My name is professor Mary, and today I am going to teach you
how to work with the Fundamental Counting Principle.
Objectives:
1. Students will learn the definition of the Fundamental Counting Principle, and how to use it in basic math problems.
2. Students will get practice applying the Fundamental Counting
Principle to real life situations.
Procedure:
1. The definition of the Fundamental Counting
Principle is: a way to figure out the total number of ways different events can
occur.
2. The Fundamental counting principle is meant to
be a short cut when you want to find out how many ways something can be done,
for example:
a.
How many different outfits can be made from 6
shirts and 5 pairs of pants?
i. To
solve this you can simply multiply 5 pairs of pants x 6 shirts and get 30 out
fit combinations.
3. Let’s elaborate on why this works: to find the
number of options someone has in any situation you simply multiple the number
of variables by each other to find the total number of possibilities. This
works because it is essentially the same as adding up all of the possible
combinations.
4. To see why the Fundamental Counting Principle is
so important to math we will look at two ways to solve the following problem
a.
How many sundae combinations can you make from
having 3 kinds of ice cream: Vanilla, strawberry, and chocolate, 3 kinds of sauces: chocolate and caramel, and
3 kinds of toppings: chocolate chips, sprinkles, and fruit.
i. The
first approach to solving this is to use the tree diagram, which is essentially
just drawing out the options.
While the tree diagram is still useful, for problems with
more variables it would be a lot harder to draw out and can get confusing and
takes more time.
ii. The second way to solve this is to use the
fundamental counting principle. By taking the numbers you see one the side of
the tree diagram in red: 3,2, and 3 we can multiply those to find the number of
options rather than counting on the tree diagram.
3 x 2 x 3 = 18
5. Jenny wants to order a custom cake for her mom’s birthday.
The bakery has 8 types of cake, 12 kinds of frosting, and 22 different
decoration fonts. How many different cake combinations are possible for Jenny
to choose from?
a. 8 x 12 x 22 = 2,112 different cake combinations.
This problem demonstrates why the Fundamental Counting Principle is so useful in saving math, and make it less likely for errors to occur when solving more complicated problems.
This problem demonstrates why the Fundamental Counting Principle is so useful in saving math, and make it less likely for errors to occur when solving more complicated problems.
This was very helpful for me to learn, I want to thank you for this! The steps that you used makes it very easy to understand, and accomplish how to use the fundamental counting principle by myself, for myself. This gives me a different perspective when I am shopping at chipotle, now I understand why they said they have so many different combinations, at first I though they were pulling that number out of there marketing room, but now I understand that there is true math behind there marketing. Thank you Mary.
ReplyDeleteThis was very helpful! thanks so much!
ReplyDeleteI love how you made the tree diagram it really helped me imagine it.
ReplyDeletethe steps are super clearly laid out I understand this way better now
ReplyDeletemary,
ReplyDeletereally nice job of using colorado standards format for the presentation of your lesson. your lesson was also easy to understand and your examples were relevant. =]
professor little