Coordinate Designs

Age

11 to 14

Challenge level

This task requires learners to explain and help others, asking and answering questions.

Thinking mathematically tags

Mathematical mindsets tags

Being curious Being collaborative Being resourceful Being resilient

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:

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 graph paper for the designs and then separate sheets for the team to recreate the designer's image.

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.

Each person needs to create a design in preparation for acting as designer. Without making anything visible to anyone else in the team, each learner draws some axes on graph paper and creates an image by joining coordinates, or drawing lines.

Tackling the Problem

The designer recreates their image so that it is hidden from the rest of the team but as s/he makes the design, s/he explains each step. This needs to include information on axes and scale as well as coordinates of points and equations of lines. The aim is for the rest of the team to 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?

Teachers' Resources

Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.

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 everybody 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:

restricting to the first quadrant or using all four quadrants,
restricting the number of points in the design,
only allowing descriptions to use equations of line graphs and given domains (i.e. the line y=3x from x= -1 to x = 5).

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.

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.

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 others asked?

Was there an answer that you found particularly helpful?

Possible extension

Other team-building tasks can be found by going to this article.

Possible support

Learners may like to try one of the other 'Explaining How' tasks. Other team-building tasks can be found by going to this article.

Or search by topic

Number and algebra

Geometry and measure

Probability and statistics

Working mathematically

Advanced mathematics

For younger learners