Keeping the Meaning in Mathematics: The Craft of Word Problems

CONTENTS OF CURRICULUM UNIT 07.06.04

  1. Unit Guide
  1. Introduction
  2. Objective
  3. Vocabulary
  4. Problem Types
  5. Picture Books
  6. Conclusion
  7. Lesson Plans
  8. Resources
  9. Appendix A
  10. Appendix B
  11. Appendix C
  12. Appendix D
  13. Appendix E

Word Problems in Picture Books: Literature as a Source of Math Word Problems

Karlene E. McGowen

Published September 2007

Tools for this Unit:

Objective

This curriculum unit will look at math word problems from a language arts point of view. I believe many times students are able to do the math computation but get stumped by the wording in the problem. If I can show them how to read the problem the same way they might read a novel or a non-fiction passage, then I believe they will have greater success at solving the word problem correctly.

The unit is divided into two sections; however these two sections are designed to be used together. The first section involves the use of math picture books. There are many books on the market today that tell a story and use math as the unifying theme. Refer to the Resources list at the end of this document for recommended picture books. I look at these picture story books as one giant word problem. By beginning with these books we can show the students that a word problem is simply a story that involves math. They are very familiar with picture books, so the idea of one that incorporates math is not a big leap for them. The unit will begin by incorporating these stories into the Language Arts curriculum. It seems natural to start in the Language Arts classroom because this is where literature lives and thrives. If the goal is for the Language Arts teachers and the Math teachers to work together, then we have to become somewhat comfortable with the curriculum in each subject. Math teachers will need to use these books in the classroom and read-aloud to the students just like the Language Arts teachers.

The Language Arts teachers would introduce a math picture book into the lesson. It can be done in a variety of ways, the simplest of which is just to perform a read-aloud of the book. This will get the students familiar with the story line. From this point the Language Arts teacher can continue with the math aspect of the lesson or turn it over to the Math teacher. Whoever takes it on will be leading a discussion on various types of word problems that are found within the text itself. This discussion and the subsequent independent or group practice will stem from additional word problems that are created based on the story characters or situation but not necessarily on the actual events of the story. This is further explained with examples in the Picture Books section of this unit. This concludes the overview of the first section.

The second section of the unit involves again the collaboration of efforts between the Language Arts teachers and the Math teachers. We will call it Word Problem(s) of the Week. The students will receive a word problem or several problems on Monday or day one. The students will take the problem(s) to the Reading teacher and they will look at it from a reader's point of view: reading the problem twice, highlighting the important information, crossing out unnecessary information, and underlining the key words that tell the operation to be used. A simple five minute lesson is all that is needed. The teacher shouldn't feel that this plan cuts deeply into their own curriculum. However, the idea of reading a passage and interpreting important information is a reading skill that is part of the curriculum already. So really it is not a deviation from the set curriculum. The next day the students would take the same problem to the English teacher and they would rewrite the problem in their own words. They will also state the question that the problem is asking. On the third day they would take the same paper which now has been looked at twice with the Language Arts teachers and take it to the Math teacher. At this time the Math teacher would help them develop a plan for solving the problem and estimate a reasonable answer for the problem. On the final day the students would take the problem again to the Math teacher and would set up the calculations of the problem, draw a diagram if necessary, solve the problem and finally check the answer to be sure it is reasonable or correct. This plan can be adjusted to fit the schedule of your school, as in it doesn't have to be a four day process. Note however, that each step in that process is relatively quick. When you do give such problems, rather than simply give one problem, another strategy might be to give a collection of problems, with various settings, and ask students to classify them according to the operation(s) required to solve them. Appendix E at the end of this document indicates the format of a worksheet to be used for this Word Problem(s) of the Week operation.

In merging these two sections, it would be ideal to use the word problems created specifically for the picture books as problems of the week. This can span as much time or as many weeks as necessary. After the picture book word problems are exhausted, word problems pulled from the released state test could be used, especially if they are grouped together by topic. In addition, word problems pertaining to the unit of study currently being practiced could be used as well. It can be adapted to fit all types of word problems from any grade.

In our school we have been exploring ways to help the math standardized test scores increase. I believe this unit will help this increase to happen. An easy way to implement this curriculum unit is to incorporate the reading and writing of the problem into a short warm up lesson for two days a week. It will become part of the daily lessons we do as Language Arts teachers. Eventually the students will no longer need to use this format. After enough practice the students should be able to read, write and solve on their own. It is not necessary to consider that this collaborative and extensive process is required throughout the school year. Hopefully students will begin to read and understand the problems naturally. They will begin to think both linguistically and mathematically.

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