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Investigating gradients

By Steve Pratchett

  • How do we measure and describe gradients on maps and in the field?
  • How does a map indicate gradients?
  • What is the relationship between gradient and land use?

One arrow indicates a gradient of 1 in 7 to 1 in 5
Two arrows indicate a gradient of 1 in 5 or steeper

Modelling the locality

To develop these ideas, children constructed a 3-D model from the Ordnance Survey map. A section of the map was enlarged in colour (to make it easier to read the contour lines). I then traced over the contour lines with a dark brown pen so that black-and-white copies could be made. The children took the copies and cut around each contour line. They glued their cut-out onto a piece of 5 mm Styrofoam® mounting board (a much cheaper option is to use corrugated cardboard from boxes). The boards gave a convenient arbitrary unit for the interval between each contour line. Although the children were using 5 mm board, the original map had been enlarged by 400%, so distortion was less than x2. The children then cut around the Styrofoam mounted contour lines using keyhole saws.

When the children viewed the model from the side they, in effect, experienced a cross section of the landscape. The children deduced that the number of arrows indicated the steepness of the hill.

A field trip with map and model

The ideal situation is to take the children on the field trip to a steep hill. When I did this the benefits were clear. On the outward journey, one group of children navigated with the map and the other with the model. They were delighted to find the model echoing even the slightest change in the incline of the road. Their fingers became the car, kinaesthetically tracing the route and mimicking its movement as it ascended and descended. This exercise also helped with map orientation skills, as the model had to be turned to face the way we were going.

Where a field trip is impractical, good discussion results can be obtained by using photographs.

Relating gradient to land use

The children were encouraged to deduce why areas of mixed woodland appeared in particular locations on their Ordnance Survey map of the Bere Peninsula. These tended to occur along the sides of stream and river valleys. The rest of the peninsula is covered by farmland belonging to numerous dairy and arable farms, such as Hole & Well Farm.

3D Model

The children offered several explanations –

'The trees grow near the rivers because they get more water.'
'The trees are planted to stop the valleys eroding.'
'The contour lines are close together so it's steep ...you can't farm the fields, it's too steep here.'


The latter response from one observant child stimulated a flurry of discussion as the children began to check all the patches of woodland on the map and model to see if they only occurred where the contour lines were closely packed. This proved to be the case. To reinforce this observation, the children were given a tiny toy tractor and tried driving it on different parts of the three-dimensional model of the peninsula. On the steeply wooded slopes, the tractor rolled over into the river or stream!

This led to a discussion of why farmers did not plough steeply sloping land for arable or cereal production and the identification of more such areas on the local map. Some humorous comments were also made about the problems dairy cows would have 'rolling down the hill!'

Try the following suggestions on modelling gradients as ratios and gradients as percentages. Lots of lovely links with numeracy!

*Styrofoam is a registered trade mark of the Dow Chemical company

Modelling gradients as percentages using metre rulers and elastic

To develop children's skills in measuring and expressing gradients as percentages, metre rulers were used. A metre ruler laid flat on the ground gives a convenient horizontal distance of 100 units (cms) and another ruler held upright at one end gives a selection of the same units for vertical climb. A length of shirring elastic can be used to link the two rulers for example, a triangle formed in this way with a 100 cm base and 20 cm height has a 20% gradient. This means that a toy car would climb 20 cms vertically for every 100 cms it travels horizontally. 20 units out of every 100 = 20%.

Using the same triangle, it is also possible to translate percentages into ratios and vice versa. If the child travels 5 cms along the horizontal ruler with a toy car and then measures up vertically from this point to the elastic slope, the height will be 1 cm. This is a 1: 5 triangle. These ratios can be multiplied e.g.:

8 cms along .......................... 1.6 cms up
12 cms along .......................... 2.4 cms up
16 cms along .......................... 3.2 cms up
100 cms along .......................... 20 cms up (20%)

Extension of work on gradients - understanding the shape of the ground

An extension to work on gradients and their corresponding contour line patterns is to model convex and concave slopes in clay. The children slice the models into horizontal layers at regular intervals and then draw around each slice to create 'contour lines'. The models can be directly compared to the configuration of contour lines they generate, highlighting the relationship between the change in gradients and the change in spacing between the contours. This work will lay a foundation for using contours to understand the shape of the ground when map-reading.

With thanks to Kim Wilde, Headteacher, at Bere Alston Primary School.

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