homework log #2

9-27-07
TIME: 1/2 hour
8:30 pm start
9:00 pm finish
HOME SCENE: both dogs have been skunked; I need to mix up skunk solution and bathe them but can’t because I must help C. with test; Andrew is tantruming upstairs; Ed has evening meeting; etc.

C. is still stacking equations vertically in order to solve; says it’s easier; says the other 8th graders do it this way, too

I tell him grownups don’t do it this way; he insists he must do it this way; yes-no, yes-no, yes-no

I attempt to demonstrate to him, a la Mathematics 6 by Nurk and Telgmaa, that when you “move” a term from one side to the other you switch signs, but he is resistant - will leave this 'til weekend & then insist

life would be far easier around here if his (male) teachers would encourage him to adopt and practice the classic, efficient mode of solving a simple linear equation, as opposed to having me do it

“Your father doesn’t stack equations vertically” etc.

[thought balloon: not fun, taxes too high....]

still mixes up and omits negative signs constantly; handwriting wasn’t taught to proficiency in IUFSD, & continues to be illegible & an obstacle to doing math problems and calculations correctly

has trouble distributing a negative [e.g. -5(x+2) ]

C. is confused by this problem, but solves it correctly:
P. 182: 35
3 - 5/6y = 2 + 16y

Needs substantial help with this one:
P. 187: 15
Solve 7(x+2) + 4(2x-3) = 47 for x.

Doesn't realize that “solve for x,” in this context, simply means “solve the equation.” Has only seen the phrase “solve for x” in the context of literal equations; his knowlege is inflexible and does not transfer.

I will need to monitor this, as the school will not.

I point out that there is only one variable in this equation; therefore it is solveable; he can find a numeric value for x. He does not know that if you have 2 variables you need 2 equations; if you have 3 variables you need 3 equations, etc. Has no sense why some equations have one number as a solution, while others have “no solution” or a “variable” as a solution.

Ed says C. doesn’t really know what a variable is (based on last night’s work).

C. can now set up and solve a simple distance problem in one variable (below). He has learned this in approximately one week’s time.

tonight’s problem:
A cargo plane left an airport at noon and flew toward New York at the average rate of 400 miles per hour. At 2 P.M. a passenger plane left the same airport for New York and flew the same route as the cargo plane at the average rate of 560 miles per hour. How many miles did the passenger plane fly before it overtook the cargo plane?

cargo plane
rate 400 mph
time x
distance 400x

passenger plane
rate 560 mph
time x-2
distance 560(x-2)

Chris sets up chart correctly, then writes equation correctly:
400x = 560(x-2)

He solves the equation correctly, coming up with:
x = 7
400x = 2800 miles

However, he does not then realize that 560(x-2) must equal 2800, too, nor does he realize that solving 400x and 560(x-2) and making sure the values are equal is the way to check his answer. Lacks conceptual understanding of what the equations he has set up actually mean in terms of the story problem.

Also, he doesn’t seem to have heard about the concept of checking one’s answer.


brainstorm
homework log #2