World of Tan 18 - Soup
Can you fit the tangram pieces into the outlines of Mah Ling and Chi Wing?
Problem
This activity follows on from World of Tan 17 - Weather.
Mah Ling and Chi Wing are about to take their lunch break. Some broth has been simmering on the stove in the kitchen. A warm, delicious smell wafts through the room. The others have gone back to work, having already eaten their lunch.
Mah Ling: They've left us a good amount for our lunch. Pass me your mug please - the broth is ready.
Chi Wing: You poured that well. It looks like we've got the exactly same amount of broth. How do you do it just by looking at it?
Mah Ling: I've had a lot of practice! You can pour out the next serving when we've finished these mugs.
Chi Wing: I can try, but I'd be worried about giving both of us fair servings.
Mah Ling: Eat up! We'll worry about that later.
A few minutes later...
Chi Wing: That was very warm and filling! Now, let me pour and see if I can get it equal for the pair of us.
Mah Ling: Stop, I have much more than you!
Chi Wing: It really isn't that easy to give two equal helpings. Can you help me try again?
Mah Ling: Okay, pour it all back into the pan. Now, choose a level in the mugs - up to the handle, say - and fill both to that level.
Chi Wing: And with what is left in the pan I can keep topping up each mug in turn. Oh, it's easy now... I've just never really had to think about it before, as I live on my own.
Mah Ling: That wasn't too difficult, but what about if we'd had mugs of two different shapes? How would you pour out fair shares then?
In the meantime, while thinking about what Chi Wing would do, you might like to complete the silhouettes of Chi Wing and Mah Ling eating their soup.
Extra activities:
- Find a jug or bowl without any markings on the side, and fill it with water. Take two differently shaped cups or mugs. Can you put water from the jug into the two cups fairly, so that each cup has the same amount of water in it? How?
- Have a look at this activity for more examples of sharing out food fairly.
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.