Area Under a Graph: 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!
The area underneath a velocity-time graph gives you the distance traveled
Trapeziums give a better estimate of area under a curve than a rectangle
Splitting the region underneath a curve into more regions gives you a better estimate of the area
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 idea 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. 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 3 different graphs, where using trapeziums
to estimate the area underneath them gives
1) An underestimate
2) An overestimate
3) A perfect answer
Sketch 3 different graphs (giving their equations if you can), that each contain a region underneath them with an area of exactly 12.