Thanks to Caroline Clissold for another great maths challenge!
One of the aims of the National Curriculum refers to children applying their mathematics to a variety of routine and non- routine problems with increasing sophistication. This month we give you some ideas of non-routine problems that also involves reasoning and tangrams! Tangrams like the one below are readily available on the internet. You could print enough out for your class to work in pairs, laminate and then cut them out for regular use. It is also possible to purchase some colourful card ones that can be punched out from a frame and used straight away.
Tangrams are Chinese puzzles consisting of, traditionally, seven shapes. The objective of the puzzle is to form a specific shape using all seven pieces which don't overlap. You could ask the children to make up the square and then try to make a triangle (which is possible). They could then move on to explore other shapes such as irregular pentagons, hexagons and octagons. They could also explore making symmetrical patterns. My favourite use of a tangram is to explore fractions. You could ask the children to work out what fraction of the whole square each smaller part is, for example the green triangles are a quarter, the blue triangle an eighth and the red triangles sixteenths.
You could then ask them to explore equivalences. This is great for enabling the children to understand that a fraction of a shape is all about its area and not the shape. The parallelogram, blue triangle and the yellow square are equivalent. How do we know? They are all the same size as the two red triangles. The square is half the size of the green triangle and the red triangle is a quarter of the blue triangle. Why? Because the two red triangles and the square are the same size as the green triangle. Another thing that you can do with the tangram is to set a problem such as this: the lengths of the outside sides of the whole tangram are each, for example, 10cm or 20cm or choose your own length, depending on the children in your class.
Can the children use this information to work out the lengths of all of the sides of the smaller shapes?
So, have some fun with tangrams and let us know how you get on. If you have other good ideas for their use please let us know and we can share them with everyone!
TagsGrammar, Spelling and Punctuation