Carnival

The 146th Playful Math Education Blog Carnival

/ ivasallay / 16 Comments

Welcome to the146th Playful Math Education Blog Carnival!

What kind of math does the number 146 make?

146 is the 6th octahedral number because 6(2·6² + 1)/2 = 146.
That means that 1² + 2² + 3² + 4² + 5² + 6² + 5² + 4² + 3² + 2² + 1² = 146.

Base ten number 146 looks interesting when it is written in some other bases:
146₁₀ = 123₁₁ because 1(11²) + 2(11¹) + 3(11º) = 146, and
146₁₀ = 222₈ because 2(8² + 8¹ + 8º) = 146.

The factors of 146 are 1, 2, 73, and 146. Coincidentally, 1 + 2 + 73 + 146 = 222.

You can read other ways 146 and the numbers from 121 to 150 make math at Pat Ballew’s Math Day of the Year Facts.

Here are the attractions at this month’s carnival. Click on one to be transported right there!

Notice Patterns, Wonder, Create Math!

Graphics that let us notice patterns and wonder about them are fun, but students don’t have to wait for some teacher somewhere to make them. Denise Gaskins, the original playful math carnival creator, reminds us that students can be Math-Makers, and she invites them to have their creations published! Check out some student creations that have already been published.

Carrot Ranch noticed that Maths Is Everywhere: Clocks, Numbers and place value, patterns and algebra, measurement and geometry, probability and statistics, and much MORE.

Anna noticed something cool about the multiplication table. Can you notice it, too?

Mathematical Art

Nisha-designs decorated mugs with some lovely Abstract Geometric Circle Triangle Art.

K’s Dreamscape has a tutorial for you to make Simple Geometric Art! using cardboard, paint, paintbrushes, and painter’s tape.

Kreativekavya of Fremont forum uses circles, lines, and rectangles in Geometric Art!

Dianna Kolawole shares bright geometry art by Maranda Russel in Wordless Wednesday Geometric Art.

RobertLovesPi made a beautiful Pentadecagon and Its Diagonals.

FracTad’s Ractopia describes how to Create a Geometric Eye Using Desmos.

Sarah Carter of MathEqualsLove has created a gorgeous 3-colored origami Harlequin Cube and shows pictures of the steps taken in her post.

Karmen of Gallery K has made math digitally in some stunning Geometric Art.

Tessellation Art

Tessellation Art is the subject of Bumbastories’ What Four?

RobertLovesPi regularly publishes tessellations like Two Versions of a Tessellation Featuring Regular Hexagons, Regular Pentagons, and Tetraconcave, Equilateral Octagons.

I especially liked how his A Tessellation of Regular Hexagons, Golden Triangles, and Rhombi turned out. It seems to change depending on where you focus your eyes.

Mathematical Photography

You can make math using a camera! Marlene Frankel, A Photo’s Worth searched for and captured lots of geometry in Lens-Artists Photo Challenge #141 Geometry.

Tina Schell of Travels and Trifles photographed some geometric examples of the Fibonacci sequence.

Oh, the Places We See found geometry everywhere but carefully selected some geometric photographs from around the world.

Jazzersten photographed More Greek Geometric Art at the Museum of Fine Arts.

Estimation Booth

Steve Wyborney has engaging Esti-Mystery puzzles ready for every day for the rest of the school year!


Chasing Unicorns humorously blogs about Organizing Jelly Beans. How many jelly beans can you eat each day to keep yourself below the estimate of refined sugar consumed per American per day?

Within 1%, how long is the hypotenuse of this right triangle? If certain criteria are met, John D. Cook’s blog post, Hypotenuse Approximation, can help you be the first to find the correct answer and win the prize.

Fractions, Ratios, and Decimals

Henri Picciotto of Henri’s Math Education Blog updates us on how to use fraction rectangles to help students make sense of adding, subtracting, or comparing fractions with different denominators.

1001 Math Problems shares an engaging and delicious Chocolate Problem involving fractions.

Third-grade teacher, Ms Victor, couldn’t help but see fractions while eating lunch in When Your Teacher Brain Is on Overdrive.

Jillian Starr shares how to transition from unit fractions to more complex fractions in Teaching Fractions Through One Whole.

Do you bake using ratios instead of measuring cups? Kat from the Lily Cafe does and will show you how to use ratios and a scale to Make Flatbread. What a tasty way to make math!

Duane Habecker of The Other Math, More Than What’s in the Textbook invites you to solve ratio problems using Tape Diagrams.

Read how much laughter can be had learning long division involving decimals in FiveHundredaDay’s post It’s not them, it’s me.

Carnival Games

Ajitadeshmukh shares the game, The Number Detective [Spying the number]. This is a game that uses an ordinary deck of playing cards and reinforces the concepts of adding, subtracting, multiplying, and/or dividing. It can be played by children in early elementary grades and up.

Primary Ideas shared how well a game of Noggle (Number Boggle) went when it was played in a Google session remotely.

Anna of one+epsilon designed a logic game called Dot, Dot Poof! Here’s a bonus: Kids 6 and up might inadvertently learn a little linear algebra playing it, too!

A Game of Linear Equations by Bethany of MathGeekMama will help students find solutions to their problems!

MakeMathNotSuck blogged about Theresa Wills’s Playing Cards.io Interactive Math Games for middle grades. It is really exciting that these games can be played in real-time with a partner.

Wendi Bernau made an Easter Egg Hunt Escape Room for her 15- and 17-year-old kids. The escape room included puzzles based on their current schoolwork. The 17-year-old had to solve a puzzle that required calculations, graphing, and trigonometry. The kids liked the escape room so much that they are already talking about doing it again next year.

Harsh Sharma writes about How Math Games and Puzzles Improves Brain Activity. It turns out that Failing/Losing is as important in brain development as Succeeding/Winning is!

Hands-on Math

The Pi Project lets you listen in on the delightful conversation about knitting and fairies and the place value police in The Beauty of Base Ten Blocks.

Melissa Packwood of The Florida Reading Coach blogged about some Affordable Math Manipulatives that can assist students in learning mathematics.

Inclusiveteach.com shares some ideas to Make Your Own Maths Manipulatives.

House of Mirrors

Reflections are important topics in geometry and coordinate math. Our House of Mirrors is full of fascinating reflections.

Ted Jennings, shared a beautiful picture of an alligator and a turtle in Reflections.

Hannah Michaela of CoC-GetFit gives a geometric definition of a mirror image, shares a few examples in pictures and a thoughtful poem about mirrors and reflections in Mirror Image.

Beth of I didn’t have my glasses on made math by photographing a reflection that is happening at the front and the back of a pond in Argo Park.

Ritva Sillanmäki wrote a poem and made math by photographing a reflection that happens on the left and the right side of a river.

Bushboys World has several amazing pictures of birds in See My Reflection.

I shared a couple of puzzles where the squares of two numbers look like they are looking in a mirror.

Museum of Mathematics

All over the world math is being made on this day, April 28. Pat’s Blog shares some famous ways math has been made in the past On This Day in Math, April 28th.

David Campbell of Culturico writes about the beloved Louis Carroll in Portrait of a mathematician in love with the art of writing.

Indrajit RoyChoudhury tells us about Bhaskaracharya, a 12th century Indian mathematician and astronomer in Arjuna’s Arrows and Algebra. Bhaskaracharya discovered differential calculus 500 years before the births of either Newton or Leibniz.

Papannasons  has written an essential biography of 20th Century Indian mathematician Srinivasa Ramanujan. Knowcusp reviews the movie about Ramanujan in The Man Who Knew Infinity: A tale of one of the Greatest Mathematicians of all times. While (Roughly) Daily mentions him and several other great mathematics in “Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.”

LA of Waking up on the Wrong Side of 50 is featured in the controversial current events area of the Math Museum in Anything Can Happen Friday: Math. LA includes the actual newsletter in which Oregon instructs its math teachers to allow for more than one correct answer. LA is upset thinking that now Oregon math teachers must accept incorrect math like 2 + 2 = 79. Perhaps Oregon is just welcoming some of Denise Gaskins’ math rebels who might say that 2 + 2 = 79 – 75, or some other of the infinite number of possible non-simplified yet still very much correct answers.

Likewise, the College Fix reported that Oregon math teachers have been instructed to let their students show their work by making TikToks, silent videos, or cartoons about the math they are learning, in other words, let students make their own math. I think about Ramanujan who taught himself math from an old textbook and then created his own mathematical symbols and terminology when he dreamed up more advanced mathematics. Later when he was told he needed to prove his ingenious mathematical formulas with rigorous proofs, did it help him or restrict him?

Esther Brunat has “curated a collection of Math TikToks” that now belong in a modern Museum of Math.

Adding, Subtracting, Multiplying, Dividing, Etc.

Have you ever experience joy when skiing? Bill McCallum of Illustrative Math compares that feeling to being fluent adding and subtracting numbers.

Laura of Riddle From the Middle describes why third-grade students often struggle with determining which operation to use in SoCs – the right teacher makes a world of difference.

Tess M Perko of River to Humility has written a sweet short story: The Imagination Grandpa Story 3: The Multiplication Staircase.

With doses of frustration and humor, Joseph Nebus of NebusResearch explains why No, You Can’t Say What 6/2(1+2) Equals.

Bethany of MathGeekMama shares her game that makes learning order of operations fun and not impossible!

Math Story Time and Other Books

1 + 1 + 1 = 3. Any number greater than one can be partitioned in a similar fashion. Patricia Nozell reviews a perfect picture book, I Am One: A Book of Action by Susan Verde. A little math can be learned while one person works with another and another to make the world a better place.

Writing this post has introduced me to Perfect Picture Book Fridays. Susanna Leonard Hill reviewed Little Ewe: The Story of One Lost Sheep, by Laura Sassi. Your 3- to 5-year-old will love counting logs, frogs, and other rhyming nouns as you read this book together.

Sue Heavenrich of Sally’s Bookshelf blogged about Bracelets for Bina’s Brothers, a picture book about estimation for 3-6-year-olds, and concluded that Math + Art > Numbers. Activities to make the math in the book more meaningful are also included in the blog post.

Wrenbeth22 of Miss Beth has a Book reviewed The Boy Who Loved Math by Deborah Heligman and LeUyen Pham. This is the story of Paul Erdös, a famous twentieth-century mathematician who made friends all over the world by sharing the math he loved.

Darlene Beck-Jacobson reviewed three biographical storybooks: Queen of Physics by Teresa Robeson, Code Breaker, Spy Hunter by Laurie Wallmark, and Counting on Katherine by Helaine Becker in Celebrate Girls and Women in STEM Day with Some Great Books.

Patricia Tilton of Children’s Books Heal reviewed Wonder Women of Science by Tiera Fletcher and Ginger Rue as part of Women’s History Month. The book is perfect for 9 to 12-year-olds. She also made me aware that Nerdy Book Club reviewed the same book. From that review, I learned the delightful true story of a human calculator named Tiera Fletcher that I am anxious for you to read as well!

MikesMathPage tells us that James Tanton’s Solve This book is full of incredible math projects to do with kids. In this post, he and his son explore a little topology in Going back to James Tantons’ amazing Möbius Strip cutting project.

In Monday’s Math Madness, Willow Croft thoroughly enjoys a 15th-century maritime manuscript called The Book of Michael of Rhodes. There is a lot of math in the book, but even if the reader doesn’t like math much, it won’t take away from the thrilling adventure. It is suitable for high school students and older.

Kelly Darke of MathBookMagic and FairyMathMother would like you to know about Math Book Wisdom: An Early Math Resource Book. It isn’t a book to read to kids, but it is filled with math wisdom for the parents and teachers who teach children.

Crow Intelligence reviewed a book that interests me a lot:  Playing with Infinity – Mathematical Explorations and Excursions by Rózsa Péter.  I only need to decide if I will read it in English or try to get through it with the little bit of  Hungarian I know!

The Enchanted Tweeting Room

Jo Morgan blogs about some wonderful ideas for teaching Place Value Tool, Powers, Simple Linear Graphs and more that she’s found on Twitter and elsewhere in 5 Maths Gems #143.

On Mondays, MathEqualsLove blogs about many must-read tweets she finds on Twitter. You will want to check out Volume 80, and Volume 81.

The Whispering Spot

Imagine someone whispering at a spot inside a building and someone else clear across the room being able to listen to them clearly! Such a whispering spot exists at this carnival! See what happens when three math teachers teach by listening to their students:

When a student didn’t understand a mathematical concept, he broke a rule by leaving the classroom. Kaneka Turner of BlackWomenRockMath details how she listened to the student with her ears, her eyes, and her heart in The Art of Listening. By so doing, she successfully helped him make the connections needed to understand the lesson while simultaneously letting him know he was truly understood. What trajectory would his life be on now, if she had not listened as she did?

The Heinemann Blog features an interview between Marilyn Burns and Lucy Calkins on Listening to Learn. By listening to the interview or reading its transcript, you can learn how Marilyn Burns interviews individual students and listens to them to advance their understanding of mathematics.

In the second half of Bill Davidson’s podcast interview with Robin Ramos, she describes how she scripts questions and listens to not just individual students but to a classroom of students at the same time!

Listening is key anytime we talk with a math maker. You can read Life Through a Mathematician’s Eyes’ interview of an up-and-coming mathematician: Akshay Thakur for the Inspirational Corner.

Of course, teachers need to be listened to as well. See Research Minutes’ Teacher Stress and Burnout in the Wake of Covid 19.

Poetry Corner and Some Trigonometry

In Math Makers Write a Poem, Denise Gaskins gives us some ideas and examples of student-written mathematical poetry.

I also have found some examples of people making math by writing poetry. Even if a poem speaks negatively about math, it gives us all an opportunity to LISTEN to students and meet them where they are.

Trigonometry for Dogs is a short, sweet poem by Lyna Galliara.

My heart broke when I read Looking at Love Lost, by murisopsis of A Different Perspective. It is a poem about falling out of love with mathematics in high school beginning with trigonometry. Simply saying Trig is Easy doesn’t help and only makes a person not feel heard. Perhaps Wyrd Smythe’s Explanation of Trig Basics might have been helpful?

Puzzles

Craftgossip.com shares an easy Easter Egg Sudoku Puzzle that even preschoolers can do.

Puzzle a Day challenges us to solve A Mathematical Multiplication Puzzle with a six-digit product without using a calculator. I can attest that it can be done!

De Graw Publishing’s blog gives us Number Problems and Easy Sudoku Puzzles for Kids: Math and Logic Games Problems for Children.

Sarah Carter of MathEqualsLove shares a new puzzle in Number Ball Puzzles by Naoki Inaba. She translates the rules from Japanese to English so that you can have some idea where to put the missing numbers in the puzzle. Be warned, for the bigger puzzles, you might need to use your eraser a lot.

Sara also shared a sequence puzzle. Her students have enjoyed predicting the next letter in the sequence.

Maggie Heffernam suggested to Brian Marks of Yummy Math that he write a math activity when a real-life man was paid in greasy pennies.

Bedtime Math has a musical mathematical puzzle for you in Mile-Long Xylophone.

Math Teaching Strategies

Some teachers have half of their students in class and half remote over zoom. Keeping the at-home kids engaged can be difficult. Libo Valencia of Fresh Ideas for Teaching has six proven strategies to engage students in these hybrid classes.

You or your students can easily make Original Which One Doesn’t Belong puzzles!


Dan Draper of Opinions Nobody Asked For explores Area Models and Grid Method.

Probability and Statistics

Joseph Nebus of Another Blog, Meanwhile posts humorous statistics every Saturday like this cumulative bar graph showing Star Wars Movies versus Star Trek Movies. His vertical axis is a hoot.

Mr. Rowlandson of Pondering Planning in Mathematics has been Thinking About Probability Trees. Do you add or multiply the fractional probabilities? His blog post spells out what to do.

Athletes are constantly making math. Greg Pattridge of Always in the Middle writes about the statistics produced with every play in It’s a Numbers Game! Baseball.

Lunatic Laboratories uses alliteration to tell a tale of tails in One-tailed vs. two-tailed tests in statistics.

Did you know that if you get 11,000 steps a day, you will walk a million steps every quarter and just over 4 million steps a year? LisaFeatherstone had a daily goal of walking 10,000 steps and still made the 4-million steps goal. She used a spreadsheet to track the data her fitbit gave her and wrote a formula to predict when she would meet her goal.

Lvonlanken of The Shy Genealogist analyses the data she’s collected to determine which John Smith is her ancestor in Sorting the Land Records. Some genealogical programs will provide you with all kinds of statistics from your family tree. See the stats the Chiddicks Family found in My Family Tree in Numbers. I was pleased that they didn’t simply accept every statistic. They made predictions of the results and compared their predictions with the statistics the program produced.

MSCNM uses probability and statistics to answer the question Should You Buy a Lottery Ticket?

Blue Ribbons

Jo Morgan of Resourceaholic recently celebrated seven years of blogging by reviewing the very best teaching ideas and resources from the previous year and naming the winners of her (Maths) Gem Awards. Check it out!

The pandemic hasn’t stopped some people from doing good. Leila Zerai writes for LondonNewsOnline about a Student Winning the Prestigious Lewisham Mayor’s Award for Offering Free Online Maths Tuition.

A short story, Advanced Word Problems in Portal Math, is a finalist in the Nebula Best Short Story Contest. The reviewer didn’t care for the story because the math references were hard to understand. Let me tell you a little secret: I think that’s the way it was meant to be because I didn’t get the math references either! The story was just a fun way to make math. Another example of purposeful over-our-heads math was in a Barnaby comic. I know how to find the determinant of a two by two matrix and how to multiply binomials, but I look forward to Joseph Nebus explaining that comic sometime soon. It is still a funny comic even if I don’t fully understand it yet.

Math Memes and Comics

Joseph Nebus of Nebusresearch explains the mathematics of a comic in Where Else Is a Tetrahedron’s Centroid.

Design a Carnival

I hope you had a wonderful time at this month’s carnival! This month the Carnival of Mathematics #192 was hosted at Eddie’s Math & Calculator Blog. Perhaps you would like to design your own carnival.

Simran M Karkera of MSCNM tells the story of a girl who loved math that used trigonometry and calculus to design a roller coaster that thrilled her previously-mocking friends in A Mathematical Ride!

Last month the 145th Playful Math Carnival was hosted by Mathhombre. Perhaps you would like to host the next carnival or one later in the year. You don’t have to go overboard like I probably did. I was having so much fun, I couldn’t stop myself! To volunteer to host a carnival go to Denise Gaskins’ Carnival Volunteer Page.

Welcome to the 140th Playful Math Education Blog Carnival!

/ ivasallay / 5 Comments

What’s Special about 140?

Ladies and Gentlemen, welcome to the 140th Playful Math Education Blog Carnival! Feast your eyes on the number, 140, the 7th member of the famous Square Pyramidal Number family. Watch as 140 performs these amazing feats:

140 is the 7th square pyramidal number because
(7³/3) +(7²/2) + (7/6) = 140.

140 has twelve factors and will now use them to make a lovely factor rainbow:

For140’s next trick, see what happens when it is divided by six of its non-factors:

Finally, 140 is the fourth harmonic divisor number, and Wolfram Math World even uses 140 to explain what a harmonic divisor number is.

Now let’s move on to the blog entries for this month’s carnival:

Children’s Literature and Math

Kelly Darke of Math Book Magic wrote a post about a brand new entry in children’s literature, The Boy Who Dreamed of Infinity.  This is the story of the great Indian mathematician, Ramanujan. The book is available for us to read now, but Kelly was able to read it for the first time last year. I felt so much joy inside of me as I read first her reaction to the description of the book and later to the book itself. I am grateful that the mere idea of that book prompted Kelly to create a blog to share the magic of good mathematical children’s literature.

Rhapsody in Books Weblog tells us about, Raye Montague, an African-American girl born in 1935. She was told repeatedly that her race and her gender would prevent her from becoming the mathematician that she dreamed of becoming. She didn’t heed her naysayers. The Girl with a Mind for Math: The Story of Raye Montague tells her inspiring story.

On world Tessellation Day, TheKittyCats blog introduced us to Tessellations!  Children will enjoy looking at the illustrations in the book and won’t even realize they are learning some math in the process unless someone shares that secret.

Games and Math

Alan Parr of Established 1962 explains how to play Dotty Six, a game played with a tic tac toe grid and a die. Because he asked himself, “What If Not?”, he was able to suggest some mathematically interesting variations of the game as well.

Mrs. O’Brien started her blog, Math Epiphany, very recently-in May 2020. She has written two posts about using games to learn mathematics. She writes about card games in Summer Math Fun: Math Games, and about board games in Summer Math Fun: Good Old Fashioned Games.

Denise Gaskins shares a math game that lets children complexify expressions or equations rather than simplify them. Making the expression or equation a little more complex than it was before can be great fun and wonderfully educational. Check out The Best Math Game Ever!

Do you know how to play Dara, Five Field Kono, Mu Torere, Pong Hau K’I, Shisima, or Triangle Peg Solitaire? I’ve never even heard of these games before. Mark Chubb of Thinking Mathematically introduces all of these games in Math Games-building a foundation for mathematical reasoning. One of the games is illustrated in the tweet below.

Math and Paper-Folding

How is making a pouch out of a newspaper doing math? Paula Krieg and John Golden explain that it can be more than simply taking measurements and using rulers in Pouch: Something from Almost Nothing #3.

Did you know that paper folding can help kids understand systems of linear equations?

Or paper folding can even help kids understand Knot Theory or Topology?

Math and Art

What creatures can be seen in these numbers? Click on the video to find out what one artist saw!

We can always count on Robert Loves Pi to create dazzling and beautiful geometric art. Here he tells us how relaxing it is to produce it:

Photographer Ming Thein shares 13 discussion-evoking photos in Photo essay: The texture of geometry. I’d love to hear some of those discussions!

Quilts can be stunning examples of mathematical art. Aby Dolinger of Abyquilts has created a quilt pattern she calls “Math Whiz,” and this mathy quilt was featured on the July/August 2020 COVER of Quiltmaker magazine! Congratulations Aby!

Geometry and Trigonometry

Laura of Mathsux² has written an explanation and created a video to take the mystery out of trigonometric ratios in How to Use SOHCAHTOA.

Jo Morgan’s website is filled with resources to make teaching and learning math more effective, and yet she always finds room for more ideas! She recently created her 133rd Maths Gems Post that included some playful ways to look at angles in a circle and areas of rectangles inside of a larger rectangle. . . Now to segway into word problems. . . If Jo writes two Maths Gems a month and her July 30th post was number 133, and the Playful Math Blog Carnival comes out ten times a year and this is the 140th post, when will the Maths Gems number and the Playful Math Blog number be the same number?

Word Problems

I love the giant Sequoia Trees. This blog post has story problem suggestions about Sequoia Trees for every age group:

A-Hundred-Years-Ago Blog explores some Hundred-year-old Food-related Math Problems when large oranges were only 60 cents a dozen. Go back in time and enjoy solving these with your students! Let them compare them with word problems from the 21st century.

Puzzles

Alan Paar of established1962 shares his last experience helping kids play with math before the lockdown. It was a series of puzzles that made A Lesson That Will Stay With Me. He has used these adventures for 30 years and kids enjoy them so much. He was especially glad that these puzzle adventures will be their last memories of attending primary school. They was so much better than Key Stage 2 SATs.

The Find the Factors puzzles I create are a playful way to get to know the multiplication table better. This level 3 puzzle can be solved by considering the factors of 30 and 90 where only factor pairs with numbers from 1 to 10 are used. After those factors are found, write them in the appropriate cells then work your way down the puzzle row by row using logic until all of the factors are found.

Singapore Maths Tuition shares an “average” math puzzle with a twist that might baffle all but those kids who enjoy math but find little challenge in traditional math work. No worries for the rest of us; a good explanation is also included.

Mathematical Humor

Emily’s Post tells a timely math joke about three ducks that will teach while it delights children in Modern Math.

Joseph Nebus has a humor blog in which he wrote a humorous post he titled What your Favorite Polygon Says about You. I’m not sure what my favorite polygon is, but I will carefully consider all the possibilities.

The Bored Side of the Phone shares a couple of stand-up-comedy-worthy jokes about Mathematics in The Truth About Maths.

Numbers

Natural Numbers:

The counting numbers/whole number set has been further categorized! Can you imagine how? Read all about it in Publications de BOULAY’s New Whole Numbers classification. As you learned about the set of ultimate numbers, how well did your imagination serve you?

Rational and Irrational Numbers: Mike of Mike’s Math Page gives us a front-row seat observing how he teaches his sons about mathematics in Sharing John Urschel’s great video on rational and irrational numbers with my son.

Imaginary Numbers: Every year Joseph Nebus lets his readers chose mathematical topics for each letter of the alphabet, and then he writes a post about each of those A to Z topics. For 2020 he wrote a serious essay on imaginary numbers that playfully included some comics about some numbers that you can imagine.

Life skills and Math

Ladybugs or ladybirds want to teach you some math concepts. Come out in the garden with the lesson plans provided by DogwoodDays in Garden Schooling: Ladybird Maths and see what you learn!

Cooking is an important life skill and a fun way to learn about fractions and other math concepts. The For-Health blog featured a post kids and adults can enjoy together: How to Cut Down Recipes: What’s Half of ½ cup, ¾ cup, 2/3 cup and More. Verifying the given measurement equivalents can be great fun for kids so do let that happen!

How can we make our lives be as well-balanced as an equation? That’s a good question for high school students to consider. A life coach’s advice on how to find success in life is given using mathematical symbols and vocabulary in Mathematics of Life, Learn from Math symbols.

Corona Virus Math

In Wheel of Theodorus – Distance Learning Edition, MrJoyce180’s shares his students’ work creating their own, and I do mean their own, Wheels of Theodorus. All of this creating occurred virtually during the lockdown. He shares both the successes and the failures. This was one of my favorite discoveries while I created this carnival.

I didn’t have my glasses on questions Cosco’s mathematical reasoning of cake buying and serving in Let (a few of) them eat cake! Can you formulate a word problem from this post?

Statistics

When Disney produces a direct to video sequel, will a Roman numeral, an Arabic numeral, or neither most likely appear in the title? Even young children will be able to explore that topic with Joseph Nebus in this Statistics Saturday Post.

World Affairs uses cleverly represented graphs to help us understand The Math of How China Surpasses USA in 5 Years. Understanding the math behind the graphs could help us improve our situation.

Poetry and Math

Beginning with irrational numbers, Prerna’s Blog uses mathematical and poetic language to describe the Mathematics of My Mind.

Math+Life connects math with life by writing poetry. After you read Set in Stone the mathematics of sets is explained followed by how they relate to life. Do we place limits on children or adults when we categorize them into sets of different types of people?

Making Math More Inclusive

Please read Sunil Singh’s powerful and thought-provoking post, How to Begin Bringing Rich and Inclusive Math History Resources Inside K to 12 Classrooms.

I am also pleased to introduce you to the brand-new BlackWomenRockMath Blog. Their first post is The Brilliance Hiding in Plain Sight in which three women share their sobering math stories. Thankfully, they each were able to overcome negative early experiences in learning mathematics to make worthwhile contributions to mathematics education today.

Mathematics Carnivals and Amusements:

Every Monday Denise Gaskins invites you over for a Morning Coffee. There she will direct you to other mathematics blogs for your edification and amusement.

There is also a Carnival of Mathematics that may interest you. The current (184th) Carnival is hosted at Tom Rocks Maths.

I really liked putting this month’s carnival together, and I hope you have enjoyed reading it as well. Feel free to stop by and hang out whenever you’d like.

The previous Playful Math Education Blog Carnival #139 was hosted by Math Mama Writes. Be sure to check it out if you haven’t already.

I am already looking forward to the next Playful Math Education Blog Carnival which will be hosted by Joseph Nebus of Nebus Research.

Perhaps you would like to volunteer to host one of the carnivals? Contact Denise Gaskins to get on the carnival calendar! I can’t wait to see what you put together!

1508 Hosting a Playful Math Carnival and Flying by the Seat of My Pants

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Blog Submission Appeal:

Please, tell me how you’ve made K-12 math education more fun. You see, later this month I’m hosting the Playful Math Education Blog Carnival. I have found several great blog posts to share, but maybe I haven’t seen yours. You can share your blog post with me by submitting this official form, leaving a comment below, or messaging me on twitter, Iva Sallay@findthefactors.com. I look forward to reading your post! Please share it with me by Saturday, August 22 so it can be included in this month’s carnival.

Today’s Puzzle:

This mystery-level puzzle was modeled after a carnival ride, the swing carousel, a ride that tilts slightly as it goes around, and lets you ride by the seat of your pants. My puzzle might not be the best representation of that ride, but it hopefully got your attention. 

Embellishing the puzzle might make it more eye-catching, but it is probably easier to solve the puzzle without distracting color and lines. (It’s a mystery-level puzzle, so I’m keeping how easy or difficult it is a secret.) Here is a plain version of the same puzzle:

Factors of 1508:

  • 1508 is a composite number.
  • Prime factorization: 1508 = 2 × 2 × 13 × 29, which can be written 1508 = 2² × 13 × 29.
  • 1508 has at least one exponent greater than 1 in its prime factorization so √1508 can be simplified. Taking the factor pair from the factor pair table below with the largest square number factor, we get √1508 = (√4)(√377) = 2√377.
  • 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 1508 has exactly 12 factors.
  • The factors of 1508 are outlined with their factor pair partners in the graphic below.

More about the Number 1508:

1508 is the sum of two squares in two different ways:
32² + 22² = 1508
38² + 8² = 1508

1508 is the hypotenuse of FOUR Pythagorean triples:
540-1408-1508, calculated from 32² – 22², 2(32)(22), 32² + 22²,
580-1392-1508, which is (5-12-13) times 116,
608-1380-1508, calculated from 2(38)(8), 38² – 8², 38² + 8²,
1040-1092-1508 which is (20-21-29) times 52.

 

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!

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)

 

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

 

1193 Math Carnival Games

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During the last week of every month, there is a math education blog carnival happening somewhere in the blogosphere. This month it will happen on my blog! Why do I get to host it? I sent an email to Denise Gaskins who coordinates the carnival and requested the privilege. If you would like to host it in the future, let her know.

In the meantime, you can help me with my carnival. Math can be so much fun for kids from preschool age and even all the way up to high school. If you blog about that, I would love to include one or more of your posts in my carnival. You’ve poured your heart and soul into your posts, so why not promote it at no cost to you?  Don’t be shy! I want to read it, and other people will want to read it, too.

The deadline for submitting posts to my carnival is Friday, August 24th. There is a form for you to submit a link to your post on Denise Gaskins website. Then the following week you will be able to enjoy the carnival even more because of your participation!

Now it will be my pleasure to tell you a few facts about the number 1193:

  • 1193 is a prime number.
  • Prime factorization: 1193 is prime.
  • The exponent of prime number 1193 is 1. Adding 1 to that exponent we get (1 + 1) = 2. Therefore 1193 has exactly 2 factors.
  • Factors of 1193: 1, 1193
  • Factor pairs: 1193 = 1 × 1193
  • 1193 has no square factors that allow its square root to be simplified. √1193 ≈ 34.53983

How do we know that 1193 is a prime number? If 1193 were not a prime number, then it would be divisible by at least one prime number less than or equal to √1193 ≈ 34.5. Since 1193 cannot be divided evenly by 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 or 31, we know that 1193 is a prime number.

1193 is the sum of five consecutive prime numbers:
229 + 233 + 239 + 241 + 251 = 1193

32² + 13² = 1193

1193 is the hypotenuse of a Pythagorean triple:
832-855-1193 calculated from 2(32)(13), 32² – 13², 32² + 13²

Here’s another way we know that 1193 is a prime number: Since its last two digits divided by 4 leave a remainder of 1, and 32² + 13² = 1193 with 32 and 13 having no common prime factors, 1193 will be prime unless it is divisible by a prime number Pythagorean triple hypotenuse less than or equal to √1193 ≈ 34.5. Since 1193 is not divisible by 5, 13, 17, or 29, we know that 1193 is a prime number.

896÷8=112. Math Teachers, It’s Carnival Time!

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  1. 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 150th 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