Lesson 1 Algebra: Roofs – isometric trapezia
Lesson plan
| Piagetian Level | Learners Thinking and Abstract of the Activity | ||
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| 3 B Mature Formal |
Recognition of the distinction between necessary and sufficient conditions. |
 Generation of a Proof strategy |
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| Expression in terms of generalised number "a,b,a,a plus b" |
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| 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’ 
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| 2B Mature concrete |
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| Mid concrete |
Episode 1
Grid and quadrilateral shape |
Episode 2
Rules for roof shapes |
Episode 3
Exploration with proof |