1322 Christmas Star

The first Christmas Star led the wise men to find the Baby Jesus.

This Christmas star can lead you to a better knowledge of all the facts in a basic 1 to 10 multiplication table.

Advertisements

1320 Christmas Factor Trees

Regardless of its size, an evergreen tree is a mighty symbol at Christmastime. Today’s factoring puzzle features a couple of relatively small Christmas trees, but don’t think for even one minute that these little trees make for an easy puzzle. It’s a level 6 puzzle so there are several places that the clues might trick you. Use logic through the entire process, and you should be able to solve it!

Print the puzzles or type the solution in this excel file: 12 factors 1311-1319

That factoring puzzle has nothing to do with the factors of 1320. In case you are looking for factor trees for the number 1320, here are a few of the MANY possible ones:

1316 Hard Candy

When I have a cold or a cough, I often have a piece of hard candy in my mouth. These red cinnamon candies are tasty, but they aren’t very good for soothing throats! Will this red hot cinnamon candy puzzle be too hard for you to solve? It may be a little bit of a challenge, but I’m sure you can solve it if you let logic be your guide the entire time. 

Print the puzzles or type the solution in this excel file: 12 factors 1311-1319

1314 Desmos Art

A teacher at my school had his students graph some polynomials and their inverses. I got to help some of his students with their graphs. After seeing the beautiful symmetry of the graphs together, I excitedly exclaimed to a few of the students, “Isn’t this a cool assignment?”

During my lunch, I put one of the graphs, its inverse, and some of their translations on Desmos and made a simple but lovely piece of art in the process. 

Before I was done, I showed it to a couple of students. One of them asked, “Are you saying that math can create art?” I loved replying, “Yes, it can!” Now that student wants to create some works of art, too. It was a privilege to show her how to use Desmos.

These are the inequalities I used to make my work of art:

MANY teachers have figured out that students could learn a lot about functions and their graphs by using Desmos to create drawings, pictures, or artwork. For example, look at this tweet and link shared by Chris Bolognese:

Here’s the final @desmos coloring book from my amazing Precalculus students. We are headed to the lower school next week to join them in some coloring fun. Pictures to come! https://t.co/iejf2RYVWX @ColumbusAcademy @CAVikesSTEAM @mathequalslove #iteachmath— Chris Bolognese (@EulersNephew) December 8, 2018

Now I’ll share some facts about the number 1314:

  • 1314is a composite number.
  • Primefactorization: 1314= 2 × 3 × 3 × 73,which can be written 1314 = 2 × 3² × 73
  • The exponents inthe prime factorization are 1, 2, and 1. Adding one to each and multiplying weget (1 + 1)(2 + 1)(1 + 1) = 2 × 3 × 2 = 12. Therefore 1314has exactly 12 factors.
  • Factors of 1314:1, 2, 3, 6, 9, 18, 73, 146, 219, 438, 657, 1314
  • Factor pairs: 1314= 1 × 1314,2 × 657, 3 × 438, 6 × 219, 9 × 146, or 18 × 73 
  • Taking the factorpair with the largest square number factor, we get √1314= (√9)(√146) = 3√146 ≈ 36.24914

1314 is the sum of two squares:
33² + 15² = 1314

1314 is the hypotenuse of a Pythagorean triple:
864-990-1314 which is 18 times (48-55-73) and
can also be calculated from 33² – 15², 2(33)(15), 33² + 15²

1313 Virgács and St. Nickolas Day

6 December is Saint Nickolas Day. Children in Hungary and other places in Europe wake up to find candy and virgács in their boots. You can read more about this wonderful tradition in Jön a Mikulás (Santa is Coming) or Die Feier des Weihnachtsmanns (The Celebration of Santa Claus). Today’s puzzle represents the virgács given to children who have been even the least bit naughty during the current year.

Print the puzzles or type the solution in this excel file: 12 factors 1311-1319

Now I’ll write a little bit about the number 1313:

  • 1313 is a composite number.
  • Prime factorization: 1313 = 13 × 101
  • The exponents in the prime factorization are 1 and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1313 has exactly 4 factors.
  • Factors of 1313: 1, 13, 101, 1313
  • Factor pairs: 1313 = 1 × 1313 or 13 × 101
  • 1313 has no square factors that allow its square root to be simplified. √1313 ≈ 36.23534

1313 is the sum of consecutive prime numbers three different ways:
It is the sum of the twenty-one prime numbers from 19 to 107.
It is the sum of eleven consecutive primes:
97 + 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 + 139 + 149 = 1313,
and it is the sum of seven consecutive prime numbers:
173 + 179 + 181 + 191 + 193 + 197 + 199 = 1313

1313 is the sum of two squares two different ways:
32² + 17² = 1313
28² +  23² = 1313

1313 is the hypotenuse of FOUR Pythagorean triples:
255-1288-1313 calculated from 28² –  23², 2(28)(23), 28² +  23²
260-1287-1313 which is 13 times (20-99-101)
505-1212-1313 which is (5-12-13) times 101
735-1088-1313 calculated from 32² – 17², 2(32)(17), 32² + 17²