Estimating Gradient of Curves: Probing Questions
Whether you are looking for a question to stimulate discussion in lesson, or a challenge at the end of a homework, then hopefully you will find these useful.
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Convince Me That... keyboard_arrow_up
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I use Convince Me That questions lots in my lessons and homeworks. Providing students with a statement and challenging them to come up with as many different ways of convincing you as possible can lead to some fascinating discussions. The different ways of seeing the same thing can also help improve the depth of students’ understanding. Thanks so much to the Thornleigh Maths Department, in particular Erica Richards, Anton Lewis and Gareth Fairclough for helping me put these together, and we will endeavour to keep adding more!
A curve does not have a single gradient like a straight line
All quadratic curves have a point where the gradient is zero
A tangent to a curve is a good approximation of the gradient of the curve at that point
Some curves may have more than one point that has the same gradient
You can work out both the gradient of a tangent, and the equation of a tangent to a curve
The gradient of a distance-time graph gives you speed
The gradient of a velocity-time graph gives you acceleration
VI3 Treatment keyboard_arrow_up
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We devised VI3 Treatment as a versatile way of giving students meaningful follow-up work at once we have marked their homework. The idea is that students are challenged to come up with 3 things with certain constraints. These are ideal to use as an extension for students who have got everything correct, and also as further purposeful practise for students who have got a particular question wrong. Use the ideas below and adapt them accordingly, using different numbers where appropriate. Either mark them yourself or better still, get other students to do it. Thanks so much to the Thornleigh Maths Department, in particular Erica Richards, Anton Lewis and Gareth Fairclough for helping me put these together, and we will endeavour to keep adding more!
Sketch the graph of y = x2, draw on 3 tangents and 3 different points, and use them to estimate the gradient of the curve at those points
Sketch a curve, draw a tangent to the curve at
a single point, and calculate the following:
1) The gradient of the tangent
2) The equation of the tangent
3) Where the tangent crosses the x-axis
Look up what "point of inflection" means and sketch 3 curves that have a point of inflection