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Multiplication with Arrays and Boxes – A Visual Model

Explore how to simplify multiplication using visual models like arrays and boxes. This guide demonstrates how to solve problems like 17 x 34 and 26 x 49 by breaking down numbers into place values. Learn to create arrays and boxes that help visualize the multiplication process, making calculations easier and more intuitive. With practice problems included, this method will enhance your understanding of multiplication and boost your confidence in solving similar math problems without a calculator.

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Multiplication with Arrays and Boxes – A Visual Model

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  1. Multiplication with Arrays and Boxes – A Visual Model

  2. How do you solve 17x34 using an array?

  3. The goal is to make easier problems that can be solved without a calculator. 34 17

  4. Split the array at the place value. For example, 17 and 34 are split into 10 and 7 and 30 and 4. 34 4 30 10 10x4=40 10 x 30 = 300 17 7x4=28 7 x 30 = 210 7 Find the product of each new array. (These are much easier problems)

  5. Finally, add up the products. 10 x 30 = 300 300 210 40 +28 7 x 30 = 210 10x4=40 7x4=28 578 17 x 34 = 578

  6. How do you solve 26 x 49 using a box? (that would be too many dots to draw)

  7. First, draw a rectangular box. Treat this box like a 26 x 49 array.

  8. 26 rows, 49 in each row. Split those numbers at the place value. 49 40 9 20x9=180 20 x 40 = 800 20 26 6x9=54 6 x 40 = 240 6 Find the product of each new “imaginary” array. (These are much easier problems)

  9. Finally, add up the products just like you did with the array. 800 240 180 +54 20 x 40 = 800 20x9= 180 6 x 40 = 240 1,274 6x9= 54 26 x 49 = 1,274

  10. Try these problems for practice. If you need help, look back at the previous slides. • 17 x 25 • 28 x 31 • 39 x 23 • 47 x 72 • 56 x 17 • 49 x 85 • 99 x 99

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