Lesson 19: Length and Distance - 2

For Grade 5 Students (Ages 10-11) - Let's master measuring length and distance!

What we will learn today:

In this lesson, you will learn to:

  • Perform multi-step conversions involving length units.
  • Multiply and divide lengths by whole numbers.
  • Solve complex word problems involving length and distance.
  • Estimate lengths and distances in real-world scenarios.

Review: Units and Conversions

Before we move to more complex problems, let's quickly review the conversions we learned in Lesson 10:

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

Remember, to convert a larger unit to a smaller unit, we multiply. To convert a smaller unit to a larger unit, we divide.

Multiplying and Dividing Lengths

Sometimes we need to find the total length of multiple identical items, or divide a total length into equal parts.

Example 1: Multiply $3$ m $20$ cm by $4$.

First, convert everything to the smallest unit (cm):
$3$ m $20$ cm = $(3 \times 100)$ cm + $20$ cm = $300$ cm + $20$ cm = $320$ cm
Now multiply:
$320$ cm $\times 4 = 1280$ cm
Convert back to meters and centimeters:
$1280$ cm = $1200$ cm + $80$ cm = $12$ m $80$ cm

Example 2: Divide $10$ m $50$ cm by $5$.

Convert to cm: $10$ m $50$ cm = $(10 \times 100)$ cm + $50$ cm = $1000$ cm + $50$ cm = $1050$ cm
Now divide:
$1050$ cm $\div 5 = 210$ cm
Convert back: $210$ cm = $2$ m $10$ cm

Exercise 1: Perform the following calculations.

$2$ m $15$ cm $\times 3 = \underline{\hspace{1cm}}$ m $\underline{\hspace{1cm}}$ cm

$8$ km $200$ m $\div 4 = \underline{\hspace{1cm}}$ km $\underline{\hspace{1cm}}$ m

Multi-step Word Problems

Many real-life problems require more than one step to solve. Read carefully to identify all the operations needed.

Exercise 2: Solve the following word problems.

  1. A tailor has a $10$ meter roll of fabric. He uses $3$ m $75$ cm for a dress and $2$ m $50$ cm for a shirt. How much fabric is left in centimeters?

  2. A cyclist rides $5$ km $800$ m in the morning and $3$ km $700$ m in the evening. What is the total distance he rides in meters?

  3. A rope is $15$ meters long. It is cut into $3$ equal pieces. What is the length of each piece in centimeters?

Estimating Lengths and Distances

Sometimes, we don't need an exact measurement. We can **estimate** to get a close idea. For example, your height might be about $1$ meter and $30$ centimeters.

Example 3: Which unit would you use to measure the length of a classroom?

You would most likely use **meters** to measure the length of a classroom, as it's too big for centimeters and too small for kilometers.

Exercise 3: Choose the most appropriate unit (cm, m, or km).

Length of a book.

Distance from Colombo to Galle.

Height of a flagpole.

Answers to Practice Time

Let's check your answers!

  1. Exercise 1: Multiplication and Division of Lengths

    • $2$ m $15$ cm $\times 3 = 6$ m $45$ cm ($215 \text{ cm} \times 3 = 645 \text{ cm}$)
    • $8$ km $200$ m $\div 4 = 2$ km $50$ m ($8200 \text{ m} \div 4 = 2050 \text{ m}$)

  2. Exercise 2: Multi-step Word Problems

    • Total used fabric: $3$ m $75$ cm + $2$ m $50$ cm = $6$ m $25$ cm ($375 + 250 = 625$ cm). Total roll: $10$ m = $1000$ cm. Remaining: $1000 - 625 = 375$ cm.
    • Total distance: $5$ km $800$ m + $3$ km $700$ m = $9$ km $500$ m ($5800 + 3700 = 9500$ m). Total distance in meters is $9500$ m.
    • Length of each piece: $15$ m $\div 3 = 5$ m. In centimeters: $5 \times 100 = 500$ cm.

  3. Exercise 3: Estimating Lengths and Distances

    • Length of a book: cm
    • Distance from Colombo to Galle: km
    • Height of a flagpole: m

You've completed Lesson 19!

Excellent work, Math Lanka students! You've deepened your understanding of length and distance, tackling more complex calculations and real-world problems. Keep practicing, and you'll be a master of measurements!

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