In this lesson, students have to find a solution to a problem where the unknowns must be non-negative integers.
This constraint means that the initial problem, which may appear to be quite open, in fact has a unique solution.
Students have the opportunity to consider related Diophantine equations and determine systematically whether they have one solution, more than one solution or no solutions.
Arriving at a point where they are sure about this allows students to see the power of mathematical thinking.
Why teach this?
Many real world problems require integer solutions. This adds an interesting constraint to students’ equation solving.
Curriculum links
- Use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships
- Make and test conjectures about patterns and relationships; look for proofs or counterexamples
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KS3 Maths Lesson Plan – Develop Students’ Algebra Skills with a Problem that Requires Integer Solutions
