4 Making a distinction between the concepts of area and perimeter

One of the issues when learning about area and perimeter is students not understanding the distinction between the two concepts. This seems to affect even mature students. Reinke (1997) reported that when elementary pre-service teachers were asked to find the perimeter and area of a shaded geometric figure, many of them incorrectly used the same method for finding both perimeter and area.

To make students aware of this distinction, in the next activity you will use the same structure as previous activities but slightly tweaked. You then ask the students to construct first shapes that have the same area but different perimeters, and then shapes which have the same perimeter but different areas.

Activity 4: Exploring areas and perimeters concurrently

This activity provides good opportunities for improving students’ performance through monitoring them and giving feedback as they work. You may want to have a look at the key resource ‘Monitoring and giving feedback’ to help you plan for this.

  • Ask the students to construct at least three shapes that have:
    • the same area but different perimeters
    • the same perimeter but different areas.
  • Ask students to share their work with others on their table, then to report back on how they constructed their favourite examples and to pay attention to the units used for measurements (for example, centimetres for perimeter and cm2 for area).
  • Ask students for their thoughts on why they think they should use these measurements.

Case Study 4: Mrs Aparajeeta reflects on using Activity 4

The first question was done quite quickly and with great enthusiasm. Once they had realised that they could rearrange the unit squares as they wanted, they could easily make squares with the same area.

Some students came up with a further question: coming up with shapes with the same area and perimeter. This led to a heated discussion about measurements and dimensions; that perimeter and area could not be the same because perimeter is expressed in a one-dimensional measurement (cm) and area is two-dimensional and expressed in cm2.

I also noted that the students looked back at the earlier examples they had made in the previous activities, linking their previous learning to the new learning – I liked that. It also made it easier for them to access the second question and explore it.

Pause for thought

  • What questions did you use to probe your students’ understanding?
  • Did you feel you had to intervene at any point?
  • What points did you feel you had to reinforce?
  • During the group work, did you notice any students who were not contributing or did not appear to understand what the task involved?
  • If so, how will you address this in your future planning?

3 Developing time-effective formulae for perimeter

5 Units of measurement and working with bigger dimensions