Philadelphia Math Trail: DoubleTree Hotel and Liberty Mall

DoubleTree Hotel 
 

Elementary: How many of the angles in the balcony wall seem to be acute?  Obtuse? Right angles?

Intermediate: Look at the angles in the balcony wall.  Assume that angles that look like they are right angles actually are, and parts of the wall that look parallel to each other actually are.  Starting with the first right angle you see on the left, what is the sum of all of the angles in the balcony wall up to the point where it intersects the glass wall?

Elementary: Look at a breakfast or lunch menu and make up four different meals that someone could have.  Find the average cost and the range of costs for those meals.

Intermediate: Measure the lengths of the two rails, and the distance between their ends, and determine if the area enclosed is the shape of a right triangle.

Elementary: How would you find out if the railing on the landing is exactly circular?

Intermediate: How many square feet of carpet is used to carpet these stairs and the landings?

Intermediate: Estimate the volume of space enclosed by the half-cylinder, using only a ruler.

Elementary: Find the experimental probability that if you drop a penny here, it will land so that it is touching a red part of the carpet.

Intermediate: At night, with only the lamps on, where would the darkest spot in this room be?

Liberty Mall

Elementary: Is this triangle equilateral?  Name two ways to prove it.

Intermediate: If this triangle is equilateral, and the length of a side is 10 feet, make a good estimate of the sum of the lengths of the parallel lines that you see in the triangle.

Elementary: There are 360° in a circle.  How many degrees separate any two of the light bulbs that you see spaced around the circle?

Intermediate: How could you figure out which of the concentric circles has a circumference which is twice that of the center circle (the one with the lights around it).

Elementary: As the escalator runs, steps appear at the bottom.  How many steps appear in one hour?

Intermediate: Suppose one person goes up one escalator while another comes down the other one, and they start at the same time.  Draw a graph that shows how the distance between the two people changes.

Elementary: Is this an isosceles triangle?  How can you tell whether it is?

Intermediate: If the diagonal of one of the small squares in the top triangle is one foot long, what is the area of the triangle?

Elementary: Name all of the polyhedrons that you see.

Intermediate: Which building has the greatest volume?

Intermediate: Make an estimate of the amount of water in this fountain, and explain how you came up with that estimate.

Elementary: You have 60 seconds to estimate the total number of people that could be seated in this area.

Intermediate: Suppose you had the job of designing this eating area.  What mathematical information would you want to have in order to decide how many trash containers to put in it?  Explain.