## GPA Calculator

Create a spreadsheet that computes a weighted average for a grade point average.

• Allow students to input course names, credits, and letter grade received.
• A student can enter at least 20 courses.
• Provide the weighted GPA (allowing for +/- grades), rounded to two decimal places.
• Have clear directions to students about how to use the spreadsheet.

## Collatz conjecture

Create a spreadsheet that explores the Collatz conjecture.

Take any natural number, $$n$$. If $$n$$ is even, compute $$n/2$$. If $$n$$ is odd, compute $$3n+1$$. Repeat the previous process until $$n=1$$. The conjecture states that all natural numbers will eventually go to 1.

• Allow a student to input a number. Then the spreadsheet will give the sequence (≤ 150 steps) and the number of steps. (Note: If the number of steps is greater than 150, you may just say so.)
• Have clear directions to students about how to use the spreadsheet.

## Linear system

Create a spreadsheet that helps students find the solution to a system of two linear equations.

• Allow a student to input two linear equations in standard form.
• Have clear directions to students about how to use the spreadsheet.
• Give answers as a clearly labeled ordered pair. If no ordered pair exists, the spreadsheet should let the student know why no solution exists: either parallel (non-intersecting) or same line (infinite solutions).

### Challenge (+1 TP)

Also show the graph of the intersection, possibly using a scatterplot with treadlines.

## Can't Stop (Monte Carlo simulation)

Create a spreadsheet to estimate probabilities for the game Can't Stop.

• Allow a student to select three input values between 2 and 12 inclusive.
• Simulate rolling dice at least 1,000 times using random numbers (Monte Carlo simulation).
• Compute the experimental probability that at least one target value occurs, based on the game rules.
• Have clear directions to students about how to use the spreadsheet.
• Explain how the spreadsheet computes the probabilities.

Game rules:

1. Choose three numbers (2-12).
2. Roll four six-sided dice.
3. Separate the dice into two pairs. There will be various ways to do this.
4. Find the sum of each pair. Is your number among one of the sums?

For example: Say a person chooses 2, 6, and 7 as a target values. Now the student rolls a 3, 3, 4, 4. Depending on how I pair up the dice, I get the following sums: 6, 7, 7, 7, 7, 8, with a total of 5 matches. That said, you should only count this result as 1 towards the probability count, not 5, because each die roll can contribute at most one to the count.

### Challenge (+1 TP)

Also compute the theoretical probability.

N/A

## SUBMISSION

1. Publish the assignment to your EduBlog by:
• using LaTeX for all non-calculator mathematics notation
• including any files that you created for the assignment
• submitting the post's URL to Canvas
2. By submitting the assignment, you acknowledge that all work is your own.

Special note: Use the "share" button to get a sharable link with "anyone can edit". Use "Data > Protect Sheet > Sheet" with "except certain cells" to keep random people on the internet from messing up your spreadsheet.

## Collab. spreadsheets scoring guide 20 TP

#### GPA calculator

Requirements

• Allows for 20 classes, weightings, and grades (1 TP)
• Computed GPA is correct (1 TP)

Directions for students are _____ clear.

• 2 - very
• 1
• 0 - not

#### Collatz conjecture

Requirements

• Student can enter number and see the Collatz sequence (up to 150 steps) (1 TP)
• Student can enter number and see how many steps (if less than 150) it takes (1 TP)

Directions for students are _____ clear.

• 2 - very
• 1
• 0 - not

#### Linear system

Requirements

• Students can input linear equations in standard form (1 TP)
• Clearly identifies "infinite solutions" because lines are identical (1 TP)
• Clearly identifies "no solutions" because lines are parallel (1 TP)
• Clearly gives an ordered pair when single solution exists (1 TP)

Directions for students _____ clear.

• 2 - very
• 1
• 0 - not

#### Can't Stop probabilities

Requirements

• Students can input a target sum for computation (1 TP)
• Probabilities are approximately correct (1 TP)

Directions for students are _____ clear.

• 2 - very
• 1
• 0 - not

Explanation for probability computation is _____ clear.

• 2 - very
• 1
• 0 - not

CHALLENGES

Shows graph of the intersection point between two lines (+1 TP)

Computes theoretical probabilities for the Can't Stop game (+1 TP)

Points: 0