Goldbach's Conjecture POW: Was Goldbach correct in

the idea that every 2 digit even number can be written as the sum of two prime numbers.

LIst the even numbers beginning with 10

10 = 5 + 5

12 = 5 + 7

14 = 7 + 7

16 = 11 + 5

18 = 13 +5 etc....What do you notice? Are there any patterns. Go all the way to 98. Would the Sieve of Erastosthenes help this problem?

Yes, this means to rewrite the question 10points

Plans can be drawing a diagram, making a chart, guess and check, finding a pattern 10 points

This means everything you do....even the scratch work. 30-40 points

This is your answer (s) 10- 20 points

Very important part where you make observations, and reveal

your thinking. You may also extend the problem here. 30-40 points

6. Rating of the problem

On a scale of 1-10 how does this problem rate for interest and learning? 1 point

Next weeks POW asks: What are the chances that your last two digits of your phone number would be = to the sum of 12? Hint: Think of all the possibilites first. The chance that something occurs is written like a fraction. My last two digits are 33 so, 3 + 3 = 6. Could a graph help?

. SUM FUN To Be Assigned 9/10

Can you find a quick and easy way to add the counting numbers from 1-100.

Plan: Try a quick and easy way to add 1-10 and let that guide you.... Don't forget to comment on the patterns you discover. (I wonder if any addition strategies we've discussed could help?) HINT: WHAT IS 9+1 and 8+2 and 7+ 3 and 6+4 and 5 more? Study that pattern......apply it to a strategy to add 1-100!

To THE PROBLEM OF THE WEEK PAGE:

Throughout the website you will discover some great problems. If you see a colored rectangular box, that could mean that I have hidden an answer. Just keep checking to see if the answer has been revealed.

Beginning the first POW is always the hardest, but then you will get the hang of it!

It is a very good idea to follow all the steps which are clearly stated below. Click on the rubric link to see how the points are calculated for your POW.

0 + 0 = 0

0 + 1 =1

0 + 2 = 2

0 + 3 = 3

0 + 4 = 4

0 + 5 = 5

0 + 6 = 6

0 + 7 = 7

0 + 8 = 8

0 + 9 = 9

The magic Square asks you to fill in the numbers 1-9 in a 3x3 grid so that every row, column, and diagonal makes the answer of 15. Be sure to think of great combinations, nice numbers and this will be a snap. Remember Comment!

What is the significance of the median for this problem?

The results found evens in the corners, odd numbers in the t zone, patterns in the adjacent blocks and a major connection to five in the middle .

B C

The Handshake problem asks for you to find a pattern of number of people in the room to how many handshakes occur if everyone shakes hands with every person only once. Do no more than 10 and start with 1 person . Make a chart to help you. You may also use geometric diagrams. Example:

A B means for 2 people there is one handshake (one line between them.

A B C would look more like a triangle with A shaking with B , Awith C and B and C have to shake too . A

Predict what would it be for 100, is there a

shortcut? B

The BASEBALL POW....

Using the diagram and the logic clues find out who is on first and all the other positions. For a little bonus where does the little joke "Who's on First" originate? Be sure to explain your comment how you solved the puzzle....

Follow the order of operations (Parenthesis first) (Exponent next, Multiply or Divide, then Add or subtract)

Make the numbers 8 4 2 1 become an equation which equals 0-10 and then 11-20 Finished in Jan of 03

Pascals TRIANGLE POW

#2 Can you devise a way of using the five digits 1 3 5 0 0 in such a way that when you write a five column addition problem you end up with the smallest possible sum. You must also never have the decimal point in the same spot, and you may never repeat any number. AND you have to use each of the digits in each of the 5 numbers.

THEN KEEPING THE SAME RULES YOU MUST DO IT AGAIN, THIS TIME WITH THE LARGEST NUMBER POSSIBLE SUM as the answer.

THE FORMATION WOULD BE SOMETHING LIKE . _ _ _ _ _

_ . _ _ _ _ etc but something is wrong.....( I didn't line up my decimal point.)

Using 4 numbers with at least three digits each, can you make the sum of your birthday as month, day and year, but do not use a 0 as your first digit.

August 15, 1992 would then be 81592

NEWSPAPER FRONT PAGE

This is to match our December project....you are to create the front page of a newspaper using a catch headline and articles that talk about the math you have learned so far this year. You can incorporate graphs too if you would like. For this POW your question, plan and comment are on a separate piece of paper in the pow folder and the Newspaper part goes in the December project after your graph!

Strategy of 13....Fill in the 8 circles with numbers 1-8 one time each to make 13 in all connective ways.

What patterns do you discover?

POW #2

Take the digits 0001234 and organize these as four separate numbers to add first to get the smallest sum possible and secondly, to get the largest sum possible. Remember this is four separate numbers. The decimal points must line up properly. You must use all the digits in each number. For example 3,124,000 and .0034210 use all the digits and are different from each other so they would be acceptable. Don't forget Q P W S C ! (The 5 steps to doing a POW are listed above)

PLace VALUE POW

Magic Square: Copy this over and over til you get it!