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# How long (on average) should it take to do one geometric proof?

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I know it will vary. I need some kind of baseline.

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My son is using TT Geometry an is only now finished with Ch 5. I can say that the average length of these proofs is about 5 -6 steps (that includes the given). I think it should be well under 10 min for each of these...my daydreaming son can take 15 min.

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Five minutes if DD *gets* right away which theorm she is probably going to use and just needs to work her way to it.

10-15 minutes if she goes down the wrong rabbit trail and tries to prove something that doesn't exist.

On strategy we have worked on is to really study the question to see which theorms/postulates will be useful. Vertical angles, right angles, congruency - all those help to classify the problem.

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Easy ones - a few minutes. Medium ones - 15 minutes.

But we have been using AoPS where a proof could easily take an hour to figure out.

It all hinges on the difficulty of the thing you need to prove- some are obvious and the main thing is to gather the theorems. Other statements are not obvious at all and require time for understanding WHAT is being proven.

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OK - after ds took 4 HOURS to do 4 proofs yesterday, I was dreading having him do more geometry today. Today I put on a timer for 15 min. With the exception of one proof that took longer and I needed to sit down with him to direct him in the right direction, they've all taken about 10 min. He actually got an entire assignment done in a little over an hour. Woo hoo! I am now rewarding him with a nerf battle between him and his sister. :laugh:

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It all hinges on the difficulty of the thing you need to prove- some are obvious and the main thing is to gather the theorems. Other statements are not obvious at all and require time for understanding WHAT is being proven.

I agree...

but it sounds like things are going better already....was he lacking confidence before? or getting distracted? anything he was worried about yesterday?

I hated doing proofs but dd loves them....but I remember being completely distracted in Geometry class because it was right before track meets and other sports - I had a terrible time concentrating...

Joan

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Just a few minutes -- longer for the harder ones. Have you tried going over one of the proofs with him using the TT CD? Stop the lecture before the answer is revealed in each step. Use the back of the textbook's definitions, properties, postulates & theorems. Let it be a quiz if he can recite it orally (or paraphrase in his own words) the statement and reason. Maybe the writing it down is tedious?????

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Dd took way too long on proofs, not an hour but long, 20 minutes? TT has three proofs during every lesson so that could mean spending an hour of math on proofs. About 3/4 of the way through the school year, I decided to drop them completely. Now what you wanted to hear, right? I don't think skipping the proofs in the last quarter hurt her one bit. It could be the way her mind works, but she's has never been inclined to work to break things down into a logical, systematic process, and always has a more intuitive approach across the board. It's not the way my mind works, and I don't really understand it. Could your ds be the same?

I wouldn't recommend skipping the proofs right away. I'd give it some time and just see how it goes. We all have our good days and bad days.

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