Chapter 7

Measurement Foundations

Identifying Measurable Attributes

Identifying Measurable Attributes

We can learn about objects by noticing how they are alike and how they are different. Some things can be measured.

A measurable attribute is something about an object that we can find out by comparing or measuring it. In 1st grade, we often talk about length, weight, and capacity.

Let’s learn what each one means and how to tell which attribute to measure.

1. Length

Length tells how long, tall, or short something is.

  • A pencil can be long or short.
  • A door can be tall or short.
  • A ribbon can be longer or shorter than another ribbon.

If you want to know how long something is from one end to the other, you are thinking about length.

Words that help us talk about length are:

  • long
  • short
  • longer
  • shorter
  • tall
  • taller
  • >

2. Weight

Weight tells how heavy or light something is.

  • A rock may feel heavy.
  • A feather feels light.
  • A backpack can be heavier than a lunchbox.

If you want to know how heavy something is, you are thinking about weight.

Words that help us talk about weight are:

  • heavy
  • light
  • heavier
  • lighter
  • >

3. Capacity

Capacity tells how much a container can hold inside.

  • A cup can hold juice.
  • A bucket can hold more water than a cup.
  • A small bottle holds less than a big jug.

If you want to know how much fits inside a container, you are thinking about capacity.

Words that help us talk about capacity are:

  • holds more
  • holds less
  • full
  • empty
  • >

How do we know which attribute to use?

Ask yourself: What am I trying to find out?

  • If you want to know how long something is, measure length.
  • If you want to know how heavy something is, measure weight.
  • If you want to know how much a container holds, measure capacity.

You can think of it like this:

  • Length = end to end
  • Weight = heavy or light
  • Capacity = how much fits inside

Worked Example 1

You have two crayons. One crayon is longer than the other. What are you comparing?

Answer: You are comparing length.

Why? You are looking at which crayon is longer and which is shorter.

Worked Example 2

You pick up an apple and a watermelon. The watermelon feels heavier. What are you comparing?

Answer: You are comparing weight.

Why? You are deciding which object feels heavy or light.

Worked Example 3

You look at a cup and a pitcher. The pitcher can hold more water. What are you comparing?

Answer: You are comparing capacity.

Why? You are thinking about how much each container can hold.

Worked Example 4

Look at a chair.

  • If you ask, “How tall is the chair?” you are thinking about length.
  • If you ask, “Is the chair heavy?” you are thinking about weight.

This shows that one object can have more than one measurable attribute.

For example:

  • A bottle has a length because it can be tall or short.
  • A bottle has a weight because it can be heavy or light.
  • A bottle has a capacity because it can hold liquid.

Let’s practice thinking

  1. You want to know which string is longer.

    Attribute: length

  2. You want to know which toy is heavier.

    Attribute: weight

  3. You want to know which bowl holds more soup.

    Attribute: capacity

Helpful clues

  • If you see words like longer, shorter, or taller, think length.
  • If you see words like heavier or lighter, think weight.
  • If you see words like holds more or holds less, think capacity.

Summary

Objects can be measured in different ways. Length tells how long or tall something is. Weight tells how heavy or light something is. Capacity tells how much a container can hold.

When you look at an object, think about what you want to find out. That will help you choose the correct measurable attribute.

Put what you read to the test

You've worked through Identifying Measurable Attributes. Try answering a few questions to see what stuck — and what might deserve a quick reread before you move on.

Direct Comparison of Length

Direct Comparison of Length means looking at two objects to see which one is longer and which one is shorter.

We can do this by putting the objects side-by-side. We line up one end of each object so they start at the same place. Then we look at the other end to see which object goes farther.

This is a very important measurement skill. It helps us compare pencils, crayons, books, ribbons, and many other things around us.

Words we use:

  • Longer = goes farther
  • Shorter = does not go as far
  • Same length = both end at the same place

How to compare two objects directly

  1. Pick two objects.
  2. Put them next to each other.
  3. Make sure one end is lined up.
  4. Look at the other ends.
  5. Decide: Which is longer? Which is shorter? Or are they the same length?

If the ends are not lined up, it can trick us. One object may look longer when it is not. That is why lining up the endpoints is so important.

Main idea: To compare correctly, the objects should begin at the same starting point.

Here is a simple way to think about it:

Object A is longer than Object B if A goes farther when the starting ends match.

We can write that idea like this: \(A > B\) for length.

Object A is shorter than Object B if A does not go as far.

We can write that idea like this: \(A < B\) for length.

If they stop at the same place, then they are the same length: \(A = B\).

Important tip: Do not guess by color, shape, or thickness. Only look at how long each object is.

Worked Example 1

Sam has a blue crayon and a red crayon. He puts them side-by-side and lines up the left ends.

The blue crayon sticks out farther on the right side.

What does that mean?

  • The blue crayon is longer.
  • The red crayon is shorter.

Answer: Blue is longer than red.

Worked Example 2

Lina compares two ribbons. At first, one ribbon looks longer.

But the ribbon ends are not lined up. So Lina moves them and matches one end of both ribbons.

Now both ribbons end at the same place.

What does that mean?

  • Neither ribbon is longer.
  • Neither ribbon is shorter.
  • They are the same length.

Answer: The two ribbons are the same length.

Worked Example 3

A pencil and a marker are placed next to each other. Their bottom ends are lined up.

The marker ends sooner. The pencil goes farther.

Let’s compare:

  • Pencil = longer
  • Marker = shorter

We can say: \(\text{pencil} > \text{marker}\) in length.

Answer: The pencil is longer than the marker.

Worked Example 4

Ben puts a spoon and a fork side-by-side, but the fork starts higher up than the spoon. Ben says the fork is longer.

Is Ben sure yet?

No. First, he must line up one end of the spoon and one end of the fork.

After lining them up, he sees the spoon goes farther.

  • Spoon = longer
  • Fork = shorter

Answer: The spoon is longer, but only after lining up the ends can we tell correctly.

Things to remember

  • Put objects side-by-side.
  • Line up one end carefully.
  • Check which object goes farther.
  • If both end together, they are the same length.
  • Do not decide before the ends are lined up.

Try thinking about these real-life objects:

  • Which is longer: your toothbrush or your pencil?
  • Which is shorter: a crayon or a marker?
  • Are two socks the same length?

You can compare many classroom and home objects this way. Just remember the rule: line up the endpoints first.

Summary

Direct comparison of length means comparing two objects by putting them next to each other.

To do it correctly, line up one end of both objects. Then look at the other end to see which is longer, which is shorter, or if they are the same length.

Put what you read to the test

You've worked through Direct Comparison of Length. Try answering a few questions to see what stuck — and what might deserve a quick reread before you move on.

Indirect Comparison (Transitivity)

Indirect Comparison means comparing two things by using a third thing.

Sometimes we cannot put two objects side by side. We can still figure out which one is longer, shorter, taller, or smaller by comparing step by step.

Today we will learn a very important idea:

If Object A is longer than Object B, and Object B is longer than Object C, then Object A is longer than Object C.

We can show it like this:

$$A > B \quad \text{and} \quad B > C \quad \Rightarrow \quad A > C$$

Here, the symbol > means longer than or greater than.

This is called indirect comparison because we learn about A and C without comparing them directly.

Why do we use indirect comparison?

Indirect comparison helps when:

  • the objects are not next to each other,
  • we compare one object at a time,
  • or we want to use what we already know to solve a new question.

It is like solving a little puzzle.

Main Idea

Let us think about three objects:

  • A
  • B
  • C

If A is longer than B, then A is the bigger one out of those two.

If B is longer than C, then B is the bigger one out of those two.

Since A is bigger than B, and B is bigger than C, A must also be bigger than C.

We can say the same kind of thing with other measurement words too:

  • longer / shorter
  • taller / shorter
  • heavier / lighter

For this lesson, we will mostly use longer and shorter.

How to solve an indirect comparison

  1. Look at the first comparison.

  2. Look at the second comparison.

  3. Find the object that is in both comparisons.

  4. Use that middle object to figure out the answer.

The object in the middle helps connect the two facts.

Worked Example 1

Question: A ribbon is longer than a pencil. A pencil is longer than a crayon. Which is longer: the ribbon or the crayon?

Step 1: Ribbon > Pencil

Step 2: Pencil > Crayon

Step 3: The pencil is the middle object.

Step 4: If the ribbon is longer than the pencil, and the pencil is longer than the crayon, then the ribbon is longer than the crayon.

Answer: The ribbon is longer than the crayon.

We can write:

$$\text{Ribbon} > \text{Pencil} \quad \text{and} \quad \text{Pencil} > \text{Crayon}$$

$$\text{So, Ribbon} > \text{Crayon}$$

Worked Example 2

Question: Tom's string is shorter than Mia's string. Mia's string is shorter than Ava's string. Which string is longest?

Step 1: Tom < Mia

Step 2: Mia < Ava

Step 3: Mia is the middle object.

Step 4: If Tom's string is shorter than Mia's, and Mia's is shorter than Ava's, then Tom's string is also shorter than Ava's.

So the order is:

$$\text{Tom} < \text{Mia} < \text{Ava}$$

Answer: Ava's string is the longest.

Worked Example 3

Question: A book is taller than a toy box. The toy box is taller than a block tower. Which is shorter: the book or the block tower?

Step 1: Book > Toy Box

Step 2: Toy Box > Block Tower

Step 3: The toy box is in the middle.

Step 4: If the book is taller than the toy box, and the toy box is taller than the block tower, then the book is taller than the block tower.

Answer: The block tower is shorter.

Worked Example 4

Question: A blue straw is longer than a red straw. A red straw is longer than a yellow straw. Put the straws in order from longest to shortest.

Step 1: Blue > Red

Step 2: Red > Yellow

Step 3: Red is the middle object.

Step 4: Blue must be longer than yellow too.

So the order from longest to shortest is:

$$\text{Blue},\ \text{Red},\ \text{Yellow}$$

Answer: Blue, Red, Yellow.

Helpful tips

  • Look for the object that shows up in both clues.

  • That object is the middle object.

  • Use the two clues together.

  • Think: If this one is bigger than the middle, and the middle is bigger than that one, then this one is bigger than that one.

Try thinking with shorter

Sometimes the clue uses the word shorter instead of longer.

Example:

A worm is shorter than a snake. A snake is shorter than a rope.

Then the worm is shorter than the rope.

We can write:

$$\text{Worm} < \text{Snake} \quad \text{and} \quad \text{Snake} < \text{Rope}$$

$$\text{So, Worm} < \text{Rope}$$

Be careful

Read the comparison words carefully.

Longer and shorter mean opposite things.

If you mix them up, the answer will be wrong.

It can help to draw a quick picture or make a line of objects from biggest to smallest or shortest to longest.

What we learned

Indirect comparison helps us compare two objects by using a third object.

If one object is longer than a second object, and the second object is longer than a third object, then the first object is longer than the third object.

This same idea works for shorter, taller, and other kinds of measurement too.

Remember: find the middle object, connect the clues, and then decide which object is longer or shorter.

Put what you read to the test

You've worked through Indirect Comparison (Transitivity). Try answering a few questions to see what stuck — and what might deserve a quick reread before you move on.

Measuring with Non-Standard Units

Measuring with Non-Standard Units

Sometimes we want to know how long something is. We can measure it.

Before children use rulers, they often measure with non-standard units. Non-standard units are small objects we use to measure, like cubes, paperclips, blocks, or even crayons.

When we measure with non-standard units, we find out how many of the small objects are needed to match the length of a bigger object.

For example, a pencil might be 5 cubes long. That means 5 cubes placed end to end are the same length as the pencil.

How to measure with non-standard units

  1. Choose one kind of unit, like cubes or paperclips.

  2. Put the units in a straight line.

  3. Start at one end of the object.

  4. Place each unit right next to the last one.

  5. Do not leave gaps.

  6. Do not overlap the units.

  7. Count the units.

The number you count tells the length.

Important rules to remember

  • Use the same size unit each time.

  • Line the units up carefully.

  • No spaces between the units.

  • No units on top of each other.

  • Start measuring at the very end of the object.

If the units are not lined up the right way, the measurement will not be correct.

Why do different units give different numbers?

Big units cover more space, so you need fewer of them.

Small units cover less space, so you need more of them.

That means the same object can have different measurements if we use different units.

For example, a book might be 4 large blocks long or 8 small cubes long. Both can be correct because the units are different sizes.

Worked Example 1

A crayon is measured with cubes. There are 6 cubes lined up from one end of the crayon to the other.

So, the crayon is 6 cubes long.

We can write:

\(6\) cubes

Worked Example 2

A spoon is measured with paperclips. The paperclips are placed in a line with no gaps. There are 4 paperclips.

So, the spoon is 4 paperclips long.

We can write:

\(4\) paperclips

Worked Example 3

Look at two ribbons.

  • Ribbon A is 5 cubes long.

  • Ribbon B is 7 cubes long.

Which ribbon is longer?

Because both ribbons were measured with the same kind of unit, we can compare the numbers.

Since \(7 > 5\), Ribbon B is longer.

Worked Example 4

A marker is measured in two ways:

  • It is 3 big blocks long.

  • It is 6 small cubes long.

Is that possible?

Yes. Big blocks are larger, so fewer are needed. Small cubes are smaller, so more are needed.

Both measurements can be correct.

Let’s think about mistakes

Sometimes children make small measuring mistakes. Here are some things to watch for:

  • If there is a gap between units, the measurement may look too big.

  • If units overlap, the measurement may look too small.

  • If different-size units are mixed together, the measurement is not fair.

Good measuring means being careful.

Try to picture it

Imagine measuring a book with cubes.

  • Put the first cube at the edge of the book.

  • Put the next cube right beside it.

  • Keep going until you reach the other end.

  • Count: \(1, 2, 3, 4, 5\).

The book is 5 cubes long.

What you should remember

  • Measuring tells how long something is.

  • Non-standard units are objects like cubes, paperclips, and blocks.

  • Put the units in a straight line, end to end.

  • Do not leave gaps or overlaps.

  • Count the units to find the length.

  • If the units are smaller, the number is usually bigger.

  • If the units are bigger, the number is usually smaller.

Summary

We can measure length using small objects instead of a ruler. These small objects are called non-standard units.

To measure well, use the same unit, line them up carefully, and count them. Then you can tell how long an object is as a whole number of cubes, paperclips, or other small objects.

Put what you read to the test

You've worked through Measuring with Non-Standard Units. Try answering a few questions to see what stuck — and what might deserve a quick reread before you move on.

The Rule of Identical Units

The Rule of Identical Units

When we measure something, we use a unit again and again.

A unit is one piece we use to measure, like one cube, one paper clip, or one step on a ruler.

The Rule of Identical Units means this: every unit must be the same size.

If the units are not the same size, the measurement is not fair and not correct.

For example, if one child measures a book with big paper clips and another child measures the same book with small paper clips, they may get different answers. That happens because the units are not identical.

Why does this rule matter?

  • It helps us measure correctly.

  • It makes measurements fair.

  • It helps different people get the same answer.

Think about lining up blocks to measure a pencil. If all the blocks are the same size, we can count them and trust the answer.

If some blocks are long and some are short, the count will not tell the true length of the pencil.

What does “identical” mean?

Identical means exactly the same.

  • Same length

  • Same size

  • Same shape if we are using shape pieces to measure

If we measure with cubes, each cube should match the others.

If we measure with paper clips, each paper clip should be the same size.

How to measure the right way

  1. Pick one kind of unit.

  2. Make sure every unit is the same size.

  3. Place the units in a line from one end of the object to the other end.

  4. Do not leave gaps.

  5. Do not overlap the units.

  6. Count the units carefully.

When we use equal units with no gaps and no overlaps, our measurement is much better.

Worked Example 1: Measuring with cubes

Lena measures a crayon with cubes. She uses 5 cubes.

All 5 cubes are the same size.

That means Lena followed the Rule of Identical Units.

So we can say:

$$\text{Crayon length} = 5 \text{ cubes}$$

This is a good measurement because each unit is identical.

Worked Example 2: Different-size paper clips

Sam measures a notebook with paper clips.

He uses 2 big paper clips and 3 small paper clips.

Are the units identical? No.

The big paper clips and small paper clips are not the same size.

So Sam did not follow the rule.

His measurement is not correct because the units changed during measuring.

Better way: Sam should use all big paper clips or all small paper clips.

Worked Example 3: Which measurement is fair?

A ribbon is measured in two ways.

  • Measurement A: 6 same-size cubes

  • Measurement B: 6 pieces, but some are long and some are short

Which measurement is fair? Measurement A.

Why? Because all 6 cubes are the same size.

In Measurement B, the pieces are not identical, so the answer cannot be trusted.

Worked Example 4: Same object, different answers

Two children measure the same table.

Mia says the table is 8 blocks long.

Jay says the table is 6 blocks long.

Can both answers be right? Maybe.

If Mia used small blocks and Jay used bigger blocks, they used different-size units.

That is why the numbers are different.

To compare their answers fairly, they need to use identical units.

Important idea

A bigger unit gives a smaller count.

A smaller unit gives a bigger count.

But this only makes sense when all the units in one measurement are the same size.

For example:

$$4 \text{ big blocks} \neq 4 \text{ small blocks}$$

The number 4 is the same, but the units are different sizes.

So in measurement, we must think about the size of the unit, not just the number.

Let's remember

  • Use one kind of unit.

  • Make sure every unit is exactly the same size.

  • Line them up carefully.

  • Count them to find the measurement.

Quick check

If you measure a marker with buttons, should all the buttons be the same size?

Yes! If the buttons are not the same size, the measurement will not be accurate.

If you measure a book with 7 same-size cubes, can you trust the answer?

Yes! Same-size units make a fair measurement.

Summary

The Rule of Identical Units tells us that every measuring unit must be exactly the same size.

When we use identical units, our measurement is fair and accurate.

When units are different sizes, the measurement is not reliable.

So whenever you measure, remember: same units, same size, good measurement!

Put what you read to the test

You've worked through The Rule of Identical Units. Try answering a few questions to see what stuck — and what might deserve a quick reread before you move on.

No Gaps, No Overlaps Principle

No Gaps, No Overlaps Principle

When we measure something, we use units to find out how long it is.

A unit can be something like a paper clip, a cube, or a ruler mark. To measure correctly, the units must go end to end.

This means there should be no gaps and no overlaps.

No gaps means there is no empty space between the units.

No overlaps means one unit does not cover part of another unit.

If there are gaps or overlaps, the measurement will not be right.

Why does this matter?

We measure to be fair and accurate. If units are spaced out, the object may look longer than it really is. If units overlap, the object may look shorter than it really is.

So when we measure, we place each unit carefully:

  • Start at one end of the object.
  • Put the first unit down.
  • Place the next unit right next to it.
  • Keep going until you reach the end.
  • Make sure there are no gaps and no overlaps.

Think about a line of blocks.

If the blocks touch side to side, they measure correctly.

If the blocks are apart, there are gaps.

If one block sits on top of part of another, there is an overlap.

Worked Example 1: Measuring with cubes

Mia wants to measure a crayon with cubes.

She puts down 4 cubes. Each cube touches the next cube. There are no gaps and no overlaps.

So the crayon is 4 cubes long.

We can write it like this: \(4\) cubes.

Worked Example 2: A measurement with gaps

Ben measures a pencil with 5 cubes, but he leaves small spaces between the cubes.

That is not correct, because there are gaps.

The cubes are not measuring every part of the pencil. The empty spaces make the pencil seem longer than it is.

To fix it, Ben should slide the cubes together so each cube touches the next one.

Worked Example 3: A measurement with overlaps

Ava uses 3 paper clips to measure a book. But one paper clip covers part of the next paper clip.

That is not correct, because there is an overlap.

The paper clips are covering the same space twice. This can make the book seem shorter than it is.

To fix it, Ava should place the paper clips end to end so they just touch.

Worked Example 4: Which measurement is correct?

Three children measure the same ribbon.

  1. Sam uses 6 cubes with spaces between them.
  2. Lila uses 6 cubes with some cubes covering each other.
  3. Noah uses 6 cubes in one straight line, touching side to side.

Noah's measurement is correct.

Why? Because his cubes have no gaps and no overlaps.

How to remember the rule

You can say:

Touching, not squishing, not separating.

  • Touching = units go right next to each other
  • Not squishing = no overlaps
  • Not separating = no gaps

Look for these clues when you measure:

  • Do the units start at the end of the object?
  • Does each unit touch the next one?
  • Are there any spaces?
  • Are any units on top of each other?

If the answers are yes, yes, no, no, the measurement is done the right way.

Let’s think with numbers

If a line of cubes has 5 cubes placed correctly, we write:

$$5$$

That means the object is 5 cubes long.

But if the 5 cubes have gaps or overlaps, we cannot trust that measurement.

The number only helps when the units are placed the right way.

Summary

When you measure, put units end to end.

Make sure there are no gaps and no overlaps.

This helps you get a correct measurement every time.

Remember: touching units measure best.

Put what you read to the test

You've worked through No Gaps, No Overlaps Principle. Try answering a few questions to see what stuck — and what might deserve a quick reread before you move on.

Direct Comparison of Weight

Direct Comparison of Weight

Sometimes we want to know which object is heavier and which object is lighter.

Weight tells us how heavy something feels when we lift it or compare it.

In this lesson, we will learn how to compare the weight of two objects by holding them or by using a pan balance.

What do heavier and lighter mean?

  • Heavier means an object weighs more.
  • Lighter means an object weighs less.
  • If two objects weigh the same, they are equal in weight.

When we compare weight, we are looking at which object feels harder to lift or which side of a balance goes down.

Ways to compare weight

There are two easy ways to compare the weight of two objects.

  1. Relative hefting: Hold one object in each hand. Feel which one is heavier and which one is lighter.
  2. Pan balance: Put one object in each pan. The lower side is heavier. The higher side is lighter.

Using your hands to compare weight

If you hold a toy car in one hand and a book in the other hand, you can feel which one pulls your hand down more.

If the book feels harder to hold up, then the book is heavier. The toy car is lighter.

This is called comparing by hefting. Hefting means lifting or holding objects to feel their weight.

Using a pan balance

A pan balance has two sides, or pans. You place one object on one side and another object on the other side.

  • If one side goes down, that object is heavier.
  • If one side goes up, that object is lighter.
  • If both sides stay level, the objects have the same weight.

You can think of it like this:

Lower pan = heavier

Higher pan = lighter

Level pans = same weight

Important idea

Do not guess by size alone. A bigger object is not always heavier.

For example, a big empty box can be lighter than a small rock.

That is why we compare by lifting or by using a balance.

Helpful comparison words

  • heavier than
  • lighter than
  • same weight as

You can say:

  • The apple is heavier than the leaf.
  • The feather is lighter than the book.
  • The two blocks are the same weight.

Worked Example 1

You hold a crayon in one hand and a textbook in the other hand.

The textbook feels much harder to lift.

What do we know?

  • The textbook is heavier.
  • The crayon is lighter.

Answer: The textbook is heavier than the crayon.

Worked Example 2

A pan balance has an orange on the left side and a banana on the right side.

The left side goes down.

What do we know?

  • The side that goes down is heavier.
  • The orange is on the left side.

Answer: The orange is heavier than the banana. The banana is lighter than the orange.

Worked Example 3

You compare a stuffed toy and a small stone by holding them.

The small stone feels heavier, even though it is smaller.

What do we learn?

  • Small does not always mean lighter.
  • Big does not always mean heavier.

Answer: The small stone is heavier than the stuffed toy.

Worked Example 4

On a pan balance, one cube is on one side and another cube is on the other side.

Both pans stay level.

What do we know?

  • Level pans mean the objects have the same weight.

Answer: The two cubes are the same weight.

Let’s practice thinking

If you compare two objects, ask yourself:

  1. Am I holding them, or am I using a pan balance?
  2. Which object feels heavier, or which side goes down?
  3. Can I say which object is heavier, lighter, or the same weight?

Try these simple questions

  • If a ball feels heavier than a sock, which is lighter? The sock.
  • If the right pan goes down, which side is heavier? The right side.
  • If both pans are even, what does that mean? The objects are the same weight.

Summary

We can compare the weight of two objects by hefting them in our hands or by using a pan balance.

Remember:

  • Heavier means weighs more.
  • Lighter means weighs less.
  • On a pan balance, the side that goes down is heavier.
  • If both sides are level, the objects have the same weight.

Now you can compare two objects and tell which one is heavier, which one is lighter, or if they weigh the same.

Put what you read to the test

You've worked through Direct Comparison of Weight. Try answering a few questions to see what stuck — and what might deserve a quick reread before you move on.

Direct Comparison of Capacity

Direct Comparison of Capacity

Capacity is about how much a container can hold.

A cup, jar, bottle, and bucket can all hold liquids like water or juice. Some containers hold more. Some hold less. Sometimes two containers hold the same amount.

In this lesson, we will learn how to compare containers by pouring. This is called direct comparison of capacity.

What does direct comparison mean?

Direct comparison means we check two containers by using them together. We can pour water from one container into another container to see which one holds more.

We use these words when we compare capacity:

  • More = holds a bigger amount
  • Less = holds a smaller amount
  • Equal = holds the same amount
  • Full = filled to the top
  • Empty = nothing inside

How to compare capacity by pouring

  1. Fill one container.
  2. Pour it into the other container.
  3. Watch what happens.

If the water does not fill the second container, then the second container holds more.

If the water spills over or does not fit, then the first container holds more.

If the water fills the second container exactly, then both containers have equal capacity.

Important idea

We are comparing the container size by how much it can hold, not by how tall or wide it looks.

A tall thin bottle may hold less than a short wide jar. That is why pouring helps us check.

Worked Example 1

Mia fills a small cup with water. She pours the water into a large bowl. The bowl is not full yet.

What do we know?

  • The bowl can hold more than the cup.
  • The cup holds less than the bowl.

So, bowl > cup for capacity.

Worked Example 2

Ben fills a jar with water. He pours it into a mug. The water spills over the top of the mug.

What do we know?

  • The jar holds more than the mug.
  • The mug holds less than the jar.

The water did not all fit, so the jar has greater capacity.

Worked Example 3

A bottle is filled with water. The water is poured into a pitcher. The pitcher becomes full exactly. No water is left, and no water spills.

What do we know?

  • The bottle and the pitcher hold equal amounts.
  • Their capacities are the same.

We can say: $$\text{bottle} = \text{pitcher}$$

Worked Example 4

Look at three containers: a cup, a can, and a jug.

First, pour the full cup into the can. The can is still not full. This means the can holds more than the cup.

Next, pour the full can into the jug. The jug is still not full. This means the jug holds more than the can.

Now we can compare all three:

  • Jug holds more than can
  • Can holds more than cup
  • Jug holds more than cup

We can write it like this:

$$\text{cup} < \text{can} < \text{jug}$$

How to talk about what you see

You can use sentence frames like these:

  • The ___ holds more than the ___.
  • The ___ holds less than the ___.
  • The ___ and the ___ hold the same amount.

Things to remember

  • Compare by pouring, not just by looking.
  • Use the words more, less, and equal.
  • If water is left over, the first container holds more.
  • If the second container still has space, the second container holds more.
  • If it fits exactly, the containers are equal.

Try thinking about these

1. A full cup is poured into a bucket. The bucket still has lots of room. Which holds more?

Answer: The bucket holds more.

2. A full bottle is poured into a small glass. Some water is left in the bottle. Which holds less?

Answer: The glass holds less.

3. A full jar is poured into another jar. It fills exactly. What can you say?

Answer: The two jars have equal capacity.

Summary

Capacity tells us how much a container can hold. We can compare capacity by pouring from one container into another. When we do this, we can tell which container holds more, which holds less, or if both hold an equal amount.

Put what you read to the test

You've worked through Direct Comparison of Capacity. Try answering a few questions to see what stuck — and what might deserve a quick reread before you move on.