Algebra/word problems

He should be on her caseload if he has language issues and CAPD…she could work with him, teaching him the vocabulary and the process he needs to use to solve the word problems.. EPS has a series that teachs the concepts behind word problems…what to eliminate what to keep, it is called It’s elementary…however, it isn’t at the algebraic level..but he may need to build up from the bottom and work up…and It’s Elementary may help you teach him….

That may be what he needs since this is his first year in a non-LD math class. He does not have an SLP because they felt he needed to be in the classroom and not pulled out. He does not receive remediation type services for anything but reading. Thank you for the information Patti I will check this program out since he has difficulty with all word problems.

Algebra is reasoning. Once the basic of the operations are acquired then the word problems you refer to will be the majority of the curriculum. That is its nature. Having your son disassemble the problem into parts is a start. Using the 4-step problem solving approach is also useful. If he is going to be successful in the rest of the Algebra, he is going to have to develop a strategy. You might start by making copies of the text pages and highlighting the data in the problem and the question. (he should be the one doing this). This is not going to go away - it is just the beginning and a strategy is what he needs.

John and Suzi have 15 apples. If 8 of the apples belong to Suzi, how many belong to John?

Would you call this an algebra word problem?

J + S = 15

S = 8

J + 8 = 15

J + 8 - 8 = 15 -8

J = 7

I’d like it better if it said John and Suzie have 24 apples, John has twice as many as Suzie - How many does each one have? Variables are important in Algebra. The problem you listed would be a pre-pre-algebra activity.
Solution: Suzie has 8, John has 16

S + 2S = 24
3S = 24
3S/3 = 24/3
S = 8
2 x 8 = 16

I’m not sure I understood the point of your question. This type of work not only requires reading skills, deductive reasoning, but a strong logic base. Relationships need to be understood. Too many people think that Algebra is just even out equations - it is everyday thinking. (not only am I SPED master but also Math)

I keep hearing this one over and over — and I keep hearing the same dead-end quick fix suggestions over and over too. So please excuse me if I sometimes sound frustrated!!

I am a math major, was in grad school math and part-time college math teaching until a thyroid problem floored me. So yes, I have done this before and this is from a long-term perspective, what actually succeeds to get you out of high school and through college.

Samantha is right that you need a strategy. Thanks.

One thing she did not mention is so-called “key words”. Some people will tell you that this is the solution. In general, they are *wrong*. This strategy will get you a bare pass, maybe, inthe first course, and leave you lost and floundering next year, with no foundation to fall back on — a bad dead end.

She is also right that so-called “word problems” are it. This is what math is all about.
I keep asking people two questions:
When was the last time you were in a business and people were running around frantically trying to fill in the answers on worksheets? Never, because worksheets aren’t what what you do in the real world; you solve real problems.
And how are problems in the real world going to be presented to you? In cartoons? No, in the real world people come up to you and explain problems in words. Or they send memos and explain problems in written words — like what you just did posting here, right?
So the phrase “word problems” is completely redundant. It’s like saying “water swimming”. What else are you going to do?

This isn’t to say that it is always easy —it isn’t. But it’s the core and purpose of the program, what you are there to learn, so it is worth taking a lot of time and effort over.

Samantha suggests the “four-step” problem-solving approach. That’s OK, but I find it sometimes not clear enough. Working with my tutoring students, I’ve come up with seven steps:

(1) *Summarize*
What facts are you given? List them in note form, in words.
What *exactly* are you asked to find? Note it down.
(2) *Visualize*
Draw a diagram
Draw a chart
Draw a graph
Make a table of values — experiment with different values and see what patterns you get
(3) *Relate*
Do you know any formulas, like d = rt? A(circle) = pi r squared? and so on?
Are you *given* any relationships, like John’s age = twice Sue’s age?
Can you *see* any relationships from your diagrams?
Did you *find* any relationships when you charted values? What system did you use to calculate values?
Do you *recognize* a familiar problem pattern that may be in an example in your text or notes?
(4) *Name*
Give SPECIFIC names to your variables. WRITE the expression “Let …”
Good: Let J = John’s age
NOT J = John (might be his weight, his height, his grade on SAT’s . . )
** Why this is a problem: the classic “mixture problem” where you mix say chlorine and water to purify, or peanuts and cashews to sell a mix; there is the *quantity* c = gallons of chlorine bleach, and then there is the *value* 0.25c = amount of pure chloride in the bleach; p = pounds or *quantity* of peanuts, but 3p = *value* of peanuts @ $3.00 a pound. You have to be absolutely clear what your variable means, or else you will have confusion coming back to bite you later.
(5) *Equation*
DO NOT write an equation without doing the first four steps. In a simple problem they may take one minute and three lines, but DO them. When you hit the hard stuff, you need the skills you were supposed to be developing while you did the easier stuff; if you skip the learning process on the practice problems, you will find out. The hard way.
With the relationships and word equations from (4) and the variables from (5), the equations should most of the time jump out at you. With a little practice, they seem fast and easy. The important point is to work through the *process* so that it *does* become easy.
(6) *Solve*
Use proper algebra techniques; don’t guess and don’t skip steps.
Sometimes in the value-charting method the correct answer falls in your lap; tha’s OK if it happens, but do the algebra anyway. The next time the answerr may not fall in your lap, and you’re here to learn the *method*. Also many problems have two or more answers, and you may get a surprise.
(7) *Check*
Any real algebra problem involves enough steps that anyone can slip up. *Everyone* makes mistakes; good mathematicians are the ones who have learned to fix them.
Check in your *first* equation, and go back and see if your answer *makes sense* in the real situation of the *original* problem. Reality check is fundamental.

At first this looks really long; it isn’t, I swear. Doing this, I can solve any high school/junior college problem as fast as I can write it. From Algebra 1 to Calculus 3, this method breaks any problem.
All the other people trying to “save time” are staring at a blank paper with blood coming out of their foreheads. Or scribbling and erasing and scribbling again. Or getting grades of F because their work was certainly fast, but it was wrong.
I strongly encourage students to *write*. For some reason, elementary teachers (most of whom became elementary teachers because they did *not* want to take math classes beyond the minimum) have the peculiar idea tha writing math down is bad and that the ideal would be to get the answer by divine inspiration and write it down in solitary splendour. This is the opposite of what real mathematicians do; real mathematicians (and scientists and engineers and technical workers) write everything down so they can keep track of all the details and check back for errors, same as any other responsible adult. Get your student to *write* the summary, *draw* the visualization, *write* the word equations for the relationships, *write* the variable naming, *write* the equations and the steps in the solution, and *write* the check (a few lines, but saves 10 to 20% on your grade).
I also have a campaign against pencils and erasing, This is a math class, not an erasing class. If you watch a weak math student, you will see that 3/4 or more of his time is spent erasing. If he just draws a line through the errors and moves on and does more *math*, instead of erasing, he will instantly be working three to four times as fast. And if, as often happens, he realizes that he was not wrong after all, he can go back to the part that was OK and continue on. Use a pen and do math, forget kindergarten training.

This is general advice; please get back to me if you have any specific questions.

I must agree with Samantha, that my example about two people having apples is more prealgebra than algebra.

In the Algebra 1A course with which I am familiar, the students spend some time learning to translate parts of word problems into algebraic symbols before they actually do problems. In Samantha’s example, the student might be asked to pick letters for John’s apples and Suzi’s apples. The answers could be j and s or x and y.

The students spend time learning to translate words like sum, difference, product, numerator, denominator, less than, increased by, and decreased by into symbols.

Some students have trouble understanding that the verbs “is” and “are” become the equal sign (=) in an equation.

Sara McName