Number Sense and Operations
for Industrial Technology
Electricity & Electronics
By
Andrew Olson- Bemidji High School
([email protected])
Overview:
This curriculum piece is an assortment of activities that will help students gain a better
understanding of the mathematics involved in the study and understanding of electricity
and electronics. This packet was designed to be implemented in an automotive or
electronics class at the high school level. The concepts and theories would be introduced
over the course of nine weeks. The class period runs 85 minutes Monday through Friday.
This allows for introduction of new material while giving time for activities.
The main areas that these activities will cover are the use of basic math facts, fractions,
decimals (scientific notation), percents, and measurement.
Most of the students will have a basic understanding of the main areas and some will be
in need of extra help. The Industrial Technology classes see a high number of students
with below grade level scores in math and science as well as all other levels.
Launch:
The launching of the curriculum will be accomplished through a combination of lecture,
and small group activities followed up by a series of discussions. The groups will discuss
how they felt about the games and activities and how the activities and games may have
helped to better understand math concepts.
Explore:
Students will explore the concepts through the games and activities in a manner that may
seem elementary but will strengthen their skills as well as introduce new concepts.
Sharing:
Sharing the answers and strategies of the games and activities in a classroom setting will
allow for all to see the different ways answers and games can be achieved. This is what I
hope to accomplish.
What's the largest number? What's a googol? How do we name large numbers?
What is infinity?
What's the largest number?
There is no largest number! Why? Well, 1,000,000,000 (1 billion) can't be the largest
number because 1 billion + 1 is bigger - but that is true for any number you pick. You can
choose any big number and I can make a bigger one just by adding 1 to it.
What's a googol?
A googol is a 1 with a hundred zeroes behind it. We can write a googol using exponents
by saying a googol is 10^100.
The biggest named number that we know is googolplex, ten to the googol power, or
(10)^(10^100). That's written as a one followed by googol zeroes.
How do we name large numbers?
There's some disagreement in the English language about how to name large numbers.
There are two systems, the American and the English:
American:
Thousand
Million
Billion
Trillion
Quadrillion
Quintillion
Number
Scientific
Notation
1,000
1,000,000
1,000,000,000
1,000,000,000,000
1,000,000,000,000,000
1,000,000,000,000,000,000
10^3
10^6
10^9
10^12
10^15
10^18
Thousand
1,000
Million
1,000,000
Thousand Million
1,000,000,000
Billion
1,000,000,000,000
Thousand Billion
1,000,000,000,000,000
Trillion
1,000,000,000,000,000,000
10^3
10^6
10^9
10^12
10^15
10^18
English:
What is infinity?
Infinity is not a number; it is the name for a concept. Most people have sort of an
intuitive idea of what infinity is - it's a quantity that's bigger than any number. This is sort
of correct, but it depends on the context in which you're using the concept of infinity (see
below).
There are no numbers bigger than infinity, but that does not mean that infinity is the
biggest number, because it's not a number at all. For the same reason, infinity is neither
even nor odd.
The symbol for infinity looks like a number 8 lying on its side: .1
Now for the fun part! Even though infinity is not a number, it is possible for one infinite
set to contain more things than another infinite set. Mathematicians divide infinite sets
into two categories, countable and uncountable sets. In a countably infinite set you can
'number' the things you are counting. You can think of the set of natural numbers
(numbers like 1,2,3,4,5,...) as countably infinite. The other type of infinity is uncountable,
which means there are so many you can't 'number' them. An example of something that is
uncountably infinite would be all the real numbers (including numbers like 2.34.. and the
square root of 2, as well as all the integers and rational numbers). In fact, there are more
real numbers between 0 and 1 than there are natural numbers (1,2,3,4,...) in the whole
number line! See One infinity larger than another? for more information.
Lastly, please realize that the concept of infinity varies depending on what mathematical
subject area you're talking about. If you're simply counting things up, then the picture
looks something like this:
If you're talking about the number line, then the picture looks something like this:
If you're talking about the number of elements in a set, here's the picture:
Do you know this number, 300,000,000 m/sec.?
It's the Speed of light !
Do you recognize this number, 0.000 000 000 753 kg. ?
This is the mass of a dust particle!
Scientists have developed a shorter method to express very large numbers. This method is
called scientific notation. Scientific Notation is based on powers of the base number 10.
The number 123,000,000,000 in scientific notation is written as :
The first number 1.23 is called the coefficient. It must be greater than or equal to 1 and
less than 10.
The second number is called the base . It must always be 10 in scientific notation. The
base number 10 is always written in exponent form. In the number 1.23 x 1011 the
number 11 is referred to as the exponent or power of ten.
To write a number in scientific notation:
Put the decimal after the first digit and drop the zeroes.
In the number 123,000,000,000 The coefficient will be 1.23
To find the exponent count the number of places from the decimal to the end of the
number.
In 123,000,000,000 there are 11 places. Therefore we write 123,000,000,000 as:
Exponents are often expressed using other notations. The number 123,000,000,000 can
also be written as:
1.23E+11 or as 1.23 X 10^11
For small numbers we use a similar approach. Numbers less smaller than 1 will have a
negative exponent. A millionth of a second is:
0.000001 sec. or 1.0E-6 or 1.0^-6 or