E. Spatial Sense · Angles, Rectangles, Grids and Measurement

Metric Prefixes: Choosing Units and Tools

E2.2 A1About 35 minutes

Learning goals

I can explain what the prefixes kilo-, centi- and milli- mean.
I can compare the sizes of metric units for length, mass and capacity.
I can choose a sensible unit to measure something.
I can choose the right tool to measure length, mass or capacity.

Words to know

prefix
A word part at the start of a word that changes its meaning, like kilo- in kilometre.

base unit
The main unit that prefixes are added to: metre (length), gram (mass) and litre (capacity).

kilo-
One thousand. 1 kilometre = 1000 metres.

centi-
One hundredth. 100 centimetres = 1 metre.

milli-
One thousandth. 1000 millimetres = 1 metre.

metric system
The system of measurement Canada uses. Its units are based on tens.

Remember from Grade 3 and the last two lessons

You know mm, cm, m and km for length, g and kg for mass, and mL and L for capacity. Did you notice that some of these names start the same way? Kilometre and kilogram. Millimetre and millilitre. That is not an accident!

Let's start with a code

The metric system uses a clever code. There are three base units:

metre (m) for length
gram (g) for mass
litre (L) for capacity

Then a prefix in front tells you how big or small the unit is compared with the base unit. Each prefix means the same thing for every base unit. Learn the prefix once, and you can use it everywhere.

Prefix	Meaning	Length	Mass	Capacity
kilo-	1000 base units	1 km = 1000 m	1 kg = 1000 g	(kilolitre, rarely used)
(none)	the base unit	metre (m)	gram (g)	litre (L)
centi-	1 hundredth: 100 make 1 base unit	100 cm = 1 m	(centigram, rarely used)	(centilitre, rarely used in Canada)
milli-	1 thousandth: 1000 make 1 base unit	1000 mm = 1 m	1000 mg = 1 g	1000 mL = 1 L

The most common metric prefixes. Milligrams (mg) are used for very small masses, like the amount of a vitamin in a pill.

Comparing sizes

A kilo-unit is the biggest: 1000 times the base unit. A kilometre is 1000 times as long as a metre.
A centi-unit is small: it takes 100 of them to make the base unit.
A milli-unit is the smallest of these: it takes 1000 of them to make the base unit.

And because 10 mm = 1 cm, a millimetre is 10 times smaller than a centimetre.

A close-up of a ruler from 0 to 3 cm. Each centimetre holds 10 tiny millimetre spaces. The same prefixes build bigger units too.

The metric staircase for length. The metre is the base unit. The common units (km, m, cm, mm) are shaded. Hectometres, decametres and decimetres exist but are not used much in everyday life.

Worked example

Example 1: Use the prefix

How many millimetres are in 1 metre? How many in 2 m?

Milli- means one thousandth, so 1000 mm make 1 m.
2 m = 2 × 1000 mm = 2000 mm.

1 m = 1000 mm, and 2 m = 2000 mm.

Worked example

Example 2: Choose a sensible unit

Choose the best unit for each: (a) the length of a hockey rink, (b) the thickness of a loonie, (c) the distance from Toronto to Ottawa, (d) the length of a pencil.

(a) A hockey rink is many big steps long: metres.
(b) A loonie is very thin, less than 1 cm: millimetres.
(c) Toronto to Ottawa is a long drive between cities: kilometres.
(d) A pencil fits in your hand: centimetres.

(a) m, (b) mm, (c) km, (d) cm.

Choosing a tool

The right tool makes measuring easier and more accurate.

To measure...	Use...	Units
a short length (a pencil, a book)	a ruler	mm or cm
a longer length (a room, a person's height)	a metre stick or measuring tape	cm or m
a long distance outside (a soccer field)	a long measuring tape or a trundle wheel	m
a trip in a car	the car's odometer or a map	km
mass of food	a kitchen scale	g or kg
mass of a person	a bathroom scale	kg
liquid for cooking	a measuring cup or measuring spoons	mL or L

Matching measuring tools to jobs.

Worked example

Example 3: Choose the unit and the tool

Lina wants to know how much flour is in a bag. What should she measure, which unit, and which tool?

"How much flour" in a bag means its mass.
A bag of flour is heavy: kilograms (or grams for a small bag).
The best tool is a kitchen scale.

Measure mass in kg with a kitchen scale.

Math talk: does my answer make sense?

After you choose a unit, picture it. "The table is 80 km long" can't be right, because 80 km is a long car trip! "The table is 80 cm long" makes sense. Checking whether an answer is reasonable is something good mathematicians always do.

Just for fun

The word millipede comes from the same Latin word for thousand as milli-. It means "thousand feet", but most millipedes have far fewer than 1000 legs. Somebody exaggerated!

Hands-on activity

Measure it right

You need: a ruler, a measuring tape, a measuring cup, a kitchen scale or bathroom scale (if you have one), paper and a pencil.

Make a table with columns: thing, what I'm measuring (length, mass or capacity), unit, tool, measurement.
Choose 6 things to measure at home, for example: your bed (length), your shoe (length), a mug (capacity), a bag of apples (mass), a soup pot (capacity), the hallway (length).
For each one, choose the unit and tool before you measure. Then measure.
Find one thing that you could measure in two units (like 1 m or 100 cm). Write both.

Grown-up note: help with heavy pots and full containers.

Math talk: "Which tool was best for which job? Was there a job where you weren't sure which tool to use?"

Your turn

What does the prefix kilo- mean?

How many centimetres are in 1 metre?

Which is the smallest unit: kilometre, centimetre or millimetre?

Choose the best unit for the mass of a horse: mg, g or kg.

Choose the best unit for the length of a ladybug: mm, m or km.

Which tool would you use to measure how much water a bucket holds?

Which is longer: 1 km or 1000 m?

More practice: warm-up

What are the three base units?

What does milli- mean?

How many mm are in 1 cm?

Which tool would you use to measure the length of a book?

Which tool would you use to measure your own mass?

More practice: on your own

Fill in: 1 kg = ___ g and 1 km = ___ m. What do you notice?

Fill in: 1 L = ___ mL and 1 m = ___ mm. What do you notice?

Ella says her classroom is 9 km long. What unit did she probably mean? Explain.

Choose the unit and tool to measure the amount of milk in a recipe.

Put in order from smallest to largest: 1 m, 1 mm, 1 km, 1 cm.

Challenge

A decimetre (dm) is 1 tenth of a metre. How many decimetres are in 1 m? How many centimetres are in 1 dm?

A vitamin pill has 500 mg of vitamin C. Is that more or less than 1 g? Explain.

Jake measures a desk and writes "120". Give two possible units that would make sense, and write the length both ways.

Check your understanding

Quiz

What does the prefix centi- mean?

How many millilitres make 1 litre?

Which unit is best for the distance between two cities?

Which tool is best for measuring the mass of apples for a pie?

Which list goes from smallest to largest?

Kilo- means 1000. Which is equal to 1 kg?

For parents and teachers

Big idea: The Ontario curriculum (E2.2) asks Grade 4 students to use metric prefixes to describe the relative size of different metric units, and to choose appropriate units and tools to measure length, mass and capacity. The key prefixes are kilo- (1000), centi- (1 hundredth) and milli- (1 thousandth). Hecto-, deca- and deci- complete the pattern but are rarely used in daily life.

Common difficulties:

Thinking a larger unit gives a larger number. The opposite is true: 1 km = 1000 m. Bigger units give smaller counts.
Mixing up centi- and milli-. Remember "cent": 100 cents in a dollar, 100 cm in a metre.
Choosing an unreasonable unit. Ask "Does that make sense?" and picture the unit.

How to help: Read labels together (mL on a juice box, g on a cereal box, km on a road sign). Let your child choose the measuring tool when you cook, sew or build something.