Tree Maths Trail
FEI educational resources ‘Only Made of Wood’
Borders FEI Cluster ‘Woodland Maths Trail’
Developing mathematical, language and mapping skills to study trees in the school grounds, local park or woodland. Suggestions are made for applying mathematics in the process of planning and planting new trees in your school grounds.
Did you know?
Scotland only has 1% of its ancient native woodland remaining. However, if you visited the school grounds seven or eight thousand years ago, they would be covered in woodland.
Before the activity
Obtain a base plan of your school site and grounds from your local authority and make multiple copies for the pupils to use, plus measuring tapes, rules and measuring wheels.
Mapping and identifying trees
Using base plans, the children locate and mark where individual or significant trees are. Measure a fixed distance on the ground and compare it to the same point on the plan to obtain the scale. Pupils can draw these on their plans, or create a map of their grounds using a Draw or CD-Rom map making package and mark them on.
The pupils can design and use symbols to represent objects – tree types, areas of plants etc – on the map. They may wish to identify the trees
(see http://www-saps.plantsci.cam.ac.uk/trees/ ) or they can make up their own names for the trees using the shape/ leaves/ colour for inspiration (see also sensory trees below) e.g. ‘jaggy edges’ or ‘wavy whisperer’ etc - or do both. There may be local names for trees types, or gaelic ones.
Is it possible to estimate the % of school grounds covered by trees? Compare this with the ‘did you know’ facts.
Measuring and estimating the girth (circumference) of a tree
Actual measuring - use a tape measure or a piece of string, which can be marked and measured. Have a look at the shape of a tree’s trunk – it an even circumference all the way up? Discuss and decide how the children will get consistency in their measurements between different trees.
Estimating – experiment with different measures e.g. handspans or armspans around the tree. This can be used to establish approximate scale.
Represent the different girth sizes of the different species measured. Is there wide variation both within the same species as between species? If so why? Are the trees different ages, or are they in different growing conditions?
What words would they use to describe the bark of the tree? Think about colour (use paint colour card strips to match), texture, surface (matt or shiny). Some tree bark is scented or aromatic too. Close their eyes - can they hear the leaves rustle?
If a tree in the vicinity has to be felled, grab the opportunity to measure its age. Remember branches will be younger than the trunks! Each ring represents a year. Are the rings evenly spaced? If they are close together, that means growing conditions were tough. If they are spread further apart, the tree was growing quickly in good conditions. (In general, softwood (conifer) trees grow faster than hardwood (broadleaved) trees, so have more widely spaced rings.) Why not make little flags on cocktail sticks, writing on the flags key dates and events, and pin these on the corresponding rings (range depending on the age of the tree). E.g. the date the school was built (was the tree growing before the school was built?), the year a pupil (or teacher!) was born, the start of the millennium, a local historic event etc.
Estimating heights of trees:
There are a number of ways to estimate height. Compare the results of different methods. Which are the most accurate? Group the results into clusters to find out how many trees in the area surveyed fall into different categories or height classes – small, medium, tall – for example.
- Measure the height of your partner. Working in pairs, one pupil stands beside the tree while their partner stands back and estimates how many times their partner fits into the height of the tree from root to crown. Estimate the height of the tree. Compare with the estimates of other pairs. Note the type of tree measured. The heights of the trees can be plotted on a graph against the measures of the girth of a tree, to see if there is a correlation i.e. do taller the tree tend to be wider in girth (circumference?).
- On a sunny day, measure the height of your partner. Note the time of day when the shadow your partner casts is the same length as his/her height. Measuring the shadows cast by the trees at this same time of day will give you a good estimate of their height.
- The ruler method. Ask you partner to stand by the tree. Holding a ruler upright extended at arm’s length, stand where the tops of the ruler ‘touches’ the top of the tree and the bottom is in line with the tree base. Now twist your wrist so that the ruler lies horizontally. Ask your partner to walk in straight line (along the ruler line) to the ‘end’ of the ruler and stop. Mark their position. The measure of distance between the tree and position of your partner is the height of the tree.
- The human clinometer: this is a fun way using the principles of right angled triangles or a clinometer – the instrument used by foresters for measuring tree height. Position yourself with your back to the tree so that when you bend over and look at it from between your legs you can see the top of it just where your legs meet! Measure this distance between you and the tree on the ground, then add your height – this is the approximate height of the tree. See how well this works when several people of different heights try it out!
- How far do your trees spread? The spread of the branches gives a good indication of how far the roots spread underground. Use a compass. In chalk mark north, south east and west on the trunk. Walk in four directions in turn- north, south, east, west - counting your paces until you reach the end of the branch tips each time. Note the distance paced. Does the tree spread evenly in all directions? (is it symmetrical?) If not, can you provide a reason why not? E.g. the growth of the branches may favour the sunnier/ less windy/ more open side etc.
Your activities may have shown you that it would be an advantage to enhance your school grounds tree resources both as a learning resource and to benefit wildlife and the landscape.
Tree planting projects should be approached in the same way as for any proposed new development – using a planning process that is holistic, participative and sustainable, to ensure they meet your school needs. Part of this planning process can include the mapping, measuring, and scale work that has been illustrated above.
The spread and eventual height of trees is important to consider when planning what to plant in your school grounds. Tree keys or nursery suppliers will provide this information. Is there room or need for a wide spreading tree to provide shade and shelter, or do you need to allow sunlight to reach other plants? How far apart should you plant your trees so that they don’t crowd each other when fully grown? If a tree reaches it full height or falls down, would it damage overhead cables? Remember, some trees can be pruned or coppiced to restrict their growth, or contained as a hedge. Will your young trees need protection from rabbits, feet, footballs, grass strimmers? What wildlife friendly species can you plant, or do you want to include orchard trees?
The Woodland Trust Trees for All teaching resources offer a range of curriculum linked activities centred around tree planting:
See Using Your Local Woodlands – Resources to support the 5-14 Environmental Studies Curriculum (Forest Education Initiative & partners - contact Rebecca Logston, FEI coordinator)
Forest Education Initiative resources:
The FEI Scottish Borders cluster group has produced resources which include the Math Trail, based at Harestanes Visitors Centre near Jedburgh (GR NT642244) is an innovative way to learn about maths. A teacher’s pack containing worksheets, risk assessments and inventory of equipment is available for download.
Forestry Commission teaching resources about trees, woods and forests.
Grounds for Learning Schoolgrounds-UK membership scheme offers ideas and inspiration on using resources, including trees, in the school grounds.