Jig Shapes
1 out of 3
Can you each work out what shape you have part of on your card? What will the rest of it look like?
Problem
Jig Shapes sheet of larger cards
This challenge is best done in a group of at least four children.
The sheet of cards will need to be cut into twelve separate cards.
Share all the cards out amongst the group.
Can you each work out what shape or shapes you have part of on your card?
Can you describe the shapes without showing it to anyone else?
What will the rest of the shape or shapes look like do you think?
How could you sort the cards?
We would love to hear your descriptions and hear about the ways you sorted or arranged the cards.
This problem is also available in French: Casse-tête de formes
Getting Started
Remember that this activity is designed for you to try in a group so try to persuade some friends or family to join you!
Can you think of a good way of arranging the cards?
Student Solutions
This problem encouraged you to work as a group to discover all of the different shapes on the cards. Part of the challenge was to describe the shapes (or part of them) on your own card and understand the explanation of others. In this way, you could work together to determine all of the different shapes in the Jig Shapes challenge.
Charlie, from The Haberdashers' Aske's Boys' School, suggested that it's good to try to describe the sides and edges that you see on your card. He also suggested describing any whole shapes.
We wonder whether any of you tried arranging the cards? Have a go - what happens?
We also received some photos of the finished problem. Thank you to both Ci Hui Minh Ngoc (who attends Kong Hwa School in Singapore) and Owen (who is home educated in the UK). Owen also recorded the different types of shapes in his solution. We wonder if you can name the shapes too and perhaps suggest some shapes that we might have included? Perhaps you might design your own puzzle for another group to solve, using some of those different shapes?
Here's is Owen's photo of his finished problem:
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?
The intention of this problem is that children will work together as a team. It should help in developing mathematical language about shape and position, as well as encouraging learners to listen carefully to others and tweak their own ideas accordingly.
You may like to read our Let's Get Flexible with Geometry article to find out more about developing learners' mathematical flexibility through geometry.
Possible approach
You'll need to print out this sheet for a small number of children or these sheets for a bigger group or the whole class. The second option has the same cards but larger versions. The sheets will need to be cut into twelve separate cards. You must give out all the cards in the set!
Either give out a set of the smaller cards to each group of four to six children, or, if you want to use the problem as a whole-class activity, one of the larger cards between two or three.
To begin with, give children time to look carefully at the shapes and part-shapes on their own cards and to describe what is on the card without showing them to others. After a suitable period of time, encourage them to ask each other about the other cards. You could suggest that one child chooses a card to describe to the others in the group and the others try to draw what is being described.
The cards have been designed to join together like a jigsaw so that the pictures of the shapes are complete, but it may be better not to tell children this immediately. Instead, invite the group to find a way to organise or sort the cards. At this stage, members of the group can help each other find adjoining cards, but discourage them from simply giving someone else their card. If you are doing the problem as a class activity you could use sticky-tack to fix the cards to the board. Encourage the children to describe the shapes they can see as the whole 'jigsaw' is built up.
Whether the children are working in groups or as a whole class, stand back and try not to intervene as learners work together. If they are organised in small groups, you could invite them to display their cards in their chosen arrangement and then give some time for everyone to move around the room to look at the way each group has sorted the cards.
A short plenary should provide an opportunity for the groups to explain the organisation they chose and for comments such as "I knew my card had half a square on it". As a follow-up children could be challenged to make their own Jig-shape puzzle for others to do. If this is done on squared paper it is more easily cut up.
Alternatively, you could invite each group to hide two of the cards and challenge them to create the jigsaw without them. Can they draw what they think is on the missing cards? Is there more than one possible solution? Does the position of the missing cards in the jigsaw make a difference to how difficult it is to draw them?
Key questions
Tell me about the shapes on your card.
Can you describe it without showing me the card?
What will the rest of it look like?
Has anyone got part of a yellow circle/blue square etc?
Have you asked the others in your group about the shapes they have found?
Did you notice anything?
Can you think of a good way of arranging the cards?
Possible extension
Learners who think this activity is trivial have not solved the problem! How can the cards be organised, arranged or ordered? Encourage them to help other members of the team in a cooperative spirit. They can also be challenged to make their own Jig-shape puzzle using all the geometric shapes they can.
Possible support
It may be appropriate for some children to share cards with someone who is more confident with language about shape than they are themselves.