Vector Geometry: 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!
You can tell if two vectors are parallel
You can use vectors to prove 3 points lie on a straight line
2a - 3b and 3b - 2a are vectors that are the same length, have the same gradient, but travel in the opposite direction
If you knew the 4 vectors that made up the sides, you would know what type of quadrilateral a given shape was
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!
Write down 3 sets of four vectors that would describe a trapezium (or parallelogram)
Write down 3 pairs of parallel vectors, each involving multiples of a and b
Sketch 3 routes around a shape the simplify to 2a - b