Post on 05-Jan-2016
Review
To introduce approaches to working out perimeter, area and volume of 2D and 3D shapes.
2
Outcomes
the perimeter of regular and composite shapes
the area of simple and composite shapes
the volume of rectangular prisms.
3
Finding ‘missing’ perimeter dimensions
8 m
1 m 1 m
If we know that the total length of the shape is 8 m . . .
4
8 m
1 m 1 m
. . . and that the two smaller rectangles are both 1 m long . . .
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8 m
1 m 1 m
. . . then the length of the large middle rectangle must be . . .
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8 m
1 m 1 m
6 m
7
Now try this one:
20 m
5 m
9 m
?8
Now try this one:
?
12 m16 m
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Finding the area of composite shapes
Divide the shape up into separate rectangles.
Find the area of each separate rectangle.
Add the areas together to find the total area of the shape.
First, you may have to work out ‘missing’ dimensions of the perimeter.
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This is a plan of a conference centre. There is a centre aisle two metres in width in the middle of the building.
20 m
22 m
20 m
15 m
10 m
10 m
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Each seat takes up a space of one square metre. How many seats could be placed in the conference centre?
20 m
20 m
15 m
10 m
10 m
22 m18
Think through ways of solving this task.
20 m
20 m
15 m
10 m
10 m
22 m19
A starting point would be to work out the ‘missing dimensions’ of the perimeter.
20 m
20 m
15 m
10 m
10 m
22 m20
Then you might begin to separate the room up into smaller rectangles.
20 m
20 m
15 m
10 m
10 m
22 m21
20 m
20 m
15 m
10 m
10 m
10 m35 m
10 m
10 m
10 m
2 m
200 m2 350 m2 350 m2200 m2
22 m22
20 m
20 m
15 m
10 m
10 m
10 m35 m
10 m
10 m
10 m
2 m
200 m2 200 m2350 m2350 m2
22 m23
20 m
20 m
15 m
10 m
10 m
10 m35 m
10 m
10 m
10 m
2 m
200 m2 200 m2350 m2350 m2
Total area = 200 + 350 + 350 + 200 m2 = 1100 m2
22 m24
20 m
20 m
15 m
10 m
10 m
10 m35 m
10 m
10 m
10 m
2 m
200 m2 200 m2350 m2350 m2
Total area = 1100 m2
22 m25
20 m
20 m
15 m
10 m
10 m
10 m25 m
10 m
10 m
10 m
2 m
200 m2 200 m2350 m2350 m2
22 m
This means 1100 chairs each taking an area of one metre square could fit in the centre.
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Area of a triangle
If the area of a rectangle is the length multiplied by the width
(and it is!) . . .
2 cm
6 cm
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Area of a triangle
. . . then what do you think the area of a triangle might be?
Use squared paper to test your theory, andwrite a formula to find the area of a triangle.
2 cm
6 cm
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Finding the volume of rectangular prisms
Height
Length
Width
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Finding the volume of rectangular prisms
3 cm
8 cm
2 cm
Volume = 48 cm3
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Summary: perimeter, area and volume
Where possible, use real, everyday examples of 2D and 3D shapes when supporting learners to understand these concepts.
Allow learners to understand through exploring ‘first principles’ to avoid ‘formulae panic’.
Use visualisation ‘warm ups’ to develop 2D and 3D spatial awareness.
Units, units, units! 35