## Stepping stones

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**Jul. 9th, 2012 | 06:56 pm**

**mood:** contemplative

(Section 4.2)

Much better for a weekend away! Today we talked about congruences, a lot. One of the things I found myself going on about, which isn't really covered in the book, is how learning about congruence (i.e. being able to tell that two figures are the same) is really all about orientation, and learning to mentally re-orient shapes. It's an important step for students to realise that the orientation of a figure is not really important.

I also suddenly realised why we did an entire section on geometry constructions: so that we can figure out what auxiliary lines can and can't be added to a figure, and also, given limited information about a triangle (for example) whether we can draw a unique triangle that satisfies the information, or not (which leads to the various tests for congruence).

It was a homework day and there were questions about one particular problem, so I put it on the board and got the class to help me complete it. After we were done, two of the students mentioned that they would not have know how to solve the problem, since it really required solving two equations simultaneously. I need to check when solving simultaneous equations comes into the syllabus - before 8th grade? And also, I think I need to put together a worksheet that helps the students figure out multistep proofs. I'm thinking maybe problems that include

Much better for a weekend away! Today we talked about congruences, a lot. One of the things I found myself going on about, which isn't really covered in the book, is how learning about congruence (i.e. being able to tell that two figures are the same) is really all about orientation, and learning to mentally re-orient shapes. It's an important step for students to realise that the orientation of a figure is not really important.

I also suddenly realised why we did an entire section on geometry constructions: so that we can figure out what auxiliary lines can and can't be added to a figure, and also, given limited information about a triangle (for example) whether we can draw a unique triangle that satisfies the information, or not (which leads to the various tests for congruence).

It was a homework day and there were questions about one particular problem, so I put it on the board and got the class to help me complete it. After we were done, two of the students mentioned that they would not have know how to solve the problem, since it really required solving two equations simultaneously. I need to check when solving simultaneous equations comes into the syllabus - before 8th grade? And also, I think I need to put together a worksheet that helps the students figure out multistep proofs. I'm thinking maybe problems that include

- filling in the blanks in a given proof
- giving the correct order for a proof whose lines have been muddled up
- drawing a mind map of possible solutions, before actually solving the problem (is this something that I can make more structured?)
- writing a list of the facts that might be applicable to the problem

(no subject)from:schedule5date:Jul. 15th, 2012 10:58 am (UTC)Link

Also, the listing of facts is a good one. I've recently seen a problem where you give a figure with some information, and then students must write down EVERYTHING that can be known about that figure i.e. all inferences etc. Then see if they can think of a question that could be set on that figure.

I've just thought of another paper I could send you - on modfying questions to change the mathematical emphasis. Really useful when trying to make up worksheets etc. Do you want it?

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