Leverage fractions
I spent about 6 hours of lesson time on fractions, and students will have had access to a couple of hours of support time on the topic. I have ‘front-loaded’ the fractions for the following reasons…
- Fraction arithmetic gives a context for ‘common factors’, ‘common multiples’ and table skills
- Adding and subtracting fractions is a good example of a ‘complex skill’ performance (see later)
- Fraction concepts generally motivate percentages and ratio problems
When students can use ‘cancelling’ to multiply fractions like 8 / 9×15 / 16 in an efficient way, they have broadened their schema for common factors and extended the range of applicability.
If you can do calculations like 3 3/4 + 2 5/9 then you must understand skills like converting fractions to top heavy, finding common denominators, expressing fractions over a new base, and finally converting from top heavy to mixed format. This bringing together of a range of skills that we have rehearsed separately is valuable for students. As I am teaching adults, we can reflect easily on the process of complex application of the skills and examine how to make notes that will remind students about the sequence and processes.
In the last 10 minutes of a lesson, I simply put the following up on the whiteboard; 3:4 = 9:12. Then I tried 5:6 = 30:? and I had 36 back as the answer instantly. I then explained what a ratio was (I use the vodka and orange for one or for twenty – still tastes the same – analogy). I expect to cover ratio problems quickly next week.
I need to explain what I am doing, and I need to reassure students that they will find that percentages and ratios are easier to understand. I also think that when students see that one piece of Maths can explain another so that the second topic is learned much more quickly, the power of Maths is being demonstrated albeit in a restricted and ‘elementary’ context.
- Download a 2 side worksheet with questions, no answers. 500Kb, PDF file.