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Day 67: Simplifying Radicals

Started the day by taking a quiz on the 30/60/90 triangles, the results of which demonstrated an incredible inability to transfer knowledge to new situations. The worksheet contains a variety of 1 triangle and 2 triangle problems (where the hypotenuse might become the long leg of a separate triangle). Students can do the simpler variety, but will stop completely at the more complex until I cover up one triangle and ask them to keep doing what they'd been doing. So on the quiz, I created *gasp* three connected triangles and gave them one side length, asking them to determine a side on the far side of the diagram.

I can't even guess how much kids left it blank or wrote a big question mark over the picture as if to say "You never taught us this so I obviously can't be held responsible for it." And these were students who did just fine on the simpler problems on the other half of the quiz. Ugh.

After the quiz we reviewed how to simplify radical expressions. Most students remember a factor tree type method from 9th grade, which is actually unfortunate, because that method is terribly unreliable (at least, the pieces of it that the students remember is). The biggest surprise continues to be the trouble students have with the square root symbol itself. They understand that add/subtract/multiply/divide are operations, and once the operation is complete, you can stop writing the symbol, but they don't make that connection to square roots. A LOT of kids will say that sqrt(144) = sqrt(12). I'm trying to combat that by reminding them that sqrt is a button on a calculator. Once you've pressed the button, you can't tell people (by writing the symbol) to keep pressing it.
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