 An array is an arrangement of objects into rows and columns. Arrays are useful in helping students understand multiplication. Okay, it looks like you guys did a great job building your arrays. Is there anybody who would like to share one that they built? Okay, Alyssa. What multiplication sentence did you write to go with your array? Six times five equals thirty. Excellent. So you can see in her array, she built one that has six columns and five rows. Now if I took this array and I turned it this way, I would now have five columns and six rows, but still thirty blocks. So it doesn't matter in what way we have the numbers written, we're going to get the same answer. This is called the commutative property of multiplication. And mine is a seven times four array. And instead, we did it five plus two and multiplied it as two separate questions. It may be easier to remember or have a strategy for figuring out a table if we've forgotten what seven times four is. So it would look like this on the board. We'd have an array that would be five times four and an array that would be two times four, which would give us our answer of twenty-eight. This is a really good strategy because a kid's kid gives the opportunity to visualize what they're multiplying to really understand what the numbers are that they are working with. It also allows them to work with easier numbers, friendlier numbers, instead of trying to work with the whole number itself. This same strategy of breaking numbers into friendlier numbers to multiply can be used when multiplying two-digit numbers. And we'll do thirty-six times forty-two. Now this can be a difficult numbers to work with on its own, but if we wanted to make this a little easier, how could we break up these numbers so a little easier to work with? How could we write these as friendlier numbers to multiply? Jack? Thirty plus six times forty plus two. Great, good job. Okay, so I've taken this question and I've made it into an array. And if you take a look at the smart board, you can see the array that would come from a question like this. There's a lot more squares and it's a much bigger array, but it is still a really good way to show up, show how we are multiplying the numbers, and how we can break them up into parts. So what we're going to do is we're going to look at each part of our array to try to figure out what thirty-six times forty-two is. So the first part of the array we're going to look at is the big blue section. So this big blue section would be thirty times forty. So if we were to start with that part, how many squares or little blocks would there be inside that thirty times forty array? Evan? Twelve hundred. Very good. There would be one thousand two hundred blocks inside of that array. To complete the question, we also need to multiply the simple equations of thirty times two, forty times six, and six times two. By adding these products together, we can easily determine the solution to our question. Does anyone know what that total would be? Rusef? One thousand five hundred twelve. Good. One thousand five hundred and twelve. Good answer, Rusef. Well done. I'm going to get you to work on a problem on your own, draw the array that goes with it, and label all the parts. So the problem I'm going to get you to work on today is fifty three times twenty eight. Okay, give that one a try. We'll see how you do. It is important for students to explain their strategy to others. I split up fifty three into fifty plus three, and twenty eight into twenty plus eight, and then I put it into an array. Then I added it all up, all four numbers up, and it equaled one thousand four hundred and eighty four. Today we're going to look at multiplying these same larger numbers without necessarily needing to draw the array, but instead always visualizing one, and remembering what the array looked like, and how we're breaking up our numbers. The problem we're going to work on today is twenty three times fifty four. So if we were to take this number, and break it up into easier parts to work with, what would we break it up into? Brianna? Twenty plus three times fifty plus four. Good. Twenty plus three times fifty plus four. Now if I were going to write that as an array, or visualize it as an array, this is what it might look like. The teacher is making the connection between the question and the drawing of an array to help students see how the written work reflects the array. So we have twenty plus three times fifty plus four. So if we were to start by looking at this array here, which is twenty times fifty, can anyone tell me how many parts or how many squares would be in that array? Owen? One thousand. That's correct. One thousand. And over here we can see in the question itself, here's our twenty times fifty, and twenty times fifty equals one thousand. To complete the question, we also need to multiply the simple equations of twenty times four, three times fifty, and three times four. Once we have all the parts of the array completed or all the parts of the question multiplied, we can add them all together to get the total. Does anyone know what the total would be? Bruce? One thousand two hundred forty-two. Perfect. Good job. One thousand two hundred forty-two. Once students understand how to multiply using an array by breaking numbers into parts, they no longer need to draw the array. I've been teaching for a long time, and I used to just teach the algorithm method that we learned, you know, when I was a kid. And when I was hesitant, as anybody is, to change to the new strategies because change is always difficult. But what I noticed immediately from the year I was only using the algorithm to the year when the kids were allowed to use arrays and other strategies was an increase in the number of kids that understood how to multiply. Thank you.