Check This Space for a new POTW every Monday.

**POTW Writeup Instructions:**

If you turn in your writeup via Google Doc, please title your Google Doc “FIRST NAME LAST NAME POTW NUMBER”. Like so: **Joel Bezaire POTW 1**

Every POTW will be turned in using the same format, with 6 parts. The 6 parts are described below:

*A) Understand the Problem*: Show me that you understand what the problem is asking. This may involve re-writing the problem in your own words, explaining what the question is asking, describing the various parts of the question, or something else. You must, however, show that you understand the question.

*B) Devise a Plan or Strategy*: Come up with a plan to solve the problem. Some possible strategies include: Guess and check, looking for a pattern, making a table, drawing a picture, sketching a graph, doing a simpler problem, using a formula, writing an equation, using inductive/deductive reasoning, examining similar problems, making a diagram, working backwards, some combination of those strategies, or something else entirely. In this section, you should explain which strategy (strategies) you are using, and why they are appropriate for the problem. **If you would like help about when certain strategies are more helpful than others, click here to see a guidelines sheet. **

*C) Solve the Problem*: Using whatever strategy you chose in B), solve the problem.

*D) Answer the Question*: Just because you correctly solve something doesn’t necessarily mean that you answer a given question! Make sure you answer the question from the problem.

*E) Check your Work:* More than just “plugging back in”, you should explain why your answer seems reasonable for the given problem and why you are confident in your answer.

*F) Reflection*: Briefly write about the problem solving process. Did you make any false steps? Was it harder/easier than you initially thought? Were there any other strategies you feel could have worked better now that you have solved the problem? In this section, you should also explain any help that you received on the problem.

Here is an example POTW question with an appropriate solution/writeup: POTW 0 Example Solution

### POTW #18 Assigned Monday May 14, Due Monday May 21

Mr. Bezaire’s hamster had babies, and he wants his family in Canada to have one of them. He discovers that it will cost $2.43 to mail one of the baby hamsters to Canada. All he has are 5¢ and 8¢ stamps. Help Mr. Bezaire by listing all of the possible combinations of those stamps that will allow him to mail one of the babies to Canada.

** ADDENDUM:** Mr. Bezaire just discovered that it is

**a good idea to send rodents/pets (really, animals of any sort) through the postal system. He would like to send a toy replica of a hamster instead. It will still cost him the same amount, which makes the problem valid. You may proceed with a clear conscience.**

*NOT*### POTW #17 Assigned Monday April 30, Due Monday May 7

Use proper POTW formatting, steps, etc. for this one.

### POTW #16 Assigned Monday March 25, Due Monday April 9 (Two Weeks)

This is an Investigation more than a Problem to Solve. Print out the pages below and answer the series of questions. You have two weeks to complete this packet. This would be a GREAT thing to bring into ERB tests next week since you can’t be on your laptop when you get finished with each ERB sub-test.

The main packet: POTW Pascals Triangle

You need this for the second-to-last question: info@usn.org_20110301_145921

You need this picture for the last question: https://www.zeuscat.com/andrew/chaos/sierpinski.html

### POTW #15 Assigned Monday March 5, Due Monday March 12

### POTW #14 Assigned Tuesday Feb 20, Due Monday March 5

### POTW #13 Assigned Monday Feb 12, Due Tuesday Feb 20

**Super Ball Problem**

A Super Ball rebounds half the height from the height it is dropped. One day, a mathematics teacher drops a Super Ball from the roof of the school. If the roof is 32 feet off the ground, what is the total distance (up and down) that the ball will have traveled when it strikes the ground for the sixth time?

### POTW #12 Assigned Monday Jan 22, Due Monday Feb 5 (Two Weeks)

There are 362880 ways to express the digits 1 through 9 as a nine-digit number using each digit exactly one time. Here is one example:

**123 456 789 **(*one hundred and twenty-three million, four hundred and fifty-six thousand, seven hundred and eighty nine*)

Here’s another:

**987 654 321 **(*nine hundred and eighty-seven million, six hundred and fifty four thousand, three hundred and twenty-one*)

There are 368878 more combinations. * *

*How many of those 362880 nine-digit combinations are prime numbers? Explain your answer.*

### POTW #11 Assigned Monday Jan 8, Due Monday Jan 22 (Two Weeks)

### OPTIONAL Holiday POTW

This will be graded IF you turn it in. But it’s optional. You don’t HAVE to complete this. To receive credit turn it in by Monday, December 11.

Here’s the link to the problem: http://chalkdustmagazine.com/blog/christmas-conundrum-1/

If you need to read up on Platonic Solids, click here: https://en.wikipedia.org/wiki/Platonic_solid

Happy Holidays!!

### POTW #10 Assigned Monday Nov 27, Due Monday Dec 4

### POTW #9 Assigned Monday Nov 13, Due Monday Nov 20

### POTW #8 Assigned Monday Nov 6, Due Monday Nov 13

Thanks to Chris Smith on Twitter for this idea

A primer on Triangular Numbers, in case you need it

A primer on Factorials, in case you need them

Bonus (worth one possible point):

### POTW #7 Assigned Monday October 20 Due Monday Nov 6

#### POTW #6 Assigned Monday October 9, due Monday October 23 (TWO WEEKS due to Fall Break)

- What is the last digit (the ones digit) of 7^131 (7 to the power of 131)? (Note: This is too big of a number to enter into your calculator, and I wouldn’t recommend trying to solve it by hand.)
- Create and answer a question similar to part (1) above, but use a base number different than 7.

**POTW #5 Assigned Monday September 25, due Monday October 9 (TWO WEEKS!)**

**POTW #4 Assigned Monday September 18, Due Monday September 25**

Can you place four *different* numbers inside the shapes (diamond, circle, hexagon, and triangle) so that the sum of the two numbers along any given side of the square is a unique square of another number (in other words, a unique square number)?

**POTW #3 Assigned Monday September 11, due Monday September 18**

Lorelei, Oliver, Frances, and BJ each have a different kind of measuring stick. Each stick is marked with equally spaced units, but the spaces are *not* necessarily the same from one stick to another. Lorelei’s, Oliver’s and BJ’s sticks each have been broken off at the beginning of their scales. Frances’ stick is *not* broken. Lorelei’s stick starts at 11 units. Oliver’s stick starts at 33 units. Frances’ stick starts at 0 since it is not broken. BJ’s stick starts at 17 units.

Each of the four students measured the depth of a pond at the same spot. Lorelei’s stick read 91 units deep. Oliver’s stick read 113 units deep. Frances’ stick read 160 units deep. BJ’s stick read 177 units deep.

Then, BJ took his stick and measured Frances’ height, and his stick read 89 units. What reading would Lorelei’s stick give for Frances’ height?

**POTW #2 Assigned Tuesday September 3, Due Monday September 11**

**POTW #1 Assigned Monday August 28, Due Tuesday September 3**

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