1423 Lollipop

Lollipops are candies that easily delight children. Will today’s lollipop-wannabe puzzle be a delight?

The puzzle number is 1423. Here are a few facts about that number:

  • 1423 is a prime number.
  • Prime factorization: 1423 is prime.
  • 1423 has no exponents greater than 1 in its prime factorization, so √1423 cannot be simplified.
  • The exponent in the prime factorization is 1. Adding one to that exponent we get (1 + 1) = 2. Therefore 1423 has exactly 2 factors.
  • The factors of 1423 are outlined with their factor pair partners in the graphic below.

How do we know that 1423 is a prime number? If 1423 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1423. Since 1423 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 31, or 37, we know that 1423 is a prime number.

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1422 Candy Corn Mystery

You can begin this candy corn puzzle easily enough, but the logic needed to solve it is a bit complicated. Good luck with this one!

Now I’ll tell you some facts about the puzzle number, 1422:

  • 1422 is a composite number.
  • Prime factorization: 1422 = 2 × 3 × 3 × 79, which can be written 1422 = 2 × 3² × 79
  • 1422 has at least one exponent greater than 1 in its prime factorization so √1422 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1422 = (√9)(√158) = 3√158
  • The exponents in the prime factorization are 1, 2, and 1. Adding one to each exponent and multiplying we get (1 + 1)(2 + 1)(1 + 1) = 2 × 3 × 2 = 12. Therefore 1422 has exactly 12 factors.
  • The factors of 1422 are outlined with their factor pair partners in the graphic below.

1422 is palindrome 1K1 in BASE 29 (K is 20 base 10)
because 1(29²) + 20(29¹) + 1(29º) = 1422.

1421 Square-shaped Sweet

This square-shaped puzzle is a Level 3 because you can start with clue 44 and work down the puzzle cell by cell to find the solution. You won’t get into a rhythm with this one, but logic will still help you to find the factors of the clues in order from top to bottom. That’s pretty sweet!

Now here are some sweet facts about the puzzle number 1421:

  • 1421 is a composite number.
  • Prime factorization: 1421 = 7 × 7 × 29, which can be written 1421 = 7² × 29
  • 1421 has at least one exponent greater than 1 in its prime factorization so √1421 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1421 = (√49)(√29) = 7√29
  • 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 1421 has exactly 6 factors.
  • The factors of 1421 are outlined with their factor pair partners in the graphic below.

1421 is also the hypotenuse of a Pythagorean triple:
980-1029-1421 which is (20-21-29) times 49.

1420 Eight-legged Creature

When you look at today’s puzzle, you might see a snowflake or perhaps an eight-legged creature. I hope you will also see lots of common factors that will help you solve this quick puzzle.

Here are some facts about the puzzle number, 1420:

  • 1420 is a composite number.
  • Prime factorization: 1420 = 2 × 2 × 5 × 71, which can be written 1420 = 2² × 5 × 71
  • 1420 has at least one exponent greater than 1 in its prime factorization so √1420 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1420 = (√4)(√355) = 2√355
  • The exponents in the prime factorization are 2, 1, and 1. Adding one to each exponent and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 = 12. Therefore 1420 has exactly 12 factors.
  • The factors of 1420 are outlined with their factor pair partners in the graphic below.

1420 is the hypotenuse of a Pythagorean triple:
852-1136-1420 which is (3-4-5) times 284.

1419 and Level 1

This Level 1 Find the Factors 1-12 puzzle is as simple as clockwork. Can you find all the factors?

Now I’ll tell you a few things about the puzzle number, 1419:

  • 1419 is a composite number.
  • Prime factorization: 1419 = 3 × 11 × 43
  • 1419 has no exponents greater than 1 in its prime factorization, so √1419 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 1419 has exactly 8 factors.
  • The factors of 1419 are outlined with their factor pair partners in the graphic below.

1419 is the difference of two squares in four different ways:
710² – 709² = 1419
238² – 235² = 1419
70² – 59² = 1419
38² – 5² = 1419

That last one means we are only 25 numbers away from the next perfect square, and that seems like clockwork, too.

1419 is only the second Zeisel number: (105 was the first.)
(4×1-1)(4×3-1)(4×11-1) = 3×11×43 =1419

1418 Challenge Puzzle

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

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

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

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

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.