Friday, December 5, 2014

Activity: Overlapping Triangles (Day 74)

At this point, the students need as much practice completing proofs as possible. Today's activity, as I promised, will involve proofs.

This weekend will be my 34th birthday. My December birth reminds me of another very contentious issue -- that of kindergarten age cutoff dates.

For years, California's cutoff date was December 2nd. That is, a child is allowed to start kindergarten at the age of four, as long as the fifth birthday is on or before the second of December -- otherwise, the child must wait a year. I might have been developmentally ready for kindergarten, since I did read and do arithmetic at a young age. But I was born five days too late to be allowed to start at four. So I ended up being one of the oldest students in my grade.

Most of the time, I didn't mind being the oldest in my grade. But one day, our school was invited to participate in the children's game show Kidquiz, where sixth graders were to compete in a trivia competition against their counterparts from other schools. But I was only a fifth grader the year we were invited -- though I would've been a sixth grader had I been allowed to start kindergarten at age four rather than five.

Recently, the adoption of the Common Core Standards brought California's late cutoff date into question, as many people thought that the kindergarten standards were too rigorous for four-year-olds to master. So the state changed the cutoff date from December 2nd to September 1st. Notice that a kindergartner born in August at a school on an early-start calendar might still be four years old for a few days before turning five. But now students born in September, October, or November will have to wait until they turn five before they can start school.

There was a new grade level created to fill the gap -- Transitional Kindergarten. Notice that TK is for four-year-olds who turn five in September, October, or November only -- that is, the students who were eligible for full kindergarten under late cutoff but not under early cutoff. Those who weren't born during those three fall months -- which would include myself -- are still not eligible for any sort of kindergarten, Transitional or otherwise, except for full kindergarten after turning five.

Here is the activity. For the bonus, notice that unlike SSSS, there is an SSASS Theorem for Quadrilateral Congruence. Just divide the pair of quadrilaterals into triangles. One pair of triangles can be proved congruent by SAS, and then the other can be proved using SSS.

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