Which operation should you use in word problems?

I was asked just recently about word problems and WHAT operation to use in them.
Can you put a better explanation of when to use addition, subtraction, multiplication, and division, because my son is having a hard time understanding.

Many children have the same problem, and I have written about it in the past as well. In a nutshell, I feel the MAIN reason students have trouble is the way word problems are presented (or not presented) in math books.

Typically (and I still see this approach), when a lesson in a math book is on some operation, then the word problems in that lesson are typically solved using that particular operation. So, any intelligent kid who notices this pattern won't take time to decipher what the problem says, but will just take the two numbers that appear in the problem, and apply the operation that the lesson is about!

(For example, if the lesson is on subtraction, then the word problems are solved using subtraction.)

I have tried to AVOID this in my books from the start, and I think all other math curricula should follow suit, that whenever there are word problems to solve, that the operation or operations used to solve it SHOULD vary within the problem set.

Even in first grade addition, you can make two kinds of problems:

"Ann had seven marbles, and Mary had two. How many marbles do they have together?" SOLUTION: 7 + 2 = 9


"Ann has seven marbles, but today she only found two. How many are missing?" SOLUTION: Think 2 + ___ = 7, or two and how many more makes seven?

So, starting in 1st grade, the word problems should never be such that they always involve the same operation. Then in 2nd grade, the word problems should proceed to easy 2-step problems.

When multiplication is introduced in 3rd grade, the word problems should be in two different ways so the child cannot automatically multiply the numbers in the problem, but has to think. For example:

Mary saw 12 duck legs. How many ducks were there?


Grandma has 12 ducks, and each wore two blue ribbons. How many ribbons could you see when looking at all the ducks?

Now, recently I had an idea for help for all these elementary students that have trouble figuring out which operation to use. I THINK it might work fairly well, but I'd like to have your input on it.

Suppose we have a student in 3rd or 4th grade who can't do word problems. What if we used the word problems in Ray's Arithmetic with him/her, starting from the beginning?

Ray's is known to be full of word problems, starting from the simplest. It sort of uses word problems to teach arithmetic. It is an old book, and therefore it is available FREE online. See the links on the left for viewing it online or downloading.

See for example the word problems on page 26.

You can also purchase Ray's as printed books.

What do you think? Could Ray's get such students up to speed with word problems?


Denise said…
One thing I did with my older kids when they were little was to have them diagram the problem (using bar diagrams), but they didn't have to solve it. We went through a whole book of Singapore Math word problems that way, but Ray's would probably work as well. The main thing was to make them think about how the numbers were related, because (imo) that's the most important step in understanding a problem.

The kids felt like they were getting off easy, not having to do the calculations. I thought they were getting lots of practice on thinking skills. We were both happy!
Kris Murphy said…
Children do have problems with word problems, don't they?

Having been educated in Singapore and later in Canada, I was pleasantly surprised to learn that Singapore math is now very popular. When I checked the Singapore math textbooks out of curiosity, I realized that the Singapore bar diagram method really helps kids visualize the word problems.

Since then, I have become a fan of Singapore math. In fact, I am teaching my twins Singapore math and they absolutely love it.

The problem with Singapore math is that there are no websites providing free Singapore math questions. To remedy that, my wife, who is an accountant, and I decided to create a free educational website for parents, teacher and kids. Living in Singapore, we have access to lots of math textbooks and workbooks. Using them as our guide, we have created thousands of questions for you. They are crazy, mindboggling and fun. Here is an example of the kind of questions we have in our website:

Fun Singapore 1st Grade Math

We have worksheets for the other grades too. Try them. And may your kids grow up to love math!
gg said…
Maria I love your blog! Many of the principles of elementary school math show up on tests like the GRE and GMAT, which are exams to get into graduate school. Great explanations.
Anonymous said…
Would'nt it be easier to teach 7-2 = 5 rather than 5+ __ = 7

Charul Patel
Maria Miller said…
I feel children do need to learn to think of missing addition problems, such as 2+ ___ = 7. They can learn to SOLVE them using subtraction, of course (or addition, whichever is easier in a particular instance).

For example, if you have $8 but you need $15, it fits better if you think of it as $8 + ___= $15. It is a situation where you want more, you want to ADD some more dollars to your wallet. Also this ties in with algebra!

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