Tuesday, September 4, 2012

Permutations and Combinations Lesson 1

Here is my lesson plan for my first lesson in Math 30-1 on Permutations and Combinations. Which covers the outcome: Apply the fundamental counting principle to solve problems.

(My students sit in groups of 4 and 5)

First show the following funny video,

Next, show this video:

After which, ask the question "How many different possible pin numbers could there be?"

Give the students about 2-3 minutes to discuss and then re-ask the last question

This is where you can go in any direction you please.  In my lesson, the gentleman in the movie has either a 4 or 5 digit PIN number (we don't know).

Now allow students to work for approximately 10 minutes.

After this is done, ask the class:

How did you arrive at your number?  Here I would actually have students come up and solve on the board

What assumptions did you make?

Is there a way we could arrive at the answer more efficiently?

Take this time to discuss that you should multiply the different possibilities of having a 5 digit pin, and the possibilities of having a 4 digit pin, and then you should ADD these answers together.

Next show the students the following picture of a hand knit mitten, and explain the following:

Jennifer makes this mitten out of four different parts, the fabric of the entire mitten, the middle "tree or leaf" part, the bead, and the strings which tie them together, and has multiple different colours for each part.

Then ask: How many different mittens can Jennifer make?

I would let students talk as long as they needed until they realized they are missing a lot of vital information.  Ask for any questions or information they might need (just like the previous question) and provide them with the following: (You can change as you see fit)

5 different colours of yarn for the mitten
3 different tree/leaf colours
5 different colours for the string.

Give time to solve and then ask

How did you arrive at your number?  Here I would actually have students come up and solve on the board

What assumptions did you make?

Is there a way we could arrive at the answer more efficiently?

Which shows that Boston Pizza currently has 4 different types of wings with 21 different flavours of each type of wing.

The problem:  Red Deer Rebels (or whichever local hockey team you want) is having dinner and orders 8 different double orders of chicken wings, how many different combinations could there be?

Again, using the same process students will need to know if you can have more than 1 flavour, and you can have up to 2 flavours PER double order, or they could be the same flavour as well.

After, ask the three crucial questions again, with some leading if needed.

If you have more time I would ask the following question:

Should Alberta, currently, be concerned with the number of phone numbers in the province and truly needed to add the 3rd area code (587)?

Following the same procedure of asking if they require more information and then the three crucial questions of debrief.