### 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?

# Matching Fractions

##### Stage: 2 Challenge Level:
We only had a handful of solutions sent in for this activity and I guess pupils played the game but did not go so far as to answer the second.question. Here are two good ones sent in.
First from the Maths Challenge Group at St. Aiden's VC school in the UK.

We all realised that there were $4$ sets of each fraction.
Billy, Noah, Luca and Benedict realised that you need to simplify the fractions e.g. $1/3 = 2/6$ Louisa added that $1/2 = 3/6$ for the pizza.
Daisy matched all her cards and had $2$ left, so realised that they must make a pair, $9/12$ (eggs) must match the red shape, which Marlo worked out to be $3/4$. Noah said that he thought people found this shape confusing due to its orientation.
Natasha matched the shape fractions by counting the shaped pieces.

Well thanks for that, a good explanation of children's thoughts. From Class 4RC  at Manor School in Didcot  UK , we had the following sent in;

Before we started, we thought that a fraction was like a pizza shared between people. You have to split it equally so everyone has the same amount. We drew pizzas split into different amounts and counted different numbers of slices.

The different pictures made us think about fractions in different ways. We knew that the grid with $9$ squares on meant it was divided by $9$. $3$ are coloured in so the fraction is $3/9$ . We used our times tables to help us simplify this fraction. We know $9$ divided by $3$ is $3$ so $3/9$ is $1/3$.

We weren't sure what $5/9$ looked like, so we took $9$ cubes and made $9$ of them white and the rest blue. $5/9$ are white, $4/9$ are blue. $5$ out of $9 = 5/9$.
This helped us to see that the balls in the grid also showed $5$ out of $9$.

We thought the purse was quite tricky, it was showing £$1$ made of two $50$p coins. Not everyone recognised that $50/100$ is $½$.
The most complicated one was the red shape. Counting squares didn't help as it was not made of whole squares, but some children noticed that if we folded the shape into triangular quarters, $3/4$ were red.

Thank you and congratulations to those two excellent contributions.