1. By : Thomas Sollberger

2. LEARNERS AND ENVIRONMENT OBJECTIVES  8 th and 9 th graders  Math students  Students who need help with using basic calculator functions in algebra and geometry  In the classroom individual by individual  Given a brief history of calculator development a student will be able to answer review questions with 80% accuracy  Given scientific calculator student will be able to with 80% accuracy know how to format and use the calculator for basic algebra problems: Sin, Cos, Tan, Area, Graphing

4. What would you like to learn about calculators today? or History Of Calculators History Of Calculators Functions

6.  Before beginning this lesson think about why one should know more about the history of calculators and calculating devices  You will need to read through the following historical information and dates, memorizing the data specific to calculator development  Click on the next or back icon to review information before completing practice quiz and the review quiz

7.  Calculator  Device used to compute arithmetic operations  An electronic or mechanical device for the performance of mathematical computations  Although many might not think it this is a form of calculator. Imagine using that for math.

8.  As long as man has needed to perform arithmetic there have existed calculating devices to perform the computations necessary to reach a solution  The earliest tool in ancient times was the abacus  Tool relying on movement of beads up and down for arithmetic

9.  The first steps towards a modern calculating device began in the 1600’s  In 1600 John Napier invents “Napier’s Bones” a device used for multiplication  In 1620 William Gunter invented the slide rule used for multiplication and division

10.  The largest development in the 1600’s was the invention of the first mechanical calculator by Willhelm Schickard in 1623.  The calculator used a version of “Napier’s Bones” for multiplication and mechanical gears for addition and subtraction.

11.  After Schickard’s invention of the first mechanical calculator in 1623, there was a long period of little to no development in mechanical calculators  The next break through didn’t come until 1872 when Frank Baldwin invented the Pin-Wheel calculator, a mechanical calculation device  This began a time period of steady growth in the development of calculators

12.  In 1874 W.T. Odhner of Sweden develops his own Pin-Wheel calculator  1878 Raymond Verea develops the first direct multiplication machine  1884 Dorr E. Felt invents the comptometer, the first successful key-driven adding and calculating machine

13.  1891 William S. Burroughs began commercial manufacturing and sale of his printing and adding calculator  1893 The Millionaire Calculator is introduced 1902 The Dalton add-listing machine is invented  The largest period of growth for mechanical calculators and their development, size reduction, electric motor drives, and additional features took place from 1900 to 1975

14.  In 1948 the Curta miniature handheld is developed Curta mechanical calculator  In 1961 the first electronic desktop calculators are invented and manufactured  These calculators used vacuum tubes  From 1963-1964 the first transistorized desktop calculators are developed and sold  Friden EC130 &132, Mathathon IME84, Sharp CS 10A

15.  In 1969 the first hand held, battery powered, electronic calculators are developed  Sharp QT8D and 8B  1970 hand held calculators take off. Even though all are very expensive  1971 the first calculator to use a microprocessor is invented, Busicom 141-PF  In 1972 a rapid development of electronic calculators and a reduction in calculator price takes place

16.  By 1975 mechanical calculator production has practically ceased  Mass production had made electronic calculators very cheap  After 1975 electronic calculators become the main tool for calculation to which improvements are made and additional function are added over time  The last major improvement occurred in 1978 when the first solar powered calculator and card sized calculator is developed

17.  Through this lesson we traced the history of the development of calculation devices from the abacus to the first modern electric calculator  Think about some of the interesting facts you learned now  Proceed to the next slide to begin the review questions over the history of calculators before taking the quiz  Take out a spare sheet of paper and fill in the blanks to the best of your ability and then check your answers at the end to see what you have learned and need to review

18.  Proceed to the next slide to begin the review questions over the history of calculators before taking the quiz  Take out a spare sheet of paper and fill in the blanks to the best of your ability and then check your answers at the end to see what you have learned

19. 1. Who invented Napier’s Bones? _________ 2. The first calculating device was the _________. 3. ____________ invented the slide rule. 4. ____________ invented the first mechanical calculator.

20. 5. Who invented the pin-wheel calculator and when? ________________ 6. When did Raymond Varea develop the first multiplication machine? __________ 7. When were the first electronic calculators created? ________ 8. What did they use? ______ 9. First transistorized calculators debuted when? _________

21. 10. When were the first handheld, battery powered, electronic calculators developed? ________ 11. What was the first calculator that used a microprocessor? _______

22. Review Answers 1. John Napier 2. Abacus 3. William Gunter 4. Willhelm Schikard 5. Frank Baldwin, 1872 6. 1878 7. 1961 8. Vacuum tubes 9. 1963-1964 10. 1969 11. Busico 141-PF

23.  Now that you have completed the review you will be taking the quiz over the history of calculators  Follow the quiz directions to complete the quiz over the material

24. Quiz Directions 1. Read Question 2. Choose best answer of multiple choices available 3. Select and answer and click, if this is not the correct answer try again 4. You will not be able to move on to the next question until you have answered the previous correctly Begin Quiz

25. 1. Who Invented the first mechanical calculator? (A.)(A.)William Gunter (B.)(B.)Willhelm Schickard (C.)(C.)John Napier

26. You answered “A” That is incorrect. William Gunter invented the slide rule. Try another Will, I mean answer. Next Question

27. You answered “B” Good job! That is correct! Willhelm Schickard invented the first mechanical calculator in 1623. Return to Question

28. You answered “C” That is incorrect. John Napier invented Napier’s Bone. This person’s calculator did however use Napier’s Bones. Try another answer. Return to Question

29. 2. The first electronic desktop calculators used: (A.)(A.) Vacuum Tubes (B.)(B.)Electronic Transistors Previous Question Previous Question

30. You answered “A” That is correct. The first desktop calculators were not developed at the time. Next Question

31. You answered “B” That is incorrect Electronic Transistors were developed after the invention of the first desktop calculator. Try again. Return to Question

32. 3. When did the first commercial transistorized desktop appear? (A.)(A.)1961 (B.)(B.)1969 (C.)(C.)1963-1964 Previous Question Previous Question

33. You answered “A” That is incorrect. In 1961 the first electronic desktop calculators were created and they used vacuum tubes. Try again. Return to Question

34. You answered “B” That is incorrect. In 1969 the first handheld batter calculators were invented much after the start of using transistors in calculators. Try again. Return to Question

35. You answered “C” That is correct. The first transistorized calculators appeared from 1963-1964 after the end of using vacuum tubes. Next Question

36. 4. The first calculator to use a microprocessor was: (A.)(A.)Sharp QT 8D (B.)(B.)Curta (C.)(C.)Busicom 141-PF Previous Question Previous Question

37. You answered “A” That is incorrect. The Sharp QT 8D was the first handheld, battery powered, electronic calculator. Try again. Return to Question

38. You answered “B” That is incorrect. The Curta is a mechanical calculating device invented in 1948. Try again. Return to Question

39. You answered “C” That is correct. The first calculator with a microprocessor was the Busico 141-PF in 1971. Submit Quiz

40. Good Job! You answered with 100% percent accuracy! Return home to take the other lesson if you haven’t already.

42.  Before beginning this lesson think about what functions will be important for math subjects  Specifically basic algebra and geometry operations  There will be a review quiz on some functions

43.  Take out a calculator, preferably a TI-83, and follow along with the examples in the lessons over functions  Test the examples and problems on your calculator  Click on the next or back arrow to navigate the information before the quiz

44. One of the most commonly used calculators a student will use is the scientific calculator. A scientific calculator has thousands of combinations of functions to solve a given problem, therefore it is of utmost importance to understand functions provided.

45. Today every calculator has the same basic functions which we all know; Addition (+) Subtraction (-) Division (/) Multiplication (x) However a scientific calculator, having a much larger amount of functions, we will need to learn how to use

46. Now look to your calculator in hand.  Each button has multiple assigned meanings.  The white label on each button is its the first function.  The yellow label is the button’s second function which can be activated by pressing the yellow “2 nd ” button in the upper right corner.  The green label is the button’s third function which can be activated by pressing the green “Alpha” button below “2 nd ”

47.  Notice the described buttons and functions they allow  Experiment with calling on other functions of the calculator

48. Some important functions for Algebra and Geometry include; sin( ), cos( ), tan( ), √, π, ^, ln, e^, Y =, and graph. These functions are essential for certain problems in theses subjects.

49. The first functions I will review are: sin( ), cos( ), and tan( ) To use these functions we must first properly define them to understand them. It is also important to know what context they can be used. These functions can only be used in problems involving right triangles.

50.  sin( θ ) = opposite / hypotenuse  This means the sin of some angle ( θ ) is equal to the opposite side of the triangle, in comparison to the angle, divided by the hypotenuse (longest side of the triangle)  cos( θ ) = adjacent / hypotenuse  This means the cos of some angle ( θ ) is equal to the adjacent side of the triangle, in comparison to the angle, divided by the hypotenuse

51.  tan( θ ) = opposite / adjacent  This means the tan of some angle ( θ ) is equal to the opposite side of the triangle, in comparison to the angle, divided by the adjacent side of the triangle

53. Another essential function maintains order among problems is the parenthesis () Although calculator’s are great arithmetic tools they do not automatically follow the order of operations This is why the function of parenthesis exists Ex. If you input 5x3-1 it will equal 14 but if you enter 3-1x5 it will equal -2 The solution to putting substitution first is using parenthesis (3-1)x5 = 10

54. ln and e^ are also important functions within algebra problems ln and e^ also happen to be inverses of one another and using them in algebra relies on knowing there rules Ex.ln(0) = DNEe^0 = 1 ln(1) = 0e^1 = e ln(e^0) = 0ln(e) = 1

55. Other important functions include the use of the ‘ π ’ function to represent pi(3.14) for questions involving shapes’ measurements, areas, and volumes and the power function(^) to operate those equations Ex. Finding the area and circumference of a circle to the nearest inch

57. Another important function to know is the graphing function. To plot a graph and understand its movement you will need to know these functions:  “Y=“ “window” and “graph”  “Y=“ allows you to assign a function to the calculator to be graphed  “window” allows you to adjust what spectrum you are viewing the graph  “graph” allows you to see the graph be demonstrated on screen and understand its movement

59.  Now that you have reviewed and learned some of the important functions you will go through and answer the questions on the practice quiz before the review quiz  Fill in the blanks to the best of your ability and compare your answers to the solutions at the end  Once complete, navigate back to review the information or begin the review quiz

60. 1. Sin(), Cos(), and Tan() are important for functions looking for ________ and ______ of right triangles. 2. To adjust the view of a graph you will adjust the _________ 3. _______ and ______ are inverse functions of one another. 4. ___________ are used to maintain order of operations.

61. 5. To input a function to be graphed you must use the ______ button. 6. To display a graph you would use the ________ button.

62. Review Answers 1. angles and lengths 2. window 3. ln and e^ 4. parenthesis () 5. Y= 6. graph

63. 1. Read Question 2. Choose best answer available 3. Select answer, if it is incorrect you will be prompted to try again 4. You will not be able to move on to the next question until you answer the previous correctly Begin Quiz

64. 1.What equation would you use to find the degrees of angle B? a = 6 b = 8c = 10 (A.)(A.)Cos(B) = 8/10 (B.)(B.)Cos(B) = 6/10

65. You answered “A” That is incorrect. Cos(B) = 8/10 would not be able to be used as 8 is not the adjacent side length for angle B. This could work if it were Sin(B) = 8/10. Return to Question

66. You answered “B” That is correct. You would use that equation and then use Cos^-1 of 6/10 to find the degrees of angle B, because 6 is the adjacent sides length Next Question

67. 2.Where would you enter the function y = 2x + 9 to make it visible when pressing “graph”? (A.)(A.)Window (B.)(B.)Y=

68. You answered “A” That is incorrect. “Window” will take you to view options on what frame to see the graph Return to Question

69. You answered “B” Correct. “Y=“ prompts you to enter the equation that will be graphed and displayed when you push “graph” Next Question

70. 3. Write the provided function in the order of operations as it is stated in. Function = two minus one, times, three plus four Function = 7 (A.)(A.)2-1x3+4 (B.)(B.)(2-1)(3+4)

71. You answered “A” That is incorrect. Without order of operations that would equal 3 Return to Question

72. You answered “B” Correct. The parenthesis maintained the order of operations and the solution is equal to 7 Submit Quiz

73. Good Job! You answered with 100% percent accuracy! Return home to take the other lesson if you haven’t already.