World of Tan 19 - A circular problem
Can you fit the tangram pieces into the outline of this teacup?
Problem
This activity follows on from World of Tan 18 - Soup.
It is almost the end of the tea break. The cups have been cleared away and the chairs are being stacked neatly in the corner, when Wu Ming poses his question...
Wu Ming: How do you find the centre of a circle?
After some discussion, it was agreed that all you had to do was fold it in half and then in half again. Where the folds crossed was the centre!
Chi Wing: Yes, that works for a circle of paper.
Wai Ping: It'll also work for a tablecloth, or even a small rug!
Chi Wing: But what about that wooden stage we have to move next week? We can't fold that!
Wu Ming: Let's ask Granma T - I've heard she enjoyed geometry at school. I'll leave a note asking for her help.
The workers went back to their tasks for the afternoon, and the next morning they were called into the office by Granma T...
Granma T: Imagine that you can walk round the edge of the circle - of any size, large or small.
Everyone seemed to understand this instruction.
Granma T: Now imagine that Mah Ling is standing still on the edge, and she is feeding out some rope attached to your waist. As you walk around the circle, the rope is kept tight at all times.
Chi Wing: The rope will get longer as I walk further around.
Wu Ming: Yes, until you get to that point when the rope starts to get shorter again.
Granma T: That is when you have gone as far out as possible and you are about to begin the journey back to where you started.
Wu Ming, Wai Ping and Chi Wing all voiced their agreement.
Granma T: Now, where is the point when the rope starts to get shorter again?
Wai Ping: At the end of the longest line across the circle - the diameter.
Granma T: Your problem about finding the centre should be easy now. Good morning!
And off she went, leaving the workers scratching their heads in confusion.
Chi Wing: Well, let's get back to furniture moving. We can all have a think and then discuss this at our tea break.
In the meantime, complete the silhouette of the teacup.
Extra activity:
- Have a look at Granma T's method of finding the centre of a circle. How does it work? Can you finish it?
The story continues in World of Tan 20 - Fractions.
Teachers' Resources
Why do this problem?
This problem is an engaging context in which pupils can consolidate their knowledge of the properties of squares, triangles and parallelograms. By attempting this activity, children will be putting into practise their visualising skills, making guesses about where the different shapes might go before trying out their ideas. When combining the shapes to make the tangram, pupils will use their understanding of translations, reflections and rotations to decide how to transform each shape. There are also links between tangrams and fractions, and children can be encouraged to work out what fraction of the whole square is represented by each smaller shape.
Possible approach
Read this story with the whole class and look at the tangram as a group. Ask pupils to suggest where a shape might go. What transformation would be needed to move the shape into that position?
When pupils are solving the tangram, they would benefit from working in pairs with a tablet or a printed copy of the shapes to cut out and move around. Working together will lead to rich discussions about the possible options for where each shape can go. When the children have solved the tangram, they can have a go at the extra activities.
At the end of the lesson, bring all of the pupils together and model the solution on the whiteboard. How does each shape need to be transformed? What fraction of the whole picture is each shape?
Key questions
What could you put with this piece to make a square?
Are all of the pieces different?
What's the smallest square you can make?
What has to go in that space? How do you know?
Possible extension
Pupils could have a go at other tangrams in the 'World of Tan' series. Some children might like to create their own tangram from the same pieces, or make their own tangram pieces by cutting up a square.
Possible support
Some children might need encouragement to experiment and 'have a go'. Using the printable tangram pieces will help all pupils try out their ideas.