### Algebra Match

A task which depends on members of the group noticing the needs of others and responding.

### Doughnut Percents

A task involving the equivalence between fractions, percentages and decimals which depends on members of the group noticing the needs of others and responding.

### Arranging Counters

A task which depends on members of the group working collaboratively to reach a single goal.

# Castles in the Middle

##### Stage: 2 and 3 Challenge Level:

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?

The team has to recreate the 3-D solid or "castle" (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 cubes (multilink or similar). The image above uses nine cubes of four different colours. You might wish to start with a fixed number of cubes each of a different colour and then work with cubes of the same colour later.

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 cubes 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 castle using some or all of the cubes available.

Using the rules for asking questions, and checking that they all agree first, the team takes turns to ask the designer questions that will help them recreate the castle.

When the team thinks they have the same castle as the designer they can check and the task ends.

At the end, the observer gives feedback about the way 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 are trying to recreate the castle using as few questions as possible.

• You must agree any question before asking the designer.
• The team can only ask questions of the type listed in the rules.
• The team must take turns in asking questions.
• The designer can only answer "Yes", "No" or give a number.

#### Designer guidelines:

• You do not have to use all the cubes.
• The cubes should be arranged so that each cube has at least one full face touching another cube and all faces must fit together exactly (no overlaps).
• You only answer a question if the team has discussed and agreed it first.
• You only answer questions of the agreed type.
• You can only say "Yes" or "No", or give a number as an answer.

#### Team question rules:

• the number of cubes,
• the number of cubes of each colour,
• the number of cubes in each row, column or layer,
• the number of cubes touching a given cube,
• the number of cubes of different colours touching a given cube,
• the colour of a cube in a particular position,
• the symmetry properties of the castle,
• any holes or gaps in the castle.