### Plum Tree

Label this plum tree graph to make it totally magic!

### Magic W

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

### Odd Differences

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

# 2-digit Square

##### Stage: 4 Challenge Level:

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 Plus Minus. 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
The problem Plus Minus is a little easier.