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.