Do you understand reciprocals?

These questions test a lot of things so use them carefully.

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Firstly there is what do we understand about reciprocals, namely:

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These are tricky concepts to grasp. This is the order in which I teach them, but I don’t think the “flow” through these 4 concepts is particularly obvious and students need to be carefully led with lots of examples using Mini Whiteboards.

Other understanding required includes:

  • Finding equivalent fractions
  • Finding common denominators and using them to find the right equivalent fractions
  • Adding fractions
  • Converting between Mixed Number and Top-Heavy fractions
  • Negative fractions

And the last question took me a good 3-4 minutes to convince myself I had the right answer.  Which always makes me stop to think – am I being fair to my students here?



3 thoughts on “Do you understand reciprocals?”

  1. But what does it mean? This is just a list of arithmetic questions saying “These are tricky concepts to grasp” with no effort to even address what the concepts are, nor how to help students gain any understanding. I don;t see the point of this,


    1. Did you read the blog post? In it was an attempt to outline the concepts. Please provide your own thoughts on how you would help students gain this understanding. We would all benefit from your ideas


      1. Yes, that’s my point. It’s a list. I don’t see what it does to help. You could start by looking at pictures rather than just a long list of rules. How does a diagram with two thirds shaded relate to one and a half? Could it be reinterpreted? What’s the link. Conceptual understanding of fractions needs objects and pictures not just words.


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