World of Tan 13 - A Storm in a Tea Cup
Can you fit the tangram pieces into the outlines of the convex shapes?
Age
7 to 11
Challenge level
Problem
This activity follows on from World of Tan 12 - All in a Fluff.
The peaceful tea break at Granma T's is being transformed into a scene that could be from a pantomime. Wai Ping and Wu Ming, two of the workers, are arguing with each other...
Wai Ping: It sticks out.
Wu Ming: No, it goes in.
Wai Ping: Out!
Wu Ming: In! I'll prove it by asking the others.
Mah Ling is the first to come in for her break, and she is immediately stopped by the workers.
Wai Ping: Does concave mean going in or sticking out?
Mah Ling: It goes in like a cave, that's why it's called concave.
Having previous experience of similar arguments, she hastily retreats to the peace and quiet of her office for the rest of her break.
Granma T enters the room for her break and also gets waylaid by the Wai Ping and Wu Ming.
Wu Ming: Does concave mean going inwards or outwards? In or out?
Granma T swears that she will buy a dictionary next time she is in town because these arguments are getting too frequent. Without answering the question, she too disappears into Mah Ling's office and shuts the door firmly.
Only the children remain to be interrogated and they won't be home from school for a while yet.
Throughout the day the yard echoes to the cousins arguing.
So in the meantime, while waiting for the children to settle the argument once and for all, complete the silhouettes of the two convex shapes that can be made.
Extra activities:
- Find out what the words 'convex' and 'concave' mean. Can you explain these two ideas to a friend or family member?
- Make a collection of things that are concave or convex. Can you find anything that's both concave and convex?
- Investigate when convex or concave lenses and mirrors are used, and find out why they are helpful.
World of Tan continues in World of Tan 14 - Celebrations.
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?