Part 2 At the end of the time limit ask the students for feedback. Part 3 For this part of the activity it is helpful to have squared paper for the students to work on. Video: Monitoring and giving feedback. Case Study 1: Mrs Aparajeeta reflects on using Activity 1 This is the account of a teacher who tried Activity 1 with her elementary students. Reflecting on your teaching practice When you do such an exercise with your class, reflect afterwards on what went well and what went less well.
Now think about how your own class got on with the activity and reflect on the following questions: How did it go with your class? Did you feel you had to intervene at any point? What points did you feel you had to reinforce?
Did any of your students do something unexpected, or take a different approach that prompted rich discussion with the rest of the class? Were there ideas that some of the students struggled to understand? How could you help them? Activity 2: Formulae and time-efficiency For this task, use the feedback of Part 2 of Activity 1 that you wrote down on the blackboard. Ask the students, in pairs, to discuss for three minutes how they could come up with a way to calculate perimeter of a rectangle that would take less time there might already be some examples on the blackboard.
Take their feedback and discuss it with the class. Let the students discuss why these different formulae will give the same results. Video: Using pair work. How did your students engage with the discussion? Did all of the students participate? If not, how could you support them to participate next time? Activity 3: Working out the area of shapes using the counting squares method To prepare for this task ask your students to point to the areas of several objects they can see in the classroom.
Part 1: Whole-class discussion on the method of counting squares to calculate area Show students a combined shape, drawn on squared paper without measurements, for which it would be difficult to calculate the area using formulae.
Figure 1 A combined shape. Part 2: Constructing shapes with the same area On squared paper 1 cm 2 squared paper works well here ask students, working in pairs, to construct at least three shapes with an area of You may wish to specify that the length of each side must be in whole units.
Video: Planning lessons. Case Study 3: Mrs Aparajeeta reflects on using Activity 3 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.
Pause for thought How did it go with your class? Did you modify the task in any way like Mrs Aparajeeta did? If so, what was your reasoning for doing so? 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. 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?
Activity 5: Finding out area and perimeter of large regular shapes using different unit measures 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. Part 1: Working out perimeter and area of large shapes 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.
Part 2: Comparing findings Back in the classroom, ask the students for their findings and write these on the blackboard. Case Study 5 : Mr Mehta reflects on using Activity 5 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. Pause for thought Identify three ideas that you have used in this unit that would also work well when teaching other topics.
Let students see mathematics as something to talk about, to communicate through, to discuss among themselves, to work together on. Resource 2: Managing pairs to include all Pair work is about involving all. To establish pair work routines in your classroom, you should do the following: Manage the pairs that the students work in.
Sometimes students will work in friendship pairs; sometimes they will not. Make sure they understand that you will decide the pairs to help them maximise their learning. To create more of a challenge, sometimes you could pair students of mixed ability and different languages together so that they can help each other; at other times you could pair students working at the same level. At the start, explain the benefits of pair work to the students, using examples from family and community contexts where people collaborate.
Keep initial tasks brief and clear. Monitor the student pairs to make sure that they are working as you want. Do this before they move to face each other so that they listen.
Make sure that students can turn or move easily to sit to face each other. References Bouvier, A. Freudenthal, H. Dordrecht: Kluwer. Reinke, K. The area of the parallelogram is 8 ft 2. Find the area of a parallelogram with a height of 12 feet and a base of 9 feet. It looks like you added the dimensions; remember that to find the area, you multiply the base by the height. The correct answer is ft 2. It looks like you multiplied the base by the height and then divided by 2. To find the area of a parallelogram, you multiply the base by the height.
This would give you the perimeter of a 12 by 9 rectangle. The height of the parallelogram is 12 and the base of the parallelogram is 9; the area is 12 times 9, or ft 2.
Area of Triangles and Trapezoids. The formula for the area of a triangle can be explained by looking at a right triangle. Look at the image below—a rectangle with the same height and base as the original triangle. The area of the triangle is one half of the rectangle! When you use the formula for a triangle to find its area, it is important to identify a base and its corresponding height, which is perpendicular to the base. A triangle has a height of 4 inches and a base of 10 inches.
Start with the formula for the area of a triangle. Substitute 10 for the base and 4 for the height. To find the area of a trapezoid, take the average length of the two parallel bases and multiply that length by the height:. An example is provided below. Notice that the height of a trapezoid will always be perpendicular to the bases just like when you find the height of a parallelogram.
Find the area of the trapezoid. Start with the formula for the area of a trapezoid. Substitute 4 and 7 for the bases and 2 for the height, and find A. The area of the trapezoid is 11 cm 2. Use the following formulas to find the areas of different shapes. Working with Perimeter and Area. Often you need to find the area or perimeter of a shape that is not a standard polygon.
Artists and architects, for example, usually deal with complex shapes. However, even complex shapes can be thought of as being composed of smaller, less complicated shapes, like rectangles, trapezoids, and triangles. To find the perimeter of non-standard shapes, you still find the distance around the shape by adding together the length of each side.
Finding the area of non-standard shapes is a bit different. You need to create regions within the shape for which you can find the area, and add these areas together. Have a look at how this is done below. Find the area and perimeter of the polygon. In upper KS2, children measure and calculate the perimeter of composite rectilinear shapes in centimetres and metres including using the relations of perimeter or area to find unknown lengths , as advised by the non-statutory guidance for Year 5.
In Year 6, children will recognise that shapes with the same areas can have different perimeters and vice versa. Perimeter is most closely linked to properties of shapes , 2D shapes and 3D shapes , and is one of the most basic and important parts of KS2 Geometry.
A good understanding of how to calculate the perimeter of a shape is needed before children can begin to learn more complex geometric ideas such as area and volume. Wondering about how to explain other key maths vocabulary to your children? Check out our Primary Maths Dictionary , or try these primary maths terms:. Calculate the perimeter of this square. Sam drew a rectangle with a perimeter of 28cm. His rectangle was 10cm long.
How wide was it? Here are some shapes on a 1cm square grid. Explain how you know. Here is an equilateral triangle inside a square. The perimeter of the triangle is 48cm. Understanding how areas and perimeters change as we change a shape is important not just mathematically but also in solving many real-life problems.
This collection of rich tasks is intended to help you to develop these useful insights into area and perimeter. Perimeter Possibilities Age 11 to 14 Challenge Level. I'm thinking of a rectangle with an area of What could its perimeter be?
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