6988
/www/nrich/html/content/id/6988/
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2011-02-01T00:00:01
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<span class="editorial">This
is one of a series of problems designed to develop learners' team
working skills. Other tasks in the series can be found by going to
this</span> <a class="editorial" href="http://nrich.maths.org/6933&part=">article</a><span class="editorial">.</span><br></br>
<div style="text-align: center;"><mdo:image width="400" height="161" src="image-of-graphs.jpg" alt="Imagre of graphs"></mdo:image></div>
<h3>What are you aiming to
do?</h3>
<h4>For the task:</h4>
<div>One member of the team is
trying to find out what is on their chosen card (the unknown
function) by asking as few questions as possible.</div>
<div>The rest of the team need
to confer and agree on a "Yes" or "No" answer to each question and
keep track of the number of questions that have been asked
altogether.</div>
<br></br>
<h4>As a team:</h4>
<ul>
<li>asking questions - making sense of your own understanding</li>
<li>being concise</li>
<li>listening</li>
<li>reflecting on what has been said.</li>
</ul>
<h3>Getting started</h3>
<div>The task is designed to
work with a team of four or five people. If you do the task several
times, members of the team can take turns at trying to find the
unknown function. You may also wish to appoint an observer.</div>
<br></br>
<div>You will need this set of
<a href="/content/id/6988/Quad%20functions.doc">function cards</a>.
Spread them out on the table so that everyone can see the sort of
functions chosen for this task.</div>
<br></br>
<div>You will each need a
sheet of paper and pencil.</div>
<h3>Tackling the problem</h3>
<h4>Rules</h4>
<ul>
<li>Choose someone on the team to keep track of the number of
questions - this might be the observer.</li>
<li>The person who has been chosen to try to find the unknown
function chooses a card and hands it to the rest of the team
without looking at it.</li>
<li>The person trying to find the function can ask up to
8 questions.</li>
<li>When a question has been asked, each of the other members of
the team writes "Yes" or "No" on their sheet of paper. If they all
agree one person gives the answer.</li>
<li>If the team do not agree, they will need to confer - preferably
out of earshot of the person trying to find the function. Once in
agreement, one person gives the answer.</li>
<li>The person trying to find the unknown can have at most two
attempts at guessing what is on the card before the task ends. Each
guess counts as one of the 6 questions.</li>
<li>The team can offer the hint "Cold" or "Warm" or "Hot" if the
first guess is incorrect.</li>
</ul>
<div>At the end of the task
the team should discuss what proved to be good questions and less
useful questions. If the person does not identify what is on the
card, discuss what questions might have worked more
effectively.</div>
<br></br>
<div>Did you work well as a
team?</div>
<br></br>
<h4>Observer guidelines</h4>
<ul>
<li>Keep track of the number of questions</li>
<li>Make a note of questions you thought were effective and
why</li>
<li>Note when the team worked well together.</li>
</ul>
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<h3>Why do this problem?</h3>
<div><a href="http://nrich.maths.org/6988&part=">This task</a> aims to encourage learners to develop their ability to communicate their reasoning and to frame and ask questions. This task requires learners to make sense of their own understanding, be concise, listen and reflect on what has been said. This is one of a series of problems designed to develop learners' team working skills. Other
tasks in the series can be found by going to this <a href="http://nrich.maths.org/6933&part=">article</a>.</div>
<br></br>
<div>This task also supports the development of knowledge of transforming graphs.</div>
<h3>Possible approach</h3>
<div>The task is designed to work with teams of four with one chosen, in turn, to find the unknown.</div>
<br></br>
<div>Using a fifth person as an observer means that feedback can be very specific and works well either using another learner or an adult.</div>
<br></br>
<p><a href="/content/id/6988/Quad%20functions.doc">Here</a> are the function cards.<br></br>
<br></br>
Give the teams plenty of time to do the task, allowing every member of the team to take the role of trying to find the unknown.</p>
<br></br>
<br></br>
<div>The observer's role should include checking discussion takes place before an answer is given and keeping track of the number of questions.</div>
<br></br>
<p>When teams have finished working on the task it is important that they spend time discussing in groups, and then as a whole class, how well they worked as a team. They can consider what they have learned from the experience and what they would do differently next time, particularly in terms of how to listen to each other and ensure that all members of the team participate. Your own
observations, as well as those of observers might inform the discussions.<br></br>
<br></br>
Finish the session by listing the most useful questions that arose whilst learners did the task and discuss why they were so effective.<br></br>
<br></br>
<em>You can read about <a href="https://www.ncetm.org.uk/resources/34332">one teacher's experience</a> of using this task in the classroom.</em><br></br>
</p>
<h3>Key questions</h3>
<ul>
<li>Was there a question that proved really useful in identifying the function?</li>
</ul>
<ul>
<li>How well did you listen to each other in your team?</li>
<li>How did you ensure that everyone had a chance to contribute?</li>
</ul>
<h3>Possible extension</h3>
<div>You may wish to keep the cards hidden from the person trying to find the rule. Learners may like to create a set of function cards of their own, or try some of the other skill-building tasks in <a href="http://nrich.maths.org/6933&part=">this article.</a></div>
<br></br>
<h3>Possible support</h3>
<div>Reduce the number of cards by focussing on cards with a particular form of transformation, such as translation along the x axis. Learners may like to try one of the other 'What am I?' tasks, which can be found by going to <a href="http://nrich.maths.org/6933&part=">this article</a>.</div>
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Which quadratic?
This task develops knowledge of transformation of graphs. By
framing and asking questions a member of the team has to find out
which mathematical function they have chosen.
Using, Applying and Reasoning about Mathematics
Team-building
Sequences, Functions and Graphs
Quadratic functions
Transformations and their Properties
Compound transformations