Video: Applying Distributive Property Using Area Model

Anthony and Olivia want to use area to find 6 × 14. Olivia splits this rectangle in half, but she can’t finish because she doesn’t know 6 × 7. Anthony says it’s easier to use the 10 times table. How would he split the rectangle? Pick the next step in his calculation. Add the areas of the two parts to figure out 6 × 14.

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Video Transcript

Anthony and Olivia want to use area to find six times 14. Olivia splits this rectangle in half, but she can’t finish because she doesn’t know what six times seven is. Anthony says it’s easier to use the 10 times table. How would he split the rectangle?

When Olivia split the rectangle in half she took the length of 14 and divided it into two parts, each measuring seven. To find the area, she would then need to multiply six times seven and six times seven and then add them together. If Anthony wants to use the 10 times table, he would need to divide the 14 up into 10 and four. We see this in the first example: 10 and four equals 14. There’s nothing wrong with breaking the rectangle up into eight and six, but Anthony wants to use the 10 times table. And that means he would need to use a 10.

Now that we’ve selected Anthony’s image, we need to pick the next step in his calculation. Remember to find six times 14, we’re finding two smaller areas and then adding them together. Anthony is using the 10 times table, which means he’ll have a piece that is six times 10 and the smaller piece is six times four. That means his next step is to find the six times 10 plus six times four. Finally, we need to add the areas of the two parts to figure out six times 14. Six times 10 equals 60. Six times four equals 24. And 60 plus 24 equals 84. What we’ve found is that six times 14 equals 84.

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