Long Division Made Simple!

As a math teacher and homeschooling mom of four, I'm not sure which is more fun to teach: making change, subtraction with borrowing, fractions or long division.  I say this with a sarcastic smile on my face.  So, when beginning the unit on long division with our second grader, I set out to find a way to teach the concept instead of a mindless algorithm.  I came up with the idea to relate division to Legos.  Before I go any further, there are two things I must clarify.  First, I know Legos is not a "real word."  I should technically use the more appropriate term, Lego playing bricks.  Secondly, this lesson has much more to do with division than with "Lego playing bricks."  I was hoping to grab our son's attention by using his absolute favorite topic of conversation.  I know it is a dirty trick, but sometimes necessary! 

Lego Dilemma:
You have been playing Legos all afternoon.  Your mom walks in and wants you to pick up everything, but throws in an added twist.  She places three containers on the floor and ask you to place equal amounts of Legos in each. Lucky you have been counting these Legos and know for a fact there are 763 Lego pieces scattered about the floor.  How many would you place in each container?

Method 1

Drop one Lego at a time into each of the three containers until they are all gone.  This might take a while!  One, two, three...

Method 2:

You have three containers and 763 Lego bricks.  So, you could subtract groups of three until you reach zero.

 

You can see this method works well for small values, but what about our problem? We have only subtracted off 6 groups of three and we have a long way to go!  This will take forever!

Method 3:

Let's think about something new: long division.  It's really not long, just a new way of thinking!

You want to divide 763 by 3.  In other words, you need to determine how many equal groups of three we can make out of 763.

Let's begin by expressing the problem in the traditional way.  We see that our dividend is 763 and our divisor is 3.

We want to first look at the hundreds place.  In the value 763, there are 7 hundreds.  If you were to split those into three equal groups, how many would go into each group?  Think: What number times three makes a number close to seven?

From the diagram, you can see that 2 hundreds would go into each group for a total of 6 hundreds and there would be one left over.  To show this traditionally, you would have:

Now, we are finished with the hundreds place.  We have 1 hundred leftover or 10 tens.  Right? 

This relates back to borrowing when subtracting.  Moving forward!  These 10 tens are now added to the 6 tens that are present.  Very quickly, you can see there are 16 tens.  We now have:

Just as we did previously, we will see how to divide these 16 tens into three equal groups.  Think: How many times will 3 go into 16 or, even better, 3 times what number makes something close to 16?

From the diagram, you can see that five tens can go into each group.  So, 3 will go into 16 five times because five times three is fifteen.  You can easily see there will be one ten left over.  Now, if we continue our division problem, you will have:

 Now that we are finished with the tens place, we must address the ones place.  Our 1 ten breaks down into 10 ones and we add that to the 3 ones already there.  This is illustrated below:

It is easy to see we have 13 ones.

Hang in there!  We're almost finished! Now, we want to see how to split these 13 ones into three equal groups.  Think: What number times three gives a number close to thirteen?

Again, it is easy to see from the diagram that we can split the 13 ones into three equal groups of four with a 1 one leftover.  Unfortunately for this last, little one it is the remainder.  There are no more places to consider and no other place for it to go.  So, our final problem looks like this:

Oftentimes, we write the quotient as 254 R.1 to show there is a remainder of one.

Solution:

Basically, we have discussed three different methods to address the dilemma of how many Legos to place in each of the three containers so there is an equal number in each.  Each method is perfectly correct!  There is no wrong way, just faster ones.  Obviously, Method 3, will provide the quickest answer to the problem.  We see you would need to place 254 Legos in each container and give the one remaining to either your little brother or sister.  Of course, the better solution would be to keep your Legos picked up so your mom doesn't have to put you in this situation.

Moral:

Keep your room clean and math is everywhere!