Arrays, Coins, and Division

What is an array?

What is an array?

An array is a rectangular picture of objects or shapes that are put together in rows and columns to show a multiplication problem.

How can we use an array to solve a multiplication probelm?

If we take a look at the image above, we will see a picture of a group of trees and a picture of a group of clouds. We could count the group of trees or the group of clouds one by one to find out how many there are in each group. Another strategy we could use is skip counting by 2s to figure out how many are in each group.

A strategy we are going to learn about today is multiplying. Multiplying means to add more than once. Taking the example of the clouds, we could say 2 clouds + 2 clouds + 2 clouds makes 6 clouds total. However, if we use multiplication we can do this in a much faster way. We count how many rows there are (3) and how many columns there are (2) and multipliy. 3 X 2 is 6 because 2 + 2 + 2 is 6. Instead of adding 2 three times, we did the math quicker by multiplying and finding out that 3 x 2 = 6.


Take this image of pennies. To find out how many pennies there are in the picture, we could count each penny one by one. But if we notice, the pennies are set up in a rectangular array pattern. In this case, we can count how many rows and columns there are to find the total amount of pennies. There are 3 rows and 4 columns. We now put it together in the form of a multiplication problem. 3 X 4 = 12 so there must be 12 pennies total. If we didn't know how much 3 x 4 was we could skip count the rows. There are 4 penneis in each row so we can count 4 (first row), 8 (second row) and 12 (last row) so there must be 12 pennies total.

What is Division?

Division is repeated subtraction. It is the opposite of multiplication and addition. Instead of adding more, we are taking away. To find out what 9 divided by 3 is, instead of saying 9-3=6 and continuing from there, We can say 9 divided by 3 is 3. It's a much faster way to do repeated subtraction.
Take the coin example from before. If we have 12 pennies and we wanted to know what 12 divided by 4 was all we have to do is circle each group of 4 and count how many groups we have. If we have 12 pennies and we create equal groups of 4, we learn that 12 divided by 4 is 3 because there are 3 groups of 4.
For homework, I would like you to complete the worksheet using the link listed above. Please print the worksheet, bring it to class tomorrow, and we will go over it.