Lesson 1 Algebra: Roofs – isometric trapezia

Lesson plan

Piagetian Level Learners Thinking and Abstract of the Activity  
3 B
Mature
Formal
Recognition of the distinction between necessary and sufficient conditions.



Generation of a Proof strategy
Expression in terms of generalised number

"a,b,a,a plus b"
3A
Early
Formal
Spontaneous testing of rules with counter examples. `So each of these on its own won’t always make a roof.
We need at least two. Which two? Let’s test.

“But 1,4,1,10 is a non-roof!”


“’But 2,1,2,2 is not a roof!”

Whatever base you start with
n-1 is the largest the other sides can be
Recognition of contradictions
2B*
Concrete
Generalisation
Expression of rules “1st and 3rd must be the same”

‘1st and 2nd make up the 4th’


2B
Mature
concrete
Mid
concrete
Episode 1

Grid and quadrilateral shape

Episode 2

Rules for roof shapes

Episode 3

Exploration with proof

License

Thinking Mathematics Lessons Copyright © by Michael Shayer and Mundher Adhami. All Rights Reserved.

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