Lesson start ideas	Give a creative idea how to begin a lesson
Which subject	Mathematics
What age group	Year or Grade 11
What topic	Permutatiom
Quantity	1
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Introduction

Welcome, young mathematicians, to today's class! We will be delving deep into the interesting and exciting world of permutations. But before we dive in, let's try something fun to get our minds working:

Warm-Up Activity: Permutation Puzzles

You will be given a set of 6 colored tiles. Each tile has one of the following colors: red, blue, green, yellow, pink, or orange.

1. Take a moment to examine your tiles and observe the different colors.
2. Now, arrange your tiles in every possible combination that you can think of.
3. Write down the number of arrangements you have come up with.
4. Exchange your tiles with your neighbor and repeat steps 1 to 3.

Discussion: What are Permutations?

Now, let's use our warm-up activity as a starting point to discuss permutations.

Permutations are the different arrangements we can make from a given set of items. Just like in our tile activity, we can arrange the tiles in different ways to create different patterns.

In Mathematics, permutations are denoted by 'nPr' and can be calculated as:

nPr = n! / (n-r)!

Where 'n' is the total number of items in the set and 'r' is the number of items we take to create each permutation.

Conclusion

Now that we have a basic understanding of permutations, we can move on to more complex problems involving them. Permutations are used in many fields including Computer Science, Statistics, and Cryptography.

So gear up students, as we are about to discover the exciting possibilities that permutations have to offer!