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A4 Fraction Subtraction

Age 7 to 11 Challenge Level:

Find a partner and start with a sheet of A4 paper and a pair of scissors each. Have a go at the activity below and compare what you've made!

The whole sheet of A4 paper represents 1 whole.

Take your sheet of paper and fold it in half into two rectangles. Unfold it and cut along the fold line. You might end up with two pieces which look like the two red rectangles below. Each of these rectangles represents $\frac{1}{2}$.

  

Take one of your rectangles and cut it in half into two smaller rectangles in the same way. By halving this you now have two rectangles which each represent $\frac{1}{4}$, like the blue rectangles below:

   

Now, take one of your $\frac{1}{4}$ rectangles and cut it in half. You will then have two new rectangles which both represent $\frac{1}{8}$ like the green rectangles below.

  

Halve one of your green rectangles to get two $\frac{1}{16}$ rectangles like the orange one below. Then throw away one of these $\frac{1}{16}$ rectangles so that you have one rectangle of each size.

  
 
You might have rectangles that look slightly different to these, depending on how you cut your rectangles!

Now, one person needs to get four pieces of A4 paper and attach one to each of their fraction pieces. Remember that the full piece of A4 paper is counted as "one whole".

You should end up with combinations that look a bit like the ones below. These are mixed numbers of pieces of A4 paper now, because they have a whole number part and a fraction part.
 
 

Can you work out which mixed number is represented by each?

The other person needs two new pieces of A4 paper so that they can make the following mixed numbers:

 
Can you work out what these shapes represent?

Take two sheets of A4 paper and put them together, like this:

 

This rectangle now represents the number 2, as there are two wholes.

We are going to subtract our mixed numbers from this. Put one of your mixed numbers on top of the two sheets, and write the subtraction calculation. 

For example, the subtraction below would give you 2 - 1$\frac{1}{2}$ = $\frac{1}{2}$, because putting the 1$\frac{1}{2}$ shape over the 2 rectangle leaves a gap of $\frac{1}{2}$.

  

How many different subtraction number sentences can you make if you always subtract from 2?
 
An addition version of this task can be found here