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Dimensions and Units

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by

Mr Mattock

on 30 May 2015

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Transcript of Dimensions and Units

Dimensions and Units
Starter
Converting Units
A cylinder has a volume of 150000 cm .
Convert this volume to m .
Convert it to mm .
Main Activity 1
Complete the jigsaw to match the units

Gold -

Silver -

Bronze -
L.O. - To understand when a formula can calculate the length, area or volume, and convert between units for these three different dimensions (Level 7/8 and Grade 5/6).
The cube is 1 metre in very dimension.
(a) Calculate the area of the front face and the volume of the cube.
(b) Recalculate the area and volume if we convert the length to cm.
(c) Recalculate the area and volume if we convert the length to mm.
Starter
The cube is 1 metre in very dimension.
(a) Calculate the area of the front face and the volume of the cube.
(b) Recalculate the area and volume if we convert the length to cm.
(c) Recalculate the area and volume if we convert the length to mm.
Length Area Volume
1 m 1m 1m
100cm 10000 cm 1000000 cm
1000mm 1000000mm 1000000000mm
2
2
2
3
3
3
x100
x1000
x100
x1000
x100
x1000
2
2
3
3
3
3
3
A triangle has an area of 6250 mm .

Evan says "this means it has an area of 625 cm ."

Explain why Evan is wrong and give the correct area in cm .
2
2
2
Converting Units
A cylinder has a volume of 150000 cm .
Convert this volume to m .
0.15 m
Convert it to mm .
150000000 mm
3
3
3
A triangle has an area of 6250 mm .

Evan says "this means it has an area of 625 cm ."

Explain why Evan is wrong and give the correct area in cm .
Evan has made the mistake that because there are 10 mm in a cm he can just divide by 10, which is converting the lengths not the areas. The correct answer is 62.5 cm .
2
2
2
2
3
3
Dimensional Analysis
(a + b)h

2l + 2w

r h
2
1
2
1
3
How can we tell which formula gives length, area
or volume?
Dimensional Analysis
(a + b)h

2l + 2w

r h
2
1
2
1
3
How can we tell which formula gives length, area
or volume?
(Length + Length) x Length = Length x Length = Area.


Length + Length = Length


Length x Length = Length x Length x Length = Area.
2
p x q
r
2
p + q
r
2
2
(p + q)r
2
p - q
2
2
(p + q )r
2
2
2
p x q
r
2
p + q
r
2
2
(p + q)r
2
p - q
2
2
(p + q )r
2
2
2
Area
Inconsistent
Volume
Length
Inconsistent
Main Activity 2
Sort the formulae into those that show:
Length
Area
Volume
Are dimensionally inconsistent
Volume
Area
Length
Inconsistent
Area
Volume
Length
Area
Length
Inconsistent
Volume
Length
Area
Volume
Volume
Area
Inconsistent
Volume
Full transcript