Mar

30

2018

Every day is special and provides opportunities to explore math with our children. National Grilled Cheese Day, which occurs on April 12th, is a fun occasion to incorporate learning into!

Celebrate National Grilled Cheese Day with some cheesy **combinatorics**! To do this, let’s get fancy with our grilled cheese sandwiches and count the number of different types we can make. While doing this, you’ll be exploring the branch of mathematics know as **Combinatorics**. This area of mathematics was studied by ancient Indian, Arab and Greek mathematicians. The idea is that by studying patterns in tree diagrams we are able to count quantities that are much too large to count using conventional methods.

For example, let’s start a tree diagram! Using only white bread with American or Swiss cheese you can make two different sandwiches.

If you also have a choice of bread, white or wheat, you would have four different sandwich choices.

If you add a third cheese choice, Gouda, you would extend your tree diagram to see that there are six possible sandwiches.

Now let’s get fancy and add turkey or bacon to your sandwich. Can you see how to extend the tree diagram to show the twelve possible sandwiches?

Now that you’ve got the idea, see if your family can solve the problems below!

In Honor of National Grilled Cheese Day, the cafeteria is serving grilled cheese sandwiches:

1. How many sandwiches can be made with exactly one bread choice and one cheese choice?

2. How many sandwiches can be made with exactly one bread choice, one cheese choice and one protein choice?

3. How many sandwiches can be made with exactly one bread choice, one cheese choice, one protein choice and one vegetable choice?

4. How many sandwiches can be made with exactly one bread choice, one cheese choice, one protein choice, one vegetable choice and one choice from the other column?

*Ready to check your work? Answers are below.*

Answers:

- 25 sandwiches;

5 bread choices x 5 cheese choices = 25 - 100 sandwiches;

5 bread choices x 5 cheese choices x 4 protein choices = 100 - 500 sandwiches;

5 bread choices x 5 cheese choices x 4 protein choices x 5 vegetable choices = 500 - 2,000 sandwiches;

5 bread choices x 5 cheese choices x 4 protein choices x 5 vegetable choices x 4 other choices = 2,000