Taming Word Problems
Written by Merak Aldebaran
(Muggle name - Bill Byles)
Last updated 1/1/2012
Young Newt Dumblesnitch, a Gryffindor house mate of Harry Potter is in danger. He has stumbled into a pit of words. Not just any words, mind you, these are the dreaded problema words, known by their Muggle name as Word Problems. Newt is struggling to remember the spell that will tame these problema words, turning them into regular numbers and operators. With a flick of his wand, sparks fly as Newt chants, "Numeris Arrangum!"' Newt looks around him, the dreaded problema words have been transformed! 'Why, this is easy!í thinks Newt, ' As easy as adding two plus Ö' Realizing that you are watching Newt stops and hands you the wand. Itís your turn to tame the problema words.
First - You will prepare a list of terms to use in decoding word problems. A worksheet will be available.
Second - You will use your list of terms to decode several practice problems found on-line.
Third - When you feel you have mastered the art of decoding word problems, you will take an online assessment.
Fourth - (part one) Using your list of code words, write two word problems appropriate for your grade level. Each problem is to be accompanied by a step by step explanation of how to "tame" the word problem.
Fourth - (part two) Last of all, write two word problems appropriate for students three years below your grade level. Include a step by step explanation with each problem. If your teacher can work out the details, you should present these problems to a class three years below your grade level.
Before you begin your Quest to learn the spell to tame word problems, you must discover who you are. No, I know you know your Muggle name, you must discover your Wizard name. Go stand in line for the Wizard Name Generator to discover your Wizard name. The line starts here. After you write down your Wizard name close the Wizard Name Generator window to return to the Quest.
To Complete Task One - Next, get a worksheet from your teacher, or download a copy of the worksheet to print. Put your Muggle name, Wizard name and Hogwarts house on the bottom of the worksheet before you begin your Quest to decode word problems. Visit the web pages listed below to collect terms to help you decode word problems.
- Visual Thesaurus has a list of key words to unlock math problems
- Purple Math has a list of keywords found in word problems
- Class Brain has a Word Problem Hint Sheet that you could print and keep with you while working on word problems [this is a .pdf sheet]
- Now, use your own Wizard brain. Look at your list of terms for addition, subtraction, multiplication, division and equals. What other words can you add to the list? Write down the words and keep your decoding worksheet with you as you continue the Quest.
To Complete Task Two - With your decoding list (your magic wand) firmly in hand, it's time to practice taming some of those problema words. Harry, Hermione, and Ron have a problem that they need your help with. When you read the problem, look at your decoding list to see if you can put the word problem in mathematical form before looking at the explanation. Don't spend too much time on the decoding, after all you are just learning how to use your magic wand (the decoding list). Next read what the Math Forum Wizards have to say about how to solve this problem. When you are finished, close that window to return to the Quest.
After helping Harry, Hermione, and Ron, it's time to do some more practice. Visit each of the web pages listed below, in the order that they are listed, and record how well you do on the check sheet. (Get a copy of the check sheet from your teacher, or download a copy to print.)
- The Parade of Legs - This is a good one to start with since it says it is for elementary students.
- The Banana Problem - This fraction problem is another good one to start with (if you can get your attention off that swinging monkey).
- Translating Word Problems - Work with a partner on this one. One person should read the words in green and the other should try to write a math statement. Swap back and forth, each of you reading two statements for the other before changing. After completing this exercise, try the age problem at Purple Math.
- Using Equations to Solve Puzzles - There are three word problems to solve on this Lesson Tutor page. Scroll halfway down the page and use your skills to solve all three of the problems; Bob and Sue picking apples, little boy eating grapes, the tree height.
To Complete Task Three - First, take the ten-question equation and word problem quiz which is posted on Quia. Each question that you get right is worth ten points. Some of the questions are about how you work with equations and others test the skill of decoding word problems. Then, take the seven-question word problem practice quiz which is also posted on Quia. Caution, this one is tough! Record your results for each quiz on the check sheet you started as part of completing Task Two.
To Complete Task Four (part one and part two) - By this point you should be more proficient at decoding word problems. The ultimate test of that will be how well you can write word problems, and how well you can explain what steps other students should take in solving your problems. Worksheets are available to submit your word problems to Professor Dumbeldore, or your teacher, whomever you find first. Get the worksheets from your teacher, or download a copy to print; (1) worksheet for your grade level, (2) worksheet for earlier grade level.
One thing must always be kept in mind when writing mathematical problems, they must be appropriate. Of course they must use appropriate vocabulary, but they also must test appropriate grade level skills. In your schooling you have not had to think about what is appropriate, the Professors have done that for you. Now you are taking on the role of a Professor and it's time to think about what is appropriate for your grades.
To see a listing of math topics by the grade levels in which they are taught (in Tennessee) take a look at the math standards for your grade, or any earlier grade; kindergarten, first grade, second grade, third grade, fourth grade, fifth grade, sixth grade, seventh grade, eighth grade. If you are a high school student using this quest you can find high school math standards at the following; Foundations of Math, Algebra I, Algebra II. As you scroll down any of these pages, take a look at the subjects listed in the column on the left side of any of the pages. You will see the kinds of things that students need to know for their specific grade. Use this same list of grades when you begin working on the word problems for earlier grades and select the grade three years earlier than your grade.
(ordinary wizard level)
(ready to teach)
How complete is your decoding list?
words from only one of the sites are listed on the student's decoding sheet most of the words from the three sites are included, however no original words are included all of the words from the three sites are included and the student added one original word in one category all of the words from the three sites are included and the student included at least one original word in each of the five categories How well did you do on the practice problems?
7 to 9 points on the seven practice problems 10 to 13 points on the seven practice problems 14 to 17 points on the seven practice problems 18 to 21 points on the seven practice problems How well did you do on the two on-line quizzes?
0 to 4 correct answers 5 to 10 correct answers 11 to 15 correct answers 16 to 17 correct answers How many original word problems did you write?
none or one two three four How well did you explain how to solve your word problems?
unclear, a person would need to be a Hogwarts professor to understand Not very clear, one would need to be an ordinary wizard to understand well enough that a fellow student could follow the instructions so well that even a muggle could understand Are the required math skills appropriate for the grade level you wrote them for?
(Implied in task four)
none of the problems were appropriate for the level they were written for, or none were written one of the word problems tested math skills appropriate for the grade level only two or three of the word problems were testing math skills appropriate for the grade level the specific math skills were listed in the grade level for which all four problems were written
Life is full of scare words. For many people the mention of "word problems" causes their thinking ability to diminish or shut down. The purpose of this Quest was to give you confidence that you can handle those dreaded problema words. The reason that this is important is that life is also full of word problems. Adults run into them all of the time. Some, those who have not developed the confidence I hope you now feel, will run to someone else for help when those problems come up. Perhaps you will be one of the ones that they run to for help.
Oh, by the way, Newt Dumblesnitch wants his magic wand back!
If you can make the arrangements, give your students the opportunity to present their word problems to a class three grades below them. This step allows the students to become teachers and will force them to think clearly about how to explain the process to someone. From your own experience, you know that when a person must teach a concept, they learn that concept at a much deeper level than surface understanding.