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Puzzling Place Value

Age 14 to 16 Challenge Level:

Why do this problem?

This problem helps students to appreciate the power of algebra for solving problems involving number and place value. It would make a good follow-up problem for students who have worked on Reversals.

Possible approach

This printable worksheet may be useful: Puzzling Place Value

You may wish to use this problem for consolidation in class or homework, after working on Reversals or Always a Multiple.

When students have had a go at tackling the questions, take some time to discuss the answers as a class, focussing particularly on their explanations of why there were only a limited number of solutions, or why the solutions they have found satisfied a particular condition.

Key questions

Is there an algebraic expression to represent the problem?
Are there any restrictions on A, B and C?

Possible extension

For students who are ready to explore algebraic representations with quadratic expressions, Factorising with Multilink and Pair Products may be suitable follow-up problems.

Possible support

Always a Multiple offers multiple representations for solving place value problems, so it might be a good problem to try before looking at this one.