Inverse operations

A complete lesson on inverse operations. Includes questions with decimals, with the intention that pupils are using calculators.

Activities included:

Starter:

• Four simple questions where pupils fill a bank in a sum, to facilitate a discussion about possible ways of doing this.
• Slides to formalise the idea of an inverse operation, followed by a set of questions to check pupils can correctly correctly identify the inverse of a given operation and a worksheet of straight-forward fill the blank questions (albeit with decimals, to force pupils to use inverse operations). I have thrown in a few things that could stimulate further discussion here - see cover image.

Main:
The core of the lesson centres around an adaptation of an excellent puzzle I saw on the Brilliant.org website. I have created a series of similar puzzles and adapted them for a classroom setting. Essentially, it is a diagram showing boxes for an input and an output, but with multiple routes to get from one to the other, each with a different combination of operations. Pupils are tasked with exploring a set of related questions:

• the largest and smallest outputs for a given input.
• the possible inputs for a given output.
• the possible inputs for a given output, if the input was an integer.
  The second and third questions use inverse operations, and the third in particular gives pupils something a lot more interesting to think about. The second question could be skipped to make the third even more challenging.
  I’ve also thrown in a blank template for pupils to create their own puzzles.

Plenary:
Your standard ‘I think of a number’ inverse operation puzzle, for old time’s sake.

Printable worksheets and answers included.

Please do review if you buy, as any feedback is appreciated!