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# Functional Skills Maths: Fixed and variable costs

Download two activities I have used with Functional Skills Maths Level 1 students recently.

These activities arose from a discussion of a question about a printer who charged 3p for each leaflet and a £10 set up charge. There were problems with writing the calculation out in a way that made sense on a calculator, where you have to show ÷100 explicitly to convert between pence and pounds. Students are used to money and simply convert without thinking of it as a mathematical operation. The online practice test provides an on-screen calculator for students to enter their calculations and document their understanding of the problem - using good 'calculator style' is important.

I used the skills questions to make sure that students were confident with the mix of pence and pounds, and could work out how to calculate the answer to the questions as a single sequence of key presses, as well as a couple of calculations with sub-totals.

The Delivery Service investigation builds on the idea of fixed and variable costs. Students worked in pairs or threes to fill in the tables. We had a discussion about what a 'quote' is, and how one company guarantees a price for a service to another for a period of time. Students had plenty of practice writing out 'calculator style' calculations like "25 ×1.25 + 10 =".

The Rival Company extension task takes things a little further on from Level 1, and I was suggesting a trial and error approach. Most of the pairs/triples worked out that the original company was better for short distances and the rival company was better for longer distances. About half the pairs found that both companies charge the same for 10 miles distance. We drafted some sentences on the whiteboard as part of the plenary for the activity.

The Widget Manufacturer investigation gave rise to a discussion about how small things are actually made. The cartridge pen adaptor actually exists, and has about 6 or 7 small plastic parts - someone had to draw those, create moulds to cast them and machine and finish the parts.Plastic fabrication has high initial costs, the figures are made up but are not too far off the mark. The worksheet specifies a large fixed and a small variable cost for making the plastic parts, and then gives a single target selling price so that the sales income is directly proportional to the number manufactured. Vocabulary included: profit, sales, income, costs, 'overheads' (energy, labour, rent &c).

Tasks 1 and 2 were not too challenging. The break-even task (3) lead to a discussion about how to estimate smarter, the break-even point being much closer to 1300 units than to 900 units. Most estimated the break even as 1220 units, with 40p under. Some thought it was 4p under because the calculator did not display the final zero - a chance for recap on the way money is always written to two decimal places in the UK. Task 4 proved harder for most, one group made it through by trial and error. A couple of groups tried working backwards...

These two investigations will lend themselves to extension when we move onto graph work soon.

Keith Burnett, Last update: Sun Oct 07 2012