Take feedback about possible solutions and how they know they have got all possible solutions. Try not to tell the students the reason two numbers that can be added together to make six , but try and let the students formulate this observation. What happened was that a few students explained how to calculate the perimeter and others looked a bit bewildered.
By spending some time on this, the other parts of the activity went very smoothly and I got the impression that most of the students now understood what they were talking about and what they were finding out, and understood better their methods for finding out the perimeter.
When Part 1 of the activity was given out they were all very enthusiastic. They took some items from their bags to find the perimeters. One brave student, Dheeraj, was trying to find the perimeter of his pencil. He got hold of a thread and tried to wrap it round the pencil to get the answer, so I asked him to note down the difficulty he had in doing this and that we would discuss this with the rest of the class.
Then we had a lively discussion about the items they had found the perimeters of, and how they had gone about finding the perimeter. At that point I asked Dheeraj to share his predicament with the rest of the class. So then while discussing it, it came out that perimeter is something they can find for two-dimensional things and so we had more discussion about dimensions and solids and if we had been working with solids then what could we find the perimeter of different faces, different cross-sections, etc.
Drawing the rectangles with a fixed perimeter was really fun for the class. They did this very quickly. Some did make a mistake because they added just two sides to get 16 cm and so there was a great discussion amongst them of how their perimeter was not 16 cm but 32 cm.
As for whether they had got all the options in Part 3, this was explained by Shanu very well. To also get the other students involved in that discussion I asked them whether they agreed with Shanu, understood the reasoning, and could explain it in another way.
When you do such an exercise with your class, reflect afterwards on what went well and what went less well. Consider the questions that led to the students being interested and able to progress, and those you needed to clarify. If they do not understand and cannot do something, they are less likely to become involved. Use this reflective exercise every time you undertake the activities, noting as Mrs Aparajeeta did, some quite small things that made a difference.
What might be the implications of this for planning future lessons? Now think about how your own class got on with the activity and reflect on the following questions:. Some students become very good at this method of learning, whilst others struggle. However, for all students the key question is, what kind of learning does memorisation afford?
Memorisation does not focus on comprehension, nor on building understanding, nor does it support an exploration of what concepts could mean, or how they are connected to other areas of mathematics. This method focuses on accurate reproduction of remembered routines.
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. Have a look at how this is done below. Find the area and perimeter of the polygon. To find the perimeter, add together the lengths of the sides. Start at the top and work clockwise around the shape. To find the area, divide the polygon into two separate, simpler regions.
The area of the entire polygon will equal the sum of the areas of the two regions. Region A is a rectangle. To find the area, multiply the length 18 by the width 6. The area of Region A is cm 2.
Region B is a triangle. To find the area, use the formula , where the base is 9 and the height is 9. The area of Region B is Add the regions together. You also can use what you know about perimeter and area to help solve problems about situations like buying fencing or paint, or determining how big a rug is needed in the living room. Rosie is planting a garden with the dimensions shown below.
She wants to put a thin, even layer of mulch over the entire surface of the garden. How much money will she have to spend on mulch? This shape is a combination of two simpler shapes: a rectangle and a trapezoid. Find the area of each. Find the area of the rectangle. Find the area of the shape shown below. This shape is a trapezoid, so you can use the formula to find the area:. It looks like you multiplied 2 by 9 to get 18 ft 2 ; this would work if the shape was a rectangle.
This shape is a trapezoid, though, so use the formula. The correct answer is 11 ft 2. It looks like you added all the dimensions together. This would give you the perimeter. To find the area of a trapezoid, use the formula. It looks like you multiplied all of the dimensions together. This shape is a trapezoid, so you use the formula.
It is found by adding up all the sides as long as they are all the same unit. The area of a two-dimensional shape is found by counting the number of squares that cover the shape. Many formulas have been developed to quickly find the area of standard polygons, like triangles and parallelograms. 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. The perimeter of a polygon is the total measurement of the length of the boundary of the polygon in a two-dimensional plane.
It is expressed in terms of cm, m, ft, inches, etc. The perimeter of a parallelogram is the sum of all its sides. Ans: The area is used to find the space or region occupied by any shape or figure. Examples are finding the space enclosed by the paths, cross-walks etc.
What are the applications of perimeter and area in our everyday life? Ans: Applications of area and perimeter can be seen in everyday life, like finding the area of the floor of the house, the area of the footpath, fencing of the park with a wire, etc. What is the perimeter formula? Ans: Perimeter formula tells that the perimeter of any figure or shape is the sum of the lengths of the boundaries. What is the distance taken around the circle? Ans: The distance around the circle is called the circumference or perimeter of the circle.
Now you are provided with all the necessary information on the application of perimeter and area and we hope this detailed article is helpful to you. If you have any queries regarding this article, please ping us through the comment section below and we will get back to you as soon as possible. Support: support embibe. General: info embibe. Skip to primary navigation Skip to main content Skip to primary sidebar K12 K
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