# Introductory Lesson: Multiplying Two-Digit by Three-Digit Numbers
## Objective
Welcome to today's math adventure! Our goal is to explore the exciting world of multiplication involving two-digit and three-digit numbers. By the end of this lesson, you'll be able to solve multiplication problems confidently and understand the area model.
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## Hook: A Multiplication Mystery!
### Scenario
Imagine you are helping a local farmer, Mr. Green, who needs your math skills to plan a new vegetable garden. Mr. Green has decided to plant his vegetables in a rectangular garden plot measuring `14 metres` in width and `125 metres` in length.
### Questions to Consider
- How many square metres of space will Mr. Green need for his garden?
- Can you help him figure out how much soil to buy if one square metre requires a bag of soil?
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## Engage: Group Discussion
Gather in small groups and discuss the following:
1. **What do you think the area of Mr. Green's garden plot is?**
2. **How can we calculate it using multiplication?**
3. **What strategies can we use for multiplying a 2-digit number by a 3-digit number?**
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## Explore: The Area Model Strategy
Let’s break down the multiplication step-by-step using the area model.
### Step 1: Set up the problem
We’re looking to multiply `14` (two-digit) by `125` (three-digit).
### Step 2: Decompose the numbers
- Break `14` into `10` and `4`
- Break `125` into `100`, `20`, and `5`
### Step 3: Create the area boxes
Now, let's create boxes to understand the multiplication better:
- **Box 1:** \(10 \times 100\)
- **Box 2:** \(10 \times 20\)
- **Box 3:** \(10 \times 5\)
- **Box 4:** \(4 \times 100\)
- **Box 5:** \(4 \times 20\)
- **Box 6:** \(4 \times 5\)
### Step 4: Calculate the area of each box
Now we'll fill in the values:
- **Box 1:** \(10 \times 100 = 1000\)
- **Box 2:** \(10 \times 20 = 200\)
- **Box 3:** \(10 \times 5 = 50\)
- **Box 4:** \(4 \times 100 = 400\)
- **Box 5:** \(4 \times 20 = 80\)
- **Box 6:** \(4 \times 5 = 20\)
### Step 5: Add the areas together
Now, we'll add all the values from the boxes:
- \(1000 + 200 + 50 + 400 + 80 + 20\)
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## Conclusion of the Hook
After completing the calculations, we will be able to determine the total area of Mr. Green's garden plot. This will help him know how much soil to buy!
Are you ready to tackle the numbers and help Mr. Green? Let's dive into some practice problems on the board and continue our adventure in multiplication!