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Mathematics Age 8-9: Geoboard Introduction: This lesson encourages children to experiment with shapes created on a Geoboard. They will examine both the perimeter and area of the shapes created, and then look for a relationship between the area/perimeter and the size of the shape. On the basis of their findings they will need to think how to work out the area and perimeter of a similar shape that is too large to be constructed on the Geoboard. The activity uses the Geoboard program from: http://nlvm.usu.edu/en/nav/grade_g_1.html Resources  A PC running the Geoboard program from: http://nlvm.usu.edu/en/nav/grade_g_1.html  An interactive whiteboard or data projector for whole class/large group teaching  A computer for each pair of children Previous learning Children need to be familiar with the concepts of area and perimeter. They should know that area of a rectangle is length x breadth and that the area of more complex rectilinear shapes can be found by breaking down the shapes into squares and rectangles. Learning Objectives  Children will learn to recognise similar shapes  They will learn to measure the area and perimeter of these shapes  They will understand that there is a numerical relationship between area/perimeter and the size of the shape. What to do Start the lesson by revising the definition of perimeter and area. Open the Geoboard program, clear the board and create a rectilinear shape. Show the children how to measure the area and the perimeter. Click on the Measure button to check the answer. Now choose a simple shape, such as the one shown below and create it on the Geoboard. Select one of the bands and then apply a click and drag technique to manoeuvre the band around the pegs. Now create a second shape that is an enlargement of the first, and then a third and fourth shape (as shown in the diagram below). For each one get the pupils to calculate the perimeter and the area and then click the Measure button to check their answers. The children have three options here: a. perimeter can be calculated by adding the length of the sides and the area can be calculated by counting the number of squares b. the area can be calculated by applying the formula for an area c. the perimeter can be calculated by extending the number sequence in the ‘perimeter’ column in the table below and the area can be calculated by extending the ‘area’ column in the table above. Hint: in this example the perimeter column increases by 8 each time, the area column involves second differences in an arithmetic sequence – that is the differences of the differences increase by a constant amount – in this case 8. However, there is an alternative. In this example, the width of the letter L is always one less than the height. The area is therefore height x (height -1) – 2

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Maths Age 8-9: Geoboard 2009


So the children can find the same answer by 3 or 4 different methods: 1. Counting squares 2. Extending number sequences 3. Applying a formula 4. Using the Measure button – but this should only be used as a check. The challenge is for the children to then to come up with the perimeter and area of enlargement 4, which is too big to be drawn on the Geoboard program. Some children may need to draw it on graph paper and use method 1 above whereas others may be able to use methods 2 or 3. Can then they produce the figures for enlargements 5 and 6?

Perimeter

Area

Starting shape

10 units

4 sq units

Enlargement 1

18 units

18 sq units

Enlargement 2

26 units

40 sq units

Enlargement 3

34 units

70 sq units

1

3 1 2

Enlargement 4

?

?

Enlargements 1 to 3 and the interface are shown below:

Once the children have grasped the idea they can then work in pairs and construct some shapes for themselves. Here are 3 possible examples:

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Maths Age 8-9: Geoboard 2009


Differentiation This lesson can be presented at a variety of levels; from drawing rectilinear shapes on the Geoboards and calculating perimeter and area to quite sophisticated ideas about creating number patterns and extending them in order to work out the perimeter and area of larger shapes without the need to draw them first. In some cases the latter may be a task more suited to a Year 5 or Year 6 lesson. The role of ICT This problem could be done as a paper and pencil exercise, but the program produces the diagrams faster and more accurately than most children could perform with ruler and graph paper. The program also checks their answers for the perimeter and area. Follow-up suggestions Those children that have developed a facility with the program and the ideas involved may then want to look at shapes involving triangles. This is not as easy as it may first appear. If they start with an isosceles right-angled triangle, they should be able to calculate and predict the area of larger triangles – even those that don’t fit on the grid. However, what do they notice about the perimeter? When they click on the Measure button they get a decimal answer. Why is this? Time to discuss Pythagoras – or may be not yet!! Assessment Children should be able to reflect on their work and draw some hypotheses about how to calculate the perimeter and area – by counting, by pattern, by formula. They should realise that there is more than one way to reach an answer to a mathematical problem. They should also realise that working out the perimeter of shapes with sloping sides can be difficult.

This lesson idea was first published as part of the Becta Direct2U subscription service for teachers, (c) Becta, 2005-2006

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Maths Age 8-9: Geoboard 2009


60_Maths_Y4_Geoboard(1)