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RPinPA

Science Advisor

Homework Helper

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## Main Question or Discussion Point

I recently started volunteer math tutoring in an after school program in a city near me. This is one of the poorest cities in the state, and the students' math preparation is about as bad as you'd expect. The after school program is not part of the school system, it's run by a non-profit. I work with whoever I'm assigned to on a given day, as the staffing and student attendees fluctuate.

My particular question has to do with one child's homework on the Pythagorean Theorem.

She had gotten this far:

##14^2 + 20^2 = c^2##

##196 + 400 = c^2##

And she seemed to understand that the next step was to add 196 to 400 to get 596, but then she was at a total loss what to do with that number. She hopefully wrote down this:

##596 + b^2##

And then at my explaining why that was wrong, tried this:

##596 + c^2##

I tried explaining that her first equation was saying ##c^2## is the same as something, so her next equation should also say ##c^2## is the same as something. And that ##=## was the sign that meant "is the same as". I could tell her that the next step was ##596=c^2## but I was not getting a feeling that she understood why. And while I was struggling to figure out what she was missing and how to bridge the gap, her ride showed up and she had to leave.

The lady who runs the program tells me that there's nothing like a structured curriculum any more, just a bunch of random topics on any given day, trying to prep them to get good test scores. So all of these students are missing fundamentals of one kind or another. This student might have never been given an equation before.

Anyway, enough of the generalities. About the specifics: Does anyone have any idea what the gap is here and how to teach it?

My particular question has to do with one child's homework on the Pythagorean Theorem.

She had gotten this far:

##14^2 + 20^2 = c^2##

##196 + 400 = c^2##

And she seemed to understand that the next step was to add 196 to 400 to get 596, but then she was at a total loss what to do with that number. She hopefully wrote down this:

##596 + b^2##

And then at my explaining why that was wrong, tried this:

##596 + c^2##

I tried explaining that her first equation was saying ##c^2## is the same as something, so her next equation should also say ##c^2## is the same as something. And that ##=## was the sign that meant "is the same as". I could tell her that the next step was ##596=c^2## but I was not getting a feeling that she understood why. And while I was struggling to figure out what she was missing and how to bridge the gap, her ride showed up and she had to leave.

The lady who runs the program tells me that there's nothing like a structured curriculum any more, just a bunch of random topics on any given day, trying to prep them to get good test scores. So all of these students are missing fundamentals of one kind or another. This student might have never been given an equation before.

Anyway, enough of the generalities. About the specifics: Does anyone have any idea what the gap is here and how to teach it?