fasten your seatbelts

I learned today that, last Thursday and Friday, C's math class -- this is Math A, algebra 1 & some geometry -- covered the following topics:

• how to solve literal equations

• how to set up and solve distance problems

• how to set up and solve number problems

• how to set up and solve algebra story problems in general

C. has never done any of these things, and, I am sad to say, was absent on Thursday and Friday when the kids did them in class.

So he missed out.

Teacher says it's not a problem. He can come in for extra help.



selected problems, 9-17-2007 thru homework 9-24-2007

• During the first 6 months of last year, the interest on an investment was $130 less than during the second 6 months. The total interest for the year was $1,450. What was the interest for each 6-month period?
  

• Find three consecutive integers such that twice the smallest is 12 more than the largest.

• Saratoga and New York are 180 miles apart. A truck traveled from New York toward Saratoga at the rate of 65 miles per hour. Another truck traveled from Saratoga toward New York at the rate of 55 miles per hour. How many miles did each travel before they met?

• (by + 2) / 3 = c, solve for y

Chris has no idea, none, how to do any of this stuff.

I know from experience that he will not learn how to do this stuff in Extra Help.



Susan J does homework

During the first 6 months of last year, the interest on an investment was $130 less than during the second 6 months. The total interest for the year was $1,450. What was the interest for each 6-month period?

This problem seems much complex that it is because of the mention of "6
months" and "interest on an investment" which has nothing to do with the
question. Here's the same problem with a different story.

The boss paid John and Fred $1450 total. John received $130 more than Fred.
How much did each receive?
Answer: John got $790 and Fred got $660.
[I think you could do this with a bar model.] [NOTE: That's exactly what I said! I have a note to myself to show C. how to do this problem using a bar model. - CJ]

On top of the other skills, have the students been taught how to determine irrelevant information? [My guess is that such a thing has never even been mentioned, but I don't absolutely know that for sure. I do know that if this subject did come up it was discussed briefly at most5.]

Find three consecutive integers such that twice the smallest is 12 more than the largest.

Here again, there is what you might call extraneous information or at least a two-part problem. The first part of the problem requires understanding what consecutive integers means and also how to solve two equations in two unknowns. Both are pretty sophisticated.

Let S be the smallest and L be the largest.
2S = L+12 (Twice the smallest is 12 more than the largest.)
L=S+2 (Consecutive integers are S, S+1, S+2, etc.)

2S = S+2+12 = S+14
S = 14

Answer: 14, 15, 16

Check 2 times 14 = 28; 28-12 = 16.
[Here I'd like to point out that C. has never, to my knowledge, been taught how to write "let x stand for _____" He has never been taught how to translate a simple algebra problem into an equation using unknowns. Never. Suddenly, he is supposed to be doing this. Or so I gather.]

Saratoga and New York are 180 miles apart. A truck traveled from New York toward Saratoga at the rate of 65 miles per hour. Another truck traveled from Saratoga toward New York at the rate of 55 miles per hour. How many miles did each travel before they met?

Are they supposed to know the distance = rate times time formula? [answer: I believe they covered it in class last Thursday or Friday. Before that he he wouldn't have known it, though he may have seen it before. - CJ]
Also, the problem does not explicitly state that they started at the same time so it requires some thought to realize that the times must be the same.

D1 = 65 * T1
D2 = 55 * T2
D1 + D2 = 180

Since T1 = T2 = T, we can substitute the first and second equations into the
third:
120 T = 180
T = 1.5

Check: 65 * 1.5 = 97.5
55 * 1.5 = 82.5

97.5 + 82.5 = 180

[C. has no idea how to set up a distance problem; nor does he know how to express one value in terms of another (e.g.. T1 = Ts). - CJ]


what my neighbor said

So I called up my neighbor to tell her C. had missed literal equations, distance problems, number problems, and general algebra story problems because he was out sick last Thursday and Friday, and, without missing a beat she said, "You need How to Solve Word Problems in Algebra. The section on number problems is really good."

"Yeah," I said. "It's supposed to be great. The Mildred Johnson book."

"Is it Mildred Johnson? How to solve algebra problems. That's the title."

"Yeah. It's Mildred Johnson. I have it on my desk."

"Oh, good. Use that."

This is an authentic Irvington school district conversation, mom to mom.

You call up your neighbor to tell her your kid missed out on literal equations, number problems, distance problems, and how to set up and solve a simple algebra problem and she says, "Use How to Solve Word Problems in Algebra."

This is why urban schools will never be high-performing.

How can urban schools be high-performing when urban moms have never even heard of How to Solve Word Problems in Algebra?<sup>*



*</sup>presumably never heard of....