### Chocolate

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?

### Doughnut

How can you cut a doughnut into 8 equal pieces with only three cuts of a knife?

### Rectangle Tangle

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

##### Stage: 2 Challenge Level:

You may like to try our Fractional Wall problem before this one.

Using the fraction wall above, can you say which is bigger, $\frac{1}{3}$ or $\frac{2}{8}$? By how much?

Which is smaller, $\frac{5}{6}$ or $\frac{3}{4}$? By how much?

What is the difference between $\frac{5}{6}$ and $\frac{1}{3}$?

What is three quarters of $\frac{2}{3}$? Can you explain how you worked this out?

Having a visual representation of fractions as a wall will aid children's understanding of both equivalent fractions and comparisons of fractions, but perhaps it will also equip them with a method to help them in the future. It is important that pupils have an appreciation of what is being taken as "the whole" and this may need some discussion before the problem as it stands is tackled. Using real Cuisenaire rods to aid manipulation of fractions is invaluable, although the lengths pose some restrictions. However, OHT rods could be used as a way into the problem by concentrating on just a few different lengths to start with.

This could be used to help older children to understand the concepts necessary for manipulating fractions to add and subtract them. It is amazing how much easier the visualisation makes the arithmetic process. Just try it yourself and see.