6989
/www/nrich/html/content/id/6989/
1
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 alt="Image fo graphs" height="152" src="image-of-hypers.jpg" width="450"></mdo:image></div>
<h3>What are you aiming to do?</h3>
<h4>For the task:</h4>
The team has to find the rule on the Ruler's card, using the minimum number of tests. A test is asking whether a particular function obeys the unknown rule or not.<br></br>
<h4>As a team:</h4>
<ul>
<li>finding out what others think</li>
<li>giving reasons for ideas</li>
<li>being concise</li>
<li>reflecting on what has been said</li>
<li>allowing everyone to contribute.</li>
</ul>
<h4>Getting started</h4>
<div>The team can be made up of four or five people of which one person is chosen to be the "Ruler". If you do the task several times, members of the team can take turns at being the Ruler. You may also wish to appoint an observer.</div>
<br></br>
<div>You will need:</div>
<ul>
<li>the set of <a href="/content/id/6989/Function%20rules.doc">function rule</a> cards.</li>
<li>a piece of coloured paper (The Box)</li>
<li>the set of <a href="/content/id/6989/Functions.doc">function</a> cards (large file).</li>
</ul>
<h3>Tackling the problem</h3>
<ul>
<li>The team has the set of function cards. The domain of each function is either the values of x visible on the x-axis or is stated.</li>
<li>The Ruler selects a rule card from the pack and keeps it hidden from the rest of the team.</li>
<li>Before deciding on a function to present to the Ruler for testing - the team must discuss and agree as a team why they think it would make a good test case.</li>
<li>If the function obeys the rule then the Ruler puts it in the Box, if it does not obey the rule it is placed outside the Box.</li>
<li>If someone thinks they know the rule, they must share their reasoning with the rest of the team, who discuss and check their reasoning before deciding if it is a suitable conjecture to put forward.</li>
<li>The Ruler then reveals the rule.</li>
<li>If the team is right, the task can start again with a different Ruler. If they are wrong, they discuss where their error in reasoning may have been before moving on.</li>
</ul>
<div>At the end of the task discuss how well you worked as a team.</div>
<br></br>
<h4>Team and Ruler Guidelines</h4>
<ul>
<li>No one should choose a card for testing without the agreement of the rest of the team.</li>
<li>You are trying to find the rule by testing the minimum number of function cards.</li>
<li>The Ruler can only put a chosen card in the Box or outside it.</li>
<li>The Ruler can only speak to state whether the rule the team have decided on is correct or not.</li>
</ul>
<h4>Observer Guidelines</h4>
<ul>
<li>Make a note of how often each member of the team contributes to the discussion.</li>
<li>Check that the Ruler only tests a function that has been chosen by the agreement of the whole team.</li>
<li>Look for occasions when someone asks someone else's opinion.</li>
<li>Look for occasions when someone listens and responds to someone else's ideas.</li>
</ul>
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<h3>Why do this problem?</h3>
<a href="http://nrich.maths.org/6989&part=">This task</a>
encourages learners to ensure all members of the team participate,
share their reasoning, listen to each other's opinions and reflect
on the outcome. 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>.<br></br>
<h3>Possible approach</h3>
<div>The task is designed to
work with teams of four, taking it in turns to be the
"Ruler."</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>
<div>The aim is for the team
to discuss and agree before selecting any card to be tested by the
Ruler. Does the function obey the rule on the chosen rule
card?</div>
<br></br>
<div><a href="/content/id/6989/Functions.doc">Here</a> are the function
cards.</div>
<div><a href="/content/id/6989/Function%20rules.doc">Here</a> are the rule
cards.</div>
<div><a href="/content/id/6989/team-ruler%20guidelines-4.doc">Guideline
cards</a> for the team and Ruler can be used to focus the learners'
attentions on the main aims of the task.</div>
<br></br>
<div>One of the roles of the
Observer is to check discussion takes place before a decision is
made and that the Ruler only responds if they feel everyone has
contributed to the decision. Guideline cards for the Observer can
be found <a href="/content/id/6989/Observer%20Guidelines-4.doc">here</a>.</div>
<br></br>
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>
<h3>Key questions</h3>
<ul>
<li>Was there a choice of house to test that was particularly
useful? Why?</li>
</ul>
<ul>
<li>Were there any ideas that proved really helpful?</li>
<li>How well did you listen to others in your group?</li>
<li>How did you ensure that everyone had a chance to
contribute?</li>
</ul>
<h3>Possible extension</h3>
<div>Learners may like to try
one of the other 'Guess the rule' tasks, which can be found by
going to <a href="http://nrich.maths.org/6933&part=">this
article.</a></div>
<br></br>
<h3>Possible support</h3>
<div>You may wish to give a
copy of all, or a selection, of the rule cards and function cards
to the team so they have a list of possible rules. There are a set
of cards with just quadratic functions in <a href="http://nrich.maths.org/6988&part=">this</a> task. Other
team-building tasks can be found by going to this <a href="http://nrich.maths.org/6933&part=">article</a>.</div>
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Guess the function
This task depends on learners sharing reasoning, listening to
opinions, reflecting and pulling ideas together.
Sequences, Functions and Graphs
Graphs
Sequences, Functions and Graphs
Graph sketching
Using, Applying and Reasoning about Mathematics
Team-building