- Welcome to the 112th Math Education Blog Carnival! There are many fabulous rides at this carnival, and hopefully you won’t get motion sickness on any of them!

At this first booth, we have the mystifying number 112. What is amazing about the number 112?

Well, not only is 112² = 2² + 4² + 6² + 7² + 8² + 9² + 11² + 15² + 16² + 17² + 18² + 19² + 24² + 25² + 27² + 29² + 33² + 35² + 37² + 42² + 50², but 112 is also the side length of the SMALLEST square that is composed entirely of smaller distinct sized squares with integer sides. Sources: Squaring a Square and OEIS.org. There are 21 different squares in this square with side length 112. Click on the image below and it will magically become bigger. You can then print it, cut it into pieces to make a puzzle, and take that home as your first carnival prize today.

I don’t know if it is significant, but 112 is 7 × 4², and 112’s square was divided into 3 × 7 different squares . 175 is also such a side length, and 175 is 7 × 5², and 175’s square was divided into 3 × 8 different squares.

**Addition, Subtraction, Multiplication, Division**

Bedtime Math has a quick math activity for kids every evening. Here’s one about adding, subtracting, and/or multiplying at the Giraffe Hotel.

**Algorithms**

Rodi Steinig leads a math circle of students ages 11-17 in a course titled “Our Algorithmic Culture,”. It may surprise you that algorithms are not just for math; they are for real, real life, too. See for yourself as several activities are described in Introducing Algorithms, a post about the first of 8 sessions on the subject.

**Math Art**

RobertLovesPi’s blog regularly features a rotating solid geometric shape or a beautiful tessellation such as this one that can be enjoyed by young or old alike.

David Mitchell of Latticelabyrinths explains how he and his friend, Jacob, made a beautiful structure for the September 1917 Wirksworth Art and Architecture Trail using a large peg board, pegs and 1302 red or blue precisely-cut wooden equilateral triangles. Amazing! I wish I could have seen it in person.

What is a Rotogon? Katie Steckles of aperiodical.com blogged about this beautiful computer generated, constantly transforming piece of art that could mesmerize young and old alike.

**Bell Ringers**

What is the Same? What is Different? has a wide variety of thoughtful activities that can get your students’ brain juices flowing.

Try Math Visuals for other great bell ringers.

Life Through a Mathematician’s Eyes sees a great deal of beauty in Pascal’s Triangle, but it isn’t the significant part of the curriculum she wishes it could be. She got around that though. In her post, Pascal’s Triangle, she shared some great articles that she turned into bell ringers for her students to contemplate when they arrive to class. She also made assignments that can be completed in class or at home.

**Bulletin Boards**

Paul Murray creates bulletin boards near the lunch room with questions on them. Some of the questions are math problems. For the last ten years or so, students have stopped by his bulletin boards, read them, and pondered the questions. Read how he does it in A Math Bulletin Board that Actually Gets Read!

**Carnival of Mathematics**

Earlier this month Just Maths published the more advanced 149th Carnival of Mathematics. It has several great links in it that could pique high schoolers’ interest even if those students aren’t able to understand all the mathematics yet. Next month Alexander at **CoDiMa** will host the 150^{th} Carnival of Mathematics.

**Math Competitions**

Some people like entering math competitions. If you have a student that likes them, look at this post from Resourceaholic. It has questions that can be a fun challenge whether you like competitions or not.

**Games**

Alan Parr often plays his envelop game with students who are learning many different mathematical concepts. His students all enjoy it. The game described in A Wow! Conversation with Amy was easy to put together, let Amy display some brilliant reasoning and provided its creator a very memorable experience, perhaps his most memorable this school year. .

**Geometry**

Paula Beardell Krieg of Bookzoompa’s wrote a post about Symmetry for 4 – 5 year olds that I adore. Even kids that young can make some gorgeous geometric art.

Mike’s Math Page does so many great math videos with his sons that its difficult to pick only one or two. I went with a couple of posts about geometry: Playing with Some Mathy Art ideas this morning which will appeal to kids of all ages and Lessons from a great geometry homework problem for older kids.

Before teaching congruent triangle proofs, Mrs. E Teaches Math recommends a paper folding, cutting, and arranging activity that helps students visualize overlapping triangles.

**Mathematical Humor: **

A little mathematical humor can help students access prior knowledge, or it can make a new concept memorable. Joseph Nebus reads lots of comics to find ones with some mathematics in them. This August 17, 2017 edition of Reading the Comics has a few that could help students remember what irrational means, what sum means, or what the < sign means.

**Math Literature Books**

Math Book Magic introduces us to a new book, *Stack the Cats* by Susie Ghahremani. The book is just right for kindergarten and earlier elementary grades. It can help you talk to kids about counting, adding, even decomposing numbers in a very fun way. Kids may not even be aware they are learning math as they find different ways to stack toy cats and other objects. Stack the Cats joins the #Mathbookmagic

Ben Orlin of Math with Bad Drawings delights us with Literature’s Greatest Opening Lines, as Written By Mathematicians.

Denise Gaskins has written Word Problems from Literature. It has a more serious but still very fun approach to exploring mathematics and problem solving through good literature.

**Math Magic**

Alex Bellos of Science Book a Day introduces us to Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks. Every trick in the book introduces a different mathematical idea, and lots of magician secrets are revealed. Sounds fun!

**Managing the Mathematics Classroom**

Mrs. G. of Give Me a Sine blogged that this school year she had the best first week of school she’s ever had. She mixed some of her tried and true favorite activities with some new ones that she learned this summer from NYC Math Lab and Sara Vanderwerf. Mrs. G gives specifics detailing what she did. Her students’ response described in the next to the last paragraph is enviable.

Years ago I made a seating chart for a Pre-Algebra class. I didn’t know the students yet and arranged my seating chart in alphabetical order by first name. It was a disaster. I had placed the tallest student in the class at a desk in front of the shortest student in the class. Once one legitimate complaint was voiced, other complaints followed. If I could have read *Mrs. E Teaches Math* post How to Create a Seating Chart before that school year, I would have had one less frustration.

**Math Music**

Coleen Young has updated the Mathematical Songs on her website to include MinuteMath’s quadratic formula sung to a One Direction song. She wrote that the song makes her students smile and sing along.

**Number Sense**

What’s your favorite number? John Golden of Math Hombre asked that question to people and got some wonderful responses. Really cool mathematics is attached to several numbers including the Top Ten Favorite Numbers.

**Problem Solving**

True problem solving is more about “Why?” than it is about an exact “What?” Denise Gaskins of Let’s Play Math has written several questions to teach students How to Succeed in Math: Answer-Getting vs. Problem-Solving

**Puzzles**

Long ago mathematicians were often philosophers and philosophers were often mathematicians. Simona Prilogan is both. Every day she posts a mathematical meme, a puzzle such as this one, and a philosophical mathematical thought. Search her site for all kinds of goodies to appeal mostly to middle school children and up.

Alok Goyal’s Puzzles Page shared a puzzle titled 10 Friends. Upper elementary students will be able to understand what the puzzle is asking but would probably need a lot of guidance to solve it.

Rupesh Gesota of Math Coach shared an interesting 6 rectangle puzzle and revealed several different methods students used to solve the puzzle.

My blog typically features a factoring puzzle such as this one that I fancied up for back to school:

This month I did something different: I wrote an elementary-school-age time management lesson plan with an object lesson that uses Tangram puzzle pieces. It was a big hit with the teachers and the students.

**Resources**

Three J’s Learning wrote math recommendations for 3 year-olds! It includes a list of measuring devices a 3 year-old would love to use and learn from.

Singapore Maths Tuition has assembled a list of the Best Online Resources to Improve Your Math Skills along with their pros and cons.

Resource Room Dot Net Blog wrote about an experience using Illustrative Mathematics (a resource for 6-8 grades) and how it is worth the effort to give feedback.

**Square Roots**

Last month’s 111 Math Teachers at Play Carnival was hosted at High Heels and No. 2 Pencils by Jacqueline Richardson. This month the Amazing Jacqueline doesn’t just guess your age, she can guess the square root of your age within a few decimal places! I have never seen anything like this before. She uses tiles and grid paper to model square roots of non-perfect squares and is amazingly accurate. Teach your students this way, and they will be amazed. They will understand square roots so well that they will be amazing as well.

**Teaching Practices**

What are the zeros of this polynomial? Julie Morgan of Fraction Fanatic lets her students give their solutions in a colorful way. This practice has become her new favorite. Lots of discussion happens. Young children could also use this fun method to give answers.

Ed Southall of Solvemymaths wrote a sobering post titled Sorry we keep lying to you… about lies our math teachers told us and we continue to perpetuate. Read it. Share it. Maybe the lies will stop.

Sara Vanderwerf explains how her Stand and Talks engage students much more than Think/Pair/Share does and REALLY gets the whole class talking about math and contributing to a whole class discussion.

**Statitistics**

Business blogger Lanisha Butterfield wrote a fascinating article titled Arithmophobia. A major portion of the article was an interview with statistician Jennifer Rogers who did well in math as a kid but HATED it until she was introduced to A-level maths and statistics in school. High School teachers and students should be especially interested in this article.

Sue VanHattum of *Math Mama Writes* detailed her first day teaching algebra, statistics, and calculus this year. When she discussed the class syllabus, she inserted some fun mathematics here and there. She summed up that first day and shared every math teacher’s universal dream, “I think the class went well. If they really feel good about it, they’ll end up thinking I’m their best teacher ever.”

To everyone who plays at this Carnival, I hope your students think that way about you!

Thank you to everyone who blogged about teaching mathematics this month, and especially thank you to those who submitted a post to this carnival.

I’d like to encourage everyone who blogs about math to submit a post to next month’s carnival which will be hosted at Three J’s Learning.

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Since this is my 896th post, I’ll also write a little bit about that number which happens to be 8 times 112. A factor tree for 112 is contained in this factor tree for 896.

896 is SS in BASE 31 (S is 28 base 10), because 28(31) + 28(1) = 28(31 + 1) = 28(32) = 896.

896 is also S0 in BASE 32 because 28(32) + 0(1) = 896.

896 is the sum of six consecutive prime numbers: 137 + 139 + 149 + 151 + 157 + 163 = 896.

Here is the factoring information for 896 with the ten factors of **112** in red.

- 896 is a composite number.
- Prime factorization: 896 =
**2**×**2**×**2**×**2**× 2 × 2 × 2 ×**7**, which can be written 896 =**2⁽⁴**⁺³**⁾**×**7**or 896 = 2⁷ × 7 - The exponents in the prime factorization are 7 and 1. Adding one to each and multiplying we get (7 + 1)(1 + 1) = 8 × 2 = 16. Therefore 896 has exactly 16 factors.
- Factors of 896:
**1**,**2**,**4**,**7**,**8**,**14**,**16**,**28**, 32,**56**, 64,**112**, 128, 224, 448, 896 - Factor pairs: 896 =
**1**× 896,**2**× 448,**4**× 224,**7**× 128,**8**×**112**,**14**× 64,**16**×**56**, or**28**× 32 - Taking the factor pair with the largest square number factor, we get √896 = (√64)(√14) = 8√14 ≈ 29.933259