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Multiplying and Dividing Fractions: 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!

$\frac{1}{2}\times \frac{1}{2}=\frac{1}{4}$

$6÷\frac{1}{2}=12$

Dividing by a half is the same as multiplying by 2

When you divide by a proper fraction, the answer gets bigger

When dividing two fractions you can flip the second fraction upside down and multiply

When dividing two fractions, you can actually divide the numerators and denominators

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 fractions multiplication/division problems that give and answer of $\frac{2}{5}$

Write down 3 fractions multiplication/division problems that give and answer of 4