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# Extending Fraction Bars

## Extending Fraction Bars

This activity follows on from More Fraction Bars.

Look at these different coloured bars: Put the bars in size order - can you do it without cutting them out?

Now focus on this bar: This bar represents one whole and two thirds, or the number 1$\frac{2}{3}$. You might find it easier to think of it as a bar which is 'one whole' that has been stuck to a bar two-thirds the size of it.

We are thinking about all the other coloured bars as fractions of this bar, so we are thinking about them as fractions of 1$\frac{2}{3}$.

For example, look at Bar A below: Drawing lines helps us measure it against the black bar: What fraction of the black bar is Bar A?

Go through each of the other coloured bars and compare them to the black bar. What fraction of 1$\frac{2}{3}$ is each bar?

Write down your ideas for each bar. For example, you could write:
Bar A is three fifths of the black bar.
or
Bar A represents $\frac{3}{5}$ of 1$\frac{2}{3}$.
or
Bar A represents a whole.

Can you work out how we came up with these three ideas?

Can you find different ideas for what fraction of 1$\frac{2}{3}$ each bar represents?

### Why do this problem

This activity gives pupils the opportunity to practise ordering and comparing fractions. It introduces the idea that as well as having a fraction of a whole number, you can also have a fraction of a fraction. Working together on this task will encourage pupils to build their fraction vocabulary.

### Possible approach

Begin by showing some rods of different lengths on the IWB. Put a row of smaller rods together and show that this is the same length as a larger rod. Can pupils work out what fraction of the larger rod each smaller rod is? What if the larger rod represents 1$\frac{2}{3}$ - what fraction does the smaller rod represent now?

In pairs or small groups, children should have access to multilink cubes, making each bar of the same colour throughout. Otherwise, pupils can use this sheet (wordpdf) along with some squared paper to make paper copies of each bar. It may be helpful for children to make multiple versions of the same bar in order to see that these can be fitted together to be the same length as the black bar.

Give pupils some time to investigate the order of size of the bars, and what fraction each bar represents. Bring the whole class together for a plenary - can the groups explain their choices? There may be disagreements between different groups and this can lead to a healthy discussion, encouraging each group to give reasons for their suggestion.

### Key questions

Why is what you've chosen true?
Can you think of a way of writing that down?
"E is 1$\frac{1}{3}$ of A as E = 32 and A = 24."
Some pupils may need support to help them understand that the bar of 48 is 1$\frac{2}{3}$. Thinking about what 1$\frac{2}{3}$ is as an improper fraction might help these children to get started with the activity.