Teaching for Understanding: Vocabulary for Long Division

Why should you take time to teach math vocabulary, 

when you are having a hard time just

 completing the provided math lesson each day?

I've been tutoring a 4th Grader, and the directions on her assigned page were:

Divide with Remainders

"The remainder must be less than the divisor. 

If it is not, increase the quotient."

OR

Multiply to check division. Add the remainder.

She was absolutely at a total loss about what they were asking her to do.  What is a remainder, divisor, dividend, or quotient? I think she understood it as much as you would if I asked you to complete a problem in which you divided polynomials like this:

One of things we can do is to stop saying, "What is the number we are dividing," and change that to "What is the dividend in this problem?"  As teachers are we always using the correct vocabulary while teaching a concept?  I know we don't say dividend because we are afraid that our students won't know what we are asking. 

How about taping a temporary place-card on each students desk while teaching this unit like this:

Next to each vocabulary word, have the student write their own student-friendly definition to each word.

 Here are some examples of what they might write:

Dividend- Number to be divided into equal groups
Divisor- Number of equal groups
Quotient- Number in each group. The answer to a division problem
Remainder- Number remaining or left over

Here's another idea.  While lining up for lunch, ask your group if we were dividing the group into groups of three, what number would we be dividing ? Yes, ___ would be our dividend.

What number would we write down as our divisor?

Then have the line, move slightly, to group into 3's (while still staying in line).

What is our quotient? (Count each group out loud..1,2,3...)

Did we have any remainders? (Count out loud...)

In the following days, divide the line into 2's, 4's, 12's...

Ask those same questions using the correct math vocabulary.  

Why will this help?  Well, it's almost like they are a "living division problem," and it's a very concrete example of the vocabulary. 

Give it a try, an let me know how it worked for you in the comment section of this blog.

Smiles,

Deborah

P.S. If you are teaching a split 3/4 Grade Class, they ALL need this exposure to the vocabulary of division.