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Sum Equals Product

The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 � 1 [1/3]. What other numbers have the sum equal to the product and can this be so for any whole numbers?

Special Sums and Products

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

Fractions Rectangle

Age 11 to 14 Challenge Level:

Rectangle Tangle


The large rectangle above is divided into a series of smaller quadrilaterals and triangles. Each of the shapes is a fractional part of the large rectangle.

Can you untangle what fractional part is represented by each of the ten numbered shapes?

Why do this problem?

This activity gives the pupils opportunities to use and develop their visualising skills in conjunction with the knowledge of fractions. It's quite a contrast to just dealing with fractions numerically.

Possible approach

The pupils will most likely need to have had some previous experience of the shapes involved. Then the pupils can be presented with the picture or for some pupils it may be better to use the picture superimposed onto squared paper.
on squares

Key questions

What shapes have you found?
How big is this shape?
Which is the biggest/smallest shape?
Tell me how you found this out?

Possible extension

Encourage the pupils who have well with the challenge to create their own problems for others to solve.

Possible support

The should probably be plenty of resources available for many children while with others you would want them to ask for particular resources to help them. [Placing resources infront of same pupils seems to tell them that they should be using them, when you really want them to use their own ideas.]