Powers, Roots and Types of Numbers: 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!
34 × 58 × 710 must be a square number.
39 × 512 × 1115 must be a cube number.
x2 = 64 has two solutions but y3 = 64 only has one solution.
28 is a triangular number but not a square number
36 is both triangular and square.
There are no prime square numbers.
It is possible for a number to be prime and triangular.
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!
1 is both a square and cube number. Find 3 more numbers where this is true.
Find 3 Perfect Numbers
Make up 3 powers questions where the final answer is 30