Lesson 23 Rates of change
Lesson plan
| Piagetian Level | Learners Thinking and abstract of the activity | ||
|---|---|---|---|
| 3 B Mature Formal |
 ‘... yes, so that means that although it is well behind the balloon af 4.5 seconds, it's actually going faster and accelerating from then on’ |
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| ‘the changes are themselves increasing at a constant rate' | |||
| 3A Early Formal |
Interpreting the graph as representing, e.g., constant speed | ‘if you look at the step and rise for the rocket between 3.5 and 4.5 seconds, you can see the rocket is going at the same speed as the balloon’ | |
'graph getting steeper means that the rises are increasing' |
‘the rocket graph is the same shape as the quadratic, so it must overtake the balloon eventually’ |
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| 2B* Concrete Generalisation |
‘the rocket starts out very slow but gets faster and faster’ | ||
 Plotting the graph and the confusion relating to the shape and the fact that both objects rise through the air |
Possibility of confusing shape of the graph with the fact that both rise vertically | ||
| Mature concrete |
Episode 1 Step and rise in linear graph |
Episode 2 Step and rise in quadratic graph |
Episode 3 Graphing and expressing |