Solving Multiplication and Division Word Problems

Are your students having difficulty with solving multiplication and division word problems? Do they find it difficult to think critically or deeper about the word problems? Is it a struggle for them to determine whether they should multiply or divide? If so, all they need is a little K.N.O.S (sounds like nose)!

This is a method I have used for the past three years and I must say it really helps my students think and break down the problems. It's an easy four step method that allows students to read the problem and understand what they know, need to know, determine the operation and solve.

K. N. O. S.

(KNOW, NEED TO KNOW, OPERATION, SOLVE)

The first step of this critical thinking method is called KNOW! What does the student know of the problem? At this point, the student should determine the important information that is given and write it out. Have them write what they know first under the word problem.

Once they have the KNOW, have students to write out what they NEED TO KNOW. This will always be the question. This is what they are looking for and what they need to constantly remember when solving the problem.

Now once the KNOW and NEED TO KNOW are determined, figure out what OPERATION should be used in order to solve. Here is where students stop to process the information and where certain terms should begin to be used.

Students should consider:

• What is given in the know? Factor and factor? Rows and Column? Groups and Group Size? If any of these, then clearly we are multiplying.
• Maybe it's none of the above. Maybe it's Product and Rows? Or product and columns? Product and groups? Products and group size, maybe? Then we are dividing.

You may be thinking, why not use the terms dividend, divisor and quotient? Those terms can easily be integrated into this method when working with division, only! But I want students to also relate the multiplication terms to the division sentence. Now it would be pretty difficult trying to incorporate the division terms and relate them to a multiplication equation. For instance, what if a student had the following problem:

       Jamie has 5 boxes. He places 4 apples in each box. How many apples does he have total? 

Would you ask students what's the divisor, quotient or dividend in this product? I think not...at least I hope not. That's why the terms groups, group size, rows, columns and product works. It may seem like a lot but it honestly works. It will take your students a while to catch on, but when they get it you'll be excited!

After the KNOW, NEED TO KNOW and OPERATION is determined, students will now be able to SOLVE.
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Let's use the steps to solve the following problem: Carlisle has 10 apples. The apples are placed into 5 baskets equally. How many apples are in each basket?

Now some students will look at this problem and say they should multiply. Some may look at the problem and say they should divide. Some will simply just say they honestly don't know! Grab those students quick and work with them on this method to start breaking down the problems.

So, we KNOW there are 10 apples (that's all we have and no more apples will be given to us). We also know there are 5 baskets that the apples were separated into equally. We NEED TO KNOW how many apples are in each basket? (Make sure students understand what they need to know)

KNOW: So, we know 10 apples are being placed into 5 baskets equally. In other words we only have 10 apples total and these apples are being separated into 5 baskets. The 10 apples must be like our product and since they are being placed into baskets these must be like our groups.

NEED TO KNOW: How many apples are in each basket? Since we have our product and our groups, we must be looking for our group size! If there will be a certain number of apples in each group, that's the group size!

OPERATION: Well, if we have the product and the groups and know that we are looking for the group size, then clearly we have to divide.

SOLVE: Now we can solve the problem (here use algorithms or pictures to help solve the problem). 10/5 = 2

This all may seem very confusing, but trust me once your students get this into practice and it becomes a constant method for them, you will see a difference in their problem solving/critical thinking skills. I've had retired teachers and even related arts teachers begin to use it or feel stunned by the way it's broken down. But if you still find this to be a little complicated, just leave your comment(s) or email below and I'll explain further.

Thanks for stopping by and Happy Teaching!