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Lesson Title: Number Systems
Class: Algebra 3/4
Date: Sept 22 - 23
Standards Covered:
A2.2.A: Explain how whole, integer, rational, real, and complex numbers are related, and
identify the number system(s) within which a given algebraic equation can be solved.
Learning Target:
I can determine which number belongs in which number system.
Time
What I Do
What
Students Do
:00 - :05
Warm up with
http://www.brainbashers.com/showpuzzles.asp?page=1&formp
ost=Y&d1=Y
:05 - :12
Questions from hmwk.
:12 - :50
Students write 5 random numbers (varied).
The Big Point: Every single number can be categorized.
Start with smallest group, the whole numbers. Explain and ask
for examples. Repeat with rationals, reals, complex #s. Show
symbol for each. Use examples of bands for each symbol!
(Zeppelin, Queen, Radiohead,
:50 - :00
Have Placing worksheet on DocCam. Students write down
answers in this manner:
1. 5 is in the _______
2. -2.5 is in the _______.
etc…
:00 - :15
Develop your own explanation for how these systems are
related; can’t be boring. Present at the end of class if willing!
Quiz on EVERYTHING on Wednesday, Hmwk Quiz on Friday.
What went well? What could be improved upon?
Official Definitions
Whole numbers: counting numbers 0 and higher
Integers: (from the Latin integer, literally "untouched", hence "whole"): positive and negative
whole numbers (-1, -6, 17, etc.)
Symbol = bold Z. (z for zahlen [German for numbers])
Rational numbers: any number that can be expressed as the quotient a/b of two integers, with the
denominator b not equal to zero. BOTH NUMBERS MUST BE INTEGERS.
Symbol = bold Q. (q for quotient).
Real numbers: include both rational numbers, such as 42 and −23/129, and irrational numbers,
such as pi and the square root of two. Real number can have infinite decimal representation.
Symbol = bold R.
Complex numbers: number consisting of a real and imaginary part.
Symbol = bold C.
Which most specific number system does x belong
in? Place x in the most specific number system
AND with the correct symbol (Whole, Z, Q, R, C).
e.g. “x is in the integers (Z)”.
1.
2.
3.
4.
5.
6.
7.
8.
x = 3π
x = -5.8
x = 6 + 3i
x=4
x = 19
x = -0.66666666666…
x = 0 + 13i
3x + 2 = 7
2x = 3 + 8
9.
10. x2 = 1
11. x2 = 10
12. 3x + 2 = 11
x 1
13. 7 = 2
14. 4x2 = 20
15. 3x2 = 48
For each of your answers for 1-15, you need to
show/justify how your answer fits into every
category that it does. For example…
8. 3x + 2 = 7
3x = 5
5
x= 3
5
By definition of rational, 3 is a rational number,
since both 5 and 3 are integers.
5
Reals contain the rationals, so 3 is also a real.
5. x = 19
19 is a whole number because it is a counting #.
19 is an integer because it is a whole number.
19 is a rational # because it can be expressed as
19
1 .
19 is a real # because it is a rational number.