Math Trail 2002

Welcome

Welcome to the University of Regina Math Trail 2002! As part of our mathematics education program we have developed an outdoor tour of our campus that includes mathematical activities at each stop. Feel free to do as many or as few as you see fit. Do one question at each stop or go to a building and try to answer all of the questions. The questions range in difficulty, but many involve estimation and are suitable for middle year students to high school students. Enjoy our campus and have fun.

The Laboratory and Classroom Building

  1. In front of the Classroom Building there is a flag pole.
    1. How tall is the flag pole?
    2. What is the area of the flag hanging on the flagpole?
  2. On the north side of the Classroom Building is a campus map.
    1. Is the map drawn to a scale?
    2. Is the scale accurate?
  3. Consider the two buildings. They look very similar.
    1. Are they the same height?
    2. Are they the same volume?
    3. About how much does a building that size weigh?

The Library and Language Institute

  1. Draw a picture of the bike rack outside of the Library Building.
    1. On your diagram indicate where the x axis and y axis would be located if the bike rack represents the graph of:
      1. A sine curve
      2. A cosine curve
    2. Given that this bike rack represents the graph of a cosine curve, what is its amplitude?
    3. What mathematical ideas or relationships could be represented by this bike rack? List as many as possible.
  2. Outside of the Library Building there is a fountain.
    1. What is the circumference of the fountain?
    2. Calculate the area of the region occupied by the fountain.
    3. Approximately how much water would this fountain hold?
    4. What is the length of the arc subtended by a central angle of 90 degrees?
  3. There are windows on the west side of the Administration/Humanities Building.
    1. What are the dimensions of one pane of glass?
    2. Using the above measurements, estimate the area of the entire section of windows.
    3. What is the ratio of the height to the width of the entire section of windows?
    4. If I wanted to install window panes that are half the height and one quarter the width of the current window panes, how many panes of glass would I need to cover the entire section of windows?
    5. How many different rectangular regions can be found in this section of windows?
  4. There is a fire hydrant by the Language Institute.
    1. What is the radius of the fire hydrant?
    2. What is the height of the fire hydrant?
    3. How much water could this fire hydrant hold?
    4. This fire hydrant is made of a material that costs 10 cents per unit area. How much would it cost to construct one fire hydrant?
  5. Outside of the Language Institute is a stair case.
    1. Using a tape measure, measure the distance from the ground to the bottom of the stairs and then measure the distance from the ground to the top of the stairs. Measure the hypotenuse and the other side.
    2. Using Pythagoreans Theorem, find the length of the hypotenuse. Comment on how close or far off you are from the measured length. Why is there some or no difference between the lengths you measured and the lengths you calculated?
    3. Find the slope of the stairs.
  6. In the courtyard behind the Language Institute there is a sculptor from the 1988 Winter Olympics.
    1. Measure the diameter of one of the circles and record the data.
    2. Assuming that all of the circles are the same size what is the area of all of the circles?
    3. Find the area of the circle that has a hole in it.
    4. Are there alternative ways of coming up with finding the area of this circle. Explain in writing and include a drawing or diagram.
    5. Find the area of the one square.
    6. Find the area of one rectangle and use this area as an estimate for the other rectangle.
    7. Find the area of the larger rectangle.
    8. Find the perimeter, area and volume of each shape. Then find the perimeter, area and volume of the whole statue. (For volume: use 0.5inches as the thickness.)
    9. Calculate the total cost of the statue if it costs 0.28 cents per square inch of steel.
    10. Using the TOTAL centimeters of the statue you found in question (8), draw a statue or object of your choice. Please include in your statue or object at least 3 squares, 2 triangles, 1 circle and 6 rectangles.
      least:

Campion and Luther Colleges

  1. There is a grid of windows on the north side of Luther.
    1. How many squares are there in a 2*2 square?
    2. How many squares are there in a 3*3 square?
    3. How many squares are there in a 4*4 square?
    4. How many total squares are there?
    5. Could you make a hypothesis about how many squares there would be in an 8*8 chessboard?
  2. On the north side of Campion, there is a window shaped in a curve.
    1. What is the mathematical name for the shape of the curve?
    2. Find the locus of the window.
    3. Why do you think the window was built that way?
  3. Using the environment outside Luther and Campion, find examples of the Fibonacci sequence (i.e. 1,1,2,3,5,8,13,....).
  4. Using the baseball field, complete the following.
    1. Hypothesize the distance between first and third base.
    2. Measure the actual distance.
    3. A pitcher fields a ball 5 metres directly left of first base. It takes the pitcher 3 seconds to prepare the ball to throw at 3 metres per second. Would it be faster to throw the ball or run it at 1.5 metres per second?
  5. Find a garbage bin outside Luther or Campion.
    1. What is the volume of the bin?
    2. Using the measurment from the volume, can you find the distance of the diagonal between the bottom left and the top right corners of the bin.

The Physical Activity Centre

  1. How much money does the University make by the University parking meters on any given 8 hr day. Suppose that on campus there are as many meters in each parking lot as their are in Lot _.
  2. What is the area of the parking lot? Hint: Find the area of one parking stall.
  3. How much sand does the volleyball pit hold?
  4. Is the PAC ramp suitable for wheel chairs? Suppose the suitable slope for wheel chairs must not exceed _.
  5. What is the probability of a random ball being stopped by you if you are stuck in one spot of the soccer net?
  6. How big is the football Field? Present your answer in metres.

The Education Building

  1. Go up the stairs on the North side of the Education Building up onto the balcony. Slightly to the right of you there is a funny looking circular object.
    1. Find the circumference and radius of this object.
    2. Figure out the volume as if the object was a complete sphere and then the volume as it stands now.
  2. If you look down at your feet, you will notice some square tiles. Estimate:
    1. the number of squares there are on the balcony.
    2. the perimeter of the balcony.
    3. the area of one of the squares and the area of the balcony.
  3. Descend the stairs at the South side of the building.
    1. Using the stairs up to the first landing only, use a right triangle and find the angle of elevation from the ground to the stairs.
    2. Confirm this angle using the second set of stairs the rest of the way up the balcony.
    3. If you were to decrease this angle, what factors would be affected?
    4. What would the measures be if the angle was 5o less?
  4. There is an arc above the doors entering the link between the Education Building and the Riddell Center.
    1. Where would the center of the circle be for this arc?
    2. What would the dimensions of the circle be (include radius, circumference)? Hint: Estimate the distance from the peak of the center triangle to the intersection of the chord and the circumference.

    The Riddell Centre

    1. Go to the parking lot and count the number of cars in the first few rows.
      1. Find the probability that you will see a red car leave, a blue car leave and a silver car leave the parking lot?
      2. Find the probability that you won't see a car leave the parking lot?
    2. Calculate the mean, median and mode of the cars that are present in the first two rows?
    3. Using a ruler and a protractor figure out the height of the building.
    4. Using the picture provided:
      1. Calculate the scale of the picture.
      2. Estimate the height of the building in the picture.
      3. Find the area of the building.
    5. Measure the height of a building by measuring your partners shadow and height and using the shadow of the building.
    6. Find the area of the flowerbed in front of the main doors.
    7. Calculate the time it requires you to walk from point A to B. Using this calculate the amount of time needed to walk between the two buildings.