Multiply 2-digit numbers by 2-digit numbers using area models
The area model is a brilliant way to visualize multiplying big numbers. It turns one big, tricky problem into four smaller, easy ones. It’s like solving a puzzle! 🧩
Concept
The area model for multiplication connects directly to the concept of area (length x width) and helps organize the multiplication of multi-digit numbers. **How It Works: The Four-Box Method** Let's solve **35 x 24**. 1. **Break apart the numbers (expand them):** * 35 becomes 30 and 5 * 24 becomes 20 and 4 2. **Draw a 2x2 grid (a box with four squares).** 3. **Label the sides** with the expanded numbers. * Write 30 and 5 across the top. * Write 20 and 4 down the side. 30 + 5 +-------+-------+ 20 | | | +-------+-------+ 4 | | | +-------+-------+ 4. **Multiply to find the area of each smaller box:** * Top-Left: 20 x 30 = 600 * Top-Right: 20 x 5 = 100 * Bottom-Left: 4 x 30 = 120 * Bottom-Right: 4 x 5 = 20 30 + 5 +-------+-------+ 20 | 600 | 100 | +-------+-------+ 4 | 120 | 20 | +-------+-------+ 5. **Add up all the partial products (the areas of the small boxes):** * 600 + 100 + 120 + 20 = 840 So, **35 x 24 = 840**. **Key Idea:** This method is also called finding "partial products" because you are finding the product of each part of the numbers and then adding them all together at the end. It guarantees you won't miss a step!
Try it
Practice using the area model! **Set up the model:** 1. How would you break apart the numbers to solve 47 x 36? 2. Draw and label an area model for 28 x 19. **Solve using the area model:** 3. 18 x 12 = ? 4. 42 x 25 = ? 5. 36 x 51 = ? 6. 29 x 33 = ? **Word Problems:** 7. A theater has 25 rows of seats, and each row has 32 seats. Use an area model to find the total number of seats. 8. A farmer plants 45 rows of corn, with 68 stalks in each row. How many corn stalks are there in total? 9. A tile floor is made of 16 rows of tiles, with 24 tiles in each row. What is the total number of tiles? **Challenge Problems:** 10. Find the four partial products for 58 x 47 and then add them. 11. What is the area of a rectangular field that is 95 yards long and 76 yards wide?