En-counters
This task requires learners to explain and help others, asking and answering questions.
Age
5 to 7
Challenge level
Problem
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 article.
Image
What are you aiming to do?
For the task:
Learners must complete the task themselves but with support and advice from other members of the team.As a team:
- helping others to do things for themselves
- responding to the needs of others - everybody helps everybody
- explaining by telling how.
Getting started
This problem needs a team of four. A fifth person can act as an observer.
You need to arrange the desks and some props so that everyone can see everyone else but no one can see what anyone else is building. One possibility is for the designer to face the other three team members and make the design inside a box whilst team members try to recreate the design behind books or folders used as screens.
You will need four sets of counters (or similar) - up to 12 in each set.
Choose someone in the group to be the designer.
If there are five people choose a person to be the observer.
If you try this task more than once, team members should take turns at playing these roles.
Give one set of counters to the designer and one set to each of the other team members.
Tackling the Problem
The designer creates a counter design so that it is hidden from the rest of the team but as s/he makes the design, s/he explains what it looks like so that the rest of the team can make a copy of the same design.
Team members can ask questions about the design at any time and the designer answers in as helpful a way as possible.
When a team member thinks they have a completed design, they ask the designer to check. If it is right they can then aid the designer in answering questions. If they do not have the correct design the task continues.
Remember that all help has to be given without sight of the enquirer's design.
At any point the task can be brought to an end to discuss the success of the questioning and answering, and how it helped or hindered completion of the task.
Observer guidelines:
- How well did the designer explain the process of creation? What words did they use that were really helpful?
- How clear were the questions the team asked? Can you give an example of a good question?
- How well were the questions answered? Can you give a good example?
Alternative version
We have written a version of this task which is suitable for one child and an adult playing together at home.
Student Solutions
As this activity is for groups to work on and there are all sorts of possible outcomes, we haven't received any solutions.
However, if you have a go at it, we'd love to hear how you got on as a group. Did you work well together?
However, if you have a go at it, we'd love to hear how you got on as a group. Did you work well together?
Teachers' Resources
En-counters
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 article.
Image
What are you aiming to do?
For the task:
Learners must complete the task themselves but with support and advice from other members of the team.As a team:
- helping others to do things for themselves
- responding to the needs of others - everybody helps everybody
- explaining by telling how.
Getting started
This problem needs a team of four. A fifth person can act as an observer.
You need to arrange the desks and some props so that everyone can see everyone else but no one can see what anyone else is building. One possibility is for the designer to face the other three team members and make the design inside a box whilst team members try to recreate the design behind books or folders used as screens.
You will need four sets of counters (or similar) - up to 12 in each set.
Choose someone in the group to be the designer.
If there are five people choose a person to be the observer.
If you try this task more than once, team members should take turns at playing these roles.
Give one set of counters to the designer and one set to each of the other team members.
Tackling the Problem
The designer creates a counter design so that it is hidden from the rest of the team but as s/he makes the design, s/he explains what it looks like so that the rest of the team can make a copy of the same design.
Team members can ask questions about the design at any time and the designer answers in as helpful a way as possible.
When a team member thinks they have a completed design, they ask the designer to check. If it is right they can then aid the designer in answering questions. If they do not have the correct design the task continues.
Remember that all help has to be given without sight of the enquirer's design.
At any point the task can be brought to an end to discuss the success of the questioning and answering, and how it helped or hindered completion of the task.
Observer guidelines:
- How well did the designer explain the process of creation? What words did they use that were really helpful?
- How clear were the questions the team asked? Can you give an example of a good question?
- How well were the questions answered? Can you give a good example?
Why do this problem?
This task encourages the development of team-building skills such as helping others to do things for themselves, responding to the needs of others, encouraging everbody to help each other and explaining to each other by telling how. 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 article.
In addition learners will gain experience at using words to describe position and orientation.
Possible approach
A team has four or more members.
You may wish to use an adult as an observer.
Before starting this practical activity you might wish to ask each member of the group to draw their design, ready for when they act as designer for the rest of the team. You may wish to constrain the range of possibilities to manage the difficulty level of the task. For example:
- The designer has up to 12 counters of different colours and arranges them in a row - each counter touching the one or two counters on either side of it. They might describe their pattern in terms of "Start with blue, place a blue counter to its right, now a yellow to its right" or "Start with a red, place a yellow below then a blue below that".
Image
- The designer can use two dimensional arrays. They might then describe their pattern in terms of "You need two blue and two yellow counters. Make a square where the blue counters are in the top right and bottom left and the yellow in the top left and bottom right".
The focus of attention for the teams is asking, explaining and helping each other. The completion of the task, whilst rewarding for all concerned, is not the main purpose of the activity.
If learners need some support with their positional language, a word list can be found here: word, pdf.
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 ask questions and answer them effectively. Your own observations, as well as those of observers, might inform the discussions.
Why not let us know how the children have got on with their group-working skills by clicking on the 'Submit a solution' link?
Key questions
Were there any questions that someone else asked that you found helpful?
How well did you listen to others in your group?
How easy was it to use the answers to the questions that were asked?
Was there an answer that you found particularly helpful?
Possible extension
Learners may like to try one of the other 'Explaining How' tasks. Other team-building tasks can be found by going to this article.
Possible support
Other team-building tasks can be found by going to this article.
Counters in the middle
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
Age
7 to 11
Challenge level
Problem
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 article.
Image
What are you aiming to do?
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
decision.
Getting started
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
task.
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
team.
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.
Task Rules:
- You must agree any question before asking the designer.
- The team can only ask questions of the type listed in the rules.
- The team members must take turns in asking questions.
- The designer can only answer "Yes", "No" or give a
number.
Try to find the pattern using as few questions as possible.
Designer guidelines:
- 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 answer.
- You must only answer questions of the agreed format.
- You only answer a question if the team has discussed and agreed it first.
Team question rules:
The team can ask
questions about:
- 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 counter.
You cannot ask about the
position and colour of a particular counter, for example:
"Is the first counter
red?",
"Is the second counter
yellow?"
You can ask questions
like:
"Is the counter to the
left of the red counter green?".
Observer Guidelines:
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 questions,
- count the number of questions the team asks.
Student Solutions
As this activity is for groups to work on and there are all sorts of possible outcomes, we haven't received many solutions.
However, Nathan from St. Helen's School in Abbotsham sent in this clear account with some suggestions:
We played counters in the middle - we thought it can be very tricky but when you get closer it gets so much easier.
Firstly we guessed the first counter and then the last counter.
After we got them right we had some counters in front of us. We used them to guess what some of the others were - you would be suprised about how much easier this is.
Good questions:
Has it got a pattern?
How many colours have you used?
How many counters are there?
How many blue counters have you used?
Less useful questions:
Is it red?
Danny, Aaron, Emma, Emily and Ella from Bacton Community Primary School sent in these comments:
What if you asked them what colours they have got.
Ask the shades of colours as well and how many. If you know your partner's favourite colour then you have a big advantage. Working in a team helps a lot as well as being good friends.
Thank you for these comments and suggestions, which will be useful to others reading this before trying the activity!
Teachers' Resources
Counters in the Middle
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 article.
Image
What are you aiming to do?
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 decision.
Getting started
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 task.
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 team.
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.
Task Rules:
- You must agree any question before asking the designer.
- The team can only ask questions of the type listed in the rules.
- The team members must take turns in asking questions.
- The designer can only answer "Yes", "No" or give a number.
Try to find the pattern using as few questions as possible.
Designer guidelines:
- 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 answer.
- You must only answer questions of the agreed format.
- You only answer a question if the team has discussed and agreed it first.
Team question rules:
The team can ask questions about:
- 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 counter.
You cannot ask about the position and colour of a particular counter, for example:
"Is the first counter red?",
"Is the second counter yellow?"
You can ask questions like:
"Is the counter to the left of the red counter green?".
Observer Guidelines:
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 questions,
- count the number of questions the team asks.
Why do this problem?
This task encourages the development of team-building skills such as sharing reasoning, allowing everyone to contribute and valuing those contributions, and coming to a consensus. 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 article. In addition learners are expected to use precision in describing an arrangement of objects.
Possible approach
If learners have never worked on this sort of problem before it is best to choose no more than six counters and two colours.
You will need a screen or cloth to hide the designer's arrangement.*
Arrange learners in groups of four or five (five allows one to act as an observer).
You may wish to ask teams to record their questions before asking them. Then, as part of their review of the task, the team can discuss what may have been a more efficient set of questions to ask.
Cards for each role:
- The rule cards for questioning can be printed from this document.
- The role card for designers can be found here.
- The role card for observers can be found here.
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, what they have learned from the experience and what they would do differently next time. Your own observations, as well as those of observers might inform the discussions.
* You may prefer to prepare some images of an arrangement first to hand out to designers. Designers then answer the team questions, making a note of the number of questions asked. The team records each question before asking it. When the groups have finished you might discuss the number of questions used and ask the team with the fewest questions to
share their ideas with the rest of the group.
Why not let us know how the children have got on with their group-working skills by clicking on the 'Submit a solution' link?
Why not let us know how the children have got on with their group-working skills by clicking on the 'Submit a solution' link?
Key questions
- What things did you hear someone else say that you found really helpful?
- How well did you listen to others in your group?
- How easy was it to come to an agreement about the questions to ask?
- Did everyone always agree and what did you do if you did not?
Possible extension
Increase the number of counters and the colours available.
Learners may like to try one of the other 'All for one' tasks, or other skill-building tasks which can be found by going to this article.
Possible support
Reduce the number of counters and colours available. Make a list of the allowed questions, such as:
- How many counters are there?
- How many red counters are there?
- Is the counter to the left of the green counter red?
- Is the counter to the right of the yellow counter green?
- Is there a counter to the left/right of the yellow counter?
What shape?
This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.
Age
7 to 14
Challenge level
Problem
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 article.
Image
What are you aiming to do?
For the task:
One member of the team is trying to find out what is on their chosen card (the unknown) by asking as few questions as possible.
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.
As a team:
- asking questions - making sense of your own understanding
- being concise
- listening
- reflecting on what has been said.
Getting started
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. You may also wish to appoint an observer.
You will need the set of shape cards. Spread them out on the table so that everyone can see the sorts of shapes chosen for this task.
You will each need a sheet of paper and pencil.
Tackling the problem
Rules
- Choose someone on the team to keep track of the number of questions - this might be the observer.
- The person who has been chosen to try to find the unknown shape chooses a card and hands it to the rest of the team without looking at it.
- The person trying to find the shape can ask up to 12 questions.
- 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.
- If the team do not agree, they will need to confer - preferably out of earshot of the person trying to find the shape. Once in agreement, one person gives the answer.
- The person trying to find the unknown can have up to three attempts at guessing what is on the card before the task ends. Each guess counts as one of the 12 questions.
- The team can offer the hint "Cold" or "Warm" or "Hot" if the first or second guess is incorrect.
At the end of the task the team should discuss what proved to be good questions and less good questions. If the person does not identify what is on the card, discuss what questions might have worked more effectively.
Did you work well as a team?
Observer guidelines
- Keep track of the number of questions
- Make a note of questions you thought were effective and why
- Note when the team worked well together.
Alternative version
We have written a version of this task which is suitable for one child and an adult playing together at home.
Getting Started
Have you found out anything about the number of sides the shape has?
Do you know anything about the angles of the shape?
Do you know anything about the angles of the shape?
Student Solutions
We had some very thoughtful comments from William, Tilly, Neve, Holly, Poppy, Caitlin, Saba, Erin, Alice, Esme, Lauren, Charlie, Ollie, Jamie, Jack, Jay and Annie from St.Helen's C of E Primary School, Abbotsham.
Here is what Tilly, Neve, Holly and Poppy said:
First we played the game and ended up with asking five questions, which is what all of our scores were (strangely!).
After three games we realised some of the questions turned over most of the cards like: Is it a shape? or Does it have a right angle? but we didn't dicuss them until the end.
Some of the shapes are easier to find because a square has four right angles and is regular (it also has other properties). In contrast we discovered that irregular shapes are much harder to find as they took up more questions.
Then we discused tactics (questions) how we could conqueror this game. Here are some good and bad questions that could be used to help win this game in the fewest questions:
Best questions:
Is it a regular shape?
Does it have right angles?
Is it a shape?
Is it an angle?
Bad questions:
Is it a strange shape?
Does it have a right angle?
Is it an angle?
We have put some of the questions in both sections because they turn over cards, but not that many.
Caitlin, Saba, Erin and William said:
If you ask a good question you can remove lots of cards and it gets you closer to the correct shape or angle.
Observe the cards set on the table and think about the different questions that could eliminate as many cards as possible, such as 'does this shape have four or fewer sides?', because this can get rid of lots of cards: squares, rectangles, circles and triangles.
When you are down to a few cards left think about a question that relates to most of the cards turned up, so it leaves you with only very few so you can easily guess the right card.
Listen carefully to all questions asked so that you can relate to the cards left turned up and eliminate any cards, also so you don't repeat a question and waste your 12 guesses.
Alice, Esme and Lauren give us some good advice:
To begin with we just asked random questions, then we began to start asking sensible ones that made more sense. Our least amount of moves that we managed to find the shape with was four, and the most was 12.
We found it quite irritating when we asked too many questions and we were out.
Our team worked ok together, but some answers we didn't agree on which caused a bit of an argument, such as 'Is the shape irregular?'.
We also found that by asking if the shape was irregular, it got rid of most of the cards and narrowed it down to just a few. This made it easier to find which shape they had chosen.
We really enjoyed this challenging task even though our team wasn't perfect.
'Is it an angle?' this got rid of fewer cards but was still useful.
Asking what the shape was directly lost us a lot of questions but came in handy at the end.
Ollie, Jamie and Jack wrote:
What we found easy:
After playing for a while we got used to all the cards and we would know what card was missing so we got the shape after one or two goes but sometimes when we chose a hard shape we took a lot longer.
What we found hard:
When we first started we found it hard because we were not used to playing with those cards and we had not memorised the cards yet.
Also some of the cards like 'Square with corner cut out' and 'Isosceles right angle triangle' we were not used to so when we first saw those shapes we thought they were a bit obscure and odd.
Some of our questions:
The first question was usally 'Is it a shape?' or 'Is it a angle?' then we would ask if it is a triangle or if it is over 90 degrees.
Then a random question if we haven't guessed the shape yet, something like 'Has it got
fewer sides than a hexagon?'. (That was one of Jack's questions).
Also Jamie said 'Has it got a line of symmetry?' but the shape was a hexagon so we
said 'It hasn't got ONE line of symmetry?' then he did realise that it must have more.
The tricky shapes:
The hardest shape was the 'Isosceles right angled triangle' because of its odd name - we all thought that it should have been 'a right angled triangle' or just an 'isosceles triangle' so because of its odd name when we picked it we never guessed the name.
The easy shapes:
The easiest shape was a square because of it being so common and a lot of people know the square also the rectangle because of it also being so common and used a lot in maths.
As well as them the other common shapes were easy like an equilateral triangle and a right angle.
Annie suggests:
The best questions to ask and get you through the game faster are: 'Is it a shape?' that gets rid of lots of cards.
Then another one is, 'Has it got fewer than four sides?' or 'Has it got more than three vertices?'.
'Has it got parallel sides?' and 'Has it got a line of symmetry?'are all good questions to ask so you can guess in the least number of questions.
Thank you all for your comments and suggestions. I am sure they will be useful to others who want to have a go at this activity.
Teachers' Resources
What Shape?
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 article.
Image
What are you aiming to do?
For the task:
One member of the team is trying to find out what is on their chosen card (the unknown) by asking as few questions as possible.
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.
As a team:
- asking questions - making sense of your own understanding
- being concise
- listening
- reflecting on what has been said.
Getting started
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. You may also wish to appoint an observer.
You will need the set of shape cards. Spread them out on the table so that everyone can see the sorts of shapes chosen for this task.
You will each need a sheet of paper and pencil.
Tackling the problem
Rules
- Choose someone on the team to keep track of the number of questions - this might be the observer.
- The person who has been chosen to try to find the unknown shape chooses a card and hands it to the rest of the team without looking at it.
- The person trying to find the shape can ask up to 8 questions.
- 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.
- If the team do not agree, they will need to confer - preferably out of earshot of the person trying to find the shape. Once in agreement, one person gives the answer.
- The person trying to find the unknown can have up to three attempts at guessing what is on the card before the task ends. Each guess counts as one of the 12 questions.
- The team can offer the hint "Cold" or "Warm" or "Hot" if the first or second guess is incorrect.
At the end of the task the team should discuss what proved to be good questions and less good questions. If the person does not identify what is on the card, discuss what questions might have worked more effectively.
Did you work well as a team?
Observer guidelines
- Keep track of the number of questions
- Make a note of questions you thought were effective and why
- Note when the team worked well together.
Why do this problem?
This task combines developing geometric understanding with speaking and and listening skills. It supports the development of basic geometric language encouraging children to talk about shapes using the correct mathematical language and accurate descriptions.This task also 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 and 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 article.)
Possible approach
The task is designed to work with teams of four with one chosen, in turns, to find the unknown.
Using a fifth person as an observer means that feedback can be very specific and works well either using another learner or an adult.
Here are the shape cards: word, pdf.
Allow 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.
The observer's role should include checking discussion takes place before an answer is given and keeping track of the number of questions.
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.
Finish the session by listing the key words associated with shape and space that arose whilst learners did the task.
Why not let us know how the children have got on with their group-working skills by clicking on the 'Submit a solution' link?
Key questions
- Was there a question that proved really useful in identifying the shape?
- What kinds of questions helped you to identify the shapes most quickly?
- How well did you listen to each other in your team?
- How did you ensure that everyone had a chance to contribute?
Possible extension
You may wish to keep the shape cards hidden from the person trying to find the rule. Learners may like to try one of the other 'What am I?' tasks, which can be found by going to this article.
Possible support
You may wish to give a copy of the shape cards to the person trying to find the unknown shape so that they have a sense of what they are aiming for. It is also possible to reduce the number of cards, perhaps focussing on polygons. Other team-building tasks can be found by going to this article.
Arranging cubes
A task which depends on members of the group working collaboratively to reach a single goal.
Age
7 to 11
Challenge level
Problem
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 article.
Image
What are you aiming to do?
For the task:
- The team has to recreate a 2-D arrangement of cubes which matches all the information on their cards without showing each team member's information to anyone else.
As a team:
- Allowing everyone to contribute
- Listening
- Asking questions and finding out what others think
- Sharing knowledge and reasoning
- Reflecting and making use of what has been said
- Coming to a consensus
Getting started
You will be working in a team of four. Ensure that you have plenty of red, green, yellow and blue cubes. You cannot use paper or pencil to help you because you need to listen to what others have to say.
Discuss how you will work together and share your ideas.
Put the pile of 8 cards face down in the centre of the table.
Tackling the problem
Each member of the team takes a card from the pile in turn (enough for two cards each).
Rules
- Team members cannot show their cards to anyone else on the team.
- A team member can describe what is on each of their cards.
- Team members can ask questions to help them make sense of what is on their cards, or on someone else's cards.
- The task is complete when everyone agrees that the arrangement they have made matches everything that is on their cards.
If you have an observer, they might find the following list of things to look for helpful and feed back to the team at the end of the task.
- Check that no one reveals their card or writes anything down.
- Identify points where team members share knowledge and reasoning, and listen to each other.
- Identify points where team members make decisions together.
- Note whether all members of the team are involved.
Student Solutions
We had some good solutions sent in for this group activity, first from Oliver and Daniel from S.U.N. School:
First, we read the statements out and found out that half of the cubes were red, a quarter were yellow and there is the same number of blue cubes as green cubes.
Secondly, Oliver said that, on the picture, there are four cubes across and two down.
Then, Daniel said that one of the lines along was: green, red, yellow.
After that, we discovered that inside the green, red, yellow sequence was the green, red combination so we didn't need to do that card.
Then Daniel found on one of his cards was a corner piece with a red block and a yellow and blue block either side so we added that in.
Then we found there was one piece left, the yellow, red, blue combination and all of the
things were somewhere in our rectangle.
This is what it looked like in a drawing.
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Then a well-presented solution came in from pupils at The Globe School in Lancing. Here it is!
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Then from Mia, Jamie-Lee, Shaneece and Spencer from Elphinstone School we had this good explanation. Thank you so much for the written details:
We went around the circle and listened to each other's explanations.
First we found out the shape and that there were eight squares (this was the most important card).
Secondly, we found that half of the squares were red, so we knew there had to be four red squares.
Then we found out that there were the same amount of blues as greens. At first we thought there were two blues and two greens, but when we found out there were a quarter yellows (this had to be two yellows because that is a quarter of eight), we realised there had to be one green and one blue.
Then we found we needed an L shape yellow, red and blue, then a line of yellow, red and blue.
Finally we added the red and blue. Finished. It looks like this:
YRBR RBRY
RYRG or GRYR
Two groups with exciting names from St. James School sent in these pictures of their work. First we have the Flying Dolphins:
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Then we have the Golden Terrifying Tigers who sent in this picture:
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Thank you for all these solutions. Maybe others will be encouraged to try the same activity.
Teachers' Resources
Arranging Cubes
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 article.
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What are you aiming to do?
For the task:
- The team has to recreate a 2-D arrangement of cubes which matches all the information on their cards without showing each team member's information to anyone else.
As a team:
- Allowing everyone to contribute
- Listening
- Asking questions and finding out what others think
- Sharing knowledge and reasoning
- Reflecting and making use of what has been said
- Coming to a consensus
Getting started
You will be working in a team of four. Ensure that you have plenty of red, green, yellow and blue cubes. You cannot use paper or pencil to help you because you need to listen to what others have to say.
Discuss how you will work together and share your ideas.
Put the pile of 8 cards face down in the centre of the table.
Tackling the problem
Each member of the team takes a card from the pile in turn (enough for two cards each).
Rules
- Team members cannot show their cards to anyone else on the team.
- A team member can describe what is on each of their cards.
- Team members can ask questions to help them make sense of what is on their cards, or on someone else's cards.
- The task is complete when everyone agrees that the arrangement they have made matches everything that is on their cards.
If you have an observer, they might find the following list of things to look for helpful and feed back to the team at the end of the task.
- Check that no one reveals their card or writes anything down.
- Identify points where team members share knowledge and reasoning, and listen to each other.
- Identify points where team members make decisions together.
- Note whether all members of the team are involved.
Why do this problem?
This task encourages the development of team-working skills such as listening, asking questions, finding out what others think, reflecting and making sense of what has been said, and eventually coming to a consensus. If you wish to learn more about these skills and find other team-building tasks look at this article.
In addition learners are expected to use precision in describing an arrangement of objects.
Possible approach
The task is based on a team of four plus an observer.You will need a collection of red, green, yellow and blue cubes or the equivalent.
Explain the rules before any equipment is handed out as it is important that teams do not look at each other's cards or make notes to help them remember what has been said. This emphasises the idea that everyone has a part to play and reduces the chance of one person taking over the problem and leaving others with nothing to do.
It is good to have an observer in this task but, if this is not possible, the observer checklist might make a good starting point for you to use for feedback.
NOTE that the card with an array of white cubes indicates the layout of the cubes.
When teams have finished working on the task it is important to spend time asking them to discuss in groups, and then as a whole class, how well they worked as a team, what they have learned from the experience and what they would do differently next time. Your own observations, as well as those of observers, might inform the discussions.
Why not let us know how the children have got on with their group-working skills by clicking on the 'Submit a solution' link?
Why not let us know how the children have got on with their group-working skills by clicking on the 'Submit a solution' link?
Key questions
- Has anyone got a card that they think has a useful piece of information to start with? Can you expain why this is a useful card?
- Have you used all the information you have been given?
- How well did you listen to others in your group?
- How easy was it to share what you knew?
Possible extension
Learners may like to try one of the other 'All for one' tasks. Other team-building tasks can be found by going to this article.
Possible support
Learners can reveal one (or more) of their cards at a time. Other team-building tasks can be found by going to this article.