Lesson 11 Setters and solvers

Episode 2

Reasoning Resources: Worksheet 2
Whole class introduction
Where there are two or more unknowns, these become a kind of ‘variable. Pupils must take one step away from the problem, and make hypotheses (however simple they are) about what one unknown might be if some assumptions are made about the other.

Give out Worksheet 2 explaining there are two steps to this activity. At first each pair act as ‘setters’ of at least three additions or subtractions of different types using only the four digits 8, 3, 5,9 for another pair to solve. Then they act as ‘solvers’ to take the other pair’s questions and find the answers to them.
Paired work and exchanges between pairs
In most cases the properties of numbers themselves, and the denary system, constrain very heavily the possible values the ‘variables’ might have, so the task is limited to choosing, and testing by trial and error, possible numbers within those constraints. Thus none of the tasks require formal operations, yet the pupils are led on the road to working with hypothetical models. Most pairs by now should have found their own ways of collaborating. You could help some pairs who find it difficult to start, by suggesting they just allocate the four digits at random first, then see if that gives one, more or no solution, then make adjustments.

Ensure that pairs exchange their set questions to solve. Once this is done, pairs should write in words their advice on best ways of solving such questions. While circulating, make mental notes on interesting and promising exchanges.
Whole class sharing and discussion
The style of classroom work here fosters collaboration and use of everyday language in handling mathematical concepts. The context also promotes a mood of empowerment and a probing attitude to arithmetic expressions, perhaps likening them to ordinary language sentences that should abide by rules. Concentrate on the ideas for setting and solving questions. Most of the ideas will be refinements of what was covered in Episode 1.
Whole class reflection
If the lesson ends ask them if it is easier to be a setter or a solver as a way of ensuring a rich and productive discussion.

Another reflective question is: What is this activity helping you to understand about calculations?


Thinking Mathematics Lessons Copyright © by Michael Shayer and Mundher Adhami. All Rights Reserved.

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