spots on different animals' skin.</p>
<p> </p>
<h3>Possible support</h3>
<div> </div>
<div>A handful of pebbles scattered on to a tray may help and be easier to count than dots on a page.</div>
<div>The difficulty is often keeping track of what has been counted and what there is still to count. See whether the children can devise strategies to help such as making a small dot beside the dots as they count or moving pebbles from one side of the tray to the other. Counting is not as easy as you might think!</div>
<div>Try working one-to-one and break the activity down into small steps. </div>
<div>Use 'we' rather than 'you' and 'you may like to start with...'</div>
<div>You could say: 'We want to find out how many dots there are.....can we do that?'</div>
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How we'd count
An activity centred around observations of dots and how we visualise number arrangement patterns.
Numbers and the Number System
Counting
Using, Applying and Reasoning about Mathematics
Visualising
Admin
Lower primary mapping document