Teachers' Notes

The Numbers Game

This activity develops pupil understanding of how managing a small business, in this case, tomato growing, relies on an understanding not only of business and management, but also of the science of photosynthesis and plant growth. It raises the concept of innovation, where a new or improved product or service can be developed by addressing issues related to the underpinning science and technology.

This activity introduces pupils to the idea that companies have to take into account a variety of variables in order to manage their business in a profitable way. The example in the activity is "hours of labour" in a tomato-growing business. In growing tomatoes for commercial sale, some factors can be controlled by management. These include the number of hours of labour that they plan for the different stages of the growth cycle, up to and including harvesting and packing for delivery to market.

Other variables:

Growing tomatoes involves monitoring and sometimes controlling various environmental factors, such as water availability, atmospheric carbon dioxide levels, sunlight and temperature in the greenhouses.

It may be useful to recap with pupils how these different factors affect plant growth, in particular the process of photosynthesis, which is responsible for producing the new biomass which causes growth.

The process of photosynthesis can be summarised as

Carbon dioxide + water → carbohydrates + oxygen. The process requires sunlight, and chlorophyll (the green pigment found in leaves).

Carbon dioxide is found in the atmosphere, making up around 0.035% of the total. Inside a closed greenhouse, the CO₂ would gradually get used up during the day, as photosynthesis occurred. It would be replenished at night, as the plant broke down carbohydrate to release energy (by the process of respiration), which produces CO₂ as a waste product. Tomato growers can increase yields if they can increase CO₂ levels, such as by burning fuel in the green house. In hot weather however, in order to reduce temperatures, greenhouses are ventilated. This provides a direct route out of the greenhouse for the extra CO₂.

Water is needed to produce new plant cells, and is also lost from leaves by the process of transpiration. At all stages in the growth cycle therefore, a supply of water is needed.

Sunlight is needed for photosynthesis to occur - the process captures light energy and transforms it into the chemical energy found in the substances which make up the tomato plants, such as carbohydrates, lipids and proteins.

Biological reactions are controlled by enzymes (biological catalysts) inside the plant cells. Like other chemical reactions, those inside cells take place faster if the temperature rises. However, a maximum rate is achieved at around 37-39°C. Above this temperature the enzymes become denatured and cease to work. It is essential, therefore, that temperatures inside the greenhouse are maintained at a temperature between 25 and 35°C: not too cold to inhibit growth, and not too high as to affect the enzymes.

The tomato grower must also be able to manage the tomato environment to optimise the levels of the factors just discussed. This could involve heating the greenhouses (using heaters which burn fuel, which also adds to the CO₂ levels), and using watering mechanisms, from manual watering to automatic 'monitor and control' systems.

As well as understanding the science, the tomato grower must also understand business and management, and a key factor to consider is when to deploy staff time to carry out all the jobs that need doing throughout the growing cycle, and through to harvesting and packing.

The activity is based on real data from a real tomato growing company, but "smoothed out" to allow a meaningful activity to be set up.

The pupils have to plan to use 1000 hours of labour time, to maximize the yield of tomato fruits. The time period they have to work with is a growing year (From January to December). 13 time periods, of 4 weeks each, are used. They have to enter the number of labour hours they would use in each time period, and then see what yield they get as a result of their decision. The optimum yield is achieved through a particular deployment of staff, based on real data. The pattern of labour use across the year to achieve optimum yield is shown in the graph below.


The optimum yield across the growing cycle, based on the deployment pattern shown above, is


This shows no yield at all until period 4 and 5, with maximum yield being in periods 9 and 10. Deployment of labour follows this pattern in general terms, but there is never a period with no labour usage. The simulation averages out the pupils suggested figures, and looks for total utlisation across several periods in order to see if the pupil has matched, in broad terms, the required deployment levels. When a pupil runs the simulation with their figures, they get some feedback, either indicating a successful labour plan, or one which needs amending. They can run the simulation several times if necessary.

Follow up activity

When pupils have arrived at a labour deployment plan which produces optimum yield, you may wish to set them a challenge. The challenge will get pupils to think innovatively, that is, new ways to use existing knowledge to improve a product, service or system. Explain that industry relies on innovative R&D in order to improve its offerings to the market.

As stated above, yield is increased if several factors are at optimum levels, including labour deployment. Discuss the following with them, and ask them to come up with ideas.

Tomato growers want to achieve optimum temperatures as well as CO₂ levels. However, in summer, temperatures are often so high that windows have to be opened to reduce temperature. This has the effect of lowering CO₂ levels, as the gas escapes into the atmosphere outside the greenhouse. Can you devise a system which allows temperatures to be maintained at optimum levels whilst keeping CO₂ levels up?