Lesson 11 Setters and solvers

Setters and solvers

Overview Resources
Worksheets 1 and 2
A lesson on coordinating place value with inverse arithmetic operations. 'Number sense’ is based on such coordination, including a sense of number size, and is necessary for using calculators and written procedures with understanding, as well as for higher levels of number work. The setting of problems with unique, multiple or no solutions allows a more mature outlook to mathematics than taught procedures.
Aims Curriculum links
  • Inverse operations,
  • Chains of reasoning (proof).
  • Place value,
  • Number operations.
    When missing digits can be found and when they cannot
    Pupils look at some addition calculations involving two-digit numbers which have missing or hidden digits and try to find them. They recognise and explain why some of the sums are impossible, while others have more than one correct solution.

    The focus is on combining place value with inversion of addition to subtraction. The lesson is designed to help pupils develop a feel for the size of numbers, rather than by using simple trial and error, which will lead to a deeper understanding of the minimum and maximum totals.

    Some classes may also look at subtraction sums.
    Setting and solving problems with missing digits
    Pairs of pupils act as setters then solvers of questions of the type they handled in the first episode. The discussion allows refinements of insights gained, a sense of empowerment in handling arithmetic questions, and use of language in describing mathematical ideas.
    Further questions on missing digits
    The ideas are extended through use of multiplication, division, and combinatory work. The challenges include handling chains of reasoning to prove calculations are possible, impossible or with multiple solutions, and some other subtleties.


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

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