You may also like 2-digit Square

A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number? Consecutive Squares

The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false? Plus Minus

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

Puzzling Place Value

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.