What is length?

Length is the distance between two points. For example, the length of your desk is the distance from one end to the other.

Tools for measuring length

There are two types of tools:

Non-standard tools give rough estimates and depend on the person measuring. Examples include:

• Handspan (the width of your hand)
• Stick
• Rope
• Footsteps

Standard tools give exact and accepted measurements worldwide. Examples include:

• Ruler
• Tape measure
• Metre stick

Units of length

The common units for measuring length are:

Important relationships

• $1 \text{ cm} = 10 \text{ mm}$
• $1 \text{ m} = 100 \text{ cm}$
• $1 \text{ km} = 1000 \text{ m}$

Worked Example

Example: Measure the length of a pencil using a ruler.

Answer: Place the pencil on the ruler. If the pencil starts at 0 cm and ends at 12 cm, the length is 12 cm. If it ends halfway between 12 cm and 13 cm, the length is 12 cm 5 mm or 12.5 cm.

What is mass?

Mass is the measure of how much matter (material) is in an object. We often say "weight" but in mathematics we use the word "mass".

Tools for measuring mass

Non-standard tools include spoons, cups, buckets, and sacks. They give rough estimates.

Standard tools are called weighing balances. They give exact measurements. Examples include kitchen scales and bathroom scales.

Units of mass

The common units for measuring mass are:

Important relationships

• $1 \text{ kg} = 1000 \text{ g}$
• $\frac{1}{2} \text{ kg} = 500 \text{ g}$
• $\frac{1}{4} \text{ kg} = 250 \text{ g}$

Worked Example

Example: A bag of rice weighs 2 kg. How many grams is that?

Answer: Since $1 \text{ kg} = 1000 \text{ g}$, then $2 \text{ kg} = 2 \times 1000 = 2000 \text{ g}$.

What is volume?

Volume is the amount of space occupied by an object or how much a container can hold.

Tools for measuring volume

Non-standard tools include cups, spoons, and buckets. They give rough estimates.

Standard tools give exact measurements. Examples include:

• Beaker
• Measuring cylinder
• Measuring jug

Units of volume

The common units for measuring volume are:

Important relationships

• $1 \text{ L} = 1000 \text{ ml}$
• $\frac{1}{2} \text{ L} = 500 \text{ ml}$
• $\frac{1}{4} \text{ L} = 250 \text{ ml}$

Worked Example

Example: A jug contains 1 litre of water. If you pour out 400 ml, how much water remains in millilitres?

Answer: First convert 1 litre to millilitres: $1 \text{ L} = 1000 \text{ ml}$. Then subtract: $1000 \text{ ml} - 400 \text{ ml} = 600 \text{ ml}$. So, 600 ml of water remains.

In Tanzania, you use these measurements every day. For example, when you go to the duka (shop) to buy cooking oil, the seller uses a litre or millilitre measure to give you the correct amount. If you buy a bag of unga (flour) or mchele (rice), the seller weighs it in kilograms using a scale. When building a house, builders measure lengths in metres to make sure walls are straight and doors fit properly. These skills help you buy the right amounts and understand measurements in daily life.