Problems Of The Week

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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 #17

Assigned 05/01/17  Due 05/15/17 (TWO WEEKS)

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 NOT 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.

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POTW #16

Assigned 03/27/17  Due 04/10/17 (TWO weeks)

This is really an Investigation of the Week.  We’re going to learn about a new topic called Pascal’s Triangle.  You won’t use the typical POTW format — just answer the following questions.  Print out all of the following pages and turn them in as a hard copy with the answers filled in by April 10 (two weeks)

POTW Pascals Triangle

For Problem #7 you need this image:  info@usn.org_20110301_145921

Picture to look at for Question #8


POTW #15

Assigned 03/06/17  Due 03/13/17

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Asher (thanks!) found this little site that lets you play the game.  Feel free to use it for the first question!  It’s still faster to use Algebra for the 15-frogs-per-side question, though 🙂


POTW #14

Assigned 02/27/17   Due 03/06/17




POTW #13

Assigned 02/13/17  Due 02/27/17  (Two weeks)

Find seven unique unit fractions whose sum is one.  In the picture below, a through g must be unique, positive integers.

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POTW #12

Assigned 01/23/17  Due 02/06/17 (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 01/09/17   Due 01/23/17


POTW #10

Assigned 12/05/16  Due 12/12/16

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Assigned 11/14/16  Due 11/21/16

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Assigned 11/07/16  Due 11/14/16



Assigned 10/25/16  Due 11/07/16

  1.  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.)
  2. Create and answer a question similar to part (1) above, but use a base number different than 7.  (You don’t have to use POTW format to answer part 2 of this POTW.  Just state and answer the question with a brief explanation).


Assigned 10/10/16    Due 10/17/16


Due to popular demand, let me reiterate:  This is a cheap alarm clock that does NOT do 24-hour military time.


Assigned 09/26/16  Due 10/03/16

Anne, Tate, Sydney, and Oliver 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. Anne’s, Tate’s and Oliver’s sticks each have been broken off at the beginning of their scales. Sydney’s stick is not broken. Anne’s stick starts at 11 units. Tate’s stick starts at 33 units. Sydney’s stick starts at 0 since it is not broken. Oliver’s stick starts at 17 units.

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

Then, Oliver took his stick and measured Sydney’s height, and his stick read 89 units.   What reading would Anne’s stick give for Sydney’s height?



Assigned 09/19/16  Due 09/26/16



Assigned 09/06/16  Due 09/19/16

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 square of another number (in other words, a square number)?



Assigned 08/29/16  Due 09/06/16

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Assigned 08/22/16  Due 08/29/16

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One thought on “Problems Of The Week

  1. Pingback: “I Learned Math From Watching *YOU*” | Pre-Algebra

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