PR3 & PR4 CBR Activities Using EasyData for CBL/CBR Apps

Transcription

1 Summer 2006 I2T2 Process Page 23. PR3 & PR4 CBR Activities Using EasyData for CBL/CBR Apps The TI Exploration Series for CBR or CBL/CBR books, are all written for the old CBL/CBR Application. Now we can use an easier program call EasyData. New Instructions: 1. Run the EasyData Applications 2. Press Setup 3. 1:Dist here is where you change units from meter to feet. Notice most programs are written in meters. 4. Setup a. If you see Ball Bounce then choose number 4 or Distance Match choose 3 b. If you don t see Distance Match or Ball Bounce then pick Time Graph i. If the instructions say SET DEFAULTS then the program is needs to have 15 seconds. You need to Press Edit and change your Sample Interval (s): and Number of Samples: to the settings below. ii. If you see 1: SETUP/SAMPLE You must look at the time and adjust your Time Graph Setting: Choose 2. Note: (The Sample Interval) times (Number of Samples) = the needed Number of seconds for Experiment Length. Press Edit 1. Sample Interval (s) {usually anything from.1 to.05} 2. Number of Samples: {usually anything from 20 to 200} Examples for experiments given the Time below MAIN MENU REALTIME: 2 seconds 3 seconds 4 seconds 5 seconds NO TIME (S): 4 DISPLAY: DIS BEGIN ON: [ENTER] SMOOTHING: LIGHT UNIT: METERS START NOW Then say OK and press Start when you are ready to start the experiment

2 Summer 2006 I2T2 Process Page 24. Transformation Application fro the TI-83 or TI-84 Steps for Transformation Apps 1. Go to your APPS and select Transfrm. Use the upperward button to get to the end of the list. Press ENTER and you will see the following screen. Press ENTER and select 2:Install. 2. Press ENTER again and you will go back to the home screen. Press Y =, you will see the follow screen. Now when you press Y =, you will see that the left margin of this screen has changed. This change is so that you know that you are in Transformation APPS. You can only do one equation in this application. You must go back to Transformation APPS and 1:Uninstall Type in an equation in y1. Use Apha keys to type in the coefficients. 3. Press Window to show that this screen has changed as well. Arrow up to settings and use the down arrow until the cursor is flashing on A and then ENTER a value such as 1. Scroll down again until the cursor is flashing on B and ENTER a value such as 1. The step should be equal to how much you want each value to change each time. I used step =.2 4. Press the right or left cursor keys and watch the values of A and B change by each step value. Now you can match your equation to your data. 5. What did the changes do? By changing the values of A and B you change the slope and y-intercept and show how these changes make the graph of the line change. 6. The second row arrow are set up to do an animated slide show. You can set the increments and the number of slides you wish to show the movement of the function.

3 Summer 2006 I2T2 Process Page 25. The Bouncing Ball If a ball is dropped from a given height, what does a Height-Time graph look like? How does the velocity change as the ball rises and falls? What affects the shape of the graphs of both the height and the velocity? In this activity, you will graph the height of a ball versus time after it is dropped from some height. You will then examine one ball bounce and investigate the parameters that affect the shape of the graph. You will also explore the relationship between the height of the ball and the velocity. The relationship is expressed mathematically as: y = ax 2 + bx + c or y = a(x h) 2 + k YOU NEED: 1 CBR Unit or CBL and Motion Detector CBL/CBR APPS Transformation APPS Racquet ball

4 Summer 2006 I2T2 Process Page 26. Instructions: APPS application CBL/CBR. 1. Connect the Ranger to the Calculator 2. Go to APPS and find the EASYDATA 3. Setup 1:Dist here is where you change units from meter to feet. Notice most programs are written in meters. Choose Ball Bounce then choose number 4 4. When you are satisfied with your data, sketch a Distance-Time plot below. Your graph should have a minimum of five bounces. If you are not satisfied with the results of your experiment, press Start, and try again. When you have a good graph go to the Data Collection sheet and graph your graph. 5. Once you have good data appearing on the calculator. Exit the program by pressing QUIT. 6. Turn your plot on. Press 2 nd y = then zoom Now you need to select a parabola to analyze. a. With the plot displayed, press 2 nd Stat (List) > OPS and select 8:SELECT( b. ENTER where you want to store the selected data. To use L3 and L4, press 2 nd L3, 2 nd L4 ) ENTER a. b. 8. To actually select a part of the graph you will use, press arrow to move the left end of the data you want to keep. Press ENTER. This sets the left bound. Press arrow to move the right end of the data you want. Press ENTER. The selected data will be placed in L3, L4 and then this data will be displayed.

5 Summer 2006 I2T2 Process Page The CBL/CBR program leaves the data connected, press 2 nd STAT PLOT 1:PLOT1 and select the unconnected scatterplot option. 10. Go to your APPS and select Transfrm. Use the upward button to get to the end of the list. Press ENTER and you will see the following screen. Press ENTER and select 2:Install. 11. Press ENTER again and you will go back to the home screen. Press Y =, you will see the follow screen. Type in an equation in y1 (Note: the Transformation APPS can not use any other letters in the equation except A, B, C, D. Letter B = H and C = K in the original equation y = a(x h) 2 + k. ) 12. Go to window and settings and set A= -1 B = 0 C = 1 Step = Go back to the graph and change the A and B. You can use the right and left mouse arrows. You can always just go to the A or B or C and type in different values. 14. Once you have figured out A, B, and C go back to Transform APPS and uninstall the program.

6 Summer 2006 I2T2 Process Page 28. Name Data Collection Graph. 1. Graph your first graph of 5 or more bounces. Label your axis QUESTIONS: 1. The goal is to capture the data of one parabola. Use the TRACE-Right Arrow key to a point near the vertex of the single parabola you selected. Record this point in the table below. X coordinate = B value Vertex Y coordinate = C value 2. The ball bounced straight up and down beneath the detector, yet the plot seems to depict a ball that is bouncing sideways. Explain why this is so. 3. The model for the distance vs. time data is quadratic. Fit your data with a quadratic function in standard form: y = a( x b) 2 + c ( or y = a(x h) 2 + k ). Where b is the x-coordinate of the vertex, c is the y-coordinate of the vertex, and a is the constant. (Hint: the value is equal to the g value, which comes from the physics formula: s(t) = - ½g t 2 + v 0 t + s 0 where g = 32 feet per second or g = 9.8 in meters per second. Remember we choose feet in the ranger APPS) 4. Write and equation of the form y = A(x B) 2 + C. a. For the B value type in your x-coordinate from the vertex. b. For the C value type in your y-coordinate from the vertex. c. Now you need to find a constant A to experiment until you get the best fit. Equation: A= B = C =

7 Summer 2006 I2T2 Process Page Use the information obtained in # 4 above to write the equation in the form of y = ax 2 + bx + c (Remember to use foil) Equation: 6. To check your work, place both equation. a. Clear out the equation and type in y1 = type in your answer from question 4 b. In y2 = type in your answer from question 5 and go to the front of Y2 and change the type of graph to 0. This will show you the path of the equation and leave a trail. 7. The TI-83 or TI-84 has a built in feature that allows you to compute the best fitting quadratic equation through a set of data. This procedure is called a quadratic regression. The values you found for A and B can be tested using a built-in feature of the TI 83 that allows it to compute the best-fitting line through a set of data. To perform a quadratic regression on the data you collect, press STAT and select QuadReg to copy the command to the home screen. On the home screen type in L3, L4, vars then y vars then y2 Home screen: QuadReg L3, L4, Y3 Write your results here and make sure the diagnostic is turned on. Answers should be given in 4 decimal places. QuadReg Y = ax 2 + bx + c a = b = c = Go to the y = menu and in front of Y3 change the type of graph to 0 this will show the graph going over the plot. How do they compare the a, b and c in #5 from above? 8. Explain the role of the a in the equation y = ax 2 + bx + c.

8 Summer 2006 I2T2 Process Page 30. EXTENSION: Use the entire graph created at the beginning of the lab and curve fit piece-wise functions to the lab. Draw the graph and record your equation below. Check your work by graphing your restrictions. Y1 = Y2 = Y3 = Y4 = Y5 =

9 Summer 2006 I2T2 Process Page 31. WALK THE LINE When one quantity changes at a constant rate with respect to another, we say they are linearly related. Mathematically, we describe this relationship by defining a linear equation. In real-world applications, many quantities are linearly related and can be represented by using a straight-line graph. In this activity, you will create constant speed distance versus time plots using a CBR (CBL and motion detector), and then develop linear equations to describe these plots mathematically. YOU NEED: 1 CBR Unit or CBL and Motion Detector CBL/CBR APPS Transformation APPS

10 Summer 2006 I2T2 Process Page 32. Instructions: APPS application CBL/CBR. 1. Connect the Ranger to the Calculator 2. Go to APPS and find the EASYDATA 3. Setup 1:Dist here is where you change units from meter to feet. Notice most programs are written in meters. 4. Choose Time Graph number 2 If the instructions say SET DEFAULTS then the program is needs to have 15 seconds. You need to Press Edit and change your Sample Interval (s): and Number of Samples: to the settings below. 5. When you are satisfied with your data, sketch a Distance-Time plot below. Your graph should have a section of straight line. If you are not satisfied with the results of your experiment, press Start, and try again. When you have a good graph go to the Data Collection sheet and graph your graph. 6. Once you have good data appearing on the calculator. Exit the program by pressing QUIT. 7. Turn your plot on. Press 2 nd y = then zoom 9. (a) In Plot 1, choose ON (b) Type: SCATTERPLOT (choice 1) (c) Xlist: L1 (d) Ylist L2 (e) Mark: 8. Go to your APPS and select Transfrm. Use the upward

11 Summer 2006 I2T2 Process Page 33. button to get to the end of the list. Press ENTER and you will see the following screen. Press ENTER and select 2:Install. 9. Press ENTER again and you will go back to the home screen. Press Y =, you will see the follow screen. Type in an equation in y1 10. Go to window and settings and set A= 0 B = 0 Step = Go back to the graph and change the A and B. You can use the right and left mouse arrows. Remember that downward slope is negative and upward slope is positive. You can always just go to the A or B and type in different values. 12. Once you have figured out A and B go back to Transform APPS and uninstall the program.

12 Summer 2006 I2T2 Process Page 34. Name Data Collection Graph your data and label your axis QUESTIONS: 1. The slope-intercept form of a liner equation is y = MX + B Where M is the slope or steepness of the line and B is the intercept or starting value. In this activity, the control variable, X, represents time and Y represents distance. Press TRACE and use the arrow keys on your calculator to move the cursor along your Distance versus Time plot. Identify the starting value (the Y-value when X = 0 ) and record this below as the intercept, B. B = 2. Go to the y = and type in y1 = Ax + B. A is equal to M the slope. You should see and A= number and B = number along with your graph. In the B= type in the number from question one. Now change the number in A until the line matches the graph of distance versus time. A = (slope) Write the equation in the form of slope intercept form y = mx + b (y = Ax + B) Equation Turn off the Transformation APPS. a. Go to the APPS menu and Transfrm then ENTER and then 1:Uninstall b. Clear out the equation and type in y1 = type in your answer from question 2 c. Check your answer compared to your graph. 3. Go to y = and turn the y1 equation off. (un-highlight the equals )

13 Summer 2006 I2T2 Process Page 35. Press TRACE. Move along the plot with the arrow keys and identify two points (x1, y1) and (x2, Y2) and record them below. Try to pick the points so that they are not too close together. X1 Y1 X2 Y2 When the coordinates of two points on the dame line are know, the slope of the line can be Computed by finding the difference in y values divided by the difference of x values. y2! y1 slope = x! x 2 1 Use this formula to compute the slope of the linear plot and record the result below. Slope = How does this value compare with the value of A you found experimentally in question 2? 4. The values you found for A and B can be tested using a built-in feature of the TI 83 that allows it to compute the best-fitting line through a set of data. This procedure is called linear regression. To perform a linear regression on the data you collect, press STAT and select LinReg (ax + b) to copy the command to the home screen. On the home screen type in L1, L2, vars then y vars then y2 Home screen: LinReg (ax + b) L1, L2, Y2 Write your results here and make sure the diagnostic is turned on LinReg Y = ax + b a = b = r = Go to the y = menu and in front of Y2 change the type of graph to 0 this will show the graph going over the plot.

14 Summer 2006 I2T2 Process Page 36. Write your results from the A and B from question one and two to the a and b from this question. 5. Remember, slope is defined as change in y-values divided by change in x- values. Complete the following statement about slope for the linear data set you collected. In this activity, slope represents a change in divided by a change in. Based on this statement, what are the units of measurement for slope in this activity? 6. As mentioned earlier, the intercept value, B, can be interpreted as the starting position or the starting distance from the motion detector (ranger). What does the value of M represent physically? Hint: think about the units of measurement fro the slope you described in question 5. Lab was modified using Real World Math with Hands-On Look at Algebra Functions, CBL System and High School CBR books from Texas Instruments.