Mathematics for Elementary Teachers

Summer 2007

Class 1 June 25

Each student will build a “Mystery Device” for later use. 

The picture to the right is of my MD.

Note that each section of the longer crossed arms has 4 beads and each shorter arm has 3 beads.

After you build one of these devices you will create several (at least 2) different number systems for it.

 

 

 

 

 

 

 

 

 

For example my first number system has each of the beads on the longer arms worth 11 and each of the beads on the shorter arms worth 1 when the beads are pushed to the center.  So for the picture below, the number represented is 25 (2(11) + 3).

A couple of questions about my first number system. 

1. How can the numbers from 1 – 100 be represented?
2. How big a number can be represented?
3. Can numbers be represented in more than one way?

 

 

 

 

My second number system each bead on the longer arms is 50 and when the short arm is out the bead is worth 1 and when the arm is in the bead is worth 5. So that the picture a the right represents the number 12.   Consider the questions for the first device. 

One possibility is to give the beads on each arm a different value.  Another is to give some of the beads a negative value.

After you build your system, create several (at least 2) systems for your device.  Try not to model your system on our base 10 number system.

After you create your system pair up and teach each other your number system and then a couple of you will be asked to come up to the front and explain your number system, give some examples and ask the class to guess what numbers are represented.  You should try to use algebraic notation to describe your numbers.

Try to write out in words how your system represents numbers.