PURPOSE:
This demonstration will present information to acquaint the audience with the mathematics behind an African children's game.

OBJECTIVE:
To demonstrate the use of mathematics in planning routes.

MATERIALS:
network rope device - board with drawer knobs
network template of dots if you need it
drawing board with a wipe-off marker
 
 
 
 
 

OUTLINE:

I. Introduction

A. Welcome the audience to the Demonstration Stage of the Maryland Science Center
B. Introduce the topic of the demonstration.
­ that games African children play have the same mathematics as that used by professional mathematicians around the world.

A. Draw a Bakuba network
B. Do a small one with rope
C. Have a volunteer try the small one
D. Show how odd vertices are the key to the solution
E. Leave the large one for the end of the demo

A. The children who play games like these can grow up to become product distributors, computer programmers, academic mathematicians, or problem solvers in their community ­ no matter where their community is.
B. There will be opportunities to do these and other games at explainers
C. There are related math activities in the Beyond Numbers exhibit
D. Any questions? Stick around.

DEMO PROCEDURES:

1. Check all materials and equipment to ensure that they are there and functioning.
a. switches are all pointing down
b. beans are in order

2. Adjust stage lighting and have the general announcement for MATH GAMES OF AFRICA played over the PA system .

We would like to invite our visitors to the Demonstration Stage on the second floor for a free live demonstration on ìMath Games of Africaî. Learn how the games played by children in Africa contain the same mathematics as that used by adult professional mathematicians around the world. Come to the demonstration stage to experience how play can help us go Beyond Numbers.

3. This demonstration show how networks **** , can be used in planning out routes, such as mail delivery , mobile health services, and garbage collection.
HistoMAPís Drawing Pictures with Just One Line presents related problems in cutting a sheet of material using a mechanical torch, and laying out a museum gallery.

Tell the audience that you are going to draw a design, like the Bakuba children (children of Kuba) draw in the sand, except that youíll do it on a marker board. You can tell the audience to count how many times you retrace lines, and how many times you lift your pen. then draw the network shown in this packet. Be certain not to lift your pen until the end of the design. Tell the audience that the children in Kuba practice these designs which can be more and more intricate.

Define vertices and what makes them even or odd -- the number of lines coming from them, and whether that number is even or odd. Then go to the board with the knobs to show an application of networks in real life. In particular, you can mention how sanitation workers, mail carriers and snowplow drivers try not to cover the same street more than necessary. Say that you can think of the smaller network on the knob board as an area of a city where each vertex is a street intersection and each line is a street. Youíre going to trace out a path with the rope without covering and ìstreetî twice. Loop the end of the rope around an odd vertex (there are only two) and begin to connect all the vertices. Remember not to use diagonals. You should end on the other odd vertex. There is a mathematical theorem that says if you have a network with exactly two odd vertices, you can only complete the network in this fashion is you start on an odd vertex and end on an odd vertex. This is called an Euler (ìOY-lerî) path. A network that has no odd vertices can be completed with the endpoints at any vertex. And a network with any other number of odd vertices cannot be completed.

Then call up a volunteer to try the same network starting from the other odd vertex to show that it is possible from the two points. You may mention that people can try the harder network after the demo.

4. Finish - Thank the audience for coming, make connections with museum exhibit components, invite questioners to stick around, and clean up.

Put away ropes and erase the board. The knob board may be placed on a cart and used immediately as an explainer.
 

SAMPLE SCRIPT:
Hello there! My name is Maura Hurst and Iíd like to welcome you to the Maryland Science Center. The demonstration Iíve got for you today is about the mathematics found in childrenís games, in particular , games from Africa.

Mathematics is used by everyone. If you can think, you can do mathematics. How many of you have ever played tic-tac-toe? Well, thatís a game involving logic and...mathematics. Some pupil would be surprised to learn that there are many children'sí games that contain the same mathematics used by professional mathematicians all around the world.

One of those games is played by the Bakuba children of Zaire. The children play the game in the sand with their fingers. This game is helping them learn craft skills and can be done with greater and greater complexity. Our pattern will only involve squares. The only rules are that you many not lift up your finger, retrace a line or draw diagonals. Iím going to do one for you now

[Draw the Bakuba network on the white board]

This is one example of a Bakuba network. Here is a board we can use to show another one [go to the board with knobs]. This will only work is we start from an odd vertex.
 

A vertex is any point that has one or more lines coming from it connecting to one or more other points. We can have odd vertices or even vertices. Do you folks know about odd and even numbers? Count with me. Odd numbers are like :1...3...5...7... How about even? Even numbers start with 0...2...4...6... [Point to the corner vertex. Show the two lines coming off the point.] Would this be an odd or even vertex? [even] Thatís right. Thereís two lines coming off of it, so itís even. [Point to the vertex in the middle of the top row] Is this one an even of odd vertex? Right. Itís got three lines so itís odd. [Highlight the three lines coming from the vertex that make it odd.]

Now letís use this Bakuba network to plan a mail delivery route. We have to deliver the mail to all the streets in this area without repeating a street, because we need to save time. Iíll show you how. Letís say this network is a part of a city. The lines are like the streets and the vertices are like the street crossings. Remember, the rules are: you canít retrace a line, and NO diagonals. [Connect all the circles the the yellow rope]. Notice that I started and ended on an odd vertex. Thereís a mathematical theorem that says that in a network with two odd vertices like this, you have to start on one odd vertex and end on the other to complete it.

Now to show that Iím not doing anything tricky, Iíd like a volunteer to solve this same problem. [Call for a volunteer. Have them work the puzzle from the vertex you ended on.] Great, you did it! Letís give our vo;lunteer a big hand.

Business professionals call these figures networks. They decide which networks are possible and which are impossible to complete in order to plan delivery routes for the mail carriers, sanitation workers, snowplow drivers and others. These puzzles will be made available to you to try at the end of the demo, if you like.

I hope that you now understand that math is more than just adding and subtracting numbers and stuff like that - that math is a part of everyoneís life and that math can take you on a fantastic journey. A journey BEYOND NUMBERS!
 

BIBLIOGRAPHY:
Chavey, Darrah; Drawing Pictures with One Line, HistoMAP module 21, COMAP,Inc. Lexington, MA, 1992
The information of African childrenís games of this type is extensive. The bookís excellent bibliography cites M. Ascherís Ethnomathematics: A Multicultural View of Mathematical Ideas as the primary source for information on Eulerian drawings in other cultures.- CB
Zaslavsky, Claudia; Africa Counts, Prinde, Weber & Schmidt, 1973
This was the book that provided us with the original idea. Ms Saslovsky was kind enough to update me on some of the terminology. - CB.
Zaslavsky, Claudia; Multicultural Math, Scholastic Professional Books, 1994

Copyright: 1995 Maryland Science Center

Authors:
From the Maryland Science Center - education department

last revised 5/22/01