**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