The 168th Playful Math Education Blog Carnival

A Couple of Carnival Puzzles for You to Solve:

Puzzle one: There are 168 prime numbers less than 1000, and four of them are consecutive primes that add up to 168. Can you figure out what those four prime numbers are? Hint: The average of the four prime numbers will be 168÷4.

Puzzle two: How many pips (dots) are on this regular set of 28 dominoes?

I’ve grouped the dominoes into groups with six dots. How many groups of six are there? Multiply six by the number of groups and you will know the number of dots. You can also count them by using this cool triangular display from Wikipedia.

Five Amazing Facts about the Number 168:

168 isn’t perfect, but it is the product of the first two perfect numbers, 6 and 28.

Most of us recognize that 168 is one less than a perfect square, so 13² – 1² = 168, but did you know that 168 is also the difference of two squares in three other ways?
43² – 41² = 23² – 19² = 17² – 11² = 168.

Here’s another square way to make 168:
18² – 17² + 16² – 15² + 14² – 13² + 12² – 11² + 10² – 9² + 8² – 7² + 6² – 5² + 4² – 3² = 168.

2¹⁶⁸ = 374144419156711147060143317175368453031918731001856. Look it over. You won’t see a “2” anywhere in that 50-digit number. 2¹⁶⁸ is the largest known power of 2 not to contain each of the 10 digits at least once.

168 is a repdigit in several other bases:
168₁₀ = CC₁₃ = 88₂₀ =77₂₃ = 66₂₇ = 44₄₁ = 33₅₅ = 22₈₃ = 11₁₆₇ = 168₁₀.

More Domino Fun:

The DewWool blog has made ten free domino worksheets for kindergarten and first-grade students to practice addition.

You can also use a double nine set of dominoes to solve an algebra problem:

And what about using dominoes to add fractions?

Autumn Math:

If your town has a scarecrow trail, you can add some learning while you take the kids around. They can learn about many subjects including mathematics as they do the activities suggested in this blog post by Curious Kids 101.

Apples have several lessons inside of them. AdamPetersonEducation suggests using apple seeds as manipulatives in Apple Activities in the Classroom.

Math Story Books:

Writer’s Rumpus’s post about a brand-new picture book, Smarty Ants, by Corey Rosen Schwartz and Kirsti Call, illustrated by Erin Taylor. The blog post includes pictures that clearly show some of the math involved in what looks like a delightful story. There’s even a song for your students to enjoy.

Way Past Embarrassed by Hailey Adelman is a picture book that will help students who are too embarrassed to ask for help in math class to speak up to get the help they need.

Tara Lazar is a children’s book writer, but she also shares other books on her blog that her readers will enjoy. Read her post and you will know what inspired Erin Dealey to write a great introduction to fractions, The Half Birthday Book. The whimsical illustrations were drawn by Germán Blanco.

Bound for Escapes Reviews The Math Kids: An Incorrect Solution, and says that “whether a child likes math or not, this is a fun story.”

Pages Unbound Reviews Talia’s Codebook for Mathletes by Marissa Moss. This is a book that is sure to appeal to students in middle grades as Talia navigates middle school, refusing to give in to those who doubt her mathematical abilities simply because she is a girl.

A Kid’s Book a Day reviewed The Probability of Everything by Sara Everett. This book will engage 4th – 7th graders in discussions about probable and improbable events. Pelicans and Prose reviewed the same book and described The Probability of Everything as one of the most powerfully written books one could read.

The Christian Fiction Girl reviewed Calculated, by Nova McBee. It is a young adult novel that’s a blend of Mission Impossible and The Count of Monte Cristo.

Numbers on the Number Line:

Positlive compares where we are in life to additions and subtractions of positive or negative numbers on a number line in Life’s Simple Equation: Number Lines, Arithmetic, and Five Life Lessons.

Poetry for Finding Meaning in the Madness, Just Poetry wrote Odd, a poem about the life of an odd number.

You can read or listen to Keith’s Ramblings story, Unlucky Numbers. How many ways can the number 13 be partitioned anyway?

Help from Heaven has a completely different take on that number in 13 is My Lucky Number.

You’ll have to scroll down to get to the 4th-grade math sections in this post from Teaching to the Beat of a Different Drummer, but it will be well worth it. On day 3 there is a Me in Numbers activity, on day 4 a rounding to the nearest hundred activity, on day 5 a doubling single digit numbers game, and on day 6 a mind-blowing partial sums strategy.

Writing from the Heart with Brian notes that 50000 doesn’t look much different from 50000000 until you can actually relate something to each of the numbers. This insight may be helpful to your students.

The Internet Effect also discusses relative place value in The Illusory  Arithmetic: A Tale of $30 K and $300 K.

Exponential Growth:

A Berg’s Eye View shares a priceless meme to help your students remember the meaning of Exponential Growth.

Lino Matteo will open students’ eyes with the role of exponential growth in Financial Literacy: Housing.

Sumant shows his work for this SAT question on Exponential Growth.

Mathematical Games and Puzzles:

Math File Folder Games has directions to play a drawing game that will reinforce several geometry concepts AND lists the standards that the game can cover.

The Bad Mathematics blog discusses the card game 24 where the players must use addition, subtraction, multiplication, and/or division on the 4 cards they are dealt to arrive at the number 24.

The Napier Local Arithmetic Board will feel like a game as students use it as they peg to multiply numbers.

Puzzle a Day invites you to determine where is the only safe place to stand in 1500 People in a Circle. Any guess is more likely fatal than not.

A safer puzzle to answer is Puzzle a Day’s The Mystery Middle Digit.

Quadratablog.blogspot has made a sudoku puzzle that is mathier than most in a Small Multiples Sudoku.


The world’s geography in geometric shapes:

The Craft of Coding very much enjoyed writing code to calculate the volume of a gugelhupf pan (what I would call an angel food cake pan.) The post explains the advantages of baking when the volume of such a pan is known.

Graphs and The Coordinate Plane:

Here’s my contribution to the carnival: I made a polygonal elephant using the Cartesian coordinate system. Using Desmos, I was able to do several reflections in mere seconds: I reflected the elephant over the x-axis and the y-axis, and then reflected the reflections into the 3rd quadrant.

Nicholas C. Rossis blogged a little about the Cartesian coordinate system and shared a hilarious video in The Shape of Stories, According to Kurt Vonnegut.

Roro’s Adventurous Blog discusses vectors in Fun with Random Numbers and Matrices.

The Golden Ratio and Fibonacci:

Puzzle a Day asks that we analyze the numbers in the Fibonacci sequence in a Fibonacci puzzle.

Nature Notes the Arb shares pictures of Fibonacci numbers in nature.

On a more serious note, HTT Network has written a beautiful post Unveiling the Enigmatic Golden Ration: Unlocking the Secrets of Beauty and Harmony.

The Graphxhub blog gives us How Math in Graphic Design Adds up to Stunning Visuals. This post helped me understand the golden ratio in art much better, but it covers so much more than that.

Lego Math:

Shapes in Blue has created some lovely blue geometric Lego art you’ll want to see.

Alison Kiddle used Legos to make 31 math conversation starters, one for each day of the month of August. These three are only a sample. Check them all out!


How about a Multiplication Magic Show from ActiveWordZ to help students learn the 2 and 3 times tables? It sounds pretty exciting to me!

The Reflections and Tangents blog teaches Area Arrangements going from one-digit multiplication problems to multiplying numbers with several place values, to fraction multiplication, and even to multiplying polynomials.

Mathematics History Museum:

Learn the history of the Rubik’s cube as you walk through MillenialMatriarch’s post on Rubik’s Magic Cube.

Sheryl, a Hundred Years Ago explains how recommended calories were calculated in 1923 and compares it to the method used today.

Cedric School of Thought describes the difficult life of self-taught mathematician, Nicolo Tartaglia, in the 16th century.

Visit Live Life King Size for a lovely presentation, What is the History of Maths? It is perfect for our Museum of Mathematics.

Math Through Music:

I saved my favorite for last:

Want more? Playlistideas has compiled a playlist of artist-produced songs about math just for us all to enjoy!

Mathematical Optical Illusions and Photography:

What carnival would be complete without a house of mirrors?

Zsolt Zsemba wrote a post explaining why a few mathematical designs turn into optical illusions.

Mathematics and art combine to make a rug that looks dangerous to step on.

Click on the video at Terryorism’s blog and watch some squares look like they’re moving, but they aren’t.

Enchanted Seashells shared these squares that are drawn to look like a stairway that changes direction while you’re looking at it.

Let’s Write… saw a picture of real stairs that look like they could be going up just as easily as they are going down and wrote about it.

Robert’s Snap Spot shared An Optical Illusion at Shelter Cove with some cool shadows. This photo really exemplifies perspective in art as well as in mathematics.

Travel with me takes us to a photo gallery highlighting triangles in each frame.

The Other Life of This Math Teacher is Photography: See the geometry in
Make Friends, Have Fun,
in Penta-licious,
and in a Chinese Pagoda.

Paper Folding, Origami, and Tangrams:

Carter in the Classroom reported to an NBC affiliate how A Texas Teacher Uses Origami to Teach Math (and a Growth Mindset).

Paula Beardell Krieg has produced some wonderful blogposts on paper folding this summer:

Paula Beardell Krieg also wrote several wonderful posts on exploring geometry through tangram play.

Geometric Designs and Tessellations:

RobertLovesPi regularly makes and shares tessellations of his blog. His tessellation of octogons, rhombi, and darts is very pretty. Be sure to check out his tessellation which includes heptagons! I don’t think they show up in other people’s tessellations very often.

You may have heard of the newly discovered tessellating hat, or maybe even the new tessellating turtle, but have you heard of David Smith’s tessellating Spectre?

Pascal’s Prism teaches us about the hidden math behind art: the fascinating geometry of tessellations.

Geometric designs might be done with plastic, paper, or cloth. Pieced quilts can certainly bring pleasure to those who make them as well as those who look at them. Take a look at these recent blog posts featuring some lovely quilted geometric designs and tessellations:

  1. Sailing Ships made from circles and squares,
  2. Intersecting Circles,
  3. Triangles,
  4. A Sampler with a variety of designs, any of which could tessellate an entire quilt.
  5. A Design made with squares in a couple of different sizes.
  6. Parallelograms (Scroll down a little to see them.),
  7. A Square and Triangle design with a free pattern and instructions,
  8. A Flower made with mini hexagons,
  9. Maple Leaf (very nice for autumn),
  10. A Mystery Halloween Quilt,
  11. A Halloween Lap Quilt,


Read and Play All Day will help us all put objects into sets with Sorting and Ordering by Size: A Precursor of Ordering Numbers.

Elorine takes 5th-graders on a few adventures. The first is Unleashing the Power of Sets, A Magical Math adventure.

The second is a virtual field trip, Exploring the Wonderful World of Sets. Find Treasures Within.

The third is Exploring the Magic of Union Sets in Mathematics.

The fourth is The Marvelous World of Equivalent Sets.

Probability and Statistics:

Wind Kisses discusses the likelihood of certain events and shares some inspirational quotes in Likely or Unlikely.

There are 23 players on a soccer team, what is the probability that at least two of the players have the same birthday? That question was examined at the Women’s World Cup, and the answer may surprise you!

Statistical Odds and Ends asks, “What is the probability of getting all heads on multiple coin flips?”

Every Saturday Nebushumor publishes a funny statistics post. For example, take a look at How I Use My Recreational Time. You and/or your students can probably relate to it. Or how about Fun, by Decade. I think he’s spot on.

Thoughts on Teaching Mathematics to All Students:

Denise Gaskins is very impressed with a fully developed, revolutionary program that teaches Algebra before Arithmetic and wishes she had access to it 30 years ago when her kids were young.

You can read the importance of a growth mindset from a parent’s perspective in The Power of Yet.

Heidi Allum asks if Math Play can be a Part of Trauma-Informed Care? I’m sure you will be interested in learning how math play affects all students including those who have experienced trauma.

Don’t let the solved calculus problem at the beginning of the post intimidate you, but Alternative Amie has several insights into the benefits of melding the arts with the teaching of mathematics.

Other Carnivals with Mathematics:

Every month The Aperiodical blog also coordinates a math carnival that includes college-level mathematics. September’s carnival is at Reflections and Tangents.

The last Playful Math Carnival was at Learning Well at Home. The next one will be at Math Hombre. How about a future carnival being on your blog? Volunteers are needed and welcome! Coordinate with Denise Gaskins for a month that is convenient to you by going to the Playful Math Carnival Volunteer Page.

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