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Investigations with the Graphing Calculator

Investigations with the Graphing Calculator. Jim Rahn LL Teach, Inc. www.jamesrahn.com james.rahn@verizon.net. Building Understanding for Constant Rate of Change with Recursion.

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Investigations with the Graphing Calculator

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  1. Investigations with the Graphing Calculator Jim Rahn LL Teach, Inc. www.jamesrahn.com james.rahn@verizon.net

  2. Building Understanding for Constant Rate of Change with Recursion

  3. The Empire State Building has 102 floors and is 1250 feet high. How high are you when you are reach the 80th floor? Explain your reasoning.

  4. A 25-story building has floors at the described heights. • How can you predict the height of the next floor based on the previous floor’s height? • This is called a recursive sequence. • Find the height of the 4th and 10th floors? • Which floor is 215 feet above ground? • How high is the 25th floor? • Explain your reasoning

  5. A 25-story building has floors at the described heights. • How can you predict the height of the next floor based on the previous floor’s height? • This is called a recursive sequence. • Find the height of the 4th and 10th floors? • Which floor is 215 feet above ground? • How high is the 25th floor? • Explain your reasoning

  6. How can we model this on the graphing calculator? Method 1 Method 2 Method 2

  7. Make figure 1-3 • Determine how many toothpicks it takes to make each figure. • Determine the number of toothpicks on each perimeter. • Record the data in a chart. • Write a recursive sequence for each that you can use on your graphing calculator.

  8. Predict the numbers for figure 4-6. • Predict the number of toothpicks in the 20th figure. • Predict the perimeter of the 20th figure. • Predict which figure will use 79 toothpicks. • Predict which figure will have a perimeter of 79 toothpicks

  9. Discovering the Effects of M

  10. Enter the equation y = 2x in your graphing calculator. • Create a graph of this line in a Zoom 4.Decimal Window.

  11. Create a table that begins at x = 0 and increases by 1. • Describe what you notice about the change in the x values? • What do you notice about the change in the y values? • What is the ratio of the change of y to the change in x?

  12. Create a table that begins at x = 0 and increases by 2. • Describe what you notice about the change in the x values? • What do you notice about the change in the y values? • What is the ratio of the change of y to the change in x?

  13. Create a table that begins at x = 0 and increases by 3. • Describe what you notice about the change in the x values? • What do you notice about the change in the y values? • What is the ratio of the change of y to the change in x?

  14. Create a table that begins at x = 0 and increases by 1/2. • Describe what you notice about the change in the x values? • What do you notice about the change in the y values? • What is the ratio of the change of y to the change in x?

  15. You worked with the same equation for each table. What did you notice about the ratio of the change in y to the change in x? • Try creating a different table by change the ΔTBL. Calculate the change in y and the change in x for each table. What do you notice? • How is the ratio related to the equation you entered in the calculator?

  16. Enter the equation y = 3x in your graphing calculator. • Create a graph of this line in a Zoom 4.Decimal Window.

  17. Create a table that begins at x = 0 and increases by 1. • Describe what you notice about the change in the x values? • What do you notice about the change in the y values? • What is the ratio of the change of y to the change in x?

  18. Create a table that begins at x = 0 and increases by 2. • Describe what you notice about the change in the x values? • What do you notice about the change in the y values? • What is the ratio of the change of y to the change in x?

  19. Create a table that begins at x = 0 and increases by 3. • Describe what you notice about the change in the x values? • What do you notice about the change in the y values? • What is the ratio of the change of y to the change in x?

  20. Create a table that begins at x = 0 and increases by 1/2. • Describe what you notice about the change in the x values? • What do you notice about the change in the y values? • What is the ratio of the change of y to the change in x?

  21. You worked with the same equation for each table. What did you notice about the ratio of the change in y to the change in x? • Try creating a different table by change the ΔTBL. Calculate the change in y and the change in x for each table. What do you notice? • How is the ratio related to the equation you entered in the calculator?

  22. Enter the equation y = (3/2)x in your graphing calculator. • Create a graph of this line in a Zoom 4.Decimal Window.

  23. Create a table that begins at x = 0 and increases by 1. • Describe what you notice about the change in the x values? • What do you notice about the change in the y values? • What is the ratio of the change of y to the change in x?

  24. Create a table that begins at x = 0 and increases by 2. • Describe what you notice about the change in the x values? • What do you notice about the change in the y values? • What is the ratio of the change of y to the change in x?

  25. Create a table that begins at x = 0 and increases by 3. • Describe what you notice about the change in the x values? • What do you notice about the change in the y values? • What is the ratio of the change of y to the change in x?

  26. Create a table that begins at x = 0 and increases by 1/2. • Describe what you notice about the change in the x values? • What do you notice about the change in the y values? • What is the ratio of the change of y to the change in x?

  27. You worked with the same equation for each table. What did you notice about the ratio of the change in y to the change in x? • Try creating a different table by change the ΔTBL. Calculate the change in y and the change in x for each table. What do you notice? • How is the ratio related to the equation you entered in the calculator?

  28. Enter the equation y = -(1/2)x in your graphing calculator. • Create a graph of this line in a Zoom 4.Decimal Window.

  29. Create a table that begins at x = 0 and increases by 1. • Describe what you notice about the change in the x values? • What do you notice about the change in the y values? • What is the ratio of the change of y to the change in x?

  30. Create a table that begins at x = 0 and increases by 2. • Describe what you notice about the change in the x values? • What do you notice about the change in the y values? • What is the ratio of the change of y to the change in x?

  31. Create a table that begins at x = 0 and increases by 3. • Describe what you notice about the change in the x values? • What do you notice about the change in the y values? • What is the ratio of the change of y to the change in x?

  32. Create a table that begins at x = 0 and increases by 1/2. • Describe what you notice about the change in the x values? • What do you notice about the change in the y values? • What is the ratio of the change of y to the change in x?

  33. You worked with the same equation for each table. What did you notice about the ratio of the change in y to the change in x? • Try creating a different table by change the ΔTBL. Calculate the change in y and the change in x for each table. What do you notice? • How is the ratio related to the equation you entered in the calculator?

  34. Building an Understanding for y=b+mx

  35. Jose’s Savings • On Jose’s 16th birthday he collected all the quarters in his family’s pockets and placed them in a large jar. He decided to continue collecting quarters on his own. He counted the number of quarters in the jar periodically and recorded the data in a chart.

  36. 1. Make a scatter plot of the data on your calculator. Describe any patterns you see in the table and/or graph. • 2. Select two points that you believe represents the steepness of the line that would pass through the data. (______, ______) and (______, ______) • Find the slope of the line between these two points.

  37. Give a real world meaning to this slope. • Use the slope you found to write an equation of the form y = Bx. • Graph this equation with your scatter plot. • Describe how the line you graphed is related to the scatter plot. • What do you need to do with the line to have the line fit the data better?

  38. Run the APPS TRANFRM on your graphing calculator. Change your equation to y=a+bx. Press WINDOW and move up to Settings. Change A to start at 0 and increase by steps of 10. Press GRAPH and notice that A=0 is printed on the screen. Use the right arrow to increase the value of A. What happens to the graph as you increase the value of A. • Continue to increase or decrease the value of A until you have a line that fits the data. Write the equation for your line.Y = _____________________ • What is the real world meaning for the y-intercept you located?

  39. Calculating Permutations and Combinations on the Graphing Calculator

  40. Go to the home screen and first press 4 Then press Math and cursor to the right to PRB Select 2. nPr Enter the second r. Press Enter to find the answer. • CALCULATING A PERMUTATION

  41. On the home screen bring the previous line back by pressing 2nd ENTER. Cursor to the 4 on the right and replace it with 3. Press Enter to find the answer. • CALCULATING A PERMUTATION

  42. Go to the home screen and first press 4 Then press Math and cursor to the right to PRB Select 2. nCr Enter the second r. Press Enter to find the answer. • CALCULATING A COMBINATION

  43. On the home screen bring the previous line back by pressing 2nd ENTER. Cursor to the 4 on the right and replace it with 3. Press Enter to find the answer. • CALCULATING A PERMUTATION

  44. Investigations with the Graphing Calculator Jim Rahn LL Teach, Inc. www.jamesrahn.com james.rahn@verizon.net

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