trying to tease it out

Just guessing here but perhaps the open book/partner tests were harder. Usually, open book tests are harder. Perhaps the fact that your son could consult a book or a partner did not make up for the test being harder. He was unable to use those resources adequately in the time allowed.

Or alternatively, he was distracted by the fact he could look in the book or talk to someone else. He was looking for perfection instead of just getting it done. He ended up doing worse.

You can ask the teacher the first question.

Beth

Maybe you could post an example of the kind of math problem either here or on the Math Board.

Just a guess here, but perhaps the partner was distracting to him and the wealth of information in the book too overwhelming to dig through to find facts (like maybe he felt he HAD to use the book and not the knowledge in his head).
Amy

Too much info and too much “help” can be very confusing!

If the temperature on a celsius scale is multiplied by eight and added to four times the reading on a farenheit scale, the result is 508. Three times the Celsius reading plus three times the Farenheit reading 306. Find the temperature on each scale.

The cost of 5 boxes of envelopes and 6 boxes of notepaper is $16.75. Three boxes of envelopes and 4 boxes of notepaper cost $10.75. Find the cost of each box of envelopes and each box of notepaper.

These are just two examples. There were questions about age, about permeter, diameter, money, and temperature.

In your original post, you said that your son “was doing well until word problems were introduced”. These problems that you have posted involve simutaneous equations. I have never seen a text book in which problems with simultaneous equations are considered to be introductory. My guess is that you may not have the real story about what kind of problems the students have studied.

Sara McName

I have reveiwed all his tests and homework assignments this year and they have not done word problems. Yes, in previous years he did word problems but had difficulty then too. He has been in LD math classes up until this year. Last year in his math class he got a D in that area. The way placement works though is the students are given an algebra placement test and based on the results are placed in the math tract at the high school. The test given was the Iowa my son scored at the 60th percentile and was placed in Algebra 1A class. There were much easier word problems on the test I just happened to pick the last question in each section. When I reviewed the questions with him he was able to tell me what times meant, less then, and some others. What seemed to trip him up was deciding what information was important and which info went with which equation.

I tutor in a school district which has a two-year algebra class that they call Algebra 1A and Algebra 1B. I probably should go look at the textbook, but my recollection is that problems with simultaneous equations come in the 1B-year. The introductory word problems in the 1A year involve equations that can be written with one variable. Problems like:

The sum of two consecutive numbers is twenty-nine. What are the numbers?

Ten nickels and dimes make 85 cents. How many are nickels?

Sara McName

He is in a 1A class also the name the name of his text is Algebra 1 published by McDougal Littell. They also use zeroxed packages. The name of the package was Problem Solving with Systems of Equations. They have not done the chapters in order for example they did Ch7, then the packet and now they are doing Ch 6. So I guess my orginal post should of read they have not been heavy into word problems until now. He has never really picked up on these types of problems. He can solve problems that are set up, he can understand the order to do things to solve.

These are absolutely typical simultaneous equation learning problems. The particular examples are a subset of the classic mixture problems. AFTER someone has learned the basics of problem setup, AND has learned about two-variable two-equation systems, these are actually fairly simple to solve. If you try to do them before that, you have a guaranteed failure on your hands.

You mentioned one key point: they are not doing the chapters in order, and they are skipping around from text to packet and back again. In math, unless very very carefully planned, this kind of working out of order is a recipe for disaster. Math is cumulative; every skill depends on having a firm grasp of a previous set of skills. If a teacher tries to do Chapter 7 before Chapter 6 because he thinks it’s “easier”, the students will be sitting there with blank faces and blank papers. Something that is “easy” because you already know it can be totally impenetrable to someone who doesn’t have the groundwork.

The only good news in this is that the rest of the class is equally stunned. The teacher will have to do a lot of review (ie actually teaching this stuff.)

In an earlier post I outlined a detailed method of how to actually teach problem-solving. That method breaks the two-variable mixture problems as well as the one-variables. Try working with him step-by step through a couple. In most cases, the light flashes in the mind — you can actually see it happening. But *before* you do this this, he will have to know how to deal with two-variable equations.

A note: some teachers try to avoid using a second variable because “we haven’t learned that yet” and go through incredible convolutions solving these problems with only one variable. Depending on the problem, the insistence on using only one variable can range from slightly tedious to absolutely impossible. The first example you gave can, with a lot of trickery, be solved with one variable (but if you’re good enough at this to get the trickery, you’re good enough to do two variables anyway). The second one is practically impossible to solve without a second variable.

As far as what belongs in 1a and what belongs in 1b, or in Algebra 2 for that matter, there is a lot of variability between texts and curricula; there is no hard and fast rule. What has to be watched out for is logical sequence: first simple problems with one variable, then more complex problems with one variable, then simple problems with two variables,. etc. If they haven’t done the one-variable problem-solving chapter yet, or if they haven’t mastered solving simple equations and the properties of equality (always do the same *mathematical* operation to both sides, in total), there’s your issue.

Have you tried Victoria’s recipe for solving algebra problems? It looks like a reasonable approach to me. Over the weekend, I should try her method with one of your problems.

Sara McName

Thank you!

I’m not sure I like the word recipe — it’s more a method of breakdown.

I typed it up fairly quickly and one thing I missed: on the second “visualize” step, you do *not* have to do all the methods on every problem! The point is to try one, try another, and find something that applies to the problem you have.
The breakdown should be quick — with practice, as fast as you can write/draw. If you find yourself doing reams of tedious work, you’ve gone a bit too far. Yes, write, but quick notes of vital info, not long reams that are more confusing than the problem itself.

In a typical mixture problem like Sara’s, say one with adult and student ticket prices, a visual thinker might draw three circles for three adult tickets and six squares for six student tickets. (or sixty, or six hundred) A person who likes playing with number and detail would make a chart and try an experiment: OK, if the adult tickets are five dollars each (just picking a number at random for an example) and the student tickets three dollars each (just picking another number at random for example), how do things work out? What about seven and four dollars? In both cases, once you have some examples on paper, then you can look for *patterns*. If you knew the prices, how *would* you calculate? OK, now name some variables, and make up an algebra exression to make that calculation (This is the part that most students find the hardest, and this is why visualizing/experimenting is the key skill).

Another point I forgot to mention: use *meaningful* letters. This is absolutely vital. Some students are trained to use only x and later only x and y; this fixation on particular letters does *not* stand them in good stead when they get into science classes or advanced math classes, where any letter of the Latin or Greek alphabet may be used. Learning that doesn’t transfer to the class you learned it for is pretty pointless. Also, even in Algebra 1, many students make totally unnecessary errors and fail tests because they muddle up who is x and who is y. But if you use J for John’s age and M for Mary’s, p for kilograms of peanuts and c for kilograms of cashews, r for the radius of the little circle and R for the radius of the big circle, then you can avoid these unnecessary errors with hardly any thought.

This is one of your sample problems

If the temperature on a celsius scale is multiplied by eight and added to four times the reading on a farenheit scale, the result is 508. Three times the Celsius reading plus three times the Farenheit reading 306. Find the temperature on each scale.

Victoria’s first step is “summarize”. My summary would be:

celcius temperature
farenheit temperature

And the problem says that it wants numberical values for each.

The next step is “visualize”. The next step is relate

number times temperature

8 x celcius
4 x farenheit These sum to 508

3 x celcius
3 x farenheit These sum to 306

The next step is “name”

celcius temperature = c
farenheit temperature = f

The next step is “equation”.

8c + 4f = 508
3c + 3f = 306

That leaves “solve” and “check”.

Thank you Victoria and Sara your help is much appreciated. Since my original post my sons algebra teacher has worked with him one one one on word problems. She plans on giving his some tutoring until he catches on better with word problems. I will work with him at home also using your suggestions. Thanks again.