Why did calculus develop and how might we use it?
Key questions
- 1
What is the gradient of a curve and how might it be useful?
- 2
What do we mean by the area ‘under’ a curve and what might it represent?
- 3
What do we mean by the rate of change of a physical quantity and how do we represent this?
- 4
How can we make deeper connections between the appearance of a graph and the features of its equation?
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Introducing...
| Resource type | Title |
|---|---|
| Building blocks | A tangent is ... |
| Building blocks | Is the Serpentine Lake really 40 acres? |
| Building blocks | Mapping a derivative |
| Scaffolded task | Zooming in |
| Problem requiring decisions | Discussing distance |
| Investigation | Talking about curves |
Developing...
| Resource type | Title |
|---|---|
| Building blocks | Gradient match |
| Building blocks | Speed vs velocity |
| Building blocks | Walk-sorting |
| Many ways problem | Rectangles in triangles |
| Problem requiring decisions | Approximating areas |
| Food for thought | Average speed |
| Food for thought | Problem areas |
| Investigation | Underneath the arches |
| Bigger picture | Newton and Leibniz |
| Bigger picture | Why are gradients important in the real world? |
Review questions
