Why do this problem?

This problem provides reinforcement of the concept of place
value and experience of reading the words in a question and forming
an algebraic expression using the information given. It also
provides practice in algebra involving the difference of two
squares, factorising and solving linear simultaneous equations.

#### Possible approach

If you think the class will not remember having learnt the
difference of two squares the class could first work on and discuss

DOTS . However this problem leads naturally into the difference
of two squares without the learner having to recognise it at first
so it could provide a useful reminder in itself. The learners could
first work individually to give them 'thinking time', then work in
pairs to support each other and to give an opportunity for
mathematical talk, and finally there could be a class
discussion.

Key questions

Give an example of a
2-digit number . [e.g. 27]

What place value does
each digit hold/stand for? [2 tens, 7 units]

Fill in the blank: 27 = 2
times____+ 7

If the digits are
reversed what will the new number be? [72]

If a 2 digit number has
tens digit a and units digit b then the number is ___times a +
___?

If you know a number is a
square what can you say about its factors?

Possible extension
What's possible? is another non-standard problem involving the
difference of two squares.

Possible support