'Master the properties of shapes and take a step closer toward mastering space itself'

Works of art, architectural and industrial designs, packaging etc. show a real mastery of forms and their properties. The triangle is the building block of many two dimensional forms and the properties that result. This activity offers the first steps towards mastery: experiment to see what polygons can be made with different triangles, using the Powerpoint or paper print-outs in the resources section. Then create a flowchart to isolate the defining characteristic of each quadrilateral, before attempting the puzzle. The final challenge will be to use all the pieces to re-create an artistic masterpiece!

Resources

Teacher's need to visit the "Teacher Notes" before reading further: Properties of Quadrilaterals

Get your "mind's eye" visualising the relationships between triangular building blocks, or use a paper version for cutting out: relationships between triangular building blocks and the rest of the 2D polygons.

With the aid of this help sheet on the properties of quadrilaterals and triangles, can you:

(a) use the flowchart to correctly classify the triangles or use this paper version to cut out the triangles and put them in the right place.

(b) On the second slide of the previous Powerpoint, or second side of the word document, can you create your own flowchart to correctly categorise the seven quadrilaterals? This activity can be done just as well on paper: cut out the quadrilaterals to place on a flowchart you have drawn on paper.

Description

• Use the first Powerpoint "triangular building blocks" to examine what polygons can be made using equilateral, right-angled and isosceles triangles. How many different 2D shapes can you make for each type of triangle? Are some more limiting than others?
• Using the second powerpoint, "classifying quadrilaterals and triangles", follow the flowchart to work out the unique properties of each of the four triangles.
• You are now ready to use the textboxes and flowchart connectors on slide 2, to copy and paste as many additional textboxes and connectors as you need to design your own questions. Use the "properties help sheet" where necessary from the resource section above. Can you isolate each quadrilaterals unique property? Can you do so using as few questions as possible?
• Open one of your classmates flowcharts and see if you can categorise all the quadrilaterals correctly. If you can't, is it your mistake or is it your classmates flowchart?
• Your teacher will give you a set of a number of different triangles. Use them to construct the quadrilaterals on the sheets your teacher has given you. If you have understood the properties of the quadrilaterals, this should help you decide a lot faster which triangles can be used for which quadrilaterals, and which can't.
• Now you've re-constructed the quadrilaterals, see if you can use all the pieces together to rebuild the original picture, created by Wassily Kandinsky.