Lesson 10: Length and Distance - 1

For Grade 5 Students (Ages 10-11) - Let's learn to measure how long things are!

What we will learn today:

In this lesson, you will learn to:

  • Identify common units of length (centimeters, meters, kilometers).
  • Convert between meters and centimeters.
  • Convert between kilometers and meters.
  • Add and subtract lengths.
  • Solve simple word problems involving length and distance.

Introduction to Length and Distance

Hello, young mathematicians! Have you ever wondered how tall you are, or how far your school is from your home? To answer these questions, we need to measure **length** and **distance**.

Length is how long something is, and distance is how far apart two points are. We use special units to measure these.

Let's learn about these units and how to use them!

Units of Length

The most common units of length we use are:

  • **Centimeter (cm):** Used for measuring small lengths, like the length of a pencil or your finger.
  • **Meter (m):** Used for measuring larger lengths, like the height of a door or the width of a room.
  • **Kilometer (km):** Used for measuring long distances, like the distance between two towns or cities.

Key Conversions:

  • $1$ meter (m) = $100$ centimeters (cm)
  • $1$ kilometer (km) = $1000$ meters (m)

Converting Units of Length

We often need to convert between different units of length.

Example 1: Convert $5$ meters to centimeters.

Since $1$ m = $100$ cm, then $5$ m = $5 \times 100 = 500$ cm.

Example 2: Convert $300$ centimeters to meters.

Since $100$ cm = $1$ m, then $300$ cm = $300 \div 100 = 3$ m.

Example 3: Convert $2$ kilometers to meters.

Since $1$ km = $1000$ m, then $2$ km = $2 \times 1000 = 2000$ m.

Exercise 1: Convert the following units.

$4$ m = $\underline{\hspace{2cm}}$ cm

$800$ cm = $\underline{\hspace{2cm}}$ m

$6$ km = $\underline{\hspace{2cm}}$ m

$5000$ m = $\underline{\hspace{2cm}}$ km

Adding and Subtracting Lengths

When adding or subtracting lengths, make sure they are in the same unit. If not, convert them first!

Example 4: Add $2$ m $50$ cm and $3$ m $20$ cm.

Add meters: $2$ m + $3$ m = $5$ m
Add centimeters: $50$ cm + $20$ cm = $70$ cm
Total: $5$ m $70$ cm

Example 5: Subtract $1$ m $30$ cm from $4$ m $80$ cm.

Subtract meters: $4$ m - $1$ m = $3$ m
Subtract centimeters: $80$ cm - $30$ cm = $50$ cm
Total: $3$ m $50$ cm

Exercise 2: Add or subtract the following lengths.

$5$ m $40$ cm + $2$ m $15$ cm = $\underline{\hspace{1cm}}$ m $\underline{\hspace{1cm}}$ cm

$8$ km $700$ m + $1$ km $200$ m = $\underline{\hspace{1cm}}$ km $\underline{\hspace{1cm}}$ m

$6$ m $90$ cm - $3$ m $20$ cm = $\underline{\hspace{1cm}}$ m $\underline{\hspace{1cm}}$ cm

$10$ km $500$ m - $4$ km $100$ m = $\underline{\hspace{1cm}}$ km $\underline{\hspace{1cm}}$ m

Problem Solving with Length and Distance

Let's solve some real-life problems involving length and distance.

Exercise 3: Solve the following word problems.

  1. A ribbon is $3$ meters long. If you cut off $120$ centimeters from it, what is the remaining length in centimeters?

  2. The distance from John's house to school is $2$ km $300$ m. He walks to school and back home every day. What is the total distance he walks in meters?

  3. A tailor uses $1$ m $75$ cm of fabric for a shirt and $2$ m $50$ cm for a pair of trousers. How much fabric does he use in total?

Answers to Practice Time

Let's check your answers!

  1. Exercise 1: Converting Units

    • $4$ m = $400$ cm
    • $800$ cm = $8$ m
    • $6$ km = $6000$ m
    • $5000$ m = $5$ km

  2. Exercise 2: Adding and Subtracting Lengths

    • $5$ m $40$ cm + $2$ m $15$ cm = $7$ m $55$ cm
    • $8$ km $700$ m + $1$ km $200$ m = $9$ km $900$ m
    • $6$ m $90$ cm - $3$ m $20$ cm = $3$ m $70$ cm
    • $10$ km $500$ m - $4$ km $100$ m = $6$ km $400$ m

  3. Exercise 3: Problem Solving with Length and Distance

    • $3$ m = $300$ cm. Remaining length: $300 - 120 = 180$ cm.
    • Distance to school and back: $2$ km $300$ m $\times 2 = 4$ km $600$ m. In meters: $4600$ m.
    • Total fabric: $1$ m $75$ cm + $2$ m $50$ cm = $4$ m $25$ cm (since $75+50=125$ cm = $1$ m $25$ cm).

You've completed Lesson 10!

Great job, Math Lanka students! You've learned about measuring length and distance and how to work with different units. Keep practicing, and you'll be able to measure anything!

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