THE ALL POWERFUL CALCULATOR!

By : Thomas Sollberger

Teacher’s Page

LEARNERS AND ENVIRONMENT

OBJECTIVES

8th and 9th 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

The All Powerful CalculatorPast to Present and The Functions

Lessons

What would you like to learn about calculators today?

or History Of Calculators

Functions

History of Calculators

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

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.

What is a calculator?

Calculator Timeline

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

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

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.

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-Wheelcalculator, a mechanicalcalculation device

This began a time period of steady growth in the development of calculators

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

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

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

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

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

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

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

Application/Review

1. Who invented Napier’s Bones? _________

2. The first calculating device was the _________ .

3. ____________ invented the slide rule.

4. ____________ invented the first mechanical calculator.

Application/Review

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? _________

Application/Review

10. When were the first handheld, battery powered, electronic calculators developed? ________

11. What was the first calculator that used a microprocessor? _______

Application/Review

Review Answers1. John Napier2. Abacus3. William Gunter4. Willhelm Schikard5. Frank Baldwin, 18726. 18787. 19618. Vacuum tubes9. 1963-196410. 196911. Busico 141-PF

Application/Review

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

Evaluation

Quiz Directions1. Read Question2. Choose best answer of multiple choices

available3. 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

Evaluation

1. Who Invented the first mechanical calculator?

(A.) William Gunter(B.) Willhelm Schickard(C.) John Napier

You answered “A”That is incorrect.

William Gunter invented the slide rule.Try another Will, I mean answer.

Next Question

You answered “B”Good job! That is correct!

Willhelm Schickard invented the first mechanical calculator in 1623.

Return to Question

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

Evaluation

2. The first electronic desktop calculators used:

(A.) Vacuum Tubes(B.) Electronic Transistors

Previous Question

You answered “A”That is correct.

The first desktop calculators were not developed at the time.

Next Question

You answered “B”That is incorrect

Electronic Transistors were developed after the invention of the first desktop

calculator.Try again.

Return to Question

Evaluation

3. When did the first commercial transistorized desktop appear?

(A.) 1961(B.) 1969(C.) 1963-1964

Previous Question

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

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

You answered “C”That is correct.

The first transistorized calculators appeared from 1963-1964 after the end of using

vacuum tubes.

Next Question

Evaluation

4. The first calculator to use a microprocessor was:

(A.) Sharp QT 8D(B.) Curta(C.) Busicom 141-PF

Previous Question

You answered “A”That is incorrect.

The Sharp QT 8D was the first handheld, battery powered, electronic calculator.

Try again.

Return to Question

You answered “B”That is incorrect.

The Curta is a mechanical calculating device invented in 1948.

Try again.

Return to Question

You answered “C”That is correct.

The first calculator with a microprocessor was the Busico 141-PF in 1971.

Submit Quiz

Good Job!

You answered with 100% percent accuracy!Return home to take the other lesson if you

haven’t already.

Functions on Calculators

Orienation

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

Directions

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

The Calculator

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.

The four Basic Functions

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

Multiple KeysNow 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 “2nd” 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 “2nd”

On the Ti-83

Notice the described buttons and functions they allow

Experiment with calling on other functions of the calculator

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.

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.

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

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

Using Sin, Cos, and Tan

Order of Operations

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 -2The solution to putting substitution first is using parenthesis(3-1)x5 = 10

Ln and e

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) = DNE e^0 = 1ln(1) = 0 e^1 = eln(e^0) = 0 ln(e) = 1

Pi “π”

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

Area of a Circle

Graphing

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

“Y=“ “Window” “Graph”

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

Application

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.

Application

5. To input a function to be graphed you must use the ______ button.

6. To display a graph you would use the ________ button.

Application

Review Answers1. angles and lengths2. window3. ln and e^4. parenthesis ()5. Y=6. graph

Quiz Directions

1. Read Question2. Choose best answer available3. Select answer, if it is incorrect you will be

prompted to try again4. You will not be able to move on to the

next question until you answer the previous correctly

Begin Quiz

Evaluation

1. What equation would you use to find the degrees of angle B?a = 6 b = 8 c = 10

(A.) Cos(B) = 8/10(B.) Cos(B) = 6/10

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

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

Evaluation

2. Where would you enter the function y = 2x + 9 to make it visible when pressing “graph”?

(A.) Window(B.) Y=

You answered “A”That is incorrect.

“Window” will take you to view options on what frame to see the graph

Return to Question

You answered “B”Correct.

“Y=“ prompts you to enter the equation that will be graphed and displayed when

you push “graph”

Next Question

Evaluation

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.) 2-1x3+4(B.) (2-1)(3+4)

You answered “A”That is incorrect.

Without order of operations that would equal 3

Return to Question

You answered “B”Correct.

The parenthesis maintained the order of operations and the solution is equal to 7

Submit Quiz

Good Job!

You answered with 100% percent accuracy!Return home to take the other lesson if you

haven’t already.