A common scenario when teaching maths is the one where you have taught a maths concept, such as area and perimeter, that pupils appeared to grasp quickly only to find that when they are asked to apply it sometime later, they appear to have completely forgotten what was taught. There can be many reasons for this, but sometimes the solutions offered focus on just one approach such as teaching through context problems. Clearly this is very important, but it can be even more effective when combined with a range of activities in order to embed the learning.
Here are ten tips for teaching area and perimeter:
1. Avoid using formulas until pupils have had lots of time to explore the concepts of area and perimeter in different ways. By using carefully chosen activities, pupils can often work out quick ways to calculate area and perimeter for themselves. Starting with formulas does not allow time for pupils to understand what we mean by the two measurements and the rules are often only retained by those who have a good memory. Of course, this will work when being asked to simply plug numbers into a formula but will not necessarily be so successful when pupils have to apply reasoning in order to solve a problem.
2. Focus on the need for equal units when working with area by presenting pupils with situations such as creating irregular enclosed spaces on the floor with chalk or rope and asking them to decide which covers the most space and how this can be worked out. They could use pupils as units but are all the pupils the same size and if not, is pupil an appropriate unit to use? Adding adults into one of the spaces and changing the unit to person can also illustrate this point. Before focusing on squares, discuss what other units could be used, for example, would circular counters be a useful unit to use?
3. Encourage the use of rectangular arrays of squares for measuring space. Even when working with irregular shapes, such as when drawing round hands and feet on squared paper, let pupils find quick ways of working out the number of squares within the area by looking for rectangular arrays rather than counting individual squares. This also helps pupils to make the connection between area measurement and multiplication.
4. Spend time on language by employing ideas used when developing vocabulary in English, such as creating sentences that contain the words area and perimeter within a set timeframe and challenging pupils to use the word, in the correct context, as often as possible during break times. Pupils could even be given points for using it a certain number of times without repetition. These activities could be sent home as homework (and they do not need marking!). Also, it can be helpful to know that the word perimeter originates from a Greek word meaning around measure.
5. Create visual images to embed the concepts of perimeter and area. Pupils can find images or create their own which can then be shared on a working wall. They could be used with younger pupils to see whether their image helps to explain the ideas of area and perimeter. However, make sure that the images do not contain any formulas. This can be extended to pupils creating physical images involving themselves or even creating a short role play that helps pupils to understand the two measures.
6. Play games that allow pupils to consolidate and embed what they are learning. One example could involve images of rectangular arrays of squares that can be matched against an area measurement. Covering some of the squares encourages pupils to use multiplication to find the area rather than counting, and this can eventually lead to a realisation that multiplication can be used even when there are no marked squares within the shape. Another game could utilise words that describe area and perimeter, and pupils have to decide which of the two concepts the word describes. Estimating the areas and perimeters of objects within the classroom by providing a range for the measurement is a quick game that can be played with the whole class, in groups. The group that provides the smallest correct range wins that round.
7. Use context problems so that pupils can apply the ideas of area and perimeter. It is even better if this can be a practical task such as working out the cost of replacing carpet or other flooring within the school or the cost (or time involved) of marking out the perimeters of tennis or netball courts or the athletics track. Another application could be looking at how much green space is enjoyed by each person living in either local areas or around the world. Asking pupils to create their own context problems can be a very challenging but worthwhile task since it encourages pupils to think carefully about the application of area and perimeter and the differences between them.
8. Provide opportunities for reasoning that can take the form of statements with which pupils have to agree or disagree, the most important part being their explanations for their choices. Examples could include: A rectangle with a perimeter of 10cm can have any length up to 5cm which would mean that the width would have to be zero or: To calculate the area of any shape, multiply the length by the width which only applies to rectangles and not to other shapes. Another format could involve pupils placing the statements under the headings Always true, Sometimes true or Never true and then explaining their placement by writing, or drawing an image.
9. Investigate any links between area and perimeter since pupils often assume that there is a link such as an increase in area results in an increase in perimeter. They are often surprised to discover that, for each area, there is a range of possible perimeters and this also holds true for each perimeter, which can surround a range of areas. If land was priced by the perimeter, rather than the area, how could those who bought and sold land benefit from this?
10. Explore the relationship between area units since pupils can struggle when converting one unit into another. It can be helpful for pupils to draw out a square metre and then label the sides in the required unit which helps them to convert between the two. Even sketches of square metres can help. Asking pupils to decide whether 100 square centimetres is the same as 100 centimetres squared can provoke an interesting discussion. Again, drawing images of what is meant by these two measurements can help pupils to see that 100 centimetres squared is a square with a side of 100 centimetres and and area of 10,000 square centimetres.
Of course, as educators we are often under pressure to get through the curriculum but given that area and perimeter has links with other areas including multiplication and units of measure, the time can be well spent.
For a prepared interactive resource that covers all of the above ideas, click the link below.