1203 and Level 3

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At the top of this level 3 puzzle are two clues that will tell you where to put three of the factors needed to solve the puzzle. After you find those three clues work down looking at the clues cell by cell until you have the entire puzzle solved.

Print the puzzles or type the solution in this excel file: 10-factors-1199-1210

Here are a few facts about the number 1203:

  • 1203 is a composite number.
  • Prime factorization: 1203 = 3 × 401
  • 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 1203 has exactly 4 factors.
  • Factors of 1203: 1, 3, 401, 1203
  • Factor pairs: 1203 = 1 × 1203 or 3 × 401
  • 1203 has no square factors that allow its square root to be simplified. √1203 ≈ 34.68429

Since 1203 is only made from three consecutive numbers (1, 2, 3) and zeros, it has to be divisible by 3.

1203 is the hypotenuse of a Pythagorean triple:
120-1197-1203 which is 3(40-399-401)

1202 and Level 2

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I am certain that you can fill in the numbers 1 to 10 one time in both the top row and the first column so that this puzzle can become a multiplication table. All you have to do is give it an honest try.

Print the puzzles or type the solution in this excel file: 10-factors-1199-1210

Now I’ll write a few things about the number 1202:

  • 1202 is a composite number.
  • Prime factorization: 1202 = 2 × 601
  • 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 1202 has exactly 4 factors.
  • Factors of 1202: 1, 2, 601, 1202
  • Factor pairs: 1202 = 1 × 1202 or 2 × 601
  • 1202 has no square factors that allow its square root to be simplified. √1202 ≈ 34.66987

29² + 19² = 1202

1202 is the hypotenuse of a Pythagorean triple:
480-1102-1202 calculated from 29² – 19², 2(29)(19), 29² + 19²

2(24² + 5²) = 2(601) = 1202 so that Pythagorean triple can also be calculated from
2(2)(24)(5), 2(24² – 5²), 2(24² + 5²)

Try out both ways to get the triple!

 

The factors of the hundred numbers just before 1201

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I’ve made a simple chart of the numbers from 1101 to 1200, but it’s packed with great information. It gives the prime factorization of each of those numbers and how many factors each of those numbers have. The numbers written with a pinkish hue are the ones whose square roots can be simplified. Notice that each of those numbers has an exponent in its prime factorization.

I didn’t make a horserace from the amounts of factors this time because it isn’t a very close race. Nevertheless, you can guess which number appears most often in the “Amount of Factors columns” and see if your number would have won the race.

Now I’ll share some information about the next number, 1201. Notice the last entry in the chart above. It had so many factors that there weren’t very many left for 1201 to have. . .

  • 1201 is a prime number.
  • Prime factorization: 1201 is prime.
  • The exponent of prime number 1201 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1201 has exactly 2 factors.
  • Factors of 1201: 1, 1201
  • Factor pairs: 1201 = 1 × 1201
  • 1201 has no square factors that allow its square root to be simplified. √1201 ≈ 34.65545

How do we know that 1201 is a prime number? If 1201 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1201 ≈ 34.7. Since 1201 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1201 is a prime number.

Even though it doesn’t have many factors, 1201 is still a fabulous number:

25² + 24² = 1201

1201 is the 25th Centered Square Number because 25² + 24² = 1201, and 24 and 25 are consecutive numbers:

1201 is the hypotenuse of a primitive Pythagorean triple:
49-1200-1201 calculated from 25² – 24², 2(25)(24), 25² + 24²

Here’s another way we know that 1201 is a prime number: Since its last two digits divided by 4 leave a remainder of 1, and 25² + 24² = 1201 with 25 and 24 having no common prime factors, 1201 will be prime unless it is divisible by a prime number Pythagorean triple hypotenuse less than or equal to √1201 ≈ 34.7. Since 1201 is not divisible by 5, 13, 17, or 29, we know that 1201 is a prime number.

1200 The 120th Playful Math Carnival

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Plinko is a fun carnival game of chance. This Plinko board is really just a portion of Pascal’s triangle. OEIS.org informs us that 120 is the smallest number to appear six times in that triangle. Why did those six times happen?
120 = 10!/3!/7! That’s why it appears twice in the 10th row of the Plinko board below.
120 = 16!/2!/14! Which is why it appears twice in the 16th row as well.
120 will appear two more times in its 120th row.

Now step right up and learn some other incredible facts like
120 = 5! because 1·2·3·4·5 = 120

120 is also the smallest positive multiple of 6 that is neither preceded nor followed by a prime number!

What kind of shape is 120 in?
120 is the 15th triangular number because 15(16)/2 = 120,
it’s the 8th tetrahedral number because (8)(9)(10)/6 = 120 (That means 120 is the sum of the first eight triangular numbers), and
it is the 8th hexagonal number because (8)(2·8-1) = 120.

Math Journals and Creative Writing

Every Playful Math Carnival contains blog links about ways to play with math and insights into teaching math. Blogging about math helps clarify thoughts, document experiences, and share the joy math brings us. It is a lot like keeping a math journal. Denise Gaskins wrote a post about the benefits of math journaling and included some prompts to help students get writing. Whether writing about joys or frustrations, math journalling has its benefits.

Abhishek Pathania wrote a clever limerick titled Maths that uses mathematical terms such as chance, calculated guess, multiply and divide. I enjoyed the limerick and I bet your students will, too. Another blogger, Roland, shared Maths Limerick, which is quite a bit of fun, too.

I hesitate a little to share this next one. However, older students may enjoy reading a little satire from the Onion that was shared this month on the Bluebird of Bitterness, Young girls creeped out by older scientists constantly trying to lure them into STEM. It certainly could give you something to talk about.

The next stop at our carnival is a house of horrors that is simply terrifying to some people. It is known as . . . . .

Math Anxiety

In Life Cameo’s post Learning, a young girl goes from liking math to feeling significantly less confident and quietly suffering from math anxiety. Thankfully her teacher intervened and she is now just starting to understand it again.

Alyssa lets you take a peek into the world of one who suffers from math anxiety in her post What Does Math Anxiety Look Like?

A young man named Dave blogged about his lifelong struggles with math in Dealing with Learning Disabilities in Math. Although he occasionally used a strong word to voice his frustrations, his is an important point of view that ought to be shared. This school year I am working with students who need specialized help with mathematics so this post gave me some food for thought.

Preventing and Treating Math Anxiety

So as you can see Math Anxiety is a real concern. What can you do about it? Josh Rappaport of Math Chat advises How to talk about math without scaring children off.

And of course, Denise Gaskins’ Let’s Play Math Blog is filled with ways to PLAY with math. Play can relieve a lot of anxiety. Recently Denise posted a quote by Rózsa Péter about math being worthy of our time and how Rózsa’s class of twelve-year-old girls begged her to let them explore the Euclidean algorithm. These girls felt no fear; it was a joyful experience for them the entire time.

Which method is better for children to learn math, discovery or traditional? The Intrepid Mathematician suggests a combination of the two and how to implement that teaching in A third path for early math education.

Mathematical Art on Exhibit

The average preschooler/kindergartner only gets 58 seconds of math instruction a day. Those who get Paula Krieg to teach them for one fascinating hour a week are really fortunate! You can see what I mean by reading her post, Little Hands, Little Books, Folds, & Math.

Number Loving Beagle shares a raw, personal story of years of yearning for artistic talent in Math is Beautiful (and other lies). Math really can make beautiful, frameable art as demonstrated in that post, but too often math has become nothing more than misery-inducing, anxiety-producing, seemingly worthless calculations. Which math will you choose for yourself and your children?

Su Leslie created a beautiful piece of fractal art in Pretty Maths. Su’s work could inspire others to see the beauty in mathematics.

Rachel Shey shares some more mathematical art and thoughts in the post Math and Art. I also liked her thoughts about two fields intersecting.

One great way to make mathematical art is to use mirrors as demonstrated in these photos by Annie Fetter when she went to Math on a Stick.

Robert Loves Pi once again has created some beautiful, rotating 3-dimensional mathematical art for us all to enjoy.

The Math Museum featuring Calculators, Castles, and Puzzles

Simona Prilogan of Let’s Math regularly posts a number puzzle on her blog, Let’s Math. Some of the puzzles may be easier to solve than others, but I’m sure students will be able to figure these two out.  Boats Tuesday Maths Puzzle and Sunshine Thursday Maths Puzzle. That second one actually contains a few carnival pictures!

I visited a type of museum inside Romania’s Corvin Castle in Hunedoara this summer. Although I didn’t know when I visited, Hunedoara is Simona Prilogan’s hometown! I was delighted to find a post she published about the castle in her poetry blog less than a month before I wrote a post with some mathematical pictures from inside the castle. I am amazed at how small the world of mathematics can be!

Life Through a Mathematicians Eyes also grew up in Romania and offers a guided tour of Calculators That Made History. When I took the tour I was amazed at how old some of those calculators are. I’m sure you will enjoy the tour very much!

Colleen Young has several different mathematical examples in her post Here’s the diagram. What’s the question? What better way could there be to learn any of those topics frontward and backward than make it feel like solving a puzzle?

I took a photo at a Hungarian museum village and turned it into a mathematical puzzle/lesson for young ones by asking a couple of simple questions. How Are They the Same? How Are They Different?

Logic

BloggingIsAResponsibility wrote a post titled Is Math Meaningless, and Is That an Insult? If you’re introducing syllogisms in your geometry class, you might want to try some of these effective but meaningless arguments!

Life Through a Mathematician Eyes offers thoughts and study videos on more advanced Logic Problems beginning with Studying Logic – Day 1.

Science Book A Day reviewed mathematician Eugenia Cheng’s book, The Art of Logic: How to Make Sense in a World That Doesn’t.

Math Literature and Books

Musings of a Mathematical Mom blogged about a mathematical adventure her children enjoyed. They counted and divided using Christopher Danielson’s book How Many. Her children even drew pictures afterward that would allow them to count and think about even more fractions. Who could ask for anything more?

Life Through a Mathematicians Eyes reviews three books that teens and teachers can most certainly enjoy in New Book Discoveries. The books reviewed are Weird Maths: At the Edge of Infinity and Beyond by David Darling and Agnijo Banerjee, Your Daily Maths: 366 Number Puzzles and Problems to Keep you Sharp by Laura Laing, and 50 Maths Ideas You Really Need to Know By Tony Crilly.

Susan mentioned Ramanujan and the book The Man Who Knew Infinity when she wrote a blog post she called The Story of the Locked Box and the Key of Dreams. Her title sounds like a mathematical fairy tale, but it is not a storybook at all. It gives a vivid description of her lucid mathematical dreams, her struggles with dyscalculia, and her triumphs in learning math. Ramanujan also had wonderful mathematical dreams, so she is in good company.

Crafts, Fashion, Souvenir booths

At this next carnival booth, you can buy a variety of clothing items. Should you buy any of them? Fashion Math-Thinking about the Cost Per Wear shares a formula created to help you make that decision.

TerifiCreations by Teri Lewis asks, “Has anyone ever written an article encouraging quilters to do math?” If any quilters out there struggle with the math, she will gladly help out.

Mathemagic or Carni Game?

How to get super-rich; millionaire math suggests 13 different ways to get to a million and would be a fun way to increase number sense for students who already know how to multiply.

Sometimes students come up with ridiculous answers to word problems. DC Gilbert shares a disastrous story and concludes, “Mathematics! It is Really That Important!”

Using statistics to tell lies: Open Mind gives an example in USA Temperatures: Can I Sucker You?

Winning Mathematical Game Skills

The son of one of Math Mammoth’s customers created a flash program that helps second-grade students practice simple addition and subtraction facts. Skills require practice so check it out!

Resourceaholic offers some fun beginning-of-the-school-year activities for year 7 students.

Dealing with histograms might seem as treacherous as getting through an obstacle on American Ninja Warrior, but Math Only Math gives step by step histogram instructions to help middle and high school students navigate through those different-height rectangles in record time.

If you’re teaching the Fundamental Counting Principle, I’m sure you can find a way to use Wrong Hands’ clever/funny comic Lesser super-hero movie title generator.

Chris McMullen can answer your students’ question, Which Calculus Skills are most essential, practical?

How do you prove that e is an irrational number? Mjlawler tackles that problem in Walking through the proof that e is irrational with a kid.

The Carnival of the Future

Joseph Nebus, who will host the carnival in September at his blog, NebusResearch mentioned some comics that could lessen geometry anxiety in Reading the Comics, Ragged Ends Edition.

Joseph also writes a humor blog that sometimes has gems like the Venn Diagram he made for his post Statistics Saturday: Trivia Night Questions, by Kind.

I can tell that Joseph is pretty pumped about writing the carnival next month. Read The Mathematics Carnival is coming! and enjoy his enthusiasm.

You can also enjoy the August 2018 edition of the Carnival of Mathematics.

Finally, no matter where or how you teach mathematics, remember these words Jennie penned in  An Open Letter to Teachers, “You have to share your love and passions.  That’s your joy.  In that way, you are sharing you.  And, all that children want to know is that you love them and love what you are teaching.  If they know that, the floodgates will open to learning.”

The future of mathematics education is in YOUR hands. Have fun!

This was my 1200th post. Here are some facts about the number 1200:

  • 1200 is a composite number.
  • Prime factorization: 1200 = 2 × 2 × 2 × 2 × 3 × 5 × 5, which can be written 1200 = 2⁴ × 3 × 5²
  • The exponents in the prime factorization are 4, 1 and 2. Adding one to each and multiplying we get (4 + 1)(1 + 1)(2 + 1) = 5 × 2 × 3 = 30. Therefore 1200 has exactly 30 factors.
  • Factors of 1200: 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 25, 30, 40, 48, 50, 60, 75, 80, 100, 120, 150, 200, 240, 300, 400, 600, 1200
  • Factor pairs: 1200 = 1 × 1200, 2 × 600, 3 × 400, 4 × 300, 5 × 240, 6 × 200, 8 × 150, 10 × 120, 12 × 100, 15 × 80, 16 × 75, 20 × 60, 24 × 50, 25 × 36 or 30 × 40
  • Taking the factor pair with the largest square number factor, we get √1200 = (√400)(√3) = 20√3 ≈ 34.64102

1200 is the hypotenuse of two Pythagorean triples:
336-1152-1200 which is (7-24-25) times 48
720-960-1200 which is (3-4-5) times 240

1200 is the sum of twin primes 599 and 601

1200 looks interesting to me when it is written in some other bases:
It’s 3333 in BASE 7 because 3(7³ + 7² + 7¹ + 7⁰) = 1200,
550 in BASE 15, because 5(15² + 15) = 1200
363 in BASE 19, because 3(19²) + 6(19) + 3(1) = 1200
300 in BASE 20 because 3(20²) = 1200, and
220 in BASE 24 because 2(24² + 24) = 1200

 

1199 and Level 1

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Here’s a puzzle that even someone just learning to multiply and divide can solve. That means you can solve it, too!

Print the puzzles or type the solution in this excel file: 10-factors-1199-1210

Here are some facts about the number 1199:

  • 1199 is a composite number.
  • Prime factorization: 1199 = 11 × 109
  • 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 1199 has exactly 4 factors.
  • Factors of 1199: 1, 11, 109, 1199
  • Factor pairs: 1199 = 1 × 1199 or 11 × 109
  • 1199 has no square factors that allow its square root to be simplified. √1199 ≈ 34.62658

1199 is the sum of the fifteen prime numbers from 47 to 109. That last one just happens to be one of its prime factors, too!

1199 is the hypotenuse of a Pythagorean triple:
660-1001-1199 which is 11 times (60-91-109)

1199 looks cool in base 10, and it’s palindrome
2F2 in BASE 21 (F is 15 base 10)

 

1198 Challenge Puzzle

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You can solve this Find the Factors 1 – 10 puzzle if you use logic. Guessing and checking will likely only frustrate you. Go ahead and give logic a try!

Print the puzzles or type the solution in this excel file: 12 factors 1187-1198

Now I’ll share some facts about the number 1198:

  • 1198 is a composite number.
  • Prime factorization: 1198 = 2 × 599
  • 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 1198 has exactly 4 factors.
  • Factors of 1198: 1, 2, 599, 1198
  • Factor pairs: 1198 = 1 × 1198 or 2 × 599
  • 1198 has no square factors that allow its square root to be simplified. √1198 ≈ 34.61214

1198 is also palindrome 262 in BASE 23

1197 Mystery Level

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The first few moves needed to solve this puzzle might not be too hard, but soon enough it might get a bit tougher. Nevertheless, its one solution can be found using logic and an ordinary 12×12 multiplication table.

Print the puzzles or type the solution in this excel file: 12 factors 1187-1198

Here are facts about the number 1197:

  • 1197 is a composite number.
  • Prime factorization: 1197 = 3 × 3 × 7 × 19, which can be written 1197 = 3² × 7 × 19
  • The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 = 12. Therefore 1197 has exactly 12 factors.
  • Factors of 1197: 1, 3, 7, 9, 19, 21, 57, 63, 133, 171, 399, 1197
  • Factor pairs: 1197 = 1 × 1197, 3 × 399, 7 × 171, 9 × 133, 19 × 63, or 21 × 57
  • Taking the factor pair with the largest square number factor, we get √1197 = (√9)(√133) = 3√133 ≈ 34.59769

1197 is the sum of these eleven consecutive prime numbers:
83 + 89 + 97 + 101 + 103 + 107 + 109 + 113 + 127 + 131 + 137 = 1197

1197 looks interesting to me when it is written in some other bases:
It’s 3330 in BASE 7 because 3(7³ + 7² + 7¹) = 3(399) = 1197,
and it’s 2255 in BASE 8.
It’s 999 in BASE 11, because 9(11² + 11 + 1) = 9(133) = 1197,
and it’s 1K1 in BASE 26 (K is 20 base 10)

 

1196 and Level 6

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In this puzzle, the permissible common factors of 48 and 72 are 6, 8, and 12. For clues 8 and 16, you can choose from common factors 2, 4, or 8. Which choices will make the puzzle work? I’m not telling, but I promise that the entire puzzle can be solved using logic and a basic knowledge of a 12×12 multiplication table. There is only one solution.

Print the puzzles or type the solution in this excel file: 12 factors 1187-1198

Here are some facts about the number 1196:

  • 1196 is a composite number.
  • Prime factorization: 1196 = 2 × 2 × 13 × 23, which can be written 1196 = 2² × 13 × 23
  • The exponents in the prime factorization are 2, 1, and 1. Adding one to each and multiplying we get (2 + 1)(1 + 1)(1 + 1) = 3 × 2 × 2 = 12. Therefore 1196 has exactly 12 factors.
  • Factors of 1196: 1, 2, 4, 13, 23, 26, 46, 52, 92, 299, 598, 1196
  • Factor pairs: 1196 = 1 × 1196, 2 × 598, 4 × 299, 13 × 92, 23 × 52, or 26 × 46
  • Taking the factor pair with the largest square number factor, we get √1196 = (√4)(√299) = 2√299 ≈ 34.58323

1196 is the hypotenuse of a Pythagorean triple:
460-1104-1196 which is (5-12-13) times 92

1196 is a palindrome in three different bases:
It’s 14241 in BASE 5,
838 in BASE 12, and
616 in BASE 14

1195 You Can Find the Answer in This Book

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The new school year is underway. Much may have been forgotten over the summer. If you don’t quite remember all the multiplication tables, this puzzle book can help you remember them AND help your brain grow. You might still find it a challenge, but that only makes it more fun!

Print the puzzles or type the solution in this excel file: 12 factors 1187-1198

Now I’ll share a few facts about the number 1195:

  • 1195 is a composite number.
  • Prime factorization: 1195 = 5 × 239
  • 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 1195 has exactly 4 factors.
  • Factors of 1195: 1, 5, 239, 1195
  • Factor pairs: 1195 = 1 × 1195 or 5 × 239
  • 1195 has no square factors that allow its square root to be simplified. √1195 ≈ 34.56877

1195 is also the hypotenuse of a Pythagorean triple:
717-956-1195 which is (3-4-5) times 239

1194 and Level 4

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The more multiplication facts you know, the easier these puzzles become. Working on these puzzles can help you learn the multiplication table better. Go ahead,  give this puzzle a try!

Print the puzzles or type the solution in this excel file: 12 factors 1187-1198

Here are a few facts about the number 1194:

  • 1194 is a composite number.
  • Prime factorization: 1194 = 2 × 3 × 199
  • The exponents in the prime factorization are 1, 1, and 1. Adding one to each and multiplying we get (1 + 1)(1 + 1)(1 + 1) = 2 × 2 × 2 = 8. Therefore 1194 has exactly 8 factors.
  • Factors of 1194: 1, 2, 3, 6, 199, 398, 597, 1194
  • Factor pairs: 1194 = 1 × 1194, 2 × 597, 3 × 398, or 6 × 199
  • 1194 has no square factors that allow its square root to be simplified. √1194 ≈ 34.5543

1194 is the sum of consecutive prime numbers two ways:
131 + 137 + 139 + 149 + 151 + 157 + 163 + 167 = 1194
283 + 293 + 307 + 311 = 1194

1194 is palindrome 424 in BASE 17