Some ideas for using map scales with primary children Steve Pratchett (2003) The Opeisometer Children can make opeisometers. These are essentially miniature 'trundle wheels'. The trundle wheel is 1 metre in circumference and a familiar piece of mathematics equipment in primary schools for measuring distances in the classroom, school and playground. The opeisometer functions in exactly the same way but measures distances on a map. To make an opeisometer the following steps need to be followed: 1. Lay a strip of cardboard along the map scale. 2. Mark off the map scale intervals along one edge of the strip of cardboard. 3. Curl the strip of cardboard round to make a cylinder. 4. Sellotape the ends of the card together to stop the cylinder unwinding, (a small overlap of the ends will create a more symmetrical cylinder). 5. Place the cylinder onto another piece of stiff cardboard and draw around its base to create a circle. 6. Use the intervals around the bottom edge of the cylinder to calibrate this circle; 7. Cut out the cardboard circle. 8. Finding the centre of this circle is difficult, so draw around it on a piece of paper, cut it out and then fold the paper circle in half and then quarters. 9. Lay the paper circle on top of the cardboard circle and pierce a hole through both in the centre where the folds intersect. 10. Throw away the paper circle and push a drawing pin through the hole in the calibrated cardboard circle and into the end of a lollipop stick. 11. The drawing pin will project slightly out of the other side of the lollipop stick so add a small blob of Blu-tac to cover the sharp point. 12. Make sure the wheel turns freely by adjusting the drawing pin. Many map and gadget shops sell opeisometers that can be set to the scale on a map and give a digital read out. Children can be shown these so that they can appreciate the relevance of their opeisometer making activity to real life. Older children can also use these but the value of making their own should not be overlooked as they can see the 1:1 correspondence between the scale bar, the horizontal distance on the map and the rotation of the wheel. This is not so apparent with digital opeisometers that can be set so that the ratio of rotation to horizontal distance is not always 1:1. That could be a fascinating piece of mathematics for some able Year 6 mathematicians!

Plate 1: 10-year-old children at Bere Alston Primary School in Devon, making opeisometers and testing them against the map scale to see how accurate they are before using them to measure distances on a map.

Plate 2

Plate 3: Children at Bere Alston Primary School, Devon, using their homemade opeisometer to calculate the distance on a large-scale map

The transparent scale bar The teacher can photocopy the map scale bar onto an overhead projector sheet to produce transparent and movable versions of the scale. The children can then move these around on the map. Being transparent is an advantage as the children can see the map features through the scale bar. This technique is most useful when measuring straight-line distances, e.g. "as the crow flies". Hence children find them useful for calculating straight-line distances on a map from lifeboat stations and helicopter bases to ships in distress and calculating "within and beyond range". The transparent scale bar is not so useful when measuring winding routes where string is more appropriate. Another advantage of directly overlaying a transparent scale bar on a map is that it avoids numerous difficult, tedious and lengthy calculations. These could get in the way of the main objective for children to enjoy geographical simulations and role-plays in which they have to make estimates of range and distance.

Plate 4: A 10 –11 year-old child using a transparent scale bar to calculate whether a helicopter is within range of a ship in distress

String and Blu-tac The children can calculate distances on a map using string, which they lay along a route. This technique is particularly useful if the route is a winding one. The secret is to use small blobs of Blu-tac along the route to be measured and then to press the string onto these blobs. This prevents the string from moving as bends and turns in the route are negotiated. The children then pull off the string and lay it along the map scale to calculate the distance.

Plate 5: Children at Bere Alston Primary School in Devon, using string and Blutac to mark out a route on a large-scale map.

Plate 6: Children remove the string from the route on the map and register it against the scale bar.

Maps lie Children may not realise that maps cannot show real distance as they are 2D representations of reality. A good way of demonstrating this is for children to use string to measure a route on an OS map of a hilly or mountainous area. Then to repeat the exercise on a 3D contour model of the same area.

Plate 7: A 10-year-old child at Estover Primary School, Plymouth, calculates the distance along a route on a 2D contour map using string which she then lays off along the scale bar.

Plate 8: Two children at Estover Primary School calculate the same distance, this time on a 3D model of the same area.

Plate 9

Fig 1: A child’s written and graphical recording of her findings regarding the real “up and down” distance over a terrain and the “as the crow flies distance” on a map.

Fig 2: The children’s recordings of distances between two points on a map. The “as the crow flies” calculated from a 2D OS map, the “up and down walking distance” calculated from their 3D model of the same area.

Dividers Children can set the gap on a pair of dividers to match an interval on the map scale bar. The dividers can then be walked along the route to be measured. The distance is then calculated by multiplying the interval by the number of "steps" taken across the map by the dividers. Alternatively the dividers can be used to develop some very useful counting skills in fractions or decimals, e.g. counting in halves, quarters, tenths of a kilometre, etc.

Plate 10: Children using dividers to "walk" a route across a map

The strip of paper Children can use a strip of paper to calculate distances from a map. The strip can be laid along a route and marked with its starting and finishing points. It can then be registered against the scale bar to calculate the distance covered. Conversely, the strip can be calibrated from the scale bar before being laid along the route. The paper strip has the disadvantage of obscuring features on the map unlike the scale bar on a transparent acetate strip.

Mathematical Calculation Children can be asked to use a ruler to measure straight-line distances on a map or string to follow winding routes, which is then measured using a ruler. They can then use the map scale to calculate distance on the ground, e.g. if the map scale is 1:25,000 then 1cm on the map is equivalent to 25,000 cm on the ground; 19 cm is equivalent to 19 x 25,000 cm, etc. The calculations will involve multiplication but also division to convert centimetres and possibly decimal fractions of a cm into kilometres. Because of the large numbers involved, this is a situation where the use of calculators would be appropriate. © Pratchett 2003 (Senior Lecturer in Primary Geography, College of St Mark & St John, Plymouth, Devon)

Photograph Codes: Plate 1: Film 22 neg. 12A Plate 2: Film 22 neg. 11A Plate 3: Film 22 neg. 10A Plate 4: Film C Air/Sea Search & Rescue neg. 22A Plate 5: Film 21 neg. 5 Plate 6: Film 21 neg. 4A Plate 7: Film 35A neg. 7 Plate 8: Film 35A neg. 9 Plate 9: Film 35A neg. 5 Plate 10: Film 14 neg. 23A