DeKalb County Math Trail: Stone Mountain

Elementary: Choose any 10 items, and estimate the total cost of buying them.  Do this in less than two minutes.

Intermediate: Suppose the smallest dolls weigh 4 ounces each, the middle-sized dolls weigh 6 ounces each, and the largest dolls weigh 10 ounces apiece.  How many different ways could you combine dolls to make a total of two pounds?

 

Elementary: 100 years ago, one dollar would buy much more food that it buys today.  

Suppose that a meal that costs $15.00 today only cost 75 cents in the year 1900.  What would it cost today to buy a meal that cost $1.25 in 1900?

Intermediate: Are these bills geometrically similar in shape to the dollar bills we use today?

 

Elementary/Intermediate:  Find the experimental probability that a quarter dropped on this sidewalk will land entirely within the borders of a single brick.

Secondary: What times of day and days of the year would this sidewalk be completely un-shaded? 

Elementary/Intermediate: If you close your eyes and pick up one of these miniature cars, look at it, put it back and then repeat the process, what is the probability that both of the cars you look at will be white?

Secondary: If you select four cars at random, what is the probability that two of them will be yellow?

Elementary: Name all of the examples of symmetry that you can see.

Intermediate: Suppose the lumber to build this cabin would have cost $50 in the year it was built, and would cost $1500 today.  Use that data to estimate how much it would have cost in the year 1900.

Secondary: Suppose this cabin needed to be moved to another location, to preserve it.  Estimate the total weight of the cabin as exactly as you can.  This will require some research.

Intermediate: What two measurements would you make to find out if the quadrilateral opening of this fireplace is exactly rectangular?

Secondary: Which would release more heat:  Burning a cord of wood (which might last four months in winter) or running a 1500 watt electric space heater for 8 hours a day for four months?  (This will require some research.)

Elementary/Intermediate: How big is this garden, in square feet?

Secondary: Is it more economical to grow vegetables in a garden like this, or to buy the vegetables in a supermarket? (This will require some research, and you will have to decide which vegetables to consider.)

Elementary/Intermediate: What would it cost for the paint needed to repaint the exterior of this plantation manor? (This will require some research.)

 

Intermediate: When this school house was built around 1840, children did not spend as much time in school as they do today.  Suppose those children spent 3 hours a day in school, for 6 months out of the year, from age 7 to 12.  Find the ratio of the amount of time they spent in school to the amount of time you will spend in school by the time you graduate high school.

 

Elementary/Intermediate: Compare the dimensions of this furniture to the dimensions of  similar modern furniture.  Do you think people are generally taller now than they were in the days when this furniture was built?  If so, by how much?

 

Elementary: Do some research to find the speed of travel for this train.  How long would it take the train to travel all the way across the United States?

Secondary: As the wheel goes around, the metal arm that is connected to it moves up and down.  How much of an angle does it travel through?

Elementary/Intermediate:  Suppose you made the wheels for this carriage, including their spokes, from one long piece of iron.  How long would the piece of iron have to be?

 

Intermediate: If you melted six of these Civil War cannonballs to make one big cannonball, how big would it be?

Secondary: Measure the weight and circumference of several of these cannonballs.  Find the equation that describes how they are related, and use that to predict the weight of a cannonball with a 15 inch circumference.

Elementary:  If the paddles on this riverboat go around 3 times a minute, how many times would you see a paddle coming up out of the water in two hours? 

Intermediate: How many degrees of arc are there between any two of these paddles?

Secondary: What percent of the time does one of these paddles spend below the surface of the water?