Philadelphia Math Trail: Locust Street, Historic District and Penn's Landing

Locust Street  

Elementary: Are these two doors congruent?  How would you prove it?

Intermediate: Assuming the two doors are congruent, what two measurements would you need to make to find the total area taken up by the doors and the semicircular windows?  Do it.

Elementary: If you choose flowers from the two buckets only, could you make 10 different arrangements where each arrangement has three flowers?

Intermediate: If you close your eyes, choose a flower and put it back and repeat that 100 times, about how many times do you think you would get a purple flower?

Elementary: Are these shapes similar? How would you prove it?

Intermediate: Are the dimensions of the shape in the middle equal to the average of the corresponding dimensions of the two other shapes?

Intermediate: The people in this mural are pictured larger than life. Find the ratio that states how much larger.

Elementary: This design is made from two polygons: squares and hexagons.  Can you create a design that is made from any two other polygons?

Elementary: Look at the polyhedron with the triangle on top.  Make a rectangular prism out of clay, and cut it so as to make a shape similar to that polyhedron.

Intermediate: Look at the polyhedron with the triangle on top. Assume that the triangle on top is an isosceles right triangle.  What two measurements would you need to make in order to find the total surface area of the polyhedron?

Elementary: On these designs, are the angles between the line segments coming out from the circle all equal, to each other?

Intermediate: Which of the triangles that you see in the window has the smallest area?  Which has the largest area?

Historic District

Elementary: Ben Franklin was born 70 years before the Declaration of Independence was signed.  In the year 2000, he would have been 294 years old if he were still alive.  Explain how you would use this information to figure out when the Declaration of Independence was signed.

Intermediate: Ben Franklin was born in 1706.  Suppose Ben Franklin had two children when he was 30 years old, and each of them grew up and had two children at the age of 30, and so on.  How many people would there be altogether who could say that Ben Franklin was their ancestor?

Intermediate: If you walked from one end of this floor to the other and stayed on the white lines, how many different routes could you take?

Elementary: If two less steps had been used to climb the same distance, how much higher and wider would each step have had to be?

Intermediate: Find the slope of the railing.  How does it relate to the height and width of the steps?

Elementary: How many days have gone by since the Declaration of Independence was signed, on July 4, 1776?

Intermediate: At the time the Declaration of Independence was signed, the population of the United States was around 4 million.  

Suppose the news was passed by word of mouth from one person to another.  If 100 people knew about it on July 4, 1776  and every day one person told two other people about it who hadn't already heard about it, how long would it take before everyone in the thirteen states heard the news?

Elementary: How many of these desks and chairs could be fit into this room?

Intermediate: Determine the volume of one of these desks.

Elementary: Measure the circumference and diameters of three different circles on this rug.  Find the ratio of circumference to diameter in each case.  What do you observe?

Intermediate: What is the area of the beige-colored part of the carpet?

Elementary: Get a schedule for the trolley and a map of its route, and compute its average speed for the entire route.

Intermediate: What information would you need to have in order to decide if running this trolley is a profitable activity?

Penn's Landing 

Elementary: Estimate how many people could sit on the steps.

Intermediate: What is the area of the beige section inside the white border?

Intermediate: Estimate the total number of square feet of canvas in these sails.

Elementary: List all of the geometric concepts that you see here, and where you see them.