What does a Primary School student has got to understand about Area & Perimeter?
Area and perimeter are two important mathematics concepts that students are exposed to during their schooling years. While seemingly straight-forward to adults, younger children may struggle to differentiate between the two and determine the correct steps to find the answer.
What is perimeter?
Perimeter is essentially the addition of the borders or lengths of a 2 dimensional shape. Take for example the square below, the perimeter would be the distance around the shape depicted by the purple lines. For straight-lined figures, to find the perimeter would simply require students to find the length of each side and add them up.
What is area?
For the area of 2 dimensional figures, it can be understood as the space that is enclosed within the perimeter of the figure, as depicted by the purple region. Different shapes have different formulas that students have to apply in order to calculate the area.
The biggest step to answering area and perimeter questions correctly is to first be able to differentiate between the two. Establishing a strong foundation for students will help them minimise careless mistakes where they apply the incorrect formula.
Let’s use post-it notes as Math manipulatives to help children better understand the concepts of Area and Perimeter!
To start off, we can scaffold their understanding by using concrete manipulatives to help students visually see what they are trying to find. An easily accessible manipulative would be square post-it notes. By arranging the post-it notes into different shapes, students will be able to physically see and move the post-it notes to help their understanding.
Starting off with perimeter, arrange post-it notes into Figure 1 and get students to count the number of sides in the figure, reiterate to them that they are only supposed to count the sides that are exposed. Get students to assume each side is 1 cm, a = 1 cm. A good habit for students to have would be to mark each side that they have already counted, so that when figures get more complex they will not accidentally miss out or double count any sides. As there are 10 exposed sides (10 a), the perimeter of Figure 1 would be 1 cm x 10 = 10 cm. After they have found the perimeter for Figure 1, move the post-it notes to form Figure 2 and get them to count again. For Figure 2, there are 12 a and hence the perimeter of the figure is
1 cm x 12 =12 cm. Explain to the children that despite the number of post-it notes being the same, the perimeter for Figure 2 is larger because there are more exposed sides.
Applying the concept of Area and Perimeter to seating arrangements
This exercise can be further explored by relating it to seating arrangements. If one side of the table can seat one person, help the students to see that different arrangements will result in the same number of tables being able to seat a smaller or larger number of people. This again will reinforce that the perimeter of a space is made up of only the exposed sides, in other words the sides which people can be seated at. All 3 figures are made up of 6 tables, however, based on how the tables are arranged, the number of people that can be seated changes. We can also encourage further thinking by asking what are the benefits or shortcomings of certain table arrangements and how they think a restaurant should arrange tables to maximise profits.
Assuming again that each side is 1cm, we can determine that the length of Figure 3 is 3 cm and its breadth is 2 cm. To find the area we will take the length and multiply it by the breadth, giving us 3 cm x 2 cm = 6 cm2. Another method that can be used in this case is by showing that each post-it note is 1 square unit because 1 cm x 1 cm = 1 cm2. As there are 6 post-it notes we will multiply 1 by 6 to get 6 cm2.
For Figure 4, it will be slightly more complex as students will need to be able to dissect the figure into two parts, the grey shaded part and the white part. They will take 2 cm x 2 cm = 4 cm2 and add it to the area of the white part which we can find by multiplying 1 cm by 2 cm, giving us 2 cm2. The sum of the two parts would give us 6 cm2. Similarly, the other method can be used where they count the number of post-it notes and multiply by 1 cm2, which would also give us 6 cm2.
Extend their understanding of Area and Perimeter by giving them real-life examples
Once the children are able to grasp the above idea, it would be a good idea to extend their understanding by giving them real-life examples of area and perimeter. You can give students a measuring tape and have them find the perimeter of things around them, for example their table or even the room. Remind them that they are only measuring the outer part of the space. Another relatable idea would be that of a school field needing to have a fence surrounding it. To find how long the fence needs to be, they first need to find the perimeter of the field which they will do by finding the lengths of the different sides and adding them together. This directly translates to how much fencing is needed.
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To help them see where the concept of area would be applicable, we can give them the scenario where they are going to paint their room, it would be strange for them to only paint the outer part of their walls leaving the inside blank. As such, area has to cover the entire wall and they need to be able to find out how much the area is in order to purchase enough paint. Furthermore, we can again use the school field as an example. Ask the students how much grass they think the school field has. They will have a visual image that the grass covers more than just the outer parts of the field, and in fact covers the whole field. As such, they will be able to relate to the idea that area is the whole region that is encompassed by the grass.
It is important that students understand the differences between the two concepts, as only then will they be able to swiftly determine which approach they will need to use in order to find the answers to their questions.
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