World of Tan 27 - Sharing
Can you fit the tangram pieces into the outline of Little Fung at the table?
Age
7 to 11
Challenge level
Problem
This activity follows on from World of Tan 26 - Old Chestnut.
As usual, Little Fung and Little Ming are arguing. Today the argument is about schoolwork...
Little Fung: I'm telling you, it's about numbers!
Little Ming: No, it's about sharing things out!
Little Fung: Numbers!
Little Ming: Sharing!
Little Fung: NUMBERS!
Little Ming: Look, it's about having equal amounts. We've been shown that it's about sharing things out fairly.
Little Fung: My teacher showed us it was all about numbers. She put them on a number line.
Little Ming: Oh, this is hopeless. I'm going into the yard to find someone sensible to talk to.
Little Fung: Good luck finding anyone! They're ALL in a meeting to talk about getting a bigger van and making alterations to the yard to allow the van in.
Little Ming: I'll see if they've finished. They've helped us with fractions before - I just hope they won't confuse us even more.
The children enter the office and find everyone - Granma T, Mah Ling, Chi Wing, Wai Ping and Wu Ming - sitting round the table enjoying cups of tea. The meeting appears to have finished, and what better time to interrupt!
Little Fung: Can you settle an argument? We can't agree about fractions.
Wu Ming: Fractions! Don't you learn about those at school?
Little Ming: That's right. So what do you remember from school?
Little Fung: You must all use them here when you're working... so what are fractions?
Wai Ping: I never use them! I can't help you, sorry.
Chi Wing: Let me ask both of you a question. Six lots of what makes two?
There is a short pause and everyone looks blankly at each other - all except one person.
Little Fung: It's a third - one over three. If you put six lots of a third together, it makes two wholes.
Chi Wing: Now that's what fractions are!
Little Ming: Hang on, isn't fractions like sharing six crackers out between three people and everybody getting two each?
Wu Ming: He's right - finding a third of something is the same as dividing by 3!
Wai Ping: I've just remembered something about fractions! Does anyone else remember that riddle? Half of a half of a half of a half of a half is what?
Mah Ling: Almost nothing. Now let's get back to our meeting - out you go, children.
Granma T: Yes, out you go. We have to decide what will happen when we buy a van that is half as big again...
In the meantime, complete the silhouette of Little Fung at the table asking about fractions.
Extra activities:
- What do you think fractions mean? What have you learnt about fractions at school? Write down all the different things that you can remember about fractions.
- What does 'half as big again' mean for the size of the van? Can you draw a line and make it half as big again? Draw a shape on squared paper and try making that shape half as big again.
The story continues in World of Tan 28 - Concentrating on Coordinates.
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?