**Drawing and identifying numerators and denominators**

First exercise was identifying a variety of numerical fractions from pictorial form and then constructing pictorial fractions from numerical forms. We spent a lot of time looking at mixed numerals and converting between mixed numerals and improper fractions using pictorial means.

eg. for 3 2/3: draw 3 lots of 3 boxes with all boxes coloured and 1 lot of 3 boxes with two boxes coloured. When students counted the coloured boxes they had 11/3.

**Investigating fractions of amounts**

It seemed strange to do this here, but funnily enough it worked well as it established relevancy of the topic for many students. We started with a problem 3/4 of $24 is to be given to John and 1/4 to Mary.

I explained it as:

3/4 of 24 is: $6 per part (24/4)

I drew a box and split it into 4 equal parts (drawing attention to the denominator)

I put $6 in each box.

I coloured in three sections that represented John's portion

then counted $6 x 3 parts = $18 for John

I then repeated the same steps for Mary

1/4 of 24 is: $6 per part (24/4) then $6 x 1 part = $6 for Mary

We checked our answer to ensure all the money had been accounted for ($18+$6=$24). Students then completed a number of examples.

**Investigating multiples and factors & Equivalent fractions**

Next day we looked at multiples and factors. I explained this through examples, showing them examples of multiples and factors, then getting them to find the first five multiples for 2,3,4,7 and then the first five multiples for 2,3,5,7 over 100. After this they found factors of 10, 15, 24 and 42. We investigated patterns in factors (none greater than 1/2 the original valure other than itself, how it helped knowing your tables, factor pairs, 2 is always a factor for even numbers)

Students were then given a fraction wall and identified equivalent fractions in preparation for adding and subtracting fractions. The idea was put forward that fractions rely on parts to be equal otherwise the idea of equivalency would not be able to be used.

**Adding and subtracting fractions**

In the third lesson we looked at the problem of 1/3 + 1/2 using paper strips. The aim was to establish why equal parts is essential to an understanding of fractions. We used our fraction wall to look for equivalent fractions that allow us to add equal parts. After a few pictorial examples I started to show students how to use multiples and factors to assist in finding common denominators.

Next lesson we look at multiplying fractions...

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