Task 97 ... Years 4 - 10
SummaryPythagoras proved that the defining property of a right angled triangle is:
The area of the square drawn on the hypotenuse is equal to the sum of the areas of squares drawn on the other two sides.A triangle is only right angled if this space/measurement property is true. Given the side lengths of any triangle these squares can easily be constructed and their areas calculated. The task makes this a tactile, colourful situation for some examples by using material that allows the areas to be created and reorganised to discover what is equal to what.
IcebergA task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.
In the first example, the area of the square built on the hypotenuse is:
The card offers another example and similar constructions apply. But the critical thing about Pythagoras is that it only works for right angle triangles. Students are asked to build another triangle where the numbers don't 'add up' and the rods can't be made to cover the square on the longer side. Explaining what does and doesn't work requires use of language such as right angle, hypotenuse and the sides adjacent to the right angle.
Whole Class InvestigationTasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.
To convert this task to a whole class lesson you only need a bag of Cuisenaire Rods for each student. Many schools have this equipment in their storeroom because it is also very useful for developing fractions content. If you don't have access you can contact the Distribution Manager and ask about having sets made up.
At this stage, Pythagoras Rods does not have a matching lesson on Maths300. However, a related lesson is Lesson 157, Pythagoras & Other Polygons which asks a different What happens if ...? question. For more ideas and discussion about Pythagoras & Other Polygons, open a new browser tab (or page) and visit Maths300.
Is it in Maths With Attitude?Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.
The Pythagoras Rods task is an integral part of:
The Pythagoras & Other Polygons lesson is an integral part of: