Writing equations

[Sue]

My grandson, whom I homeschool, is working on beginning Algebra. Fortunately, I remember enough so that so far I have been able to help him. Since he was little, he always had his own way of solving math problems, getting the correct answer in half the time it took anyone else & that is why I am writing.

He is working on writing equations for word problems, but is doing it his way (still getting the right answer), but I can’t remember enough Algebra to know if this will get him in trouble down the road, because he is doing it differently & is not writing the equation using a variable. I will give 3 examples & appreciate any feedback. (Hopefully the math symbols will print OK.)

#1 Jed figures the prom will cost him $160. He has saved $46 and can earn $6 an hour at his job. How many hours will he have to work?

Tyler’s Solution:
160 - 46 = 114
114 ÷ 6 = 19
Answer: 19 hours


#2 Matt wants to call his mother long distance. The rate is 80 cents for the first 3 minutes and 20 cents for each additional minute. How long can he talk for $3.00?

Tyler’s solution:
300 – 80 = 220
220 ÷ 20 = 11
11 + 3 = 14
Answer: 14 minutes

#3 Anna is in a phone booth with $1.35 in change. A call home costs 60 cents for the first 5 minutes and 15 cents for each additional minute. How long can she talk?

Tyler’s solution:
135 – 60 = 75
75 ÷ 15 = 5
5 + 5 = 10
Answer: 10 minutes

Thanks so much for any help!
Sue

 

[tkhunny]

trouble down the road

It is great to be able to conceptualize the solution. Please don't try to discourage that. On the other hand, a goal of the teaching of algebra is to encourage conceptual abstraction, to pick something and have it represent some quantity or value as yet unknown. Another goal of the teaching of algebra is to create experience in the manipulation of abstract symbols. This will be very useful when the problems become more complicated.

The biggest problem I have seen with forcing a student to write stuff down when the student already sees the answer is boredom. The student should be encouraged to learn patience. The student should be encouraged to try to understand that there will be additional benefit sometime later and that there is great benefit in learning multiple ways to solve problems.

#1 Jed figures the prom will cost him $160. He has saved $46 and can earn $6 an hour at his job. How many hours will he have to work?

Abstraction
H = # of hours of work
Conceptualization
$46 + H*($6/hr) = $160
Manipulation
H*($6/hr) = $160-$46
H*($6/hr) = $114
H = $114/($6/hr)
H = 19 hr
Realization
The student can see how his thought process appears on the page and in the abstract symbols. Solving the problem is not the only goal. Learning to communicate the process is equally important. We are not alone in this world.

#2 - How does he solve this one if the total expense is $2.00?
#3 - How does he solve this one if the total expense is $1.40?