Arrays of Multiplication

Mr. Squeak's workshop has gotten very messy from all of his recent projects. It's time for him to organize his materials so that he knows where everything is. Luckily, Imani has volunteered to help out. She can scan the room to locate the scattered items and represent the amount with a multiplication expression. But, they will need our help to organize with "Arrays of Multiplication!” An array is a model that can be used to find the product, or total, of a multiplication problem. We use arrays to lay out multiplication problems in rows and columns, then count the number of marks to find the product. When drawing your own array, it's common to use exes, dots, or circles. Let's try this out with the example two times three. To start, look at the first factor. This tells us how many rows we need, so here we need two rows. Neatly mark the two rows accordingly. Then, look at the second factor and neatly make three circles on each of the rows. Finally, count the total number of circles made to calculate the product: two times three equals six. Let's use this knowledge to help Mr. Squeaks and Imani. First, Mr. Squeaks holds up a wrench. Imani scans the rooms to locate all the scattered wrenches. She comes back with the expression three times six. Let's use an array to determine how many wrenches Mr. Squeaks has and how he should organize them. The first factor in this expression is three. This tells us to mark three rows. The second factor, six, tells us how many marks to put on each row. Finally, we count each mark to calculate the product. There are eighteen marks, so the product of three times six equals eighteen. Mr. Squeaks can hang all of his wrenchs in three rows of six! Second, Mr. Squeaks holds up sandpaper. Imani scans the rooms to locate all the scattered pieces of sandpaper. She comes back with the expression eight times seven. Let's use an array again to determine how many pieces of sandpaper Mr. Squeaks has and how he should organize them. But, they will need our help to organize with... This tells us we mark eight rows. The second factor, seven, tells us how many marks to put on each row. Finally, we count each mark to calculate the product. There are fifty-six marks so the product of eight times seven equals fifty-six. Mr. Squeaks can organize his sandpaper in a cabinet with eight rows of seven! Lastly, Mr. Squeaks shows Imani a nail. Iman scans the rooms to locate all the lost nails. She comes up with the expression ten times five. How can we solve this? We can use an array to determine how many nails Mr. Squeaks has and how he should organize them. The first factor in this expression is ten. So how many rows should we draw? We should draw ten rows. What does the second factor tell us? The second factor, five, tells us how many marks to put on each of the ten rows. What is the final step? The final step is to count each mark to calculate the product. How many nails does Mr. Squeaks have? He has fifty nails so the product of ten times five equals fifty. Mr. Squeaks can organize his nails in ten rows of five on a piece of wood! Wow! Mr. Squeaks workshop looks tidy now, thanks to all our hard work! When using arrays with multiplication, remember: Arrays are models of rows(...) and columns that are used to lay out the product of a multiplication problem. To draw an array, look at the first factor in the expression and neatly draw the same number of rows. Then, look at the second factor and neatly put that number of marks on each row. Finally, count the total number of marks drawn... to calculate the product. "Wow, I can see where everything is now!" "Hey, what's this?!" “I was wondering where my giant magnet went!”