Long divison is a concept most often misunderstood by children at about age 9 or in the fourth grade. When you see a child struggling with this concept - early intervention is crucial to ensure the child doesn't begin to detest math and to support understanding (which doesn't mean memorizing the sequence of steps to be followed.)
Where we go wrong:
Let's begin with the question 73 divided by 3.
Think about the 'confusing' steps involved in this question:
1. How many times does 3 go into 7?
(It's really not a 7 is it? It's 7 10's which means it's a 70.)
2. Put a 2 on the top.
(Why? Answers previously have been put to the left or on the bottom.)
3. What is 2 x 3?
(Multiply? Isn't this a division question?)
3. Now, put a 6 under the 7 and subtract 6 from 7.
(What? Now the answer goes on the bottom and then subtract?)
3. Bring down the 3.
(Another step to remember that doesn't quite make sense.)
4. How many times does 3 go into 13?
(All this to determine how many times 3 goes into 73?)
5. Put your answer on the top.
(Answers on the top, on the bottom, how does all of this get remembered?)
6. Subtract 12 from 13.
(Subtraction again? But this is a division question!)
The above process is too confusing to a child. They can't remember the steps involved and therefore find long division completely confusion and lacking any sense. Typically, the child says 'what do I do next' because they lack the understanding.
A Better Way to Teach Long Division:
We need to get concrete to ensure that the process is understood. We will need strips for 10's and small squares for 1's. Just like you use buttons or counters for addition and subtraction.
Put the question into an authentic context, something like: " There are 73 pieces of fudge to be shared by 3 people"
Ask the child to 'represent' or build' the number 73. It will look something like this:
|||||||... (7 tens to represent 70 and 3 dots to represent 3)
Now ask the child to physically begin sharing into 3 groups.
1 Group of 10 will be left out which means the group will need to be exchanged for 10 ones. The child now has 13 ones to divide and will see that 1 one is left over which becomes the remainder.
... Remainder of 1
The child then has a complete visual of what 73 divided into 3 groups looks like.
The child counts how many are in a group and states 24 with a remainder of 1.
Why does this work? Because the child has visually seen what it looks like to divide. Many of experiences with this concrete method of dividing will eventually lead them to understand the actual algorithm above and then be able to use it which is exactly how they learned to add and subtract - concretely first!
Therefore here are the steps to master long division:
1. Use tens and ones (strips or base 10 pieces work fine) to model the question and answer.
2. When understanding is evident, move to the written form. Allow the student to use notations beside the division question to show the 10's and 1's, circling the groups as they perform .
Try some with this pdf.
An excellent collection of PDF ready to use worksheets for fractions, addition, subtraction, algebra and much more.
Great trick to help with quick division.