# World of Tan 7 - Golden Goose

This activity follows on from World of Tan 6 - Junk.

It was almost a week after Mr Cheung moved into his new restaurant that everything went wrong. The gold plaque of the goose that had been passed down through generations of Mr Cheung's family could not be found anywhere. Obviously, those at Granma T's had lost it or stolen it.

Mr Cheung was both angry and disappointed. At first, Granma T was calm and composed. She tried to reassure Mr Cheung that the plaque would be found. If all else failed, she would pay for a replacement! It was then that Mr Cheung exploded, "The plaque is a priceless family heirloom, it cannot simply be replaced! Besides, the beak of the goose alone would cost one thousand Chinese yuan."

Granma T slumped into her chair. She was shaking and there was a tremor in her voice as she barked orders at everyone. The children were sent off to thoroughly search the packing cases. The workers were sent back to the old business premises. They were to search every corner of the building and back yard. No stone was to be left unturned!

"How could we have been so careless?" wondered Granma T.

In the meantime, complete the silhouette of the Golden Goose plaque as last seen.

Extra activities:

- Imagine that each shape in the tangram is made of the same type of gold, and the white space around the plaque doesn't cost anything. Can you work out the full cost of the plaque if the cost of the beak is 1000 Chinese yuan?
- Design a new plaque that has at least one line of symmetry.

The story continues in World of Tan 8 - Sports Car.

### 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?