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'Counters in the Middle' printed from http://nrich.maths.org/
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
What are you aiming to
For the task:
The team has to recreate
the row of counters (created by the designer) by asking as few
questions as possible.
As a team:
- Listening and finding out what others think
- Giving reasons for ideas
- Pulling ideas together
- Finding out whether the group is ready to make a
You will be working in a
team of four or five. You will need two sets of counters. The image
above uses 6 counters of 3 different colours. You might wish to
start with just two colours until you have some experience of the
Choose someone in the
group to be the designer. If you try this task more than once, team
members should take turns at playing this role.
Give one set of counters
to the designer and the other identical set to the rest of the
You may also wish to
choose someone to be the observer (a really good idea if there are
more than four people in the team).
Tackling the problem
Without the rest of the
group seeing, the designer creates a line of counters using some or
all of the counters available.
Using the rules for
asking questions, and checking that they all agree first, members
of the team take turns to ask the designer questions that will help
them recreate the line of counters.
When all of the team
think they have the correct design they can check with the designer
and the task ends.
At the end, the observer
gives feedback about the way members of the team worked together,
highlighting strengths and ways that they could improve next time.
The team discuss the feedback and how they think they worked.
- You must agree any question before asking the designer.
- The team can only ask questions of the type listed in the
- The team members must take turns in asking questions.
- The designer can only answer "Yes", "No" or give a
Try to find the pattern using as few questions as possible.
- You do not have to use all the counters.
- The counters should form a line.
- You can only say "Yes" or "No", or give a number as an
- You must only answer questions of the agreed format.
- You only answer a question if the team has discussed and agreed
Team question rules:
The team can ask
- the number of counters,
- the number of counters of each colour,
- the colours of touching counters,
- the symmetry properties of the design,
- the colours, or numbers, of counters to the left or right of a
You cannot ask about the
position and colour of a particular counter, for example:
"Is the first counter
"Is the second counter
You can ask questions
"Is the counter to the
left of the red counter green?".
Your role is to:
- identify the times when reasons for ideas are given by members
of the team,
- check that everyone agrees before a question is asked,
- check that the questions fit those allowed in the rules,
- check that members of the team take it in turns to ask
- count the number of questions the team asks.