A short instructional YouTube lesson by Rob Langman (who introduces himself as Ben) showing how to use blank arrays (a grid/grid-method variant) to multiply both small and larger numbers. The video walks through two worked examples: 17×19 (partitioned into tens and ones; partial products 100, 90, 70, 63 recombined to 323) and 326×56 (partitioned into hundreds/tens/ones and tens/ones; partial products recombined to 18,256). The presenter emphasizes place-value awareness and proportional boxes to help children understand relative magnitude before recombining partial products.
Questions this video answers
323
18,256
He says, 'Hi, my name is Ben,' though metadata lists Rob Langman.
Chapters
Hi, my name is Ben, and in this video I'm going to be showing you how to use blank arrays to multiply numbers together. It's a very similar method to the grid method, and it just bridges that gap, just to help the children and enables them to understand the process. So here's our question. We have 17 multiplied by 19. Now we need to partition the numbers 17 and 19 into tens and ones. So here we have 10 and 9. And here we have 10 and 7. And now we need to start multiplying them in the same way that we'd have the arrays going up in this rectangular form. This is what we've got here. But to draw this many dots would be far too time consuming. So the children need to make that progression into looking at numbers. So we have 10 multiplied by 10, which equals 100, then 10 multiplied by 9, which is 90. Then 7 multiplied by 10, which is 70, and then 7 multiplied by 9, which is 63. Now we've got our four boxes full again. When you use this method, it's really good to get the children to understand that the largest answer in these boxes will be in the top left and the smallest answer will be in the bottom right. And it doesn't matter how large the box, that will always be the case. So then we're going to recombine all of these answers together because we've partitioned them. So now we have 100. Add 90, which is 190. And we have 70. Add 63, which is 133. And we need to total these. So three. Nine of three is 12. Carry the one. And now we have three. So our answer to 17 times 19 is 323. Now, this next question, we're dealing with much larger numbers. We have 326 times 56. I'll show you this method, but it's worth noting that your children may well be wanting to use an alternative method, maybe column multiplication. Here you can see that I've divided the boxes up so it's all proportional. So the largest number here, which will be 300 times 50, and the smaller ones down here, the ones six times six, so the children get that idea of the largeness or the smallness of the numbers. So here we have 326. Again, we're partitioning those numbers. And here we have 50 and 6 and exactly the same procedure. So we have 300 times 50, which is 15,000, and then we have 50 multiplied by 20, which is 1000. And then 50 multiplied by 6, which is 300 and now onto the bottom. So we have 300 multiplied by 6, which is 1800. And then we have 6 times 20, which is 120. And then 6 times 6, which is 36. So there we have our numbers, and you can see there are a lot larger. And children need to be confident with those larger numbers, adding them before we move on. So we can add. So we have 15,000, 16,300. So the total of the top row, 16,300. And then at the bottom row, we have 1800, 19, 20, 1956. Always paying due care and attention to place value. And we're going to recombine those two again. So 6, 5, 3, and 9 is 12, 6, 7, 8, and 1. So you can see our answer to 326 times 56 is 18,256. And there you have using arrays to help you calculate even much larger multiples.
