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’
‘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’
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

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

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