Let’s Think Secondary Maths, Lesson 11 – Setters and Solvers
Overview
Thinking Strands: Number (exploring place value and inverse operations)
Setters and solvers develops thinking concerning place value and inverse arithmetic operations.
Learners ‘number sense’ is developed by coordinating their sense of number size, mental and
written calculations with understanding. The use of problems with unique, multiple or no
solutions allows for a more mature discussion of mathematics as opposed to a focus upon
standard and taught procedures.
Aims
 To use inverse operation to solve calculations involving the four operations.
 To use chains of reasoning to see the importance of proof.
Vocabulary
Digit, number, place value, inverse operation
In-school resource preparation
Materials – Supplied
 Resource Sheet A: The corner shop (Hook)
 Resource Sheet B: Sample addition questions (Activity 1)
 Resource Sheet C: Addition problems (Activity 2)
 Resource Sheet D: Subtraction problems (Activity 2)
 Resource Sheet E: Further questions
Overview of Activities – please see video tutorial for full details of how to develop this lesson
with your class.
Hook: The hook sets the scene for the learning to come and serves as a visual cue to introduce the
idea of calculating totals when shopping. The discussion should flow naturally and the class
should be encouraged to share their calculation strategies when not in school.
Activity 1: This is a quick warm-up activity based around the four sample questions, A - D.
The aim is to challenge the class to think of the complexity that can be involved in solving sums
where the answer is not obvious. The discussion here should draw out the range of thinking
within the class. Hiding digits makes routine number work tricky and focuses upon the ideas
involved. It helps if a range of alternative solutions are shared to focus upon the chains of reason
that are being shared, each step of which is fully proved to be true. Highlight instances where
thinking through questions is easier and faster than trial and error on a calculator. Pairs could then
work on the remaining addition questions.
You may wish to extend this aspect of the lesson to include subtraction questions or three
digit problems of the same type. Draw out the rules that allow us to discern which questions are
impossible, unique or that have multiple answers.
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Activity 2: Using the blank sheets pairs can work at setting addition then subtraction
problems for another group. This means each pair will go through a round of setting and then
solving addition and subtraction problems – the time you allow for this is very much dependant
upon how well the class respond to this task. The video tutorial for this lesson highlights the
reasoning involved in this aspect of the activity. This style very much seeks to foster
collaboration and the development of the language for handling mathematical concepts. This
lesson seeks to promote a mood of empowerment and a probing attitude to arithmetic
expressions.
Activity 3: Sheet E provides a sample of the possible extensions for this lesson. For some
several could be set for homework that is followed by a discussion on methods and discoveries
made, expressed in their own ways. A useful discussion upon the role of estimation and
approximation can develop which should help learners to develop proficiency in these through
understanding rather than memorising.
End of activity reflection: The initial hook could be used to encourage the class to reflect
upon the idea that have arisen and also how they may help those (adults, shop workers etc)
who struggle in such tasks.
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