This seems related to a post from a while back (yours?) that if a number ends in 0 then it’s even, so 5.0 must be even.

Procedural approaches are fine if the test checks for it. You can have a test that is designed to find out if a student knows how to use “the” quadratic equation, or even how to do long division. The evil thing is when a test-writer knows which procedures the students have learned and then uses it against them (as if that’s not a hollow victory). I’d make a bet that I can make a grade-level question which breaks ANY procedure that is taught in K-12 schools. This doesn’t mean procedure should be avoided, but its limitations should he known and given as a warning to the user.

E.G. for |…|

remove the negatives? -|5|

only remove negatives inside? |-(3 + -5)|

only remove the first negative inside? |-3*-3|

compute the value inside and then remove any negative |2x-4x|

I was thinking about rolling two dice. There is one combination for 2 and 12. Two combinations for 3 and 11, three combinations for 4 and 10, four combinations for 5 and 9, five combinations for 6 and 8, and six combinations for 7 = 36 possible combinations. I feel this is related to pascal’s triangle but can’t see how.

]]>That is endless and lacking in joints.

If you give it a bend

Or give it an end,

This results in you losing some points.

Ray Charles, Ray Parker got praise.

Their duets were starting a craze

On heavy rotation

Throughout all the nation.

Their angle? A merging of Rays.

With a triangle right and scalene

(Or isosceles, isn’t that keen?)

The height of the hunk

Is the root of the chunks

As a product… not to be mean.

Pythagoras (“Fred” to his crew)

Was found fretting the square root of two

They said, “Here’s a theorem,”

But he couldn’t quite hear ’em

Since Fred was irrational, too.

That’s not the point, though. The point is, Euclid visualized mathematics in geometric terms, and this is another case of that. I think it’s interesting to see how different people see the same concept.

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