6926
/www/nrich/html/content/id/6926/
8
2011-02-01T00:00:01
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<p>Before starting to explore Charlie's mapping, you might want to watch a short video explaining how to use the NRICH Number Plumber.<br></br>
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Charlie has created a new mapping which you can access by clicking on the picture below. The initial challenge is to figure out what Charlie's mapping does. You can drop some numbers into the mapping, and see what comes out.<br></br>
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Test your ideas by predicting the outputs for some different inputs.<br></br>
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Then try to build your own mapping which does the same job.<br></br>
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There are many ways of doing this which are not as complicated as the way Charlie chose! Try to find more than one, and explain why they do the same job.<br></br>
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Only reveal the hidden parts of Charlie's mapping once you have been succesful.<br></br>
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Click on the picture to explore Charlie's mappings.<br></br>
<a href="http://nrich.maths.org/DataFlow/DataFlow.html?config=/content/id/6926/CharlieMapping.xml" style="font-weight: bold;" target="_blank"><mdo:image alt="" height="100" src="icon.png" width="100"></mdo:image></a><br></br>
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As you explore Charlie's mappings, you will notice points appearing on the graph. The input number is the x coordinate, and the output number is the y coordinate.<br></br>
Create some other function machines using the <a href="http://nrich.maths.org/DataFlow/DataFlow.html?config=/content/id/6926/Stage3NumberPlumber.xml">NRICH Number Plumber</a>, and observe the outcomes on the graph.<br></br>
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Mathematicians like to ask themselves questions about what they notice.<br></br>
<span style="font-weight: bold;">What possible questions could you ask?</span><br></br>
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These questions may lead you to make conjectures - something which you believe to be true but need to investigate further in order to convince yourself.</p></mdoxml>
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<h3>Why work on this project?</h3>
<div>This month's NRICH site has been inspired by the way teachers at Kingsfield School in Bristol work with their students. Following an introduction to a potentially rich starting point, a considerable proportion of the lesson time at Kingsfield is dedicated to working on questions, ideas and conjectures generated by students.</div>
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<div>Working on this project will encourage students to work together, discuss ideas, develop conjectures, suggest new lines of enquiry, solve problems and generally experience how a mathematical community functions.</div>
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<h3>Possible approach</h3>
<div><a href="http://nrich.maths.org/6926&part=">Charlie's Mapping</a> is one of several starting points. Here are the sort of questions that might emerge:</div>
<div style="margin-left: 40px;">When are lines parallel?</div>
<div style="margin-left: 40px;">When are they perpendicular?</div>
<div style="margin-left: 40px;">What affects the direction and steepness of a graph?</div>
<div style="margin-left: 40px;">Can I tell from a function where its graph will cross the axes?</div>
<div style="margin-left: 40px;">Which functions give straight lines, and which give curves?</div>
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<div>The interactivity could be used as a starting point to encourage students to make conjectures about functions and graphs, in a similar way to how students at Kingsfield School are introduced to the topic. </div>
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<div>Read the article <a href="http://nrich.maths.org/6808&part=">Kingsfield School - Building on Rich Starting Points</a>, which has links to a description of a Kingsfield teacher's first lesson on functions and graphs, and a video showing how these ideas are put into practice in the classroom.</div>
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<div>For teachers who want to create their own alternatives to Charlie's Mapping for use in the classroom, here is an introductory video explaining how to build, load and save your own examples.</div>
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To read more about the Number Plumber, visit <a href="http://grumplet.wordpress.com/2010/02/23/the-nrich-number-plumber/" target="_blank">Grumplet's blog</a> where you can comment on how you have used the number plumber and share links to files you have created. We are continuing to develop this resource so your feedback and ideas will be very useful.</p>
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<h3>Key questions</h3>
<div>What do you think this function machine does?</div>
<div>Can you predict an output, and test it?</div>
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<div>What possible questions could we ask?</div>
<div>Can you make any predictions about what might happen when we change the function machine?</div>
<div>What's the same? What is different?</div>
<div>Can you explain?</div>
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<h3>Possible extension</h3>
<p><a href="http://nrich.maths.org/6929">Alison's Mapping</a> provides a starting point based on quadratic functions.</p>
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<h3>Possible support</h3>
<p><a href="http://nrich.maths.org/6928">Become Maths Detectives</a> encourages exploration of numerical patterns.<br></br>
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Charlie's Mapping
Charlie has created a mapping. Can you figure out what it does?
What questions does it prompt you to ask?
Sequences, Functions and Graphs
Graphs
Sequences, Functions and Graphs
Linear functions
Using, Applying and Reasoning about Mathematics
Making and proving conjectures