Our monthly picture that you could use with your pupils, or your department, or just by yourself, to make you think about something in a different way
These pictures were taken from the exercise books of two Year 7 pupils. The left hand picture seems to indicate that this pupil has a good understanding of equivalent fractions; what of value can we take from the right hand photograph?
Securely understanding equivalence is crucial if pupils are to be fluent and confident when operating with and on fractions. Using these or similar photographs, you could ask your pupils to
- justify the “ticked” equivalences for 2⁄5;
- suggest a fraction that is equivalent to 2⁄5 but with a constraint, for example the denominator is more than 50, or is odd, or equals 12;
- select the correct equivalences for 2⁄5;
- explain why the incorrect equivalences are wrong (why 2⁄3 ≠ 10⁄10 etc.);
- suggest the (mistaken) thought processes behind the pupil writing the incorrect equivalences;
- write rules to explain how you can and cannot operate on a fraction so that the answer is equivalent to the original fraction;
- devise questions that test the depth of the first pupil’s conceptual understanding. How could the teacher be sure that this pupil really “gets it”?
If you try successfully other ideas, please do share them with us.
If you have a thought-inducing picture, please send a copy (ideally, about 1-2Mb) to us at firstname.lastname@example.org, with a note of where and when it was taken, and any comments on it you may have.
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