The trouble with word problems

It's time to talk about WORD PROBLEMS!

Why is it that many children have such trouble with them?

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Licensed with CC BY-NC-ND 2.0

I've written some thoughts about this issue... I feel it is fairly comprehensive article, and hopefully helpful! Let me know what you think.

Here's the outline of the article:

• The problem
• The solution
• Problems to ponder/solve
• Student's Misguide to Problem Solving
• Resources

And here's the beginning:

The problem

Have you ever noticed this kind of "recipe" for math lessons in many math books?

LESSON X

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Explanation and examples.
Numerical exercises.
A few word problems.

In other words, the word problems are usually in the END of the lesson, and just a few. But worse... if the lesson is about topic X, then the word problems are usually about the topic X too!

Children might be learning about multi-digit multiplication, or subtraction, or dividing decimals. After the calculation exercises come some word problems, which oddly enough are solved by using the exact operation just practiced!

Worse YET... typically the word problems in elementary grades only have TWO numbers in them. So, even if you didn't understand a word in the problem, you might be able to do it. (The misguide to problem solving at the end of this article refers to this also.)

Just try: the following made-up problem is in FINNISH... and let's say it is found within a long division lesson. I assume now that you do NOT know Finnish — but can you solve it?

Kaupan hyllyillä on 873 lakanaa, 9:ää eri väriä. Joka väriä on saman verran. Kuinka monta lakanaa on kussakin värissä?

Continue reading...

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Word problems involving "four times as many as"

Someone asked for help to explain the concepts of multiplicative word problems involving "as many as", like the ones below:

1) Haley had four times as many dollars as her sister. Together they had $60. How much money does Haley have?


2) Rachel had 5 times as many dollars as her sister, Nora. They had a total of $90. How much money did each of them have?

The BAR MODEL is an excellent tool for helping children understand what is going on in these types of word problems.

In (1), draw a bar for Haley and another for her sister. Divide Haley's bar into four parts, and make the other bar just one such part long.

Haley |---|---|---|---|

Sister |---|


Now you will see that the TOTAL needs divided into FIVE equal parts — and from then on it is easy-peasy.

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Additionally, you can use Thinking Blocks website to build such bar models INTERACTIVELY.

For problems like (1) and (2) above, choose the fourth model from the left (rightmost) in the top row that is bluish in color. Then click "Start modeling" button. Video tutorials exist also. This is not my site, but it's a very nice interactive tool for this concept!

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More practice with bar models and problem solving

Someone asked me about the BAR MODELS in the problem solving lessons in Math Mammoth grade 5.

This person said that they had just completed every problem in the lesson Problem Solving with Bar Models 1, but her son is still having a hard time knowing how to make the bar model after reading the problem, and knowing what to do with the fractional part once it is figured out.

She was wondering if there was something else for supplemental practice, and if she should look for mastery in this area at this point.

MY ANSWER:

I feel it would be good to achieve some degree of mastery at this point (in 5th grade). I suggest  using the website Thinking Blocks for additional practice, in particular the "Multiplication and Division" and "Fractions" subsections.



Also, if the problem solving lessons are difficult, consider spreading out the study of these lessons in Math Mammoth by starting the child simultaneously on the next chapter. For example, one could study problem solving every other day, and the next chapter every other day. That way, if it's spread out to a longer period of time, the student's brain has more time to "mull it over". :)

I hope this advice helps the person who asked -- and maybe some of you others out there also!

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Math Stars - for summer math and more

I have used Math Stars problem solving sets with my girls for several years, and they have always greatly enjoyed them.

Math Stars include various puzzles and challenging math problems. They  come as PDF files (free and ready to download & use) in sets for grades 1-8. They're great to use for summer math  or for some fun problem solving at any time.

I tend to use the problems from one grade level below the grade the student is in.

One reason I like these so much is the variety of the problems - geometrical puzzles, number puzzles, logical thinking, etc. --  all of it is included!

Another reason is that the sets go all the way from grade 1 upward. There exist actually lots of problem solving resources but not so many for the early grades.

Each set per grade has 10 two-page "newsletters", and each "newsletter" has 8-10 problems. The number of stars in each problem marks the level of difficulty. Answers are included.

Math Stars Problem Solving Newsletters

I hope you enjoy them as much as we have!

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