How do you measure a journey?

Liri spread out her notes: distances, the weight of her cargo, how much drinking water was left, how many days the journey would still take, and how much her collected star gold was worth.

Liri: “So many different numbers – but they all mean something completely different!”
Erklärus: “Exactly. There are five big areas of measurement that you need for your journey: length, weight, capacity, time and money. Each has its own units – but they all follow the same rules.”

🎯 Being able to estimate – a feeling for sizes

Before you measure, it is worth estimating. That sharpens your feeling for which unit makes sense in the first place.

An ant is about…
5 mm long
5 m long
A big dog weighs about…
15 g
15 kg

🎲 Game idea: find an object that you think weighs exactly 500 g – and then weigh it. Whoever gets closest wins!

📏 Length: from mm to km

Millimetres (mm) for very small distances, centimetres (cm) and metres (m) for everyday things, kilometres (km) for long journeys. In between there is also the decimetre (dm) – each unit is exactly ten times as big as the one before.

0
1
2
3
4
5
6
7
8
9
10
km
→ ×1000← ÷1000
m
→ ×10← ÷10
dm
→ ×10← ÷10
cm
→ ×10← ÷10
mm
🐜5 mman ant
🧽5 cma rubber
🚪2 ma door
🏫2 kmthe way to school
UnitConversion
1 cm= 10 mm
1 dm= 10 cm
1 m= 10 dm = 100 cm
1 km= 1000 m
How many millimetres are 4 cm?

⚖️ Weight: g and kg

Grams (g) for light things (an egg weighs about 60 g), kilograms (kg) for larger amounts (a bag of flour weighs 1 kg).

kg
→ ×1000← ÷1000
g
🥚60 gan egg
🌾1 kga bag of flour
🐕15 kga dog
UnitConversion
1 kg= 1000 g
How many grams are 2 kg?

🥛 Capacity: ml and l

New in Grade 3: millilitres (ml) for small amounts (a small juice carton holds 200 ml), litres (l) for larger ones (a bucket holds 10 l).

250 ml
500 ml
750 ml
1000 ml

The fuller the measuring jug, the more millilitres – with a whole litre it is full to the brim with 1000 ml.

UnitConversion
1 l= 1000 ml
How many millilitres are 3 l?

⏱️ Units of time at a glance

New: seconds (s). Time works differently from the other measures – not in tens, but in steps of 60!

h
→ ×60← ÷60
min
→ ×60← ÷60
s
💓1 sa heartbeat
🦷3 minbrushing your teeth
🏫6 ha school day
UnitConversion
1 min= 60 s
1 h= 60 min
1 week= 7 days
1 year= 12 months
How many minutes are 2 hours?

💶 Units of money: € and c

Calculating with amounts of money up to €1,000, and handling the decimal point with confidence: €2.50 = €2 and 50c.

€
→ ×100← ÷100
c
1csmallest coin
€1big coin
💶€100a banknote
How many cents are €2.50?

🔢 The place value chart against decimal-point frustration

When converting, zeros are often added or crossed out wrongly. A place value chart helps: write the lengths in columns one under the other.

m
tens of cm
ones of cm

3 m and 5 cm is not 3.5 m (that would be 3 m 50 cm) – it is 3.05 m! The chart shows straight away where the missing zero belongs.

🍰 Word problem: Baking with Liri

A recipe needs 500 ml of milk. But Liri’s measuring jug only shows litres. Where does she have to pour to?

Erklärus: “500 ml is half of 1000 ml, so half of 1 litre: 0.5 l – exactly in the middle up to the mark.”

⏳ Word problem: The timeline

Training begins at 15:45 and lasts 50 minutes. When does it finish?

15:45
→
+10 min
15:55
→
+10 min
16:05
→
+10 min
16:15
→
+10 min
16:25
→
+10 min
16:35

Jump in 10-minute steps up to the full hour, then carry on – training ends at 16:35.

🌌 Measures in the universe

The Moon is about 384,000 km away from the Earth.
An astronaut in space drinks about 2,000 ml (2 litres) of water a day – measured exactly, because nothing may be wasted.
A rocket often weighs several hundred thousand kg at launch – by far the largest part of that is fuel.

❌ Common mistake

With the decimal point the zero is often forgotten: 1 kg 50 g is 1.050 kg, not 1.5 kg (that would be 500 g)!

Tip: use the place value chart – there you can see straight away how many zeros really belong.

📏 Exercise 1 – Length
How many metres are 3 km?
⚖️ Exercise 2 – Weight
How many kilograms are 5000 g?
🥛 Exercise 3 – Capacity
How many litres are 4000 ml?
⏱️ Exercise 4 – Time
How many seconds are 3 minutes?
💶 Exercise 5 – Money
Liri has €3 and 25c. Write that with a decimal point.

A journey, measured five ways

Liri rewrote her travel notes: the distance in km, the weight of her cargo in kg, her water supply in litres, the remaining time in hours, and her collected star gold in euros.

Liri: “Now I can describe every part of my journey exactly – how far, how heavy, how much, how long, how expensive. Nothing stays vague any more.”
Erklärus: “And with every exact number you get a little closer to home – because now you know exactly what you still need.”
“Five areas of measurement: length (mm, cm, m, km), weight (g, kg), capacity (ml, l), time (s, min, h…), money (€, c). First estimate, then use the place value chart to convert safely.”
What you learned today
1 km=1000m · 1kg=1000g · 1l=1000ml · 1h=60min · €1=100c
First estimate, then convert safely with the place value chart
🌟

Chapter 17 mastered!

Liri can now estimate, measure and safely convert in all five areas of measurement.

Erklärus’s notebook – page 17:
“Five areas of measurement: length, weight, capacity, time, money – each with its own units, but the same rules. First develop a feeling (estimate), then convert safely with the place value chart.”
← Back to overview 17 – Measures & Units