Extending Fraction Bars

Thank you to everybody who sent in their thoughts about this task.

Jacob from Stirling East Primary School in Australia explained how they started the activity:

I did it by counting the squares on the graph so that I could figure out how long the bars are so I could put them in size order.

Good idea, Jacob - it's really helpful to work out how long each bar is to begin with. James from Radstock Primary School in England used the lengths of the bars to work out what fraction each one represented:

Firstly, you need to count the number of squares in the black line (40). The black line is worth 1 and $\frac{2}{3}$ which is equal to $\frac{5}{3}$. Then, you can divide 40 by 5 which will get you 8. This is $\frac{1}{3}$ because you are dividing $\frac{5}{3}$ by 5.

$\frac{1}{3}$=8 If you halve this you will get $\frac{1}{6}$=4. Next, you have to count the number of squares in A(24), B(36), C(20), D(28) and E(32). You can now divide the number of squares in each bar by 4 which will tell you how many sixths there are in each bar. You can simplify these to make it easier to read.

A = $\frac{6}{6}$ = 1
B = $\frac{9}{6}$ = 1 and $\frac{3}{6}$ = 1 and $\frac{1}{2}$
C = $\frac{5}{6}$
D = $\frac{7}{6}$ = 1 and $\frac{1}{6}$
E = $\frac{8}{6}$ = 1 and $\frac{2}{6}$ = 1 and $\frac{1}{3}$
Now you can put them in ascending order (lowest to highest). C,A,D,E,B

We also had similar solutions sent in by Connie and Harry from Radstock Primary School - well done to all of you for explaining your ideas so clearly.

Reuben from New Cangle Primary School in the UK sent in the explanation below. Reuben has written each bar as a fraction of one whole, but also as a fraction of the black bar:

Thank you for sending in these ideas, Reuben. It's really interesting to see how we can represent numbers as a fraction of other numbers (in this case, as a fraction of 1$\frac{2}{3}$) even when those numbers are fractions themselves!