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Week 3: Defining Midpoints

Last week was our 3rd 4 day week in a row, making this feel like a slow starting school year. Three weeks in and I haven't given a significant assessment. Perhaps that is okay as I have given several small skills quizzes to Algebra and two in Geometry. They are getting feedback from me and I know which topics to spend more time on.

This week in geometry included learning more basic terms, triangle inequality (activity inspired by someone in the #mtbos), starting proofs and developing definitions for midpoint and bisect.

I really like how my lesson on the definition for midpoint and bisect went this year. I facilitated a math talk punctuated by discussions in pairs.

Step 1:
Show them this image and ask them to come up with an If-then definition for point M that is general and doesn't name any points or segments from the diagram.

Step 2:
Gather ideas from the class and polish the grammar until it makes sense. Other possible items to clarify might be using congruent rather than equal and saying line segment rather than line. Often students used all three key terms (bisect, midpoint and congruent) in interesting ways in one definition.

Step 3:
After we decided on a clear definition for midpoint, I gave them the rest of the rules. The objective for the next 8 minutes would be to write all six If-then definitions using the terms midpoint, bisect and congruent twice each (once in the hypothesis and once in the conclusion). They worked on this with their partners while I walked around asking questions.

Common phrasing issues: If there is a midpoint, then a segment has been bisected. While not terribly incorrect, our class get the chance to discuss grammar.

Keep the subject (point, line, ray, etc), the thing doing the doing, in the hypothesis. Then get to the verb immediately in the conclusion.

"...a segment has been bisected," always makes me giggle as it makes me think of some sort of divine intervention for the segment. This is just geometry, nothing too grandiose, so let's keep the language to the point!

Their homework included a construction to bisect a line segment. After my little clip art placement malfunction, I am a little worried about how seriously they will take the compass work. :)

In Algebra, we continue to spend a decent amount of class time taking questions on homework. Students corrected a skill quiz from last week and took another. We are working on word problems which are fairly traditional - coin, interest and age. I am bothered that these problems lack a real world application. However, they are excellent for students to show their translating skills. We wrapped up with summarizing their stock projects via their blogs. As such, they got to download and learn to use Daum Equation editor for the matrices.

Only downside to algebra this week: no PrBL or games.

In both courses, I am still doing a ton of explaining SBG - which isn't unexpected as this grading system is different for them. I also haven't found the time to do a formal lesson on brain based study strategies, though our effective effort wall is coming along. I also haven't yet had time to lead a meditation or take read about mindsets.