Ratio problem that was solved by the teacher

Steven G

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My eighth grade daughter had this ratio problem solved by her teacher (yes Denis, I have a daughter).

Paul earns $5 per hour as John earns $6 per hour. If John earns $5 more than Paul, then how much does each earn per hour?

The teachers work: P:J = 5:6 = 25:30. So John earns $25 per hour and Paul earns $30 per hour

How can someone say this when it clearly says that John earns $5 per hour and Paul earns $6 per hour?

What the author meant to say but did not come close to saying in my opinion is : Paul earns $5 as John earns $6. If John earns $5 per hour more than Paul, then how much does each earn per hour?


I have no idea what to say to this teacher let alone the author!!
 
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My eighth grade daughter had this ratio problem solved by her teacher (yes Denis, I have a daughter).
So do I....and daughters are very important.

The way that problem is written is completely moronic, I agree...
 
So do I....and daughters are very important.

The way that problem is written is completely moronic, I agree...
Yes the author listed a moronic problem but the teacher 'solved' it. Amazing! I wonder what color she things George Washington's white horse was. Actually it was grey but I doubt she knows this. Oh, by the way in 8th grade the teacher teaches just one subject--the one which they mastered.
 
My eighth grade daughter had this ratio problem solved by her teacher (yes Denis, I have a daughter).

Paul earns $5 per hour as John earns $6 per hour. If John earns $5 more than Paul, then how much does each earn per hour?

The teachers work: P:J = 5:6 = 25:30. So John earns $25 per hour and Paul earns $30 per hour

How can someone say this when it clearly says that John earns $5 per hour and Paul earns $6 per hour?

What the author meant to say but did not come close to saying in my opinion is : Paul earns $5 as John earns $6. If John earns $5 per hour more than Paul, then how much does each earn per hour?

I have no idea what to say to this teacher let alone the author!!

Another correction of the problem would be:

Paul earns $5 per hour and John earns $6 per hour. If John earned $5 more than Paul in the same amount of time, then how much did each earn?

Possibly teachers get so accustomed to ignoring errors in textbooks that they automatically read the problem as if it made sense, and don't comment on how they had to twist their minds to do that.

I suppose it's also possible that your daughter copied part of the problem and answer incorrectly.
 
Another correction of the problem would be:
Paul earns $5 per hour and John earns $6 per hour. If John earned $5 more than Paul in the same amount of time, then how much did each earn?

Possibly teachers get so accustomed to ignoring errors in textbooks that they automatically read the problem as if it made sense, and don't comment on how they had to twist their minds to do that.

I suppose it's also possible that your daughter copied part of the problem and answer incorrectly.
I saw the problem in the textbook along with the teacher's solution in my daughter's notebook. She couldn't have possibly copied down 25:30 by mistake.

Maybe I did not word it correctly but it did not say Paul earns $5 per hour and John earns $6 per hour. It was in the form of a ratio. Something like: The ratio of John's salary to Paul's salary is $5 per hour to $6 per hour. I wrote in my OP Paul earns $5 per hour as John earns $6 per hour
 
I saw the problem in the textbook along with the teacher's solution in my daughter's notebook. She couldn't have possibly copied down 25:30 by mistake.

Maybe I did not word it correctly but it did not say Paul earns $5 per hour and John earns $6 per hour. It was in the form of a ratio. Something like: The ratio of John's salary to Paul's salary is $5 per hour to $6 per hour. I wrote in my OP Paul earns $5 per hour as John earns $6 per hour
\(\displaystyle \text {John's hourly salary is to Paul's as } 5 \text { is to } 6\)

\(\displaystyle \text {and Paul's salary is } 5 \text { dollars more than John's.}\)

A reasonable problem if decently worded. The teacher's answer, however, is abysmal. It does not say how to get the answer. The teacher apparently "saw" the answer. That is worse than no explanation because it convinces kids that math involves some super-powerful intuition and discourages them.

Eighth grade means your daughter has been introduced to algebra.

\(\displaystyle \dfrac{j}{p} = \dfrac{5}{6} \text { and } j + 5 = p \implies WHAT?\)

leads to comprehension.

Executing (in a humane way) all grade school and high school teachers would be a reasonable first step. After my first parent-teacher conference, my wife would not let me go again.
 
\(\displaystyle \text {John's hourly salary is to Paul's as } 5 \text { is to } 6\)

\(\displaystyle \text {and Paul's salary is } 5 \text { dollars more than John's.}\)

A reasonable problem if decently worded. The teacher's answer, however, is abysmal. It does not say how to get the answer. The teacher apparently "saw" the answer. That is worse than no explanation because it convinces kids that math involves some super-powerful intuition and discourages them.

Eighth grade means your daughter has been introduced to algebra.

\(\displaystyle \dfrac{j}{p} = \dfrac{5}{6} \text { and } j + 5 = p \implies WHAT?\)

leads to comprehension.

Executing (in a humane way) all grade school and high school teachers would be a reasonable first step. After my first parent-teacher conference, my wife would not let me go again.
I'm against the death penalty but to execute high school teachers I might go for that. In a humane way, that goes out the window.
I still laughing about your comment regarding parent-teacher conference!
 
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