Grade by Grade
E. Spatial Sense · Spatial Sense: Shapes, Grids, Angles, Area and Surface Area

Metric Units: Measuring and Converting Both Ways

E2.1 A1About 45 minutes
Learning goals
  • I can choose a sensible metric unit to measure length, area, mass and capacity.
  • I can convert from a smaller unit to a larger unit, like 2350 m to 2.35 km.
  • I can convert in both directions to solve problems.

Words to know

convert
To change a measurement to a different unit without changing its size. 100 cm and 1 m are the same length.
millimetre (mm), centimetre (cm), metre (m), kilometre (km)
Units of length. 10 mm = 1 cm, 100 cm = 1 m, 1000 m = 1 km.
gram (g), kilogram (kg)
Units of mass. 1000 g = 1 kg.
millilitre (mL), litre (L)
Units of capacity. 1000 mL = 1 L.
square centimetre (cm²), square metre (m²)
Units of area. 1 cm² is a square 1 cm on each side, and 1 m² is a square 1 m on each side.

Remember from Grade 5

In Grade 5 you converted larger units to smaller units, like 8 km = 8000 m and 4.5 L = 4500 mL. You multiplied, because it takes more of the small units to measure the same amount. This year you'll also go the other way: smaller units to larger units.

Let's start with a winter run

The school cross-country ski trail is 2350 m long. The sign at the trailhead says the length in kilometres. What should it say?

A kilometre is much bigger than a metre, so we'll need fewer kilometres than metres. When you go from a smaller unit to a larger unit, you divide.

2350 ÷ 1000 = 2.35. The sign says 2.35 km.

A groomed cross-country ski trail with two ski tracks winding through a snowy forest of pine and birch.
Trail lengths are measured in metres but often posted in kilometres. A 2350 m trail is 2.35 km long. AI-generated image
To change…into…do thisExample
mmcm÷ 1045 mm = 4.5 cm
cmm÷ 100340 cm = 3.4 m
mkm÷ 10002350 m = 2.35 km
gkg÷ 1000750 g = 0.75 kg
mLL÷ 10002500 mL = 2.5 L
kmm× 10001.2 km = 1200 m
kgg× 10003.6 kg = 3600 g
Smaller to larger: divide. Larger to smaller: multiply.
kmmcmmm× 1000÷ 1000× 100÷ 100× 10÷ 10Going DOWN toa smaller unit:MULTIPLYGoing UP toa larger unit:DIVIDEMass and capacity: g ↔ kg and mL ↔ L use 1000.
The metric staircase for length. Going down to a smaller unit, multiply. Going up to a larger unit, divide by the same number.

Dividing by 10, 100 or 1000

When you divide by 10, each digit moves one place to the right (to a place worth 10 times less). Divide by 100: two places. Divide by 1000: three places.

  • 45 ÷ 10 = 4.5
  • 340 ÷ 100 = 3.4
  • 2350 ÷ 1000 = 2.35

A quick check: the answer in the larger unit should be the smaller number.

0123456cmThe line is 45 mm long. 45 mm = 4.5 cm.
A centimetre ruler with millimetre marks (drawn larger than real size, but every mark is evenly spaced). A line from 0 to halfway between 4 and 5 is 45 mm, which is 4.5 cm.
Worked example

Example 1: Millimetres to centimetres

A beetle is 18 mm long. How long is it in centimetres?

  1. mm to cm is smaller to larger, so divide by 10.
  2. 18 ÷ 10 = 1.8

1.8 cm

Worked example

Example 2: Millilitres to litres

Lily drinks 3 bottles of water with 350 mL in each. How many litres is that?

  1. Total: 3 × 350 = 1050 mL.
  2. mL to L is smaller to larger, so divide by 1000.
  3. 1050 ÷ 1000 = 1.05

1.05 L

Worked example

Example 3: Compare in the same unit

Which is heavier: a 1.2 kg bag of apples or a 950 g bag of carrots?

  1. Change both to the same unit. 1.2 kg × 1000 = 1200 g.
  2. 1200 g is more than 950 g.

The bag of apples is heavier.

Just for fun

Which is heavier: 1 kg of feathers or 1000 g of rocks?

Neither! 1 kg = 1000 g, so they have the same mass. (The feathers just need a much bigger bag.)

Choosing a unit

Before you measure, choose a unit that fits the size of the thing:

  • Length: mm for tiny things (a seed), cm for small things (a book), m for rooms and fields, km for trips.
  • Area: cm² for small surfaces (a sticky note), m² for floors and gardens.
  • Mass: g for light things (a pencil), kg for heavy things (a backpack, a pumpkin).
  • Capacity: mL for small amounts (a spoon of medicine), L for big containers (a pail of water).

Does my answer make sense?

After converting, ask: "Is the number bigger or smaller, and should it be?" A larger unit means a smaller number. If you converted 2350 m and got 2 350 000 km, you multiplied by mistake. Catching your own mistakes this way is a sign of a strong mathematician.

Hands-on activity

Kitchen measuring lab

You need: a ruler with millimetres, a measuring tape, a kitchen scale (if you have one) and a measuring cup marked in millilitres. Ask a grown-up before using kitchen tools.

  1. Length: measure a spoon, your hand span and the length of a table. Choose mm, cm or m for each. Record each measure, then convert it to the next larger unit (for example, 175 mm = 17.5 cm).
  2. Area: trace a sticky note or a coaster on centimetre grid paper and count the squares to estimate its area in cm².
  3. Mass: read the mass on 3 packages in the cupboard (it's printed on the label). Convert grams to kilograms.
  4. Capacity: fill a cup with water using the measuring cup. Record the millilitres and convert to litres.
  5. Make a table: object, measure, converted measure.

Math talk: "Which unit was the easiest to use for each object? Why?"

Your turn

1

3000 g = ? kg

2

2500 mL = ? L

3

65 mm = ? cm

4

340 cm = ? m

5

A walk to school is 1850 m. How many kilometres is that?

6

Which is longer: 0.8 km or 750 m?

More practice: warm-up

1

5000 m = ? km

2

4000 mL = ? L

3

70 mm = ? cm

4

600 cm = ? m

5

To go from a smaller unit to a larger unit, do you multiply or divide?

More practice: on your own

1

450 g = ? kg

2

75 cm = ? m

3

Put these in order from shortest to longest: 1.5 m, 140 cm, 1600 mm.

4

A party has 6 juice boxes with 200 mL in each. How many litres of juice is that?

5

3.6 kg = ? g

Challenge

1

A school track is 400 m around. Maya runs 7 laps. How many kilometres is that? How many more laps would she need to reach 5 km?

2

A bag holds 2.5 kg of flour. Each batch of bannock in Mr. Lee's recipe uses 375 g of flour. How many full batches can he make, and how much flour is left?

3

A tablecloth is 2 m long and 1 m wide. Find its area in m² and in cm². How many cm² are in 1 m²?

Check your understanding

Quiz

1.

2350 m = ? km

2.

85 mm = ? cm

3.

750 g = ? kg

4.

Which is the most sensible unit for the mass of a pumpkin?

5.

Which amount is the greatest?

6.

4.2 km = ? m

For parents and teachers

Big idea: The Ontario curriculum (E2.1) asks Grade 6 students to measure length, area, mass and capacity using appropriate metric units, and to solve problems that require converting smaller units to larger ones and vice versa. In Grade 5 they converted larger to smaller (multiplying); now they also divide to go from smaller to larger.

Common difficulties:

  • Multiplying when they should divide. Ask: "Will I need more or fewer of the bigger unit?" Fewer means divide.
  • Decimal places. 450 ÷ 1000 is 0.45, not 0.045 or 4.5. Practise with a place-value chart.
  • Comparing different units. Change both to the same unit first.

How to help: Read labels on food packages together (grams, millilitres) and convert them. Measure things around the house with a ruler and a tape measure and talk about which unit fits best.