# MATH

• WELCOME TO MATH!

I understand some students found last Friday's work of Arrangements and Combinations to be a bit confusing.
I understand. This type of math can be very challenging to understand just via written explanations.

Today let's go to your Math Workbook, page 86.
At the top you will find the organized list a boy named John made to show how many ways he could make that 3-section flag out of three different colors.

It makes sense that he considered first the color of the top triangle. He decided to begin with red. Because there were two more colors for the other sections, he created the combination of those two colors once in each place. There were two possible arrangments with RED as the color of the top triangle.
Then he made the top triangle green and created the two possible remaining combinations for the other parts of the flag.
Finally, he made the top triange yellow and created the two possible remaning combonations for the other parts of the flag.

We can do the same thing.

Let's work on Number 1 together:
They gave you the two possible combinations that can occur if you are involving quarters in the coins.
► one quarter and one dime. (QD)
OR
►one quarter and two nickels. (QNN)
(Remember, using pennies is not an option.)
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NEXT, our job is to think about the possible combinations that DON'T involve quarters.
Let's start with the next largest value of coin first, which is a dime.
►Three dimes and one nickel (DDDN) = 35¢
►(Let's cut back to two dimes.) Two dimes and three nickels (DDNNN) = 35¢
►(Let's cut back to one dime.) One dime and five nickels (DNNNNN) = 35¢
►(Let's cut back to zero dimes.) Seven nickels (NNNNNNN) = 35¢

VOILA! THERE WERE A TOTAL OF SIX POSSIBLE COMBINATIONS, AND WE FOUND THEM ALL! (OKAY, THEY GAVE US THE FIRST TWO, BUT WE FOUND ALL THE REST! :)
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Let's work on #2 Together, and this time we will put it in a chart format so you can more easily see the possible combinations.
For our chart,
S = Spinach / T = Tomatoes / C = Cucumber

Spinach in the first row.       S   T   C   T
Spinach in the first row.       S   C   T   T

Now, put  Cucumber in the first row.    C   T   T   S
Cucumber in the first row.    C   T   S   T
Cucumber in the first row.    C   S   T   T

Next, put  Tomatoes in the first row.     T   T   C   S
Tomatoes in the first row.     T   T   S   C
Tomatoes in the first row.     T   C   T   S
Tomatoes in the first row.     T   C   S   T
Tomatoes in the first row.     T   S   T   C
Tomatoes in the first row.     T   S   C   T