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 #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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