Standards: The Jumping Dog Quadratic Activity A2.4.1 Identify the family of function best suited for modeling a given real-world situation. A2.4.3 Using the adapted general symbolic form, draw reasonable conclusions about the situation being modeled. A3.3.1 Write the symbolic form and sketch the graph of a quadratic function given appropriate information. A3.3.2 Identify the elements of a parabola given its symbolic form or its graph and relate these elements to the coefficients of the symbolic form of the function. Goals: Students will be able to look at this real-life situation and be able to: (1) understand why this data fits into the quadratic family of functions. (2) demonstrate their knowledge of the different formats of quadratic equations and pick which one to use based on the information given in the problem. (3) demonstrate their knowledge of many important quadratic ideas such as domain, range, intercepts, vertex, independent vs dependent variables, etc (4) create a quadratic equation for the situation using their method of choice. Materials: Worksheet(s) Vertical Motion Model WS, Distance/Height Model WS, Jumping Dog WS Pick one WS or more than one depending on your situation and focus of the lesson The Jumping Dog WS is the same activity with less direction in the questions more open ended for students to discover their ideas about the activity. Graphing Calculators Computer/Internet Access for watching slideshow and dog jumping videos
Jumping Dog Data Collection Distance/height Model Teacher Notes 2. What function family models the path of the jumping dog? Quadratic function family you can discuss the different forms of the quadratic function 3. What is the independent variable? horizontal distance a. What are the units? the fence is 8 feet in length discuss the option of converting to inches 4. What is the dependent variable? height a. What are the units? units marked in feet, 0.5 feet intervals beginning with 1 foot discuss the option of converting to inches 5. How can you collect the data? Play the video and let the students discuss the options 6. What information do you need to find the equation? Leave this open for the students to determine Support materials include the page with 9 frames of screen shots, 2 slow motion videos Choose a scale, label each axis and graph the path of the jumping dog. (The width of the fence is 8 feet)have students determine their units and scale each axis 7. Write the equation of the function that you graphed. determine which form of the equation is best 8. What is the maximum height of the dog? discuss how to find the vertex 9. What do the zeros of the graph represent? how do the zeros help determine the horizontal distance? 10. What is the real world domain of the graph? 8 ft
Jumping Dog Data Collection Vertical Motion Model Teacher Notes 1. Write the equation that models vertical motion. h = -16t 2 + vt + s 2. What is the independent variable? time is the independent variable a. What are the units? seconds 3. What is the dependent variable?height a. What are the units?units marked in feet, 0.5 feet intervals beginning with 1 foot discuss the option of converting to inches 4. What type of data do you need to collect? leave this open for discussion 5. How can you collect the data? support materials, page with 9 screen shots, video in real time, slow motion and super slow discuss what part of the dog to follow when collecting data, back feet, front feet, shoulder 6. What are the different forms of the quadratic equation? Intercept form, standard form, vertex form 7. What form of the equation will work best with your data? leave this open for discussion, allow students to make their own choice 8. Write an equation to model the path of the dog. answers will vary depending on units, form chosen, data collection method Choose a scale, label each axis and graph the path of the jumping dog. 9. What is the maximum height of the dog? what is the best way to determine the vertex? Which value is the height? 10. How long does it take the dog to reach the maximum height? again emphasize that the vertex is a maximum value, which value is the time? 11. How long is the dog in the air? I used the timer on my ipod and timed the real time jump at 0.6 sec. 1/5 time jump at 3.4 sec (3.4 x 1.5 = 0.68) 1/20 time jump at 13.2 sec (13.2 x 1/20 = 0.66) timing back feet leaving ground and landing on ground 12. What is the real world domain of the graph? discuss what real world means, compare with the theoretical graph
Jumping Dog Data Collection Name Distance/height Model Hour Date 1. What function family models the path of the jumping dog? 2. What is the independent variable? a. What are the units? 3. What is the dependent variable? a. What are the units? 4. How can you collect the data? 5. What information do you need to find the equation? Choose a scale, label each axis and graph the path of the jumping dog. (The width of the fence is 8 feet) 6. Write the equation of the function that you graphed. 8 ft 7. What is the maximum height of the dog? 8. What do the zeros of the graph represent? 9. What is the real world domain of the graph?
Jumping Dog Data Collection Name Vertical Motion Model Hour Date 1. Write the equation that models vertical motion. 2. What is the independent variable? a. What are the units? 3. What is the dependent variable? a. What are the units? 4. What type of data do you need to collect? 5. How can you collect the data? 6. What are the different forms of the quadratic equation? 7. What form of the equation will work best with your data? 8. Write an equation to model the path of the dog. Choose a scale, label each axis and graph the path of the jumping dog. 9. What is the maximum height of the dog? 10. How long does it take the dog to reach the maximum height? 11. How long is the dog in the air? 12. What is the real world domain of the graph?
THE JUMPING DOG Teacher Notes Problem: Can you write a mathematical model for the jumping dog? 1. What information do you know for sure about this problem? (function family, equation, variables, ) It is a quadratic equation because the shape is a parabola, or it has to do with gravity which makes it a quadratic equation. The equation we should use is : h = -16t 2 + vt + s where h is the height of the dog (dependent variable) and t is the time during the jump (independent variable). The starting height, s, is 0 because it is on the ground. 2. What information do you need to find out to complete the mathematical model for the jumping dog? How can we find this information? You need to find the velocity that the dog jumps with. You can find this if you know any time and height of the dog other than the starting height because that is (0, 0). If we watch the video we can find time and height of the dog. 3. Show all of your work for the equation of the jumping dog and explain how you found your answer. 4. Is there any other way that you could have found the equation for the jumping dog? Explain. You could enter the points from the slides of the dog jumping in the stats menu in your calculator and do a quadratic regression for the data.
THE JUMPING DOG Problem: Can you write a mathematical model for the jumping dog? 1. What information do you know for sure about this problem? (function family, equation, variables, ) 2. What information do you need to find out to complete the mathematical model for the jumping dog? 3. Show all of your work for the equation of the jumping dog and explain how you found your answer. 4. Is there any other way that you could have found the equation for the jumping dog? Explain.
Jumping Dog Data Collection Screen Shots The total time from slide 2(beginning of the jump) to slide 9(end of the jump) is 0.66 seconds Students can use this page to determine the height while watching the slow motion video TEACHER NOTES 1 2 3 4 5 6 7 8. 9.
Jumping Dog Data Collection Screen Shots 1 2 3 4 5 6 7 8 9