Division Strategies

Division Strategies – We will begin learning about division this week.  Division is when you take a whole, big group of objects and break them into smaller, equal-size groups.  We will start by learning about some important strategies we can use when we want to divide.

Number of Equal Groups – When dividing, one strategy is to take the whole group and break it into smaller equal-size groups.  Then, you can count how many groups you made.

For example, if you want to solve the problem 24 / 6 you could make groups of 6 until you get to 24 and count how many groups you made:

XXXXXX          XXXXXX               XXXXXX                  XXXXXX

In this example, I have made groups of 6 and there are 24 X's in all.  When I count how many groups I have made, I count 4 groups.  So, 24 / 6 = 4.

Size of Equal Groups – A second strategy is to make your groups first, then share the whole group of objects into the smaller groups so that each group has the same amount of objects.  Then, you can count how many objects are in each group.

In this strategy, you will make a number of equal groups and share the objects into each group.  Then, you will count how many objects are in each group.  So, if you want to solve 24 / 6, you would make 6 groups and share the 24 objects equally into each group:

XXXX     XXXX      XXXX       XXXX      XXXX      XXXX

In this example, I have made 6 groups and shared the 24 objects equally into each group.  When I count how many are in each group, I find that there are 4 in each group.  So 24 / 6 = 4.

Here's a video about division and equal groups:

Repeated Subtraction – In multiplication, we learned that we could use repeated addition to solve multiplication problems.  In the same way, you can use repeated subtraction to solve division problems.  You can start with the total number and keep subtracting the same number until you have 0 objects left.  Then, you can count how many times you subtracted.

In repeated subtraction, you just keep subtracting the smaller number from the larger number until you have 0.  Then, you count how many times you subtracted.  So, if you want to solve 24 / 6 you would start with 24 and keep subtracting 6 until there are 0 left:

24 - 6 = 18
18 - 6 = 12
12 - 6 = 6
6 - 6 = 0

In this example, I subtracted 6 each time until there were 0 left.  When I count how many times I subtracted, I find that I subtracted 4 times.  So, 24 / 6 = 4.

Here's a short video that shows repeated subtraction:

Arrays – We learned about arrays in multiplication.  You can also use arrays when dividing.  When dividing, you take the whole number of squares or circles and you can either make a number of rows with the same amount in each row, or you can make rows with a  certain number in each row and keep making rows until there are none left.

When you make an array for division, you start with the whole group of objects and either fill in by rows or by columns.  So, if you want to solve 24 / 6:

These are my 24 objects:

XXXXXXXXXXXXXXXXXXXXXXXX

Now, I can make an array in two different ways.  First, I can make rows of 6 until I have 24:

XXXXXX
XXXXXX
XXXXXX
XXXXXX

Then, you count how many rows you made.  In this case, I made 4 rows so 24 / 6 = 4.

Second, I can make 6 rows and fill them in until I have 24 in all:

XXXX
XXXX
XXXX
XXXX
XXXX
XXXX

Then, you count how many are in each row.  In this case, there are 4 in each row, so 24 / 6 = 4.

Multiplication – If you know your multiplication facts (keep studying them!), you can use your multiplication facts to help you figure out division facts.

In this strategy, you can use your multiplication facts to solve division problems.  So, if you want to solve 24 / 6:

24 / 6 =           

When I look at 24 / 6, I see the numbers 24 and 6.  When I think about my multiplication facts, I know a fact that has 24 and 6 in it.  The multiplication fact is 6 X 4 = 24.  The three numbers in that fact are 6, 4, and 24.  When I go back to the division fact 24 / 6, I see that it has the numbers 24 and 6.  It is missing the 4.  So, 24 / 6 = 4.

Here's a short video about using multiplication and division facts: