Arrays of Multiplication

Mr. Squeaks' workshop has got rather messy from all of his recent projects. It's time for him to organise his materials so that he knows where everything is. Luckily, Imani has volunteered to help him. Imani can scan the room to locate the scattered items and represent the amount with a multiplication expression. But, they will need our help to organise 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, you might use crosses, dots or circles. Let's try this out with the example two times three. To start, look at the first number in the equation. 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 number 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 spanner. Imani scans the room to locate all of the scattered spanners. They come back with the expression three times six. Let's use an array to determine how many spanners Mr. Squeaks has and how he should organise them. The first number in this expression is three. This tells us to draw three rows. The second number, six, tells us how many crosses to put on each row. Finally, we count each cross to calculate the product. There are eighteen crosses, so the product of three times six equals eighteen. Mr. Squeaks can hang all of his spanners in three rows of six! Secondly, Mr. Squeaks holds up a piece of sandpaper. Imani scans the room to locate all of the scattered pieces of sandpaper. They come 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 organise them. The first number in this expression is eight. This tells us we need to draw eight rows. The second number, seven, tells us how many crosses to put on each row. Finally, we count each cross to calculate the product. There are fifty-six crosses so the product of eight times seven equals fifty-six. Mr. Squeaks can organise his sandpaper in a cabinet with eight rows of seven! Lastly, Mr. Squeaks shows Imani a nail. Imani scans the rooms to locate all of the lost nails and 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 organise them. What is the first number in the expression? The first number in this expression is ten. So how many rows should we draw? We should draw ten rows. What does the second number tell us? The second number, five, tells us how many crosses to put on each of the ten rows. What is the final step? The final step is to count each cross 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 organise his nails in ten rows of five on a piece of wood! Wow! Mr. Squeaks' workshop looks tidy now, thanks to all of 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 number in the expression and neatly draw the same number of rows. Then, look at the second number 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!”