A First, break the task into small steps to build their confidence. The technique I have found most useful is described below.
When they think they have found the correct values, it is important that they then check on the graph. Tell them that you are going to begin with an easy example to demonstrate the idea.
Here are some techniques that you could demonstrate as examples. The first involves whole-number divisions and the second includes subdivisions that are decimals. I have shown only one axis of the graph.
The main division on the axis is 10km and so the scale is marked in units of 10km (Fig 1). Focus the students' attention on the scale between two of the divisions. Here I have chosen 30km and 40km; show this as an expanded diagram (Fig 2). Point out that there are five subdivisions (arrowed) between the main divisions; count them to convince your audience.
To read the scale accurately, it is necessary to know how many kilometres make up one of the subdivisions. There are five subdivisions, and when we divide the available 10km by 5, each subdivision is 2km.
Encourage students to tot up the subdivisions by counting along the axis or by filling in a part of the diagram to convince themselves of the unit of the subdivision, as shown in Fig 3.
For a second example, use a scale of 5km on the graph paper. The main division on the axis is 5km (Fig 4). Count the number of subdivisions between these - in this case, there are 10 subdivisions.
To work out the value to allocate to each subdivision divide the available 5km by 10. Thus, each subdivision is 0.5km. Encourage the students to count between two of the main divisions, using this unit to convince themselves that they have the right measure. I have demonstrated this in Fig 5.
Student needs convincing? Check the scale.
When they get really good, have a bit of fun and ask them to challenge each other with different scales using graph paper.
Wendy Fortescue-Hubbard is a teacher and game inventor. She has been awarded a three-year fellowship by the National Endowment for Science, Technology and the Arts (NESTA) to spread maths to the masses. Email your questions to Mathagony Aunt at email@example.comOr write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX