# World of Tan 20 - Fractions

Can you fit the tangram pieces into the outlines of the chairs?

This activity follows on from World of Tan 19 - A Circular Problem.

Little Ming and Little Fung have homework to do before they can go into the yard to help the workers.

**Little Ming:**Mah Ling, why were fractions invented? Why are they so complicated?

**Little Fung:**I'm sure it isn't just us who don't understand fractions.

**Little Ming:**All I can remember is that what you do to the top you must do to the bottom.

**Mah Ling:**Yes, if you multiply or divide the top number by another number you must do the same to the denominator.

**Little Ming:**Does it matter if you do it to the bottom number first?

**Little Fung:**Does that apply to adding and taking a number from the numerator or denominator?

**Mah Ling:**No, no, no! You two sound so confused and you're confusing me.

**Little Ming:**Perhaps we should start again at the beginning.

**Little Fung:**What are fractions?

**Mah Ling:**They are part of a whole.

**Little Ming:**A hole?

**Mah Ling:**If something is divided into equal parts, one or more of these parts are called fractions.

**Little Fung:**You mean like a half or two thirds or three twenty-fifths?

**Mah Ling:**Yes, that's one type of fraction...

**Little Ming:**Oh no, you mean there are more types?

**Mah Ling:**There are also improper fractions...

**Little Ming:**No, no! I've had enough for today.

**Little Fung:**Let's finish this tomorrow when we don't have school and our heads aren't buzzing!

In the meantime, complete the silhouettes of the two chairs that Little Ming and Little Fung were sitting on.

Extra activities:

The story continues in World of Tan 21 - Almost There Now.

- Write down all the things you know about fractions!
- Have a go at this activity involving fractions of bars of chocolate. Where would you choose to sit to get the most chocolate? Why?

The story continues in World of Tan 21 - Almost There Now.

### 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?