Month: September 2019

1418 Challenge Puzzle

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The 19 clues in this Find the Factors Challenge Puzzle are enough to find its unique solution. Can you find it?

Print the puzzles or type the solution in this excel file: 10 Factors 1410-1418

Now I’ll write a few facts about the puzzle number, 1418:

  • 1418 is a composite number.
  • Prime factorization: 1418 = 2 × 709.
  • 1418 has no exponents greater than 1 in its prime factorization, so √1418 cannot be simplified.
  • The exponents in the prime factorization are 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1418 has exactly 4 factors.
  • The factors of 1418 are outlined with their factor pair partners in the graphic below.

1418 is the sum of two squares:
37² + 7² = 1418

518-1320-1418 calculated from 2(37)(7), 37² – 7², 37² + 7².
It is also 2 times (259-660-709)

 

1417 Mystery Puzzle

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How hard is today’s puzzle? It’s a little harder just because I’m not telling what the level number is. Are you going to let that stop you from finding the unique solution? I hope not!

Print the puzzles or type the solution in this excel file: 10 Factors 1410-1418

1417 is just the puzzle number, but in case you want to know something about it, here are some facts:

  • 1415 is a composite number.
  • Prime factorization: 1415 = 13 × 109.
  • 1415 has no exponents greater than 1 in its prime factorization, so √1415 cannot be simplified.
  • The exponents in the prime factorization are 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1415 has exactly 4 factors.
  • The factors of 1415 are outlined with their factor pair partners in the graphic below.

1417 is the sum of two squares in two different ways:
29² + 24² = 1417
36² + 11² = 1417

1417 is the hypotenuse of FOUR Pythagorean triples:
265-1392-1417 calculated from 29² – 24², 2(29)(24), 29² + 24²
545-1308-1417 which is (5-12-13) times 109
780-1183-1417 which is 13 times (60-91-109)
792-1175-1417 calculated from 2(36)(11) , 36² – 11² , 36² + 11²

1416 A Birthday Mystery

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Today is my sister’s birthday, but the cake is tipped over and there’s a big hole in it! And what happened to the candle? Can you solve this mystery? Happy birthday, Sue!


Print the puzzles or type the solution in this excel file: 10 Factors 1410-1418

Now I’ll share some facts about the puzzle number 1416:

  • 1416 is a composite number.
  • Prime factorization: 1416 = 2 × 2 × 2 × 3 × 59, which can be written 1416 = 2³ × 3 × 59.
  • 1416 has at least one exponent greater than 1 in its prime factorization so √1416 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1416 = (√4)(√354) = 2√354.
  • The exponents in the prime factorization are 3,1 and 1. Adding one to each exponent and multiplying we get (3 + 1)(1 + 1) (1 + 1) = 4 × 2 × 2 = 16. Therefore 1416 has exactly 16 factors.
  • The factors of 1416 are outlined with their factor pair partners in the graphic below.

1416 is the difference of two squares four ways:
355² – 353²  = 1416
179² – 175²  = 1416
121² – 115²  = 1416
65² – 53²  = 1416

131 Playful Math Carnival

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Welcome to the Playful Math Education Blog Carnival featuring the amazing prime number 131, whose digits can mutate into other prime numbers right before your eyes!

131, a permutable prime number

make science GIFs like this at MakeaGif
Yessiree, 131 is prime, and so is 113 and 331. Do I need to mention that 3, 11, 13, and 31 are also prime numbers?
131’s next trick happens when you add up all the 2-digit PRIMES that begin with a 4:
41 + 43 + 47 = 131.
Because 131is a palindrome, it reads the same forwards and backward. Here’s another trick: 131 is 65 in BASE 21 and 56 in BASE 25.

 

We have many different attractions this month. You can go to any category quickly here:

Carnival Attractions:

Arithmetic

You’ve heard of the three R’s, reading, and writing and ‘rithmetic, but what is arithmetic? Joseph Nebus shares a few comics about basic arithmetic and explains what they mean:

Arithmetic is also television’s Lisa Simpson’s favorite subject in school and she will miss it greatly as she recovers from the mumps. In this blog post, Safi explains Dr. Hibbert’s comforting words to her about polygons, hypotenuses, and Euclidean algorithms.

Art

You can always count on Robert Loves Pi to produce a beautiful and complex geometric design. This one he calls Two Rhombic Polyhedra with Tessellated Faces. Here’s another one:

Paula Beardell Krieg helped students create big, beautiful geometric artwork and origami in Summer Projects with Teens.

Also, check out Paula’s Paper, Books, and Math Workshop for many more ways to learn math through art.

Big Prize, Little Chance of Winning

Several years ago Mental Floss wrote about carnival games that offer big prizes but have very little chance of being won. This carnival has a couple of those as well. They are called unsolved math problems. Even if winning probably isn’t going to happen, that doesn’t mean the games and activities aren’t fun. Explaining Science updates us on a very famous unsolved problem, The Goldbach’s Conjecture. Supercomputers have worked on it, but we are no closer to a solution.

In A Neat Unsolved Problem in Number Theory That Kids Can Explore, Mike’s Math Page explores the new-to-me Collatz conjecture that for every positive n, the sum 3 + 8n will equal a perfect square plus an even number. It’s a simple enough conjecture for kids to understand and it is fascinating, yet mathematicians have not been able to prove or disprove it yet!

Creative Writing

Subha laxmi Moharana (Angel Subu) writes creatively about some tough topics in high school mathematics in Math Poem. I think her words could be turned into a rap.

Poetrywithmathematics shares Doug Norton’s lovely mathematical poem Take a Chance on Me.

What if graphs were self-conscious about their looks? High School aged students can consider that thought as they read the imaginative blog post, To Infinity and Beyond.

Displays

There’s a cozy classroom place that promotes mathematics in Our New Math Space. It was designed for older students by Continuous Everywhere But Differentiable Nowhere and includes many pictures.

Have you considered displaying a weekly math joke? MathEqualsLove shares a fun joke and a puzzle for kids to gather around and enjoy.

Factoring Quadratics

Super Safi uses another episode from the Simpsons to teach about the quadratic formula.

Food for Thought

Anybody can cook or do math. Really? What does that even mean? Math4Love explains both in What We Mean When We Say, “Anyone Can Do Math.”
Math with Bad Drawings makes a similar point in The Adventures of Captain Math.

Games

Joyful Parenting made a simple kindergarten-age counting game and called it Snack Math, but even older kids might enjoy figuring out exactly how many crackers are required to play the game.

How many are in the jar. What is a good estimate? Add Steve Wyborney’s clues one by one to get an even better estimate. He has 51 New Esti-Mysteries that also happen to teach several different math concepts.


For older students, Kent Haines a free game he calls Last Factor Loses. I played it a few times with a student. Making prime factorization a game really did make it more fun.

Geometry

Bn11nb enjoys the geometry of architecture. The pictures in this post are worth a look and could be an inspiration to your students.

House of Mirrors (Reflecting on Mathematics Teaching)

We often reflect on the effectiveness of our teaching methods. Sometimes we are advised to require students to use more strategies. We might ask them to notice or wonder about a concept. These two thoughtful posts will certainly give you cause for reflection:

“The More Strategies, the Better?

Noticing and Wondering: A powerful tool for assessment

 

Robert Kaplinsky shares ten things he’s embarrassed to tell you. Has he been reading your mind and mine?

Money

What is your favorite part of a cupcake? What if you could buy just that part? What if you wanted to put a whole cupcake together? How much would that cost? Your child can learn about money and decimals exploring those answers with Mathgeekmama’s  Money Math Problems.

Museum of Mathematics

Beads can be a fun manipulative when learning mathematics. Joseph Nebus has begun his 2019 Mathematics A-Z series by writing about the Japanese abacus. He compares it to a slide rule and the Chinese abacus. He also describes how to use it to add, subtract, and multiply numbers. Students could have some fun using it to understand place value, too.

Life Through a Mathematician’s Eyes is giving museum tours in A History of Mathematics-August. K-12 students could be fascinated by the mathematical relics from the Smithsonian founded in August 1846 as well as the Seven Bridges of Königsberg solved by Euler in August 1735.

Pumpkin Patch

Erin of Sixth Bloom’s Pumpkin Math-Preschool Activity will engage your little ones as they learn to count and sort pumpkin-shaped macaroni or candies.

They will also love decomposing numbers using pumpkin seeds and  Mathgeekmama’s cute Pumpkin cards.

Posters

Digital Educators Alliance offers free posters of admirable women in math and related fields:

While Sara Van Derwerf set of 112 New Math Fail Posters will delight students as they notice and wonder about and LEARN from grown-ups’ computing mistakes.

Puzzles

7Puzzle gives some clues about a 3-digit number. Can you figure out what it is?

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Alan Parr writes about a newspaper puzzle called Evens Puzzles. He suggests that students can make their own and hints that he has thought up several variations of it. I look forward to reading about those!

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American Calendars for September had more than a week’s worth of palindromes. Would palindromes make a good puzzle? Yes! Print off a 100 chart and try Denise Gaskins’s A Puzzle for Palindromes. Also, check out her new Morning Coffee feature each week for more math teaching tips.

Next Month’s Carnival

That’s it for this month’s Math Education Blog Carnival. The 132nd Carnival will be next month at Arithmophobia No More. Would you like to share a post or host the carnival? Go to Let’s Play Math for details!

1415 and Level 6

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Very likely when you look at this puzzle common factors of 40 and 10, 8 and 16, 9 and 18, and 20 and 40 will pop into your head. Will they be the right common factors that work with all the other clues in the puzzle to produce a unique solution? Let logic be your guide when finding the factors.

Print the puzzles or type the solution in this excel file: 10 Factors 1410-1418

Now I’ll tell you something about the puzzle number, 1415:

  • 1415 is a composite number.
  • Prime factorization: 1415 = 5 × 283.
  • 1415 has no exponents greater than 1 in its prime factorization, so √1415 cannot be simplified.
  • The exponents in the prime factorization are 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1415 has exactly 4 factors.
  • The factors of 1415 are outlined with their factor pair partners in the graphic below.

1415 is also the hypotenuse of a Pythagorean triple:
849-1132-1415 which is (3-4-5) times 283.

1414 Your Math Education Post Will Add So Much to This Month’s Carnival!

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Have you written a blog post that would bring delight to a preschool, K-12 or homeschool mathematics teacher or student? Then submit it to this month’s Playful Math Education Blog Carnival or message me on Twitter by Friday, September 20th! I’m hosting the carnival this month, and I would love to read your post. So come join the fun!

Today’s puzzle looks a little like a wild, but fun? carnival ride. The numbers 36 and 12 went together on the ride. They managed to stay with each other but the ride went so fast, you can see 36 and 12 in two different places at the same time. There’s also poor number 40. You can see it in THREE places at the same time.

Oh my! Can you use logic to find where the numbers 1 to 10 need to go in both the first column and the top row so that this wild ride will behave like a multiplication table? It’s a level 5 so it won’t be easy to find its unique solution. Are you brave enough to try?

Print the puzzles or type the solution in this excel file: 10 Factors 1410-1418

That puzzle’s number is 1414. Let me tell you a little about that number:

  • 1414 is a composite number.
  • Prime factorization: 1414 = 2 × 7 × 101.
  • 1414 has no exponents greater than 1 in its prime factorization, so √1414 cannot be simplified.
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 1414 has exactly 8 factors.
  • The factors of 1414 are outlined with their factor pair partners in the graphic below.

1414 is also the hypotenuse of a Pythagorean triple:
280-1386-1414 which is 14 times (20-99-101)

 

DNA Evidence at Ellis Island

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About the middle of August, Ancestry.com contacted my husband informing him that he had a new DNA match who was his second or third cousin. I was very excited to look into it. This new match is my husband’s second-best match. The two of them share 204 centimorgans (cM) across 3 DNA segments. There were several shared matches between them, and based on them, I was confident that the DNA they shared was from his mother’s side of the family. The surname on the match was Kovacs (Equivalent to Smith in English), and I was hopeful that there would be a connection to one of the known or probable siblings of my husband’s grandfather, Frank Kovach.

I immediately looked at the match’s pedigree. The names of the living were not given, but it appears that the match was the grandchild of a Mr. Kovacs and Betty Baker who were married on 26 February 1960 in Trumbull, Ohio. Mr. Kovacs was the son of William Ray Kovacs Sr and Barbara Bernice Jennings who were married 13 April 1937 in Pomeroy, Washington.  That marriage record indicated that William Sr’s parents were Samuel Kovacs and Elizabeth Jenney. I didn’t find any other records for Samuel, but I did find several for Sandor Kovacs and Elizabeth Jeney. Perhaps, the clerk had mistakenly written Samuel instead of Sandor on that marriage record. The 1940 Census shows a William R Kovacs, his wife, Barbara, and their two children living in Trumbull County, Ohio. That’s where Sandor eventually settled.

Samuel or Sandor.  I was hoping to see John, Stephen, or Julia. I was feeling a little disappointed that I wasn’t seeing the connection I had hoped for. I looked at this DNA match’s ethnicity tab on Ancestry.com. My husband is 98% Eastern Europe and 2% Baltic States. This match was only 4% Eastern Europe, 0% Baltic States, and 96% other places. Doubt crept in. How could these two possibly be 2nd or 3rd cousins? That just seemed too close with so little shared ethnicity.

After I got over my initial disappointment, I looked at my husband’s grandfather’s 1938 petition for naturalization. It stated that he, Frank Kovach, was born in Szürthe, Czechoslovakia (previously Hungary, but currently part of Ukraine) and that he immigrated to the United States on 16 June 1902. I was able to find this page of the 16 June 1902 New York arrival manifest for the ship Vaderland when he arrived at Ellis Island.  I had not seen this manifest before, and it gave me some wonderful information:

  • Ferencz Kovach is the fourth name from the bottom of the manifest. (Ferencz is the Hungarian equivalent of Frank.)
  • The ship, Vaderland, set sail from Antwerp, Belgium on 7 June 1902. It was nine days later when Ferencz got to Ellis Island. (The ship probably arrived at New York sooner than nine days, but each ship had to wait its turn in the harbor for its passengers to be processed.)
  • When he arrived at Ellis Island, Ferencz was a 19-year-old single male in good health, yet he had only one dollar in his pocket. He told officials that his occupation was a laborer. He came here to work!
  • There were a few other Hungarians listed on this same page of the manifest, but Ferencz was the only one from Szürte. Still, he had at least a few people he could speak to in Hungarian on the voyage.
  • It was his first trip to the United States. His brother, Alexander Kovacs, paid for his passage. Ferencz was going to McKeesport, Pennsylvania where his brother lived at 817 Jerome Street. Alexander is the English equivalent of the Hungarian given name Sándor! That meant that Sandor Kovacs was Ferencz’s big brother, AND he was the one who helped him get to America! It also means that the third great grandfather of my husband’s DNA match was indeed named Sandor and not Samuel.

Here is a descendant chart showing how my husband is connected to this DNA match. I would have expected the DNA match to have 12.5% Eastern European ethnicity, so 4% is remarkably low. Ancestry.com says there is only a 2% chance that two people sharing their amount of DNA would only be 2nd cousins, twice removed. We each get 50% of our DNA from both parents, but the 50% we get isn’t necessarily evenly distributed from every previous generation!

Now I wanted to know all I could about this Alexander/Sandor Kovacs! I found out that Sandor and his wife welcomed a new baby boy into their family just a few months earlier. They named him Chas, and he was born on 23 November 1901. Sandor was a miner at the time, a very dangerous occupation. Note that Chas’s birth was not registered until 6 January 1902.  That may be why his birth year was mistakenly listed as 1902 on his birth certificate. His birth certificate lists his father’s birthplace as Szürte and his mother’s birthplace as Gönc. I was so happy to see those birthplaces!

When Ferencz arrived at Ellis Island, he must have been very excited to see his brother, his wife, Elizabeth, and their 6 1/2-month-old baby boy.

I constructed a table of the household of Sandor Kovacs from 1910, 1930, and the 1940 Censuses.  The dates of birth were found in other records that are included at the bottom of this post.

The April 1910 Census had Alexander Kovacs employed as a helper in the steelworks industry and living at 917 Chestnut Street in Duquesne, Allegheny, Pennsylvania. The census indicated that he immigrated to the United States in 1895 and was now a naturalized citizen. It also includes his brother-in-law, John Jeney, who was an engineer in the Steelworks industry.

That census record led me to the manifest showing Sándor Kovács at Hamburg on 21 August 1895 as he traveled to Amerca. His is the sixth surname from the bottom on the right side of the manifest. Szürte is in Ung county, the previous residence listed for him on the manifest.

The 1910 census record stated that AlexanderJr was born in Hungary in 1905. What was that all about? I found 1905 civil registration records from Gönc, Hungary for this family!

In the margin of the right side is the civil registration of their marriage, we learn that Kovács Sándor and Jenei Erzsébet were married in the Reformed Hungarian Church in Pittsburgh on 6 November 1900 and that Jenei Erzsébet had been born 11 July 1878 in Gönc.  I wondered if I could get a copy of the marriage record from the church in Pittsburgh. Then it occurred to me that it might be in the Family History Library in downtown Salt Lake City.  It was! I went to the library the first day I could after work and found it! Click on it to see it better.

Indeed, in Pittsburgh on 6 November 1900, 28-year-old Kovács Sándor, the son of the late Kovács Péter and Péntek Mária wed 22-year-old Jeney Erzsébet, the daughter of Jeney János and Laczkó Mária. He was born in Szürte and she was born in Göncz. I did not know before I saw this record that Sandor and Ferencz’s father, Péter, had died before Ferencz left Szürte to go to America.

I would have preferred to have the entire page from the anyakönyv, but the projector at the library didn’t focus very well when I tried to get the entire page, and I could only get a blurred copy of the full page below.

Thus, DNA led me to Ellis Island where I found my husband’s wonderful great uncle. I am beyond thrilled! I can tell that he was a very kind man because he paid for his little brother’s passage to America and he allowed his grown children to live with him in 1940 as the country was getting over the Great Depression.

Here are the family records that I found for this family:

Károly Kovács (AKA Carl, Chas, Charles) born 23 November 1901 in West Virginia. The record indicates that both Sándor and Erzsébet were living in Gönc in 1905 when this civil registration occurred.

Sándor Kovács (AKA Alex, Alexander) born 3 January 1905 in Gönc, Hungary. 

1930 Census

1940 Census Page 1 includes his daughter Helen Haught and her husband Terrance Haught.

1940 Census Page 2 includes granddaughter Helen Haught and his daughter, Mary Kovacs Collins, who lived next door with her husband and three children. (See Grave Stone and Obituary for Mary Kovacs Collins born 18 Jun 1908 and died 18 Jul 1987).

8 Jan 1953 Death record of Sandor Kovacs from his Find A Grave Memorial.

Edna Kovacs Staub born 19 Feb 1911, married Wayne Staub 11 Jan 1930

Alex Kovacs married Mary Ann Rusky 20 Dec 1948 in Mt Clemens, Macomb, Michigan

19 Oct 1995 Warren, Trumbull, Ohio Death Record for James Kovacs who was born on 29 Nov 1909

4 Sept 2004 death index of Helen Kovacs Waldron who was born 24 Mar 1912, daughter of Kovacs and Jenei

21 Mar 2000 Death of William R. Kovacs Sr who was born 29 June 1914

1413 and Level 4

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You find a rhythm as you solve this level 4 puzzle. The logic is quite easy for most of it, but there is at least one place that will require you to think things through before proceeding.

Print the puzzles or type the solution in this excel file: 10 Factors 1410-1418

Now I’ll share a few facts about the puzzle number, 1413:

  • 1413 is a composite number.
  • Prime factorization: 1413 = 3 × 3 × 157, which can be written 1413 = 3² × 157.
  • 1413 has at least one exponent greater than 1 in its prime factorization so √1413 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1413 = (√9)(√157) = 3√157.
  • The exponents in the prime factorization are 2 and 1. Adding one to each exponent and multiplying we get (2 + 1)(1 + 1) = 3 × 2 = 6. Therefore 1413 has exactly 6 factors.
  • The factors of 1413 are outlined with their factor pair partners in the graphic below.

1413 is the sum of two squares:
33² + 18² = 1413

That means that 1413 is the hypotenuse of a Pythagorean triple:
765-1188-1413 calculated from 33² – 18², 2(33)(18), 33² + 18².
It is also 9 times (85-132-157)

1412 and Level 3

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If you know the greatest common factor of 56 and 48, then you have taken the first step in solving this puzzle. Once you put the factors of 56 and 48 in the appropriate cells, work down from the top of the puzzle to the bottom, cell by cell, until you have put all the numbers from 1 to 10 in both the first column and the top row.

Print the puzzles or type the solution in this excel file: 10 Factors 1410-1418

Here are a few facts about the puzzle number, 1412:

  • 1412 is a composite number.
  • Prime factorization: 1412 = 2 × 2 × 353, which can be written 1412 = 2² × 353.
  • 1412 has at least one exponent greater than 1 in its prime factorization so √1412 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1412 = (√4)(√353) = 2√353.
  • The exponents in the prime factorization are 2 and 1. Adding one to each exponent and multiplying we get (2 + 1)(1 + 1) = 3 × 2 = 6. Therefore 1412 has exactly 6 factors.
  • The factors of 1412 are outlined with their factor pair partners in the graphic below.

1412 is the sum of two squares:
34² + 16² = 1412

1412 is the hypotenuse of a Pythagorean triple:
900-1088-1412 calculated from 34² – 16², 2(34)(16), 34² + 16²

1411 and Level 2

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Four of the fourteen clues, 18, 24, 16, and 40, appear twice in this puzzle, but do they lead you to the same factors? Where do the factors from 1 to 10 belong that will make this puzzle function like a multiplication table?

Print the puzzles or type the solution in this excel file: 10 Factors 1410-1418

Now I’ll write a little bit about the puzzle number, 1411:

  • 1411 is a composite number.
  • Prime factorization: 1411 = 17 × 83.
  • 1411 has no exponents greater than 1 in its prime factorization, so √1411 cannot be simplified.
  • The exponents in the prime factorization are 1, and 1. Adding one to each exponent and multiplying we get (1 + 1)(1 + 1) = 2 × 2 = 4. Therefore 1411 has exactly 4 factors.
  • The factors of 1411 are outlined with their factor pair partners in the graphic below.

1411 is the hypotenuse of a Pythagorean triple:
664-1245-1411 which is (8-15-17) times 83.