Puzzles and Brainteasers, Set 4

I'm trying to learn how to eat lunch again — like really sitting down and chewing on the food.  Students are always in my room at lunch; some come in to get help, others show up just to hang out.  Although I make lunch for my kids every morning, I just grab a granola bar and an apple for myself.  BUT, yesterday — for the first time in months — I went to the cafeteria and got myself a real lunch.  Our cafeteria ladies know I want everything on my tray and lots of it.  We also have a great salad bar, but I try to get there before the students sneeze, cough, and drool on the lettuce and tomatoes.  I like our school's spaghetti.  Well, that was yesterday.  Today I didn't have a lunch

Patterns in Area and Volume

Back in October I had presented at the Ventura County Math Council's Mini-Conference.  The theme for the workshop was "Puzzles, Patterns, and Problem Solving."  We had around 30 middle school teachers and student teachers in the audience.  Below are two patterns (Cut-Block and Blocks) of the five patterns that I'd asked the group to work on and discuss.

The equation I came up with for the "Area" of the Blocks (second pattern) just doesn't look elegant and would love to see what others get.

If the edge of each cube has a length of one unit, what is the surface area of the figures in each set?  What is the volume of the figures in each set?  Fill in the table accompanying each set of figures.

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This is one of the rate problems on a worksheet that my Algebra kids work on.

Burning Candles

One candle burns entirely in 6 hours, and another burns entirely in 9 hours.  The candles were lit at the same time, and they were the same height when lit.  After how many hours will one candle be half the height of the other?

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My geometry students get this one for their weekly PS.

The radii of circles C and D are each 3 units long.  The two circles are tangent at point E.  Side AB of rectangle ABCD is tangent to circle D at point A and tangent to circle C at point B.  What is the area of the shaded region?

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