World of Tan 23 - Transform this into that
Can you fit the tangram pieces into these outlines?
Problem
This activity follows on from World of Tan 22 - An Appealing Stroll.
It is Saturday morning. There is no school today and Little Ming and Little Fung are fast asleep. As usual, Granma T has already been up for hours!
The smell of fresh bread drifts upstairs and gradually wakes the children...
Granma T: Come on you two! There is much to be done.
Only groans can be heard as the children argue about who gets to use the bathroom first...
Granma T: It's no good putting it off with stories about 'transformations' or whatever it was you did at school. The yard has to be transformed. So...
Little Ming: Why did you have to go on about the transformations we did at school? Granma T seems to have found a perfect excuse to get us doing chores...
Little Fung: Again! Surprise, surprise...
Granma T: Come on now, no more moaning. Get your breakfast then get out into the yard. Let us put the theory into practice.
Little Ming: Ugh!
Granma T: Yes, I was very interested in what you had to say about transforming one thing into another... my mind has been racing with things that transform... from one state into another... and into another.
Little Fung, yawning: Oh yes?
Granma T: Flour, water and yeast are transformed into bread. Bread gets eaten and transformed into energy. Children who are full of energy go out into the yard and tidy it up... it's the perfect example.
Little Ming: What was that about being full of energy?
Little Fung: Granma, you've got the right idea about transformations. But we were only talking about mathematical transformations and the things that stay the same after some change has taken place...
Granma T: Things that stay the same? Are you sure that makes sense?
Little Fung: Yes! We could go into the yard and do nothing!
Granma T: It's already seven o' clock. The yard must be tidy before the others appear and they begin to transform our closed removal firm back into an open one.
Little Ming: Come on Little Fung, let's just get on with the yard...
In the meantime, transform this:
into that!
Extra activities:
- Write down some ways that a shape can transform. Do these transformations turn the shape into a new shape, or is it still the same shape after the transformation? Why/why not?
- Look up 'word ladders' and have a go at transforming one word into another by changing one letter at a time.
The story continues in World of Tan 24 - Clocks.
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.