Exploring word problems

I enjoy solving word problems.  I think they can be quite fun, actually. As a child, as a teacher, as a parent, I have always found it stimulating to read a story, identify the problem, and look for critical information that would help me solve it. Sherlock Holmes, looking for clues, solving the mystery, here I come.

And I hope to pass this on to my children: the joyfulness of problem solving.

You can find thousands of word problems on the internet, by grade level, by operations. Often, however, I just made them up, based on Rosie’s interests and competence. But for any word problem, we always take the time to discuss

  1. what the problem is,
  2. how it can be solved.

We usually go through 5 different steps (one step / finger, Pinky comes last and bring the solution), that Rosie enjoys and that I have found helpful to lead the discussion. Here is, as an example, a problem that I did recently with Rosie. I know, it is very simple, but I did it on purpose: it gave us a chance to focus our effort on how to solve a problem, rather than on the solution. We will work on more complicated tasks later, throughout Summer. I also hope this simple problem, and Rosie’s representation hereafter, helps you see the steps, so that you can use them on word problems you may do at home with your child. Even at a upper level.

Rosie has an aquarium, with 1 very lonely fish. For her birthday, Rosie receives 2 more fish. How many fish does Rosie have?

Step 1 – Read the problem. Thoroughly. Sometimes Rosie reads the problem, sometimes I do. In the present example, I did it, as I did not want her to get frustrated over a word like aquarium. We look for relevant information in the text (e.g. the fact that there is 1 fish in the aquarium is relevant to solve the problem, the fact that he is lonely is not). Then, Rosie has to retell the problem on her own.

Step 2 – Represent the problem. Sometimes, we draw a picture. Sometimes, we use manipulative, such as Legos or buttons. Often, we do both. And we add the numbers from the text to our visual representation.

Step 3 – Discuss the strategy to solve the problem. What should we do next? Which kind of operation are you going to do? (e.g. ” I am going to add the 2 fish I had for my birthday to the lonely fish”). Step 3 is sometimes done with step 2, but still, I always ask Rosie to explain, using her own words, her strategy.

Step 4 – Solve the problem. And when we write the equation, we connect each part of the equation, to the visual representation (with a code of color, for instance, see picture hereafter).

Step 5 – Answer the problem i.e. write/say a complete sentence answering the question that was asked in the problem. “Rosie has 3 fish in her aquarium” is an answer. “3” is not.

Fish problem

Representation of the problem “Rosie has an aquarium, with 1 very lonely fish. For her birthday, Rosie receives 2 more fish. How many fish does Rosie have?”

I do not know what your experience is with solving word problems. Your child may be unfamiliar with, or even reluctant to, explaining his/her answer. If so, you may want to start with just asking him/her to represent the problem with 2 different ways (i.e the equation and something else such as, depending the grade level, drawing a picture, a chart, tally bars, using manipulative, etc, anything that could motivate your child).

I always seek for opportunities to help Rosie build up strong math foundation and strength her logical thinking, and word problems are a great way to do so. Have fun solving problems !


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