Mathematics notes, unit 6
Length, Mass and Volume of Liquid
Textbook Mathematics Year 2 (DLP), Part 1 and Part 2 (one combined PDF), pages Part 2, 53–76
What this chapter covers
- You can use the units centimetre (cm) and metre (m), and know that 1 m = 100 cm (6.1.1)
- You can measure the length of objects with a ruler and draw straight lines (6.1.2)
- You can estimate lengths and say "more than" or "less than" (6.1.3)
- You can use the units gram (g) and kilogram (kg), and know that 1 kg = 1 000 g (6.2.1)
- You can read a weighing scale and estimate the mass of objects (6.2.2, 6.2.3)
- You can use the units millilitre (mℓ) and litre (ℓ), and know that 1 ℓ = 1 000 mℓ (6.3.1)
- You can measure and estimate the volume of liquid (6.3.2, 6.3.3)
- You can solve simple everyday problems about length, mass and volume of liquid (6.4.1)
In this unit we measure how long things are (length), how heavy they are (mass) and how much liquid they hold (volume of liquid). Each one has a small unit and a big unit.
| We measure | Small unit | Big unit | The big unit is |
|---|---|---|---|
| Length | centimetre (cm) | metre (m) | 1 m = 100 cm |
| Mass | gram (g) | kilogram (kg) | 1 kg = 1 000 g |
| Volume of liquid | millilitre (mℓ) | litre (ℓ) | 1 ℓ = 1 000 mℓ |
6.1Length: centimetres and metres
Length tells us how long, tall, short or wide something is. Short things are measured in centimetres (cm). Long things are measured in metres (m).
1 m = 100 cm
1 m = 100 cm
A pencil is about 15 cm. A door is about 2 m tall. The symbol for centimetre is cm and the symbol for metre is m.
Which unit? A pencil, a rubber, a leaf: use cm. A classroom, a lorry, a road: use m.
Measure with a ruler
Each space on the ruler is 1 cm. Start from 0 and read the number where the object ends.
Start from 0. If an object starts at 2 cm, the end number is not its length. The leaf below goes from 2 to 8, so it is 8 − 2 = 6 cm, not 8 cm. Better still: move the object so that it starts at 0.
Draw a straight line
To draw a line 9 cm long: mark a dot at 0, mark a dot at 9, then join the two dots with the ruler. Do not move the ruler. Write 9 cm. To draw a line 1 m long, put the dots at 0 and 100 and write 1 m.Estimate length
To estimate is to make a good guess. Use words like "about", "more than" and "less than". Then measure to check.
Example (textbook p. 59)
Aini says a crayon is about 10 cm. Its real length is 9 cm. Her estimate is almost accurate because 10 is close to 9.a) Which unit is better for the height of a school gate, cm or m?
b) 1 m = ___ cm
c) A ribbon starts at 0 and ends at 7 on a ruler. How long is it?
b) 1 m = ___ cm
c) A ribbon starts at 0 and ends at 7 on a ruler. How long is it?
Show answerHide answer
a) m
b) 100 cm
c) 7 cm
b) 100 cm
c) 7 cm
6.2Mass: grams and kilograms
Mass tells us how heavy something is. Light things are measured in grams (g). Heavy things are measured in kilograms (kg).
1 kg = 1 000 g
1 kg = 1 000 g
A slice of bread is about 40 g. A bag of rice is 5 kg. The symbol for gram is g and the symbol for kilogram is kg.
Read a weighing scale
- Before you weigh, make sure the needle points to 0.
- Look at the graduation: how much is each small mark worth?
- Read where the needle stops.
Compare: 1 kg is the same as 1 000 g. The apples (800 g) are a little less than 1 kg. The oranges (2 kg) are much heavier.
Big does not mean heavy. Mass does not depend on size. A big sponge can be lighter than a small stone.
Check the unit. 400 g and 400 kg are very different. 400 kg is as heavy as a big cow, and 400 g is only a loaf of bread.
a) Which unit is better for a mango, g or kg?
b) 1 kg = ___ g
c) A mango is about 300 g. About how much are 2 mangoes?
b) 1 kg = ___ g
c) A mango is about 300 g. About how much are 2 mangoes?
Show answerHide answer
a) g
b) 1 000 g
c) about 600 g (300 + 300)
b) 1 000 g
c) about 600 g (300 + 300)
6.3Volume of liquid: millilitres and litres
Volume of liquid tells us how much liquid there is. Small amounts are measured in millilitres (mℓ). Big amounts are measured in litres (ℓ).
1 ℓ = 1 000 mℓ
1 ℓ = 1 000 mℓ
A box of milk is 1 ℓ. A glass of juice is about 250 mℓ. A spoon of medicine is 5 mℓ. The symbols are mℓ and ℓ.
Measure liquid
- Use a beaker, a measuring cylinder or a measuring jug.
- Look at the graduation first.
- Look at the water level at eye level. Then read the volume.
Estimate volume
If a jug of juice is 1 ℓ, then a container that looks twice as big holds about 2 ℓ. Say "more than" or "less than" and then measure to check.
Do not mix up the units. 8 ℓ is a lot of water (a bucket). 80 mℓ is only a little (a small cup).
a) Which unit is better for a bucket of water, mℓ or ℓ?
b) 1 ℓ = ___ mℓ
c) The beaker above shows 60 mℓ. How much more water to make 100 mℓ?
b) 1 ℓ = ___ mℓ
c) The beaker above shows 60 mℓ. How much more water to make 100 mℓ?
Show answerHide answer
a) ℓ
b) 1 000 mℓ
c) 100 − 60 = 40 mℓ
b) 1 000 mℓ
c) 100 − 60 = 40 mℓ
6.4Solve everyday problems
Read the question slowly. Ask: What do I know? What must I find? Then pick the unit that fits.
Example 1: comparing lengths (textbook p. 72)
Sarina uses 8 cm of red thread and 10 cm of blue thread. Which thread is longer?10 cm is more than 8 cm. The blue thread is longer.
Example 2: height limit (textbook p. 73)
A child shorter than 90 cm gets a free cable car ticket. Kamal is 1 m tall (100 cm). His little brother does not pay. So his brother is less than 90 cm, for example about 80 cm.Example 3: between two numbers (textbook p. 74)
Julia is 27 kg and Saiful is 30 kg. Nisha is heavier than Julia but lighter than Saiful. Nisha could be 28 kg or 29 kg.Example 4: choose a container (textbook p. 74)
Sue Chin wants to wash her bicycle. She needs a lot of water, so she should choose the 8 ℓ bucket, not the 80 mℓ cup.Do not forget the unit in your answer: cm or m, g or kg, mℓ or ℓ.
A lorry is 3 m high. A tunnel can only take vehicles less than 250 cm high. Can the lorry go in?
Show answerHide answer
3 m = 300 cm. 300 cm is more than 250 cm, so the lorry cannot go in.
Summary
- Length: cm for short things, m for long things. 1 m = 100 cm.
- Mass: g for light things, kg for heavy things. 1 kg = 1 000 g.
- Volume of liquid: mℓ for small amounts, ℓ for big amounts. 1 ℓ = 1 000 mℓ.
- Start measuring from 0, check the graduation and write the unit.
- Estimate with "about", "more than" and "less than", then measure to check.