Which Solid?

'Which Solid?' printed from https://nrich.maths.org/

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Which Solid?

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.

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 the person asks, and keep track of the number of questions that have been asked in total.

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 unkown solid. You may also wish to appoint an observer.

You will need the set of solids cards. Spread them out on the table so that everyone can see the solids 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 solid chooses a card and hands it to the rest of the team without looking at it.
The person trying to find which solid 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 solid. Once in agreement, one person gives the answer.
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 8 questions.
The team can offer the hint "Cold" or "Warm" or "Hot" if the first 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 aims to encourage learners to develop their ability to communicate their reasoning and to frame and ask questions. The 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 article.

This task also supports the development of language asssociated with, and properties of, 3D shapes.

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.

The solids cards are available as a word or pdf document.

Give the teams plenty of time to do the task, allowing every member of the team to take the role of trying to find an 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 3D shapes that arose whilst learners did the task.

Key questions

Was there a question that proved really useful in identifying the solid?
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 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

Why not use real solids? Put them in a bag and ask one of the team members (not the person who is trying to guess the shape) to choose a solid from the bag. It is also possible to reduce the number of cards, perhaps focusing on prisms. Other skill-building tasks can be found by going to this article.