Lesson 13: Volume and Capacity - 1

For Grade 5 Students (Ages 10-11) - Let's learn about how much space things take up!

What we will learn today:

In this lesson, you will learn to:

  • Understand the difference between volume and capacity.
  • Identify common units of capacity (milliliters and liters).
  • Convert between liters and milliliters.
  • Add and subtract capacities.
  • Solve simple word problems involving capacity.

Introduction to Volume and Capacity

Hello, young mathematicians! Have you ever poured juice into a glass, or filled a bottle with water? When we talk about how much liquid a container can hold, we are talking about its **capacity**.

**Capacity** is the amount a container can hold. **Volume** is the amount of space an object takes up. For liquids, we often use these terms interchangeably, but it's good to know the difference!

Let's learn about the units we use to measure liquids and how to perform calculations with them.

Units of Capacity

The most common units of capacity we use are:

  • **Milliliter (ml):** Used for measuring small amounts of liquid, like medicine in a spoon or a small bottle of perfume.
  • **Liter (L):** Used for measuring larger amounts of liquid, like a bottle of water, a carton of milk, or fuel in a car.

Key Conversion:

  • $1$ liter (L) = $1000$ milliliters (ml)

Converting Units of Capacity

We often need to convert between liters and milliliters.

Example 1: Convert $4$ liters to milliliters.

Since $1$ L = $1000$ ml, then $4$ L = $4 \times 1000 = 4000$ ml.

Example 2: Convert $2500$ milliliters to liters and milliliters.

Since $1000$ ml = $1$ L, then $2500$ ml = $2000$ ml + $500$ ml = $2$ L $500$ ml.

Exercise 1: Convert the following units.

$7$ L = $\underline{\hspace{2cm}}$ ml

$3000$ ml = $\underline{\hspace{2cm}}$ L

$1$ L $250$ ml = $\underline{\hspace{2cm}}$ ml

$4750$ ml = $\underline{\hspace{1cm}}$ L $\underline{\hspace{1cm}}$ ml

Adding and Subtracting Capacities

When adding or subtracting capacities, make sure they are in the same unit. If not, convert them first! Remember to regroup (carry over or borrow) $1000$ ml as $1$ L, or $1$ L as $1000$ ml.

Example 3: Add $2$ L $300$ ml and $1$ L $500$ ml.

Add liters: $2$ L + $1$ L = $3$ L
Add milliliters: $300$ ml + $500$ ml = $800$ ml
Total: $3$ L $800$ ml

Example 4: Subtract $1$ L $700$ ml from $5$ L $200$ ml.

We cannot subtract $700$ ml from $200$ ml. So, we borrow $1$ L from $5$ L (making it $4$ L) and add $1000$ ml to $200$ ml, making it $1200$ ml.
Now, $1200 - 700 = 500$ ml.
And $4 - 1 = 3$ L.
Total: $3$ L $500$ ml

Exercise 2: Add or subtract the following capacities.

$3$ L $450$ ml + $2$ L $100$ ml = $\underline{\hspace{1cm}}$ L $\underline{\hspace{1cm}}$ ml

$6$ L $800$ ml + $1$ L $300$ ml = $\underline{\hspace{1cm}}$ L $\underline{\hspace{1cm}}$ ml

$7$ L $600$ ml - $4$ L $250$ ml = $\underline{\hspace{1cm}}$ L $\underline{\hspace{1cm}}$ ml

$9$ L $100$ ml - $3$ L $400$ ml = $\underline{\hspace{1cm}}$ L $\underline{\hspace{1cm}}$ ml

Problem Solving with Capacity

Let's solve some real-life problems involving capacity.

Exercise 3: Solve the following word problems.

  1. A water bottle holds $1$ L $500$ ml of water. If you drink $700$ ml, how much water is left in the bottle?

  2. A chef uses $2$ L $250$ ml of oil for cooking in the morning and $1$ L $800$ ml in the evening. How much oil does he use in total?

  3. A jug has a capacity of $3$ liters. If it contains $1500$ ml of juice, how much more juice can it hold?

Answers to Practice Time

Let's check your answers!

  1. Exercise 1: Converting Units

    • $7$ L = $7000$ ml
    • $3000$ ml = $3$ L
    • $1$ L $250$ ml = $1250$ ml
    • $4750$ ml = $4$ L $750$ ml

  2. Exercise 2: Adding and Subtracting Capacities

    • $3$ L $450$ ml + $2$ L $100$ ml = $5$ L $550$ ml
    • $6$ L $800$ ml + $1$ L $300$ ml = $8$ L $100$ ml (since $800+300=1100$ ml = $1$ L $100$ ml)
    • $7$ L $600$ ml - $4$ L $250$ ml = $3$ L $350$ ml
    • $9$ L $100$ ml - $3$ L $400$ ml = $5$ L $700$ ml (since $100 < 400$, borrow $1$ L from $9$ L, making it $8$ L and $1100$ ml. $1100-400=700$ ml, $8-3=5$ L)

  3. Exercise 3: Problem Solving with Capacity

    • $1$ L $500$ ml = $1500$ ml. $1500 - 700 = 800$ ml. So, $800$ ml is left.
    • $2$ L $250$ ml + $1$ L $800$ ml = $4$ L $50$ ml (since $250+800=1050$ ml = $1$ L $50$ ml). Total oil used is $4$ L $50$ ml.
    • $3$ liters = $3000$ ml. $3000 - 1500 = 1500$ ml. So, $1$ L $500$ ml more juice can be held.

You've completed Lesson 13!

Excellent work, Math Lanka students! You've learned about volume and capacity, and how to measure liquids. Keep practicing, and you'll be able to measure anything!

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