## Saturday, October 25, 2008

### Revisiting fractions

My 10D class has revisited fractions over the last week. For many fractions is like another language others have managed it in the past but have forgotten basic principles. The sequence I have used leading up to percentages of amounts is as follows

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.