This will really twist your students’ minds and possibly create a deeper understanding of our own decimal, or base ten, number system.
Computers use a base two system known as binary in which there are only two numeric symbols: 0 and 1. As a result, when you add 1 + 1, there is no 2. Instead, you regroup and reach 10. Here’s a fantastic use of the Socratic Method to teach binary.
The following are correct equations in binary:
- 1 + 1 = 10 (10 is equivalent to 2 in decimal)
- 10 + 10 = 100 (same as 2 + 2 = 4 in decimal)
- 10 – 1 = 1
Hexadecimal (or base sixteen) is also commonly used in computer science and uses sixteen numerals (0 through 9 and A – F). In this system A is equivalent to our 10. Here are some true equations in hexadecimal:
- 9 + 1 = A (since A is the 11th numeral)
- A + 1 = B
- B – A = 1
- B + A = 15
Historical Use Of Non-Decimal Systems
These non-decimal systems are not restricted to computers. The Mayan’s used a base twenty system while the Babylonians used a base sixty system. Imagine having sixty distinct numeric symbols! How would it change arithmetic?
Non-Arabic Numeral Systems
In the same vein, increase students appreciation of our Arabic system by trying arithmetic using Roman Numerals. Or investigate how did Chinese used number rods to perform arithmetic. Look into the abacus and its use as an early calculator.
These activities make great explorations for students who have already demonstrated mastery of grade-level standards and will encourage them to think about math from multiple points of view.