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Jurgensen/Dolciani Geometry C level proofs - 22 steps - how to get there?


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Jane in NC or someone who has done this level or understands Geometry....

 

We're in 6-5 Proving Corresponding Parts Equal question 31 p207 (c1962, 1965)...

 

In the answer there are 22 steps and dd is wondering....

 

In general - this is a big jump from the B-level problems that have average 7-8 steps.....How do you plan for arriving at the "Prove"....ie how do you prepare the path mentally? She doesn't want to go down too many dead ends....

 

Ahhh - strategies?

 

I was terrible in Geometry...

 

Thanks for any help,

Joan

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Sounds like it is time to "talk, talk, talk".

 

How about asking your daughter for her strategy--what does she have to do to prove this? A number of the steps are preliminaries that lead up to the main ideas in the proof.

 

If it is overwhelming to do all of the C level proofs in detail, I would discuss some of these problems. Ask first what needs to be proved. How would you go about doing this? Have her point out the issue at hand via the diagram..Why did you choose this path over that path?

 

I think this sort of discussion can be as valuable as writing out all of the steps--particularly after succeeding at the B level proofs.

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I view the C-level proofs as "bonus" -- when they get them it's terrific, but I do not expect them to get them routinely.

 

Like Jane said, talk. What do you know? What would you like to know? How can you bridge the two?

 

Like a maze, in a really difficult proof, when working forwards from the beginning is too hard, I work backwards from the end, trying to figure out what I need to know before I can prove that last step.

 

And sometimes in math, when you can't figure out what to do, you just do what you CAN do. Honestly, I can't even tell you the number of times I've asked my kids, "What CAN you do next?" They will say something, try it, and it will be the key, even though going that route didn't look promising to them.

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I view the C-level proofs as "bonus" -- when they get them it's terrific, but I do not expect them to get them routinely.

 

 

Good point, Gwen. One idea might be to assign one of the C problems for discussion. Then if you feel your daughter's confidence is growing, have her write out the bare bones of a proof on a C problem in the next set. Basically let her work her way into them without completely frustrating her.

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Thank you Jane and Gwen!!!

 

Your answers are bolstering my courage and helping me realize there are feasible ways of approaching this...

 

I think one thing about the C-levels in geometry - at least for this particular problem - is that there is a huge jump in the liberties that they take. Eg. they have you draw in a bisector and other lines on this pyramid - which makes complete sense for solving a problem but it was a new concept for her - that she could 'add' lines that weren't given :-)

 

Then there's the other area where I'm really over my head - realizing all the itsy bits pieces of info that you have to put into the proof. She will sometimes skip steps....

 

We'll try again later today...:-)

Thanks!!!

Joan

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Then there's the other area where I'm really over my head - realizing all the itsy bits pieces of info that you have to put into the proof. She will sometimes skip steps....

Regarding those itsy bits...High school geometry texts usually want justification for every breathe you take. What is different in higher level math is that if you go through a proof or series of steps once, you don't need to repeat everything again down the line. I think that the high school text authors believe that having the minutia helps the student but I sometimes wonder if it turns them off. "Hey, I just did this--why do I need to do it again?"

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