Lesson #1

                       "Kemit Mystery" (Scientifc Mysteries of the Land of Kemit )                                                

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Painting on a cave wall in Egypt                                                                                                                                                                                       of a man working                             Click on photos  (Giza)                                                                       

 

The Great Pyramid And Pi.Click here for more about Egytpian Mathematics

The Great Pyramid's designed height (481.3949 ft) bears the same relationship to its base perimeter (3023.16 ft) as does the circumference of any circle to its radius, namely 2 Pi.

Pi is not supposed to have been known until the Greeks discovered it in the 3rd century BC, yet the pyramids were built as long ago as 2,500 BC at least.

 

OBJECTIVE:  To show how the ancient Egyptians supplied the Kemetic Theorem of  the Right Triangle (aka The Pythagorean Theorem):  to the building of  the Great Pyramid   ( The Pyramid of Khufu)   Kemetic Theorem (In a  right triangle, the square of the measure of  the  hypotenuse equals the sum of the squares of  the measure of the two legs is: The  square of   the hypotenuse of a right triangle is equal to the square of the sum of  the two sides):

                                                                        c2 = a2 + b2)

Materials:  Paper, pencil, 3 x 5 index cards, sugar cubes.  Text:  The African Roots of  Mathematics, Publisher: Professional educational Services,   Detroit, Michigan 48315,  (313) 824-MATH.

Getting Sarted:  The teacher will introduce the lesson by leading a discussion on the major concepts  concerning the Great Pyramid. 

"A famous mathematical theorem named after a Greek was applied by ancient people of  the Nile Valley to build The Pyramid of   Khufu in 2500 B.C.

                                                                        c2 = a2 + b2

Kemet was  the name  used to refer to the land of  Egypt 2500 B.C. where  the pyramids were built.  Kemit which means black refers to the people and the land they inhabited.  The Great Pyramid of Giza is one of  the 7 wonders of the world.  The mysteries of the Great Pyramid continues to be a riddle that fascinates historicans, scientists and mathematicians, as well as   the average person, young and old thousands of  years after they were built. For centuries, questions such as who built the Pyramids, why and how remain to be unanswered conclusively. Many of the world's greatest leaders and thinkers such as Herodotus, Plato, Pythagoras, Sir Isaac Newton, Napolean studied the pyramids and have tried to unravel its secrets. Many scholars have proposed theories, but few have been able to prove their ideas."

Ask the students these questions: Who built them?  What materials were they constructed from? 

Procedure:  Construct a pyramid measuring 10 centimeters on each side.  Fit each sugar cube together with the next forming a square cube 10 x 10 x  10 x 10 centimeters on each side.  This  will be the base.  The next layer of cubes shoud be place on top of the former layer.  The length of eachs ide of its shou be 8 cm.  Continue placing sugar cubes in the form of a square making each successive layer two centimeter shorter than the former layer.  The final layer should consist of on cube.  The end result should be subar cubes arranged in the form of a pyramid with four triangular sides.

The teacher should check the student's MDW NTR numbers for accuracy.  Check to make sure student's pyramids are arranged correctly.  Did the students take notes on teacher's discussion on the pyramids of Egypt?  What were some of the building materials ancient engineers used to construct the pyramids

Next:  Provide the students with the dimensions of  The Pyramid of Khufu ( The Great Pyramid)

Length of the four sides of Pyramid                          Height of  Pyramid

755.43 ft. north side                                                   481 ft.                                       

756.08 ft south side                                                                                                                                                755.88 ft. east side                                                                                                                                                755.77 ft. west side

According to the Kemetic Theorem of the Right Triangle,

     Taking one half of the average of the four sides 1/2 (756)=378 feet

substituting the above dimensions into the Kemetric Theorem of the Right Triangle formula and solve the equation below to determine the third side ( the hypotenuse).  Check the equation is correct and it balances show all steps

                            c2 = a2 + b2   or     c2= (481) 2 + (378)2

The correct number for side c us oriif tgtthe ancient Kemetic people knew and applied the Pythagorean Theorem in the building of the The Great Pyramid more than 1500 years before Pythagoras the Greek.

Click here for more about Egytpian Mathematics

                                                Lesson # 2    

                                                How a Jet plane flies   

OBJECTIVE: To demonstrate Sir Issac Newton's Third Law of Motion:  Every action has an equal and opposite action

Materials:     Balloons for each student in the classroon

Blow up a balloon and hold the end tightly with your fingers.  Now, in the balloon there is a higher air pressure that in the air around it which pushes the rubber outwards with equal pressures in all directions.  So the balloon gets its shape-a large ball. 

What happens if you now suddenly let go of the balloon?   Try it!  The balloon shoots away in the opposite direction to the air escaping from the mouth.  This agrees completely with Newton's Third Law.  ( The third law of motion, states"  Every action has an equal and opposite reaction.)

The  air escaping backwards produces a force also acting backwards.  A forward reaction follows, and so the balloon moves in a forward direction.  You can also think of it like this: the air escaping backwards pushes against the balloon and so the balloon goes forwards.  While the balloon was held tightly, the air was pressing strongly and equally against the inside.  The forces inside were in equilibrium, cancellling each other out, and so the balloon had no tendency to move.  But he moment you opened the outlet the equilibrium was disturbed.   The air pressure against the front of the balloon was no longer in equilibrium with the pressure against the back of the balloon and so it forced the balloon forwards.   The different explanations which have been given for the forward movement of the balloon really amount to the same thing.

Now, perhaps, you will ask: what has all this got to do with a jet plane?  A jet plane isn't a balloon, is it?  In a jet plane there is a combustion chamber which is open at the back.  By burning a certain kind of fuel, hot gases at high pressure are produced in it.  The gases can only escape in a backward direction.  The backward forces, which are set up, have a forward reaction as a result of which the aircraft is pushed forwards.  Rockets work in the air, as many people suppose.  The rocket works best in airless space because ther is no air resistance to act as a brake.

                                            Lesson # 2a  

                                     Make a Cannon from a  Bottle

OBJECTIVE:  To demonstrate Newton's Third Law of Motion:  Every action has an equal and oppoisite action

Put into the bottle just enough vinegar so that none runs out when the bottle is laid on its side.  Roll a teaspoonful of baking powder in a paper serviette, twist the ends rightly and push the paper "bomb"into the bottle.   Quickly put the cork in and lay the bottle on the two round pencils.  Because of the pressure produced by the carbon dioxide which is generated, the cork is blown out of the bottle with a bang while the bottle runs backwards just like a real cannon.

                                           Lesson #3

                                Electricity:  A Simple Series Circuit

Objective:  1.  Define an electron and demonstrate its presence.

                   2.   Define voltage of electric force

                   3.   Define electrical resistance and identify  various resistors

                   4.   Define a series electrical circuit and demonstrate the presence of  voltage,  resistance and electric                            current.                                      

Material: Radio Shack 50 in one Project Kit or equivalent

 Electrons

The loose electrically charged particles that move in conductors are called electrons.  The charges are negative  by a minus sign on drawings and idagrams.  If something has a surplus (extra) of electrons it is negatively charged.

      If  it has less lectrons than it ordinarily should it is positively charged. 

EXPERIMENT A:  Use a comb in your hair.   Now touch bits of torn up paper.  Are they attracted or repeled by the comb?   (Attracted)  Why? (The comb has picked up extra electrons from your hair and caused it to exert an electro static force on other materials).

If we charged a piece of paper with positive charge and suspended it freely it would be attracted to the comb.  Why:  ( Unlike charges attract each other);   If  we charged up two combs and suspended them they would move away from each other.  Like charges repel.

Now suppose you were to shuffle your feet on a wool rug on a dry winter day and then touch someone.  What happens?  (He would see a spark and experience a mild shock).  Why?  Because he would discharge you of the extra lectrons you accumulated when you shuffled your feet on the rug.

The flow of electrons is call electrical current.

We shall study the flow of electrons thru wires supplied by a battery instead of our feet because it is more practical for our daily uses.

Electric current in the form of  electrons always move thru a conductor from the negative battery terminal to its positive terminal.

Electrons move best thru metals such as gold, silver, copper, or aluminum.   Unfortunately gold and silver are too expensive and aluminum is too brittle to make wire of.  Most wire is copper.

                                                     Voltage

A battery is like a pump.  It creates pressure to push electrons from its negative side thru wire to its positive terminal.  We measure the size of electrical pumps in Volts.  (Show the class batteries of various sizes and voltages).  Voltage then is the electrical force in the cricuit.

                                                 Resistance

Now if we didn't use something with the wire to slow down the electrons, they travel so fast that the wire would overheat and burn.  We call these "slower downers" RESISTORS.

We can open the wire at one or more points and insert resistors.  We now have a simple series circuit.

Of course we want to add a switch and maybe a horn or light to make some real use of the electricity.

EXPERIMENT B Construct an electric cirucit such as experiment 4 in the Radio Shack 50 in 1 project kit.

EXPERIMENT C:  Construct the electric circuit in experiment 5

EXPERIMENT D:  Construct the electric light cirucit in experiment 15.

EXPERIMENT E:  Add any additional experiments as required to satisfy the demands of more demanding students.

                                   Review and Application

Now that we understand what a DC series circuit is (it consists of a switch or switches, a battery or batteries, a resistor or resistors or lamps connected in a loop by wires), we can learn to read as well as draw schematics of electrical circuits.

1.  What is the schematic symbol for a single cell battery?  Draw it.

2.  Draw the schematic symbol for a switch.  Make it open.

3.  Draw the symbol for a resistor.

4.  Draw the symbol for a wire.

5.  Draw they symbol for a lamp.

6.  Draw a schematic diagram of a series circuit consisting of a battery, two resistors, a  lamp, and two switches.

             Lesson #2-  Parallel Electrical Circuits

OBJECTIVE:   1.  Identify electrical circuits with parts in parallel

                          2.   Draw schematics with batteries, resistors,  switches, relays, light or buzzers in                                  parallel.

                          3.   Construct parallel electrical circuits.

Material:            Radio Shack- 50 in 1 Electronic and  Magnetic Project Kit or equivalent electrical                             parts and batteries.

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                                 Parallel Batteries

Not all electrical circuits are series.  it is necessary at times to put some parts in parallel.  For example, two batteries connected in parallel with supply power for a longer period.  However, the cirucit has the same voltage.

EXPERIMENT A: Using battery symbols draw a schematic of two batteries connected in parallel.

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                                   Figure 2-1 

                             Parallel Switches

Sometimes an electrical circuit is turned on or off from two different places.   Two or more switches are needed.

EXPERIMENT B:  Using electric symbols.  Draw two switches in parallel, make one on and one off.

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                         Parallel resistors or Lamps

                                   Figure 2-3

When it is necessary to pwer many lamps with the same voltage they are wired in parallel.

EXPERIMENT C: Draw a schematic necessary to wire 3 lamps in parallel with a series switch and 3 volt battery.

There is an endless number of ways to wire resistors, switches, batteries and lamps in series or parallel circuits or some combination of  each.

EXPERIMENT D:  Try to identify whether the cirucits in the following kit experiments are series or parallel or series-parallel.  Do kit experiments 2, 8, 10, 18, and 44.

                                 Review and Application

To test and apply your understanding of parallel wiring in electric cirucits draw a schematic diagram with the following:

1.  Two batteries in parallel.

2.  Two switches in parallel with each other but in with the  positvie side of the batteries.

3.  Two lamps in parallel with each other but in series with the switches and in parallel with the batteries.

Now have your instructor check your cirucit, then hook it and turn it on.