Dr. E and Jessica Edens 7/9/03 Earth Algebra Temperature Activity 1. What kind of function would most accurately describe temperature during the months from April through September? The function would be a quadratic because the temperature increases and then decreases over this period of time. 2. Would the function be different for different parts of the world? Yes, because there are parts of the world whose temperature does not change the same rate as other parts (i.e. equator). For example, at the equator the function would be flatter because the temperature remains about the same. In contrast, in Australia the temperatures alter between cold and hot; therefore, the function would go up and down. Comparing US to Australia, it would be a reflection of Australia’s quadratic. 3. What function would accurately describe temperature over only one day? Here in the US, over one day, the function would look quadratic because our day changes temperature through the course of 24 hours. Early in the morning the temperature is low (about 70 degrees in the summer), then increases throughout the day, peaks, then decreases throughout the evening. 4. Why is it important to know about the average temperatures over a period of time? It is important to know for agricultural purposes, habitat, decisions on where to live, kinds of houses including air conditioning needs, etc. Also, to observe any changes over a period of time is critical in order to measure impacts on the environment, such as global warming. 5. How does temperature affect precipitation? The colder the temperature the more frozen the precipitation. As temperatures increase, precipitation increases. However, if the temperature is too hot, precipitation decreases. 1. Make points from the average temperature data provided; the first coordinate will be the mid-point of the month and the second coordinate will be the average temperature for that month. Plot these points on the applet screen. 2. Use regression to fit the given data with a quadratic function A(t). Graph the function showing an appropriate domain and range. Use this function to answer the remaining questions. The function reads as follows: f(t) = -3.456t2 + 46.871t - 99.938 3. What will the average temperature be on May 15? On August 15? On April 6? On September 21? May 15: 41 f(4.5) = 40.9975 August 15: 57 f(7.5) = 57.19 April 6: 15 f(3.2) = 14.6 September 21: 46 f(8.7) = 46.255 4. When will the daily average temperature be 50 degrees? When will it be freezing? Daily average temperature of 50 degrees: June 7 September 11 Daily average temperature of 32 degrees: April 30 October 15 f(5.23) = 50 f(8.4) = 50 f(4.0) = 32 f(9.55) = 32 5. On what day will the average temperature be the warmest? The average temperature would be the warmest on July 26 according to the function graph. It would be 59 degrees. However, according to the data, it was actually higher in July and August. Reflection Examination of the model 1. Do you think that this model would work for long periods of time, i.e. decades or centuries? Why or why not? We think this model would work for small periods of time, such as decades. However, not for longer periods of time, such as centuries. The impact of global warming will either change the function or shift it up over longer periods of time. 2. Could this function be used to predict the temperature at a specific time on a given day? This function does not allow for precision per day. It gives average temperatures over several months. 3. Could we use this function to predict average daily temperatures during the other months (January, February, March, October, November or December)? We could not use this function to predict the other months because we only used a small period of time to create this function and cannot be extended beyond April to September. We would have to create a new function. 4. What do you see as advantages to the use of this function? Disadvantages? Advantages: allows for predictions on specific days of the month within the range of April to September; finding the day when certain temperatures occur Disadvantages: limited to certain months of the year rather than the whole year; precision of function might be improved with more data points Using Earth Studies Materials in Your Classroom 1. What module did you choose? We chose the Streamflow Temperature module. 2. What course do I teach? Sixth Grade Pre-Algebra Where does this fit into your course? This particular module does not fit into pre-algebra because it is not a linear module. Does the level need to be modified? Yes, if used in sixth grade. 3. Do you need any additional applets? I have not had enough experience with earth algebra to know at this time. 4. Do you need any additional review topics? N/A Supplementary materials? I’d be interested in more materials pertinent to a pre-algebra skill level. 5. How will you evaluate the students? N/A 6. Is there a meaningful local connection that you and your students could discuss? I would relate the information to how it pertains to the region they live in and what this has to do with climate and agriculture. For example, the temperatures in Georgia are different than the temperatures in this example.