It can therefore become problematic when studying more complex aspects of a subject or learning formulae and algorithms that entail complex steps. Because there is little or no understanding of the underlying meaning, elements get missed out, details muddled up, stress increases and exams can be failed. These barriers to learning about formulae can be overcome if the students are given the opportunity to deduce the formulae themselves and give meaning to the formulae, even from a young age.
In the next activity the aim is to give your students the opportunity to deduce formulae themselves by building on the understanding they developed in Activity 1. This entails using their examples and asking them to construct different ways to express formulae for calculating the perimeter of rectangles.
You will also ask them to think about why these different expressions are equivalent, and tell them the purpose for developing formulae, which is to become more efficient and save time.
I liked doing this activity. It was very fast paced. There were quite a few examples on the blackboard from Activity 1, but I still asked quickly for some more examples.
I did this because I wanted to make the link clear with Activity 1, give the students even more ownership of the mathematics they were doing, and also because I thought it might give students a better opportunity to experience generalising from many examples. Asking the students to first discuss with a partner also worked well.
It gave them the opportunity to phrase their thinking, to sort out any questions they had between themselves and not be exposed to comments from the whole class. This also worked for me, as the teacher, because they had practised what they would be saying and so we got really nice and comprehensible arguments in the class discussion! To prepare for this task ask your students to point to the areas of several objects they can see in the classroom.
Show students a combined shape, drawn on squared paper without measurements, for which it would be difficult to calculate the area using formulae.
The idea is that the students have to think of another approach to working out the area instead of using formulae. An example is the shape in Figure 1. However, if you choose not to set this condition, you may find that some of your more enterprising students experiment with fractions of units to create additional shapes. This will help them to extend their thinking further.
Ask students to share their work with others sitting near to them, and then to report back on how they constructed their favourite example. As with the first part of Activity 1, the students actually found it hard to point out what the area and perimeter were for the shape. They wanted to calculate it using formulae. But I insisted, and asked students to come to the blackboard to show with their hands and fingers the area and perimeter.
One of the misconceptions that surprised me was when a student pointed to the longest length and the longest height and said that was the area, suggesting that they actually did not know what area is. So I am really pleased I persevered and did not just tell them, or point out what the area and perimeter were.
When I asked the students to find the area of the combined shape, at first some of the students were puzzled. Some of the students even partitioned the shape into rectangles and squares and calculated the area of these using the formula that they remembered.
So I prompted them to think of another method that would work. Student Sarika and her group then suggested counting the squares. Once that idea had been explored and demonstrated with the whole class I asked the students to make at least three shapes with an area of 12 cm 2.
I was amazed at the number of examples the students came up with, and their complexity. The activity also made me think about tweaking tasks that I know are good and rich to turn them into other rich tasks.
In the coming weeks I will put aside the tasks I use that I think are rich, and think about how I could tweak them so I can also use them as rich tasks for teaching other mathematical concepts. 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 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.
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 cm 2.
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.
In the last section you focused on the measurements used in working out area and perimeter. Students tend to be told to use units of measurements such as metres, centimetres, inches, etc. A unit of measurement is a measure defined and adopted as a standard by convention or by law, such as a metre, a gram or a litre. In the next activity you will ask your students to explore in groups any areas and perimeters they can find outside the classroom using their own measures, and then to compare and discuss their findings with other students in the class.
Taking the mathematics outside of the classroom in this way also allows the students to become aware that mathematics is all around us. At the same time, it gives them the opportunity to experience working with larger shapes than pencil and paper allow. This out-of-the-classroom activity works well when students work in groups of four or five and they have been assigned roles within their groups.
For example, two students can be asked to measure, one student to oversee, one or two students to record the observations. If your students have access to digital cameras or mobile phones with an integral camera, these could be used to take photographs of the shapes that the students measure in their groups. Alternatively, a tape recorder could be used to record the measurements instead of writing them down when the students are working out-of-the-classroom.
The task you are asking the students to do is to measure and work out the perimeter of as many large shapes as they can within a certain time period outside of the classroom. For example, they could measure the perimeter and area of the playground, the flower bed, the water pump area.
Decide with the students on a list of which shapes to measure so that the measurements can be compared later. Ask the students whether they came up with the same measurements. What was the same and what was different?
Did they encounter any difficulties when measuring? Can they think of more effective and accurate ways to make such measurements? The class thought it would be very easy to complete this activity but when they actually started they found that there were a lot of challenges.
Some used a piece of wood they found, some used their tread length, some used their arm length and so on. During the discussion we found that the pupils had been wondering what to write for units. They came up with the suggestion themselves that using standard units of measurement might be a good idea! During the discussion, the students talked about aspects of dimension as well as different dimensional measurements in a playful way, such as describing the area in twig 2!
This unit has focused on exploring the mathematical concepts of area and perimeter by helping the students to develop an understanding of and distinction between the concepts. The activities asked the students to use examples and objects that they can find around them and build on their intuitive understanding. In reading this unit you will have thought about how to enable your students to create examples themselves, think mathematically and reflect on the thinking processes involved.
You will also have considered how to help your students to understand the concepts of area and perimeter by learning through talking in pairs, in groups and in whole-class discussions. Identify three ideas that you have used in this unit that would also work well when teaching other topics. Make a note of two topics that you have to teach soon where those ideas can be used with some small adjustments.
Pair work is about involving all. Since students are different, pairs must be managed so that everyone knows what they have to do, what they are learning and what your expectations are. The area is the space occupied by shape whereas the perimeter is the total distance covered around the edge of the shape. We define area as the amount of space covered by a flat surface of a particular shape.
It is measured in terms of the "number of" square units square yards, square inches, square feet, etc. Most objects or shapes have edges and corners. The length and breadth of these edges are considered while calculating the area of a specific shape. On the other hand, the perimeter is the measure of length covered by the boundary of the shape. First, have a look at the image given here to understand what area of any shape means:.
Similarly, the area of a square as seen above is a 2 , while the perimeter of that square is 4a. Let us have a look at the formulas for the area and perimeter of some of the common shapes:. For more practice and enhance your learnings about perimeter check out few more interesting articles listed below. Example 1: Your favorite chocolate bar is made up of equal-sized squares with each side of the square measuring 1 in. Calculate its perimeter. If we count and add the sides of squares along the length of the bar, we get 3 in.
The sides of squares along the breadth of the bar add up to 2 in. Example 2: What is a perimeter of a rectangular-shaped notebook if the length of the notebook is 7 units and breadth is 4 units? The total length of the boundary of any closed 2-dimensional shape is called its perimeter. In the case of a circle , we call it circumference. Perimeter is the measure of the length of the boundary covering a particular shape.
Hence, it has the unit of length. For example, let us find the perimeter in feet of a square. Consider a square of a side 4 meters. Consider a rectangular table with length 30 in and breadth 25 in. Perimeter is very useful in real life and plays a crucial role. If you are planning to construct a house then an accurate perimeter is required of doors, windows, roof, walls, etc. Hence, the perimeter of that shape is measured as the sum of all the sides.
For more on ellipses, see our page on circles and curved shapes. The more elongated the ellipse becomes, the more inaccurate the answer. Mathematicians have come up with several complex formulae for solving this problem. There are many professions and occupations that may require you to take physical measurements of perimeters and boundaries, such as civil engineering, surveying, landscape architecture, garden design and sports ground maintenance.
It is necessary to not only have an understanding of the basic mathematical principles above, but also more advanced numeracy tools, such as trigonometry. It is not only the lengths of the lines that are important, but accurate measurement of the angles between those lines.
Apart from mathematical knowledge, there is also an interesting and varied toolkit needed for these sorts of occupations. Relatively short distances can be measured using steel tapes, or measuring wheels. Electronic distance measurement EDM devices, which use electromagnetic waves, are more often used by land surveyors.
These are used in conjunction with other instruments such as levels and theodolites, which ensure the accuracy and precision of angular measurements, using a mathematical technique called triangulation. However, if you just need to replace your garden fence, you will probably be fine with just a tape measure and a ball of string!
This eBook covers the basics of geometry and looks at the properties of shapes, lines and solids. These concepts are built up through the book, with worked examples and opportunities for you to practise your new skills. Whether you want to brush up on your basics, or help your children with their learning, this is the book for you.
Perimeter is the mathematical term used to define the total length of the edges of a multisided two-dimensional enclosed shape polygon. In the case of circular shapes, it is called a circumference. Many professions require these mathematical skills, often used in conjunction with much more complex geometry and trigonometry.
However, a basic understanding of the principles will allow you perform jobs around the house and garden with more mathematical confidence. You will now be able to work out how many bricks are required to go around the edge of a circular pond! Search SkillsYouNeed:. We'll never share your email address and you can unsubscribe at any time. Perimeter or Boundary?
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