Teachers’ Notes: The Beginners’ Guide to Reciprocals

The Beginners’ Guide to Reciprocals is a simple activity that is intended to help students to learn some very basic ideas.

The aims are:

  1. Know how to calculate a reciprocal of a whole number
  2. Know how to calculate a reciprocal of a simple fraction
  3. Know how find reciprocals using the function key on a scientific calculator

The guide starts with a definition, then allows students to ‘magically’ change n to 1/n with Marvo’s Magical Reciprocal Calculator. They can enter any value here – I wanted to emphasise that it is 1 divided by anything. Except zero, obviously.

Speaking of zero, at the moment it is possible a value of zero, which simply leads to 1/0 being displayed as the answer. I use this as a discussion point. I’m undecided as to whether to leave this as it is and let the students work out that 1/0 is a problem or whether to put in a message to warn them about it. (Suggestions/opinions are welcome in the comments.)

In the next section, fractions ‘magically’ turn upside down. Once again, students can enter any values and I’ve used ‘silly’ answers as a talking point. The guide doesn’t explain why the fractions end up upside down – I encourage my students to work that out for themselves (with a few nudges in the right direction).

Finally, students learn to use their scientific calculators to find reciprocals.

The Beginners’ Guide to Reciprocals can be used on an interactive whiteboard or students can work through it themselves. This worksheet [download in doc format] [download in RTF] might help with that.

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