Grade by Grade
E. Spatial Sense · Spatial Sense: Angles, Triangles, Transformations and Area

Choosing Metric Units: Estimating and Measuring

E2.1About 40 minutes
Learning goals
  • I can choose a sensible metric unit to measure length, area, mass or capacity.
  • I can use benchmarks to estimate measurements.
  • I can measure length, area, mass and capacity with the right tools.
  • I can find the area of a shape on a grid by counting full and half squares.

Words to know

length
How long, wide, tall or far something is. Units: mm, cm, m, km.
area
How much flat surface a shape covers. Units: cm², m², km².
mass
How much matter is in an object (how heavy it feels). Units: g, kg.
capacity
How much a container can hold. Units: mL, L.
benchmark
A familiar object whose measure you know, used to help you estimate.

Remember from Grades 3 and 4

You have used mm, cm, m and km for length, cm² and m² for area, g and kg for mass, and mL and L for capacity. You learned that kilo means 1000, centi means one hundredth and milli means one thousandth. This lesson puts all of these together, so you can choose the right unit and make good estimates.

Let's start with a backyard rink

The Nguyen family is building a backyard skating rink. They need to know:

  • how long and wide the rink is (metres),
  • how much ground it covers (square metres),
  • how much water to flood it with (litres),
  • and the mass of the bags of sand that hold down the tarp (kilograms).

Four different questions, four different kinds of units! Choosing the right unit is the first step to measuring well.

A rectangular backyard skating rink with wooden boards and a white tarp, a garden hose beside it and lights on the fence.
A backyard rink. Its length is in metres, its area in square metres, and the water to flood it in litres. AI-generated image
What you measureUnitsBenchmarksTool
Lengthmm, cm, m, kmA dime is about 1 mm thick. Your fingernail is about 1 cm wide. A door is about 2 m tall. Walking 1 km takes about 10 to 15 minutes.ruler, metre stick, measuring tape
Areacm², m², km²Your fingernail covers about 1 cm². A square 1 m on each side covers 1 m². Big areas, like a city, are measured in km².grid paper, or measure length and width
Massg, kgA paper clip is about 1 g. A 1 L carton of milk is about 1 kg.kitchen scale, bathroom scale, pan balance
CapacitymL, LA measuring teaspoon holds 5 mL. A milk carton holds 1 L.measuring cup, measuring spoons
Metric units, benchmarks and tools.

How to choose a unit

  1. Decide what you are measuring: length, area, mass or capacity.
  2. Think about how big it is. Small things get small units (mm, cm, g, mL). Big things get big units (m, km, kg, L).
  3. Ask: will the number be sensible? "The pencil is 0.00015 km long" is true, but silly. "The pencil is 15 cm long" is much easier to understand.
Worked example

Example 1: Pick the unit

Which unit would you use for each? (a) the mass of a pumpkin, (b) the area of a basketball court, (c) the capacity of a juice box, (d) the distance from Thunder Bay to Sudbury.

  1. (a) A pumpkin is heavy, like several cartons of milk: kg.
  2. (b) A basketball court is a big flat surface: m².
  3. (c) A juice box holds a small amount, less than a milk carton: mL.
  4. (d) Two cities are far apart: km.

kg, m², mL, km

Estimating strategies

  • Compare with a benchmark: "This bag feels like about 2 cartons of milk, so about 2 kg."
  • Count benchmarks: "The hallway is about 6 of my long steps, and each step is about 50 cm. 6 × 50 = 300 cm, which is 3 m."
  • Break it into parts: "The table looks like about 2 metre sticks long."

An estimate doesn't have to be exact, but it should be close and sensible.

Worked example

Example 2: Estimate a length

Amir's bedroom is 8 of his heel-to-toe steps wide. Each of his steps is about 25 cm. About how wide is the room?

  1. 8 steps × 25 cm = 200 cm.
  2. 200 cm is the same as 2 m.
  3. Check: that's about the height of a door. Seems sensible for a small bedroom.

About 2 m wide.

Amir's bedroom: 8 heel-to-toe steps25 cm25 cm25 cm25 cm25 cm25 cm25 cm25 cm200 cm8 × 25 cm = 200 cm = 2 mabout the height of a door
Counting a benchmark: 8 steps of about 25 cm each make about 200 cm, which is 2 m.

Measuring area on a grid

When a shape isn't a rectangle, cover it with a grid of squares.

  1. Count the full squares.
  2. Count the half squares. Two halves make one whole, so divide the number of halves by 2.
  3. Add the results.

If some pieces are not exactly halves, put small pieces together to make about one square, and say "about".

½½½½each square = 1 cm²10 full squares4 half squares
A house shape on a grid. Each square stands for 1 cm² (the picture is not actual size). The shape covers 10 full squares and 4 half squares, marked ½.
Worked example

Example 3: Area of a house shape

Find the area of the house shape on the grid.

  1. Count the full squares: the bottom part is 4 × 2 = 8, and the roof has 2 more full squares. That's 10 full squares.
  2. Count the half squares: there are 4. Two halves make 1 whole, so 4 halves make 2 whole squares.
  3. Add: 10 + 2 = 12.

The area is 12 cm².

Worked example

Example 4: Estimate, then measure capacity

About how much does a coffee mug hold? Then measure it.

  1. Benchmark: a milk carton holds 1 L, which is 1000 mL. A mug is much smaller, maybe a quarter of the carton.
  2. A quarter of 1000 mL is 250 mL. Estimate: about 250 mL.
  3. Measure: fill the mug with water, then pour it into a measuring cup. Read the scale at eye level.
  4. Compare your measure with your estimate. Mugs come in different sizes, so your answer may be different.

The estimate was about 250 mL. The measure depends on your mug!

Estimate, measure, reflect

Every time you estimate and then measure, you get better at estimating. If your estimate was far off, ask "Which benchmark could I have used?" That's how your brain learns.

Just for fun

Silly what if: Imagine a store labelled its pencils in kilometres: "New! Extra-long pencil, 0.00015 km!" True, but not very helpful. Choosing a sensible unit matters!

Hands-on activity

Measurement scavenger hunt

You need: a ruler, a measuring tape, a kitchen scale, a measuring cup, grid paper and a pencil.

Find and measure each of these. For each one, write the unit you chose, your estimate, and your measure.

  1. Length: the length of a spoon, and the height of your fridge.
  2. Area: trace your hand (fingers together) on centimetre grid paper. Count full and half squares to find its area in cm².
  3. Mass: an apple, and a bag of flour or rice (read the label too).
  4. Capacity: a mug, and a cooking pot. (Use cold water, and ask a grown-up before using kitchen pots.)

Which estimate was the closest? Which was the farthest?

Math talk: "Why do we use different units for different things?"

Your turn

1

Which unit would you use for the length of a hockey rink: mm, cm, m or km?

2

Which unit would you use for the mass of a pencil: g or kg?

3

Which unit would you use for the capacity of a bathtub: mL or L?

4

Which unit would you use for the area of a classroom floor: cm² or m²?

5

Which unit would you use for the area of a postage stamp: cm² or m²?

6

Which unit would you use for the distance between two cities: m or km?

7

A shape on a centimetre grid covers 6 full squares and 4 half squares. What is its area?

More practice: warm-up

1

What has a mass of about 1 g?

2

About how many millilitres does a measuring teaspoon hold?

3

About how wide is your fingernail?

4

About how tall is a door?

5

Which tool measures mass: a measuring cup, a scale or a ruler?

More practice: on your own

1

A hallway is 12 of your long steps. Each step is about 50 cm. About how long is the hallway in metres?

2

A desk top is a rectangle 60 cm long and 40 cm wide. What is its area?

3

Which is a sensible mass for a full school backpack: 4 g, 4 kg or 400 kg?

4

A shape on a centimetre grid covers 9 full squares and 6 half squares. What is its area?

5

Why would it be silly to measure the area of a soccer field in cm²?

Challenge

1

Estimate the area of a door that is about 2 m tall and 1 m wide.

2

You trace a leaf on centimetre grid paper. It covers 14 full squares and 8 partial squares that are each about half a square. Estimate the area.

3

A 1 L bottle is filled with water. Lucas says the water has a mass of about 1 kg. Is he right? Explain.

Check your understanding

Quiz

1.

Which unit is best for the mass of a watermelon?

2.

Which unit is best for the area of a book cover?

3.

Which is the best estimate for the capacity of a juice box?

4.

A shape covers 5 full squares and 6 half squares on a 1 cm grid. What is its area?

5.

Which tool would you use to measure capacity?

6.

Your steps are about 50 cm. A path is 20 steps long. About how long is it?

For parents and teachers

Big idea: The Ontario curriculum (E2.1) asks Grade 5 students to use appropriate metric units to estimate and measure length, area, mass and capacity. The focus is on choosing sensible units, using benchmarks, and measuring accurately.

Common difficulties:

  • Mixing up mass and capacity. Mass is how heavy (g, kg); capacity is how much a container holds (mL, L).
  • Forgetting the square units for area. Area is always in cm², m² or km².
  • Not reading scales at eye level. Crouch down to read a measuring cup.

How to help: Cooking is a great measurement activity. Read food labels together ("454 g", "1.89 L"). Before measuring anything, ask for an estimate first. Supervise any kitchen activities.