E. Spatial Sense · 3D Objects, Directions and Measurement

Mass: Using a Pan Balance

E2.4 E2.5About 35 minutes

Learning goals

I can compare the masses of objects with a pan balance.
I can estimate and measure mass using non-standard units like cubes.
I can explain that bigger objects are not always heavier.
I can explain why a smaller unit gives a bigger count, even though the mass stays the same.

Words to know

mass
How much matter is in an object. We often think of it as how heavy something is.

pan balance
A tool with two pans on a beam. The heavier side goes down.

balance (balanced)
When both sides are level, the two sides have the same mass.

heavier / lighter
Words to compare masses. The heavier object goes down on a pan balance.

non-standard unit
A unit that is not an official unit, like a linking cube or a LEGO brick. Every unit must be the same.

Let's start with a guess

Which is heavier: a pumpkin or a pine cone? Easy! The pumpkin.

But which is heavier: an apple or a banana? That's harder to tell just by looking. Hold one in each hand. Can you feel a difference? A tool can help us find out for sure.

How heavy something is tells us about its mass.

The pan balance

A pan balance has a beam with a pan on each side.

The side with the heavier object goes down.
The side with the lighter object goes up.
If the beam is level, the two sides have the same mass. We say they balance.

An apple on the left and 3 cubes on the right. The apple's side is lower, so the apple is heavier than 3 cubes.

Measuring mass with units

To measure the mass of an apple:

Estimate: "I think the apple has the same mass as about 10 cubes."
Put the apple on one side.
Add cubes to the other side one at a time.
Stop when the beam is level. Count the cubes.
Say the number and the unit: "The apple has a mass of about 14 cubes."

All the units must be the same (the same kind of cube), or the measurement won't make sense.

The beam is level: the apple has the same mass as 14 cubes.

Worked example

Example 1: Compare two fruits

An apple balances 14 cubes. A banana balances 9 cubes. Which is heavier? By how many cubes?

Both were measured with the same cubes, so we can compare the numbers.
14 is more than 9, so the apple is heavier.
14 − 9 = 5.

The apple is heavier, by 5 cubes.

When it won't balance exactly

Sometimes 13 cubes is too light and 14 cubes is too heavy. Then the mass is between 13 and 14 cubes. You can say "about 14 cubes" or "between 13 and 14 cubes".

Bigger is not always heavier

A big balloon is bigger than a small rock. But which has more mass?

A big balloon and a small rock on a pan balance. The rock's side goes down, so the small rock is heavier.

The rock is heavier! Size doesn't tell you mass. A big pillow can be lighter than a small can of soup. To know for sure, measure.

Worked example

Example 2: Order three objects

On a pan balance:

An orange is heavier than a lemon.
A lemon is heavier than a lime.

Order them from heaviest to lightest.

The orange is heavier than the lemon.
The lemon is heavier than the lime.
So the orange must also be heavier than the lime. The orange is the heaviest and the lime is the lightest.

Orange, lemon, lime.

Same mass, different units

What if we measure the apple with bigger blocks? If each big block has the same mass as 2 small cubes, the apple balances only 7 big blocks.

The apple didn't change! Bigger units give a smaller count. Smaller units give a bigger count. The mass stays the same.

14 small cubes balance 7 big blocks, because each big block has the mass of 2 small cubes.

Worked example

Example 3: Change the unit

A book balances 10 big blocks. Each big block balances 2 small cubes. How many small cubes will the book balance?

Each big block is the same as 2 small cubes.
10 big blocks = 10 groups of 2 small cubes.
Count by 2s: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.

The book balances 20 small cubes.

Just for fun

A pan balance has a big pile of feathers on one side and a few rocks on the other, and the beam is level. Which side is heavier?

Neither! They have the same mass. The feathers just need a much bigger pile.

Hands-on activity

Make a hanger balance

You need: a plastic clothes hanger, 2 paper cups or small bags that are the same, string or tape, and lots of the same small unit (LEGO bricks, linking cubes, or identical coins).

With a grown-up, tape or tie a cup to each end of the hanger.
Hang the hanger from a door handle or a broom handle resting across two chairs.
Check that the empty cups balance (the hanger is level). If not, move a cup a little until it is.
Pick 4 small things (a crayon, a spoon, an eraser, a toy car). Estimate the mass of each in bricks.
Measure each one. Write your estimate and your measurement.
Order your objects from lightest to heaviest.

Grown-up note: coins and small bricks are a choking risk for babies and toddlers.

Math talk: "Was the biggest object also the heaviest?"

Your turn

On a pan balance, which side goes down: the heavier side or the lighter side?

What does it mean when the beam is level?

A pear balances 12 cubes. A plum balances 7 cubes. Which is heavier? By how much?

Is a bigger object always heavier? Give an example.

A toy car balances 8 big blocks. Will it balance more or fewer small cubes? Why?

Why must all your units be the same?

A carrot is heavier than a celery stick. A celery stick is heavier than a strawberry. Which is the lightest?

More practice: warm-up

What tool compares masses?

Which is heavier: a watermelon or a grape?

A spoon goes up on the balance. Is it heavier or lighter than the other side?

What should you do before measuring?

An eraser balances 5 cubes. What is its mass in cubes?

More practice: on your own

A shoe balances 25 cubes. A mitten balances 6 cubes. How many more cubes does the shoe balance?

Kate says her mug's mass is between 15 and 16 cubes. What does she mean?

Hana measured a ball with marbles and got 10. Ian measured it with LEGO bricks and got 6. Did they make a mistake? Explain.

Order from lightest to heaviest: book 30 cubes, pencil 2 cubes, apple 14 cubes.

Mo estimated a toy truck is 20 cubes. It balanced 22 cubes. Was his estimate reasonable?

Challenge

A potato balances 18 small cubes. Each big block balances 3 small cubes. How many big blocks will the potato balance?

On a balance: 2 lemons balance 1 grapefruit. 1 lemon balances 9 cubes. How many cubes does the grapefruit balance?

Lucas has a small box and a big box. He thinks the big box must be heavier. How could he check? What might surprise him?

Check your understanding

Quiz

On a pan balance, the heavier side ...

The beam is level. What does that tell you?

A book balances 20 cubes. A pencil case balances 12 cubes. How many more cubes does the book balance?

Which is true?

A melon balances 8 big blocks. Each big block balances 2 small cubes. How many small cubes does the melon balance?

Why do you get a bigger number when you measure with smaller cubes?

For parents and teachers

Big idea: Children compare, estimate and measure mass using a pan balance and non-standard units (Ontario E2.4), and see that using a different-sized unit changes the count but not the mass (E2.5). Grams and kilograms come in later grades.

Common difficulties:

Thinking bigger means heavier. Try a balloon or a pillow against a can of soup.
Reading the balance backwards. Remind: "The heavy side sinks down, like a heavy person on a teeter-totter."
Mixed units. All units must be identical (all the same kind of LEGO brick, for example).

Safety: coins, small bricks and cubes are choking hazards for babies and toddlers. Hang the hanger balance where it can't fall on anyone. Balloons (whole or popped) are a choking hazard for young children: supervise balloon play and throw away broken pieces right away.

How to help: Ask "Which is heavier?" while unpacking groceries, then let your child check by holding one in each hand, then with your homemade balance.