Worksheet 6

Activity 1: 'Tree Tops'

* Lesson is generated from the nrich mathematics tool: 'Tree Tops'

Possible support

Students might begin by exploring each type of tree separately. Encourage them to consider the possibility of combining trees - for example, if they try to maximise profits over 100 years, they could plant one type of tree for 60 years and then a different type for the next 40 years. Students could then work towards a strategy for managing a forest with a cycle of planting, thinning and harvesting, that would give a sustainable and regular profit over time.

The Getting Started section goes through the calculations for the first forty years for the Sitka Spruce. Students could use this example to repeat the calculations with the other two tree types, and make comparisons.

Then set the class to work on some of their questions. Some students may wish to draw tables by hand and use calculators. Others might prefer to use a computer and create a spreadsheet with the data, and use formulae to calculate the profit for each type of tree and each timescale. As the class are working, circulate to see the different approaches people are using and the different strategies they come up with for organising the data. It might be appropriate to bring the class together to share some of these strategies, so that students can learn from each other's approaches.

At the end of the lesson, set aside some time for students to explain the strategy they would recommend for planting the forest, together with their reasoning. Allow the students to discuss the following:

1. What strategy will maximise the profits for you and your family in the decades to come?
2. What's the maximum profit you could make after 100 years?

Key questions

• Does it help to put the information in a table?
• Are there any diagrams or graphs that could be used?
• Is a spreadsheet useful?