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Secondary Magazine - Issue 70: An idea for the classroom


This page has been archived. The content was correct at the time of original publication, but is no longer updated.
Created on 27 September 2010 by ncetm_administrator
Updated on 12 October 2010 by ncetm_administrator

 

Secondary Magazine Issue 70   two isoceles triangles
 

An idea for the classroom - 'the same' and 'different'

There are some kinds of mathematical task that ALL learners can access, and to which they can apply their natural thinking.

For example, if you show two examples of something and ask ‘what is the same?’ or ‘what is different?’ about them, all students are able to respond. If you choose the examples carefully, mathematical concepts can be developed naturally, using nothing more than the students’ questions and natural thinking.

A simple starting point might be two isosceles triangles:

A simple starting point might be two isosceles traingles - two isosceles triangles

What is the same about the triangles? Students may notice that:

  • in both triangles two sides are equal
  • in both triangles the two angles that are between one of the equal sides and the third side are equal
  • the ‘bases’ or ‘third sides’ are equal.

What is different about the triangles? Students may notice that:

  • the angle opposite the ‘third side’ is smaller in the red triangle than in the blue triangle
  • the equal angles in the red triangle are bigger than the equal angles in the blue triangle
  • the red triangle is ‘taller’ than the blue triangle
  • in the red triangle the equal sides are longer than the base, but in the blue triangle they are shorter.

Questions will arise naturally, such as:

  • ‘as the top corner of the red triangle moves down vertically towards the base what happens to the angles?’
  • ‘what happens to the length of the equal sides?’
  • ‘what are the smallest and largest possible sizes of the top angle/the base angles?’

A slightly different starting point will generate other questions.
 

A slightly different starting point will generate other questions - two isosceles triangles

 

  • ‘as the base of the red triangle grows longer what happens to the angles?
  • ‘what happens to the length of the equal sides?’
  • ‘what are the smallest and largest possible sizes of the top angle/the base angles?’

Even with a situation involving just two triangles, the possibilities are endless!

These naturally arising questions are rich starting points for mathematical activity and, if they come from the students, they will carry commitment and motivation.

 
 
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