DeKalb County Math Trail: Avondale School and Vicinity
	Elementary/Intermediate: Suppose you wanted to paint this building. What would you do to estimate the amount of money it would cost to buy the paint? Secondary: The curved part of the roof looks like it might be an arc of a circle. What would you have to do to find out if it is in fact exactly circular?
	Intermediate: If the center of the free-throw line is 20 feet from the basketball pole, and the circle is 8 feet across, how far it is from one of the ends of the free-throw line to the basketball pole?
	Elementary: Is the shape of the window on the right similar to the shape of the doorway? How would you prove it?
	Intermediate: The contents of this fire extinguisher are under pressure, and so they are pushing out against the container. Use the gauge and make measurements to find out how many total pounds of force are being applied to the container from the inside.
	Elementary/Intermediate: Estimate the total number of gallons of water that flow through this drinking fountain in a month, and explain how you made your estimate. Secondary: If there is enough pressure and the valve is open all the way, the water in the drinking fountain will form a curve which is parabolic in shape. Find the equation of that parabola.
	Intermediate: Use a yardstick on a sunny day to find the height of the goal post, based on its shadow. Secondary: To make a field goal from the 50 yard line, the kicker must kick the ball almost exactly straight toward the goal posts. Assume the kicker is positioned halfway between the sidelines. At what angle can the ball be kicked and still pass through the goal posts? Compare that to the angle at 40 yards and 30 yards.
	Elementary: If you wanted to paint these locker doors so that no two lockers that are next to each other are the same color, how many colors of paint would you need? Intermediate: Suppose you and a friend of yours are assigned lockers along this wall. What is the probability that your lockers will be less than 15 feet apart?
	Intermediate/Secondary: Use what you know about the tangent ratio to cut a sheet of paper at an angle of 50°.
	Elementary: Suppose that, on the license plates of these cars, there are a total of 200 digits. How many 1's do you think there would be? Why? What ratio is this? Now count the actual number of digits and the actual number of 1's. Did you get the ratio that you expected? Intermediate: If a license plate has three digits and three letters on it, how many different license plate numbers could you have?
	Elementary/Intermediate: Point out all of the pairs of angles that are equal to each other, and explain why you think they are.
	Secondary: If this parabolic satellite dish were pointing straight up, how high above the ground would the directrix be?
	Intermediate: The 10 digits that can be shown on the scoreboard are made by lighting up some of the seven line segments that form the figure "8". How many possible combinations of lit up line segments are there?
	Elementary/Intermediate: What percent of the floor is colored dark blue? Secondary: Find the equation for a sinusoidal path down this hallway that stays only on white tiles.
	Intermediate: For a race that goes all the way around the track, the runners must start in different positions, because the inside lanes are shorter than the outside lanes. Verify that the markers for starting positions for such a race are correctly placed. Secondary: Determine whether or not the arc of the turn on this track is exactly circular. If so, find its radius of curvature.
	Elementary: How many different combinations of snacks could you buy with $3.00?
	Elementary/Intermediate: Choose a log and find out how many cubic inches of wood it contains. Secondary: About how much heat would be released by burning this wood? (This will require research as well as an accurate estimation of the amount of wood.)
	Elementary/Intermediate: If you had to replace all of the soil in these pots, how much soil would it require?
	Elementary: Using a yard stick or meter stick, estimate how many bricks were used to make the front of this house.
	Intermediate: How would you determine whether or not the two triangles that you see here are similar? Secondary: Write the equation for the step function that represents the steps going up to the porch.
	Intermediate: Measure the distance between the posts and the size of one of the angles in the base of the roof triangle. Use that information to find the area of the roof of this building.
	Secondary: The lengths of the leaves on this fern get longer as you move farther away from the central branch. Find an equation that represents this relationship for one of the side branches.