Arranging cubes

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

Age

7 to 11

Challenge level

Primary

Geometry

Drawing and Constructing

Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving

Being curious Being resourceful Being resilient Being collaborative

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.

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.

Then a well-presented solution came in from pupils at The Globe School in Lancing. Here it is!

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:

Then we have the Golden Terrifying Tigers who sent in this picture:

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.