Problem of the week #2

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**the gum ball dilemma**

For this problem we had to find a formula to fit a situation where you can find the amount of money, in pennies, a parent must spend if her kids want gum balls of the same color from a gum ball machine where "X" amount of gum balls costs one penny per gum ball.

What I did to solve this dilemma was to use the mathematical trait of Conjecture and Test in many ways. I created a simple data table with all the information, created a diagram of the gum balls and tried to find a connection to the total amount of gum balls/Pennies spent, the amount of kids wanting gum and the amount of gum ball colors. After I found the connection I created a formula that fit the connection accurately and proved all the solutions I got.

When you keep the kids constant and just change the amount of colors you get the same results as you would keeping the colors constant and changing the number of kids and using multiple tests for the data used to form the formulas. For both situations I got the following formulas:

K = Kids

C = Colors

P = Pennies

2K:

C + 1 = P

3K:

2C + 1 = P

4k:

3C + 1 = P

5K:

4C + 1 = P

6K:

5C + 1 = P

The only way I think you could extend this problem would be to change the amount the parent has to pay for the gum balls, while still paying in pennies. Though this wouldn't change a big part of the problem to would bring a change to the problem making the mathematician think just a little bit more. An example is:

2 Kids

Gum Balls - $0.10

2 2 ?

Gum balls: 1,2/1

2 2 3

C + 1 = total # of gum balls

10(C + 1)

10[(2) + 1)

10(3) = 30

Parent pays $0.30 for the Gum Balls

During this problem I learned how a set of data can be connected in such a way that if you change different factors of the problem the solution still comes to be the same one. It was a problem where you had to put to uses three Mathematical traits: Be Persistent and Patient, Look for Patterns and Conjecture and Test. I used the trait of being Persistent in looking for all my data to support my solutions, I used the trait of Conjecture and Test while solving my data to find the information for my solutions and, finally, I used the trait of looking for patterns when I analyzed my data looking for the connections (patterns) that would come together to create the solutions (the formulas). I think that in this problem I would give myself a 9 out of 10 because I consistently making data to create an accurate solution, I tried multiple ways of doing the problem and created a way of extending it to make it a little more complex.

__Process:__What I did to solve this dilemma was to use the mathematical trait of Conjecture and Test in many ways. I created a simple data table with all the information, created a diagram of the gum balls and tried to find a connection to the total amount of gum balls/Pennies spent, the amount of kids wanting gum and the amount of gum ball colors. After I found the connection I created a formula that fit the connection accurately and proved all the solutions I got.

__Solutions:__When you keep the kids constant and just change the amount of colors you get the same results as you would keeping the colors constant and changing the number of kids and using multiple tests for the data used to form the formulas. For both situations I got the following formulas:

K = Kids

C = Colors

P = Pennies

2K:

C + 1 = P

3K:

2C + 1 = P

4k:

3C + 1 = P

5K:

4C + 1 = P

6K:

5C + 1 = P

__Extension:__The only way I think you could extend this problem would be to change the amount the parent has to pay for the gum balls, while still paying in pennies. Though this wouldn't change a big part of the problem to would bring a change to the problem making the mathematician think just a little bit more. An example is:

2 Kids

Gum Balls - $0.10

__K C P__2 2 ?

Gum balls: 1,2/1

__K C P__2 2 3

C + 1 = total # of gum balls

10(C + 1)

10[(2) + 1)

10(3) = 30

Parent pays $0.30 for the Gum Balls

__Evaluation:__During this problem I learned how a set of data can be connected in such a way that if you change different factors of the problem the solution still comes to be the same one. It was a problem where you had to put to uses three Mathematical traits: Be Persistent and Patient, Look for Patterns and Conjecture and Test. I used the trait of being Persistent in looking for all my data to support my solutions, I used the trait of Conjecture and Test while solving my data to find the information for my solutions and, finally, I used the trait of looking for patterns when I analyzed my data looking for the connections (patterns) that would come together to create the solutions (the formulas). I think that in this problem I would give myself a 9 out of 10 because I consistently making data to create an accurate solution, I tried multiple ways of doing the problem and created a way of extending it to make it a little more complex.

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