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Exploring Gradients of Curves
This activity uses a combination of dynamic techniques and data capture to explore the gradient of various simple polynomials using the traditional chords method. The TI-Nspire allows students to see that, as a chord is shortened, its gradient gets close to the gradient of the curve itself. The notation δx, δy and δx/δy is introduced and students are able to experience dynamically that, as δx tends to zero, so δx/δy tends to the gradient of the curve at the point.
This enables students to find the results experimentally before then going on to prove them algebraically.
There is 20-page TI-Nspire document called GradientsByChords.tns that can be used by students working alone on TI-Nspire handhelds. This activity could either be used on a class set of TI-Nspire handhelds with students working individually or in small groups, or it could be used with the software and projected onto a screen for class discussion.
There is also a 2-page Student Worksheet that can be used in conjunction with the TI-Nspire document.