A Multiplication Based Logic Puzzle

This snowflake puzzle isn’t for beginners, but making snowflakes goes very well with the idea of carrying your own weather.

Print the puzzles or type the solution in this excel file: 10-factors-986-992

I like when I can sneak a little bit of mathematics into a completely unrelated lesson. This lesson is about being proactive and is called “Carry Your Own Weather”.

Carry Your Own Weather (Be Proactive) discussion:

  1. If you could choose the weather, what kind of weather would you choose? (Sunny weather and snowy weather seem to be chosen the most.)
  2. If the weather outside was ALWAYS sunny, would you like that? Would that be a good thing? Would you appreciate the sunny days if every day was sunny? (Variety is good. Without rain and snow, how could food grow?)
  3. Does your mood depend on the weather?
  4. How do you feel when it’s sunny outside?
  5. How do you feel when it’s gloomy outside?
  6. The author of the 7 Habits of Highly Effective People, Stephen R. Covey, talked about carrying your own weather. What do you think that might mean? (Decide for yourself how you will feel. Don’t let the outside weather or other people make that decision for you.)
  7. Let’s listen as Stephen R. Covey talks about Carrying Your Own Weather:

7Habits – CARRY YOUR OWN WEATHER VIDEO.flv.

Have you ever made a snowflake before? Did you know that you can decide how the snowflake will look before you make a single cut? Choosing how the snowflake will look ahead of time is like deciding what kind of weather you will carry with you. You will not leave it up to chance. You will begin with the end in mind. You will decide ahead of time how your snowflake will look. In real life, a snowflake has 6 sides, but you can choose to make your snowflake have four sides, six sides or eight sides. Several layers of a napkin are much easier to cut than the same number of layers of regular paper so you will use white paper napkins to make your snowflakes. Afterwards, you can glue your snowflake onto a sheet of dark blue construction paper. Then you can use a white crayon to sign your name and decorate the dark blue construction paper around your snowflake.

First, you need to fold your napkin. Folding into eighths is the easiest. Just find the corner where all the folds in the napkin already meet and fold that corner again, thus making a 45° angle. Fold that corner in half again and you’ll get the 22.5° angle that you see at the bottom of the napkin in the picture below. The other napkin is folded into sixths and then into twelfths. If you don’t cut off the uneven edges at the top of those napkins, your snowflake will only have four sides, but if you do cut off the uneven edges, you will get a six-sided or an eight-sided snowflake. (Depending on that cut, you might also get a twelve-sided or sixteen-sided snowflake. They’ll look great, too!)

Making a perfect six-sided snowflake is a little more difficult than an eight-sided one. I recommend reading this post from Paula Beardell Krieg for complete instructions on six-sided snowflake cutting: ‘Tis the Season to Make Paper Snowflakes (She is the one who told me about using easy-to-cut paper napkins for the snowflakes, too.)

I found these three triangles helpful in making snowflakes with perfect 60° angles.

 

Place the center of the folded napkin at the bottom center of triangles. You can easily see through the napkin to see where the folds need to go.

When each side of the napkin has been folded up, it will look have a 60° angle at the bottom. The red line shows where to cut the top off the napkin to get a perfect hexagon folded into an equilateral triangle.

Fold the napkin in half again so that bottom angle becomes a 30° angle before making your decorative cuts. These next instructions tell how to make those cuts to get the exact snowflakes that you want. These tips were made for six-sided snowflakes, but you can also apply the tips to eight-sided snowflakes:

Paper Snowflake Cutting Tips

Please be aware that these snowflakes are delicate. They can rip easily. I suggest you mount them on sturdy paper as soon as possible.

After you finish making your snowflakes, I’m sure you will enjoy a story that I like very much, even though you have heard it many times before. The main character felt sorry for himself because he was bullied and nobody thought he was good at anything. When he decided to find a way to be helpful, he started to carry his own weather. He became proactive. Doing so not only lifted him but lifted everyone around him, too. Can you guess the name of the story? (Rudolph the Red-Nosed Reindeer)

Rudolph the Red-Nosed Reindeer story and song from youtube

***********************************

This is my 991st post, so I’ll tell you a little bit about the number 991:

991 is a prime number that can be written as the sum of consecutive prime numbers two different ways:
127 + 131 + 137 + 139 + 149 + 151 + 157 = 991; that’s seven consecutive primes.
191 + 193 + 197 + 199 + 211 = 991; that’s five consecutive primes.

991 is a palindrome two different ways:
33133 in BASE 4 because 3(4⁴) + 3(4³) + 1(4²) + 3(4¹) + 3(4⁰) = 991
131 in BASE 30 because 1(30²) + 3(30) + 1(1) = 991

  • 991 is a prime number.
  • Prime factorization: 991 is prime.
  • The exponent of prime number 991 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 991 has exactly 2 factors.
  • Factors of 991: 1, 991
  • Factor pairs: 991 = 1 × 991
  • 991 has no square factors that allow its square root to be simplified. √991 ≈ 31.48015

How do we know that 991 is a prime number? If 991 were not a prime number, then it would be divisible by at least one prime number less than or equal to √991 ≈ 31.5. Since 991 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 991 is a prime number.

 

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Tag Cloud