Tuesday, September 16, 2014

252: Circle and Quarter-circles






What do you notice about the blue figure and the yellow one?

What could we do to find perimeter?
How about area?

Monday, September 15, 2014

251: Semicircles 1


Let's talk about perimeter. What do you notice about the perimeter of the big semicircle alone and all of the smaller ones together?

What will happen if we changed this so that all the small semicircles were really, really, really small. Wouldn't that essentially be a straight line?

Sunday, September 14, 2014

250: The Shadow Knows






The man is walking down the sidewalk in the evening, at a constant speed. As he walks away from the streetlight, he casts a shadow in front of him.

If a second man were to try and keep up with the very front tip of his shadow, would he be walking at a constant speed, accelerating or decelerating, or what?

How do you know your answer is correct?

Saturday, September 13, 2014

249: Create some data

Can you create a set of data (more than 12 numbers, please) with a mean of 17 and a median of -17 and a mode of 0?

Friday, September 12, 2014

248: Raising one out of two.

Can you create a data set of more than 5 numbers so that when you add one additional number to the set, you can raise the median but not the mean?


Thursday, September 11, 2014

247: SAT Number theory






This is an actual SAT question, from later in a section so it is one that a lot of test-takers got wrong because it was a hard question, was worded strangely, had too many undefined letters, or was near the end of a section and the test-takers simply ran out of time.

What are some of the difficulties you think most students would have with it? What are some things we could do to rewrite the question so it's more clear?

Wednesday, September 10, 2014

246: Square and Circle






Two opposite vertices of a square lie on a circle. Sure as sunrises, someone is going to ask about area.


What information do we need?

What would be the easiest scenario?

Is there more than one easy scenario?

source.