Number crunching

Calculating the number of people you need in a year is a complex process. Sam Ellis attempts to shine some light on an arithmetical challenge.

About 15 years ago, I had a regular jazz guitar gig at a restaurant called Chaplin's which paid £25 a week for playing thousands of chords to three people. Compare that to a rock guitarist playing three chords to thousands!

At home, the unit of disposable income became the 'Chaplin'. A visit to IKEA easily produced a bill of £100 or four Chaplins. The curriculum has a similar currency unit: the teacher period. If the average teacher costs £40,000, including National Insurance and superannuation, and they deliver 20 out of 25 periods a week then a teacher period is worth £2,000 - or 80 Chaplins.

The numbers above are for ease of illustration. If you add the expenditure on CFR lines E01 (teaching staff), E02 (supply staff) and E26 (agency staff) to get the overall cost of a teacher you may get a better, more scary result. I guarantee it will be a lot of Chaplins.

When I started timetabling in the pencil and rubber days I would regularly get asked, "How many staff will we need for next year's curriculum?" Given an impatient headteacher I sometimes had to answer the question before I had a curriculum plan, so I evolved a way of making an initial estimate.

In Key Stage 3, pupils were sub-divided into a fairly constant number of groups of just under 30 across the year for all subjects except PE and technology (Tk). Assuming a 25-period week with two periods for technology and two for PE, the calculations of teacher periods (TP) might look like this:

Year group	Roll	Notes	TP
Year 7	151	5 groups for 21 periods = 5×21 = 105 TP 6 PE groups for 2 periods = 6×2=12 TP 8 Tk groups, 8×2=16 TP	105+12+16=133
Year 8	156	6 groups for 21 periods = 6×21 = 126 TP 6 PE groups = 6×2=12 TP 8 Tk groups, 8×2=16 TP	126+12+16=154
Year 9	150	6 groups for 21 periods = 6×21 = 126 TP 6 PE groups = 6×2=12 TP 8 Tk groups, 8×2=16 TP	126+12+16=154

It might be reasonable to teach year 9 as five groups of 30 but in this example we have six groups of 25 or equivalent.

I noticed that an average class size around 20 in Key Stage 4 gave reasonable flexibility for option choices and setting. Dividing the roll by 20 and multiplying by the periods in the week gave the target for the total teacher periods. Something like this:

Year group	Roll	Notes	TP
Year 10	158	158×25/20 = 197.5 rounded to 198 TP	198
Year 11	147	147×25/20 = 183.75 rounded to 184 TP	184

For this 11-16 school I need 133+154+154+198+184 = 823 TP, which is £1,646,000 or around 66,000 Chaplins when you work out the cost.

A key question is "How much do the teachers teach?" Patterns of PPA time and management time vary from school to school. The contact ratio is usually quoted as a decimal fraction. If we assume that in this school the contact ratio is 0.76 then the average teacher provides 0.76×25 = 19 TP. (I have chosen 0.76 because it produces a round figure answer for the average teaching load. It does not represent a recommended value.)

A contact ratio of 0.76 means we need 823/19 = 43.3 FTE teachers. The roll is 762 so the pupil teacher ratio is 17.6. You can benchmark your value against other schools on the Schools Financial Benchmarking website.

Real schools might add teacher periods and hence have more staff for learning support, inclusion and intervention.

How many periods you need for a post-16 curriculum is like asking "How long is a piece of string?" It is almost certain that adding a post-16 curriculum will mean operating at a pupil-teacher ratio lower than 17.6. In the example above that would mean an increase in the 43.3 FTE.

Finding the balance between the staffing level calculated from a timetable point of view and that calculated from a financial point of view (see Leader June 2010) is where meaningful discussion in the senior team can be invaluable.

Teacher pay is about 60 per cent of revenue expenditure or about two million pounds in the example above. What is the benefit? Can we afford it? Can we afford not to have this staffing level?

A shift in the contact ratio or average class size will have a significant impact on the final FTE. For example in the 11-16 model above, changing the contact from 0.76 to 0.79 makes a difference of about 1.6 FTE teachers or over £65,000 or 2,600 Chaplins.

There are no easy answers to the "How many staff?" question but a poor decision will add up to a lot of Chaplins somewhere along the line.