InnerworldWe may not have it all together, but together we have it all. —Ellen Marie Wiseman
Denise Gaskins' Let's Play MathPlayful Math 184: Carnival of Living Math
Welcome to the 184th edition of the Playful Math Education Blog Carnival — a smorgasbord of delectable tidbits of mathy fun. It’s like a free online magazine devoted to learning, teaching, and playing around with math from preschool to high school.
With all the links, a blog carnival can feel overwhelming. Bookmark this article, so you can take your time reading the posts.
“Living math” means bringing our children face-to-face with the big ideas of mathematics to help them develop their reasoning skills. When the ideas of math come to life for our children, their minds delight in seeing how numbers and shapes connect to each other and exploring these relationships.
Scattered between the playful math links below, you’ll find quotations from my new book Charlotte Mason’s Living Math, along with several paintings of children playing and learning which I considered for the book but ran out of room.
“The lesson” by Rafael Frederico, 1895.By tradition, we start the carnival with a puzzle/activity in honor of our 184th edition. But if you’d rather jump straight to our featured blog posts, click here to see the Table of Contents.
Puzzle: Playing with Primes
Prussian mathematician Christian Goldbach, in correspondence with Swiss polymath Leonhard Euler, posed several ideas about number theory (the study of natural numbers) which he couldn’t prove. The version we know now as Goldbach’s Conjecture is:
Every even natural number greater than 2 is the sum of two prime numbers.
Goldbach’s Conjecture is one of the oldest and best-known unsolved problems in math. It has been shown to hold for numbers less than 4 × 10^18, but remains unsettled for larger numbers.
Our carnival number can be written as the sum of primes in eight ways:
184 = 181 + 3
= 179 + 5
= 173 + 11
= 167 + 17
= 137 + 47
= 131 + 53
= 113 + 71
= 101 + 83
184 can also be written as the sum of four consecutive prime numbers:
184 = 41 + 43 + 47 + 53
Play around with Goldbach’s Conjecture and prime numbers.
- What do you notice about sums of primes?
- What do you wonder?
- What other questions can you ask?
Did you know the prime numbers come in a pattern? While it can be hard to prove for sure which large numbers are prime, there are infinitely many numbers that we can be confident are not prime.
- List some large numbers that you know are not prime. How do you know?
- Fill in this worksheet and consider the patterns.
- Now can you list more large numbers that are not prime? Can you tell some that might be?
Contents
And now, on to the main attraction: the blog posts. Some articles were submitted by their authors; others were drawn from the immense backlog in my rss reader. If you’d like to skip directly to your area of interest, click one of these links.
- Talking Math with Kids
- Exploring Elementary Arithmetic
- Adventuring into Algebra and Geometry
- Scaling the Slopes of High School Math
- Enjoying Recreational Puzzles and Math Art
- Teaching with Wisdom and Grace
- Giving Credit Where It’s Due
Talking Math with Kids
“From their birth, children have minds just like ours, hungry for knowledge and able to digest solid mental food. They enter life full of wonder, questioning, investigating the world, reasoning, and drawing conclusions.”
—Denise Gaskins
- Dan Finkel invents Trifle — a new, very small game. “I invented a small game off the cuff last night. I needed a super quick game to play with my 6.5-year-old before bedtime.”
- Christopher Danielson shares the conversations that launched his yet-unpublished book: On vehicles and the meanings of words. “These questions are simple yet deep. They can inform our current conversations in which we seek to regain our understanding of truth, meaning, and empathy.”
- Digging through Christopher Danielson’s delightful archives, I find: A circular conversation, and Doll years, and Does the Earth have an end?. “If you are new to talking math with your kids, don’t worry about getting the timing right. Just start to make a habit of asking those questions. The first few times, you may not get much. That’s OK. It can be like introducing new foods — children need multiple exposures to new things before they accept them.”
- Tom Hobson tells how to build A State-of-the-Art Preschool Playground (for under $200) that will prompt all sorts of math (and other) talk. “As educational as these kinds of spaces are for children, these wonderlands of loose parts, dirt, rocks and compost, these bastions of junkyard chic, they are often perceived as eyesores by the uninitiated. Before going too far, you might want to save up to build a fence.”
- Writing is talking on paper. Dylan Kane tries Incorporating more writing in 7th grade math. “Slowing down and writing about a topic is a great way to think deeply about it, to make connections, to consider hypotheticals, to reason about cause and effect.”
- Jenna Laib gets 4th-graders writing math: How Many Nivelsnorts: Assessing Silly Story Problems. “Perhaps this speaks to who I was as a child, but there is a playfulness and a creativity to getting to write about nivelsnorts and flying tomatoes, and I don’t see a need to deny students that.”
- Karrie E. suggests 5 Easy Ways to Add Writing into Your Math Class. “The goal isn’t to create more work for your or your students. It’s to make thinking visible.”
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Exploring Elementary Arithmetic
“That he should do sums is of comparatively small importance; but the use of those functions which ‘summing’ calls into play is a great part of education.”
—Charlotte Mason
- Patrick Vennebush explores the Mathematical Mysteries of 2026. Meanwhile, Iva Sallay collects 2026 Math Facts and Factors, including a “powerful” math joke. You may also enjoy George Sicherman’s Roman New Year puzzle.
- Sarah Dees explains one of my favorite math games: How to Play Target Number. “This is a fabulous math game that works for third grade all the way up through 6th. You can choose the complexity of the game by choosing how many dice to use.”
- Erick Lee poses A Problem Worth Solving. “I liked this problem because there are so many different ways to approach it and so many interesting patterns to see while solving it.”
- Susan Smith and Kim Montague explore Factor Puzzles: Helping Math Make Sense. “That’s the challenge we pose to students: What do you notice about the puzzle you see? What relationships pop out to you?”
- Pat Ballew plays around with The 3×3 Magic Square, More Magical than You Thought! And Greg Ross shares a magic Venn diagram: Set Piece.
- For my contribution to the carnival, I finish up my series on mental math with Advanced Multiplication, Part 1, followed by Advanced Multiplication, Part 2, and then Advanced Division to wrap things up. “The more time our children spend playing around with numbers and making sense of these relationships, the better they’ll be prepared for algebra and beyond.”
- Jenna Laib shares important information: The 8 Fast Food Chains in the US Most Likely to Get Your Drive-Thru Order Right. And some good news: Extreme Poverty Fell Sharply Worldwide – Even Excluding China. Slow Reveal Graphs “invite learners to examine trends, relationships, and possible interpretations.”
- John Golden teaches Statistics and Probability for K-8 Teachers with some fun resources: Who Wins? “Lots of great discussion about variation, mean, median and their limitations.”
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Adventuring into Algebra and Geometry
“If students find our lessons boring, that is because we are not engaging their minds. Children learn by thinking, imagining, reflecting, reasoning, arguing, justifying, and communicating, putting their thoughts into words. Learning, like digestion, is active.”
—Denise Gaskins
- Iva Sallay graphs a Cat Rotating Around a Bouncing Ball. “This year, the 9th-graders I work with at school need to know how to rotate a shape around a point that is NOT the origin. This is a topic I had never thought about before. To patch up this hole in my math knowledge, I decided to play with rotations in Desmos.”
- Ramsha Waseem reports on 14-year-old Miles Wu’s origami invention. “I was really shocked by how much [weight] these simple pieces of paper could hold,” says Wu.
- Karen Latham offers suggestions for Making the Most of Probability. “I like to have students work several counting problems by hand, so they have experience simplifying expressions with factorials. Then they can move on and let the calculator do the work.”
- David Butler plays with a geometric puzzle: When perimeter is equal to area. “One answer I discovered to this question is completely surprising and delightful to me. You may want to attempt to prove it yourself before I show you my proof…”
- Andrew Staccy categorizes Catriona Agg’s Puzzles by Topic. “The various techniques are grouped into categories and ordered roughly by complexity. Puzzles may appear more than once as they can have multiple ways of being solved.”
- Pat Ballew takes a look at Heron and his Formula(s). “Heron is also remembered for his invention of a primitive steam engine and many early automatons, and a coin operated vending machine, and one of the earliest forerunners of the thermometer.”
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Scaling the Slopes of High School Math
“Never are the operations of Reason more delightful and more perfect than in mathematics. There is great joy in standing by, as it were, and watching our own thought work out an intricate problem.”
—Charlotte Mason
- Christopher Burke posts a series of Geometry Problems of the Day from the Regents Exam, with solutions. “This is a silly question because it’s obvious that both Choices (1) and (2) cannot both be true, so one of them must be the answer.”
- Oliver Johnson explores the probability that your shopping receipt ends in .00: Time’s Arrow. “This ‘everything has the same chance’ collection of probabilities is called the uniform distribution, and it’s really important. But what might be surprising is how easily we reach it, and how few items we need to pick up in a supermarket to make it appear.”
- Nicola Rennie discusses How to create a more accessible line chart. “It’s a myth that accessibility means compromising on aesthetics. Instead, accessibility means prioritising communication.”
- Sue VanHattum needs beta-readers for Althea and the Mysteries of Calculus, version 8.2. “I’m still finding places where I need to add a bit to make the math clearer. Adding a touch of color here, removing something out of place there. I feel like a sculptor or painter.”
- Erick Lee shares A Calculus Esti-Mystery. “Instead of using basic number properties for the clues, I leveled it up. To unlock the clues, my students had to evaluate derivatives.”
- And don’t miss the 249th Carnival of Mathematics.
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Enjoying Recreational Puzzles and Math Art
“We take strong ground when we appeal to the beauty and truth of Mathematics. Mathematics are to be studied for their own sake and not as they make for general intelligence and grasp of mind. But then how profoundly worthy are these subjects of study for their own sake!”
—Charlotte Mason
- David Butler (and daughter) explore a math/art puzzle: Jenga Views. “One thing I particularly like about them is that you don’t need an answer key, because you can just look at your construction and tell if it looks right or not. There’s something empowering about being able to check it yourself.”
- John Golden shares a couple of shape puzzles: Five by Five, and his variation on the theme: Seven by Seven. “Easier to solve, but more solutions. Better for free play. If you made something cool, tangram style, I would love to see it!”
- Rick Mohr welcomes us to a world of Tiled Art. “enjoy a gallery of artworks as each emerges from an underlying grid. And try creating your own tessellation, with the tiles staying interlocked automatically.”
- I post two excerpts from my new book, Charlotte Mason’s Living Math: Discover Math in Art, and the math equation journaling prompt True-False-True. “This puzzle pushes students to consider the structure of mathematical expressions. Make it a game by letting your children challenge you, too.”
- Andrew Taylor creates things with math. I’ve been enjoying his puzzle game Celtix. “Celtic knots are a rich tradition, but for the sake of reducing them to a game mechanic you can think of them as ribbons which ‘bounce’ off ‘walls’ which you can add by clicking anywhere that the ribbons cross each other.”
- Paula Beardell Krieg demonstrates how to make a Cube with an Open Pocket. You may also enjoy her Snow Day Octahedrons. “I’ve been at my desk, working on geometric solids, doing art and math together. I find focus and comfort here.”
- Jonathan Halabi plays with a couple of Birthday Puzzles. Greg Ross finds some harder Words and Numbers. And Pat Ballew digs deeper into Some History Notes about Alphametic Puzzles (and some early versions of a Topology Gem).
- Ben Orlin seeks play-testers: Puzzle Planet. “Your collective generosity and wisdom help me to clarify confusing bits, fine-tune difficulty levels, cull inferior puzzles, spotlight superior ones, and sprinkle play-testers’ insight and wit throughout the text.”
- Laura looks at the math of bell ringing: I can hear the bells. “Each bell ringer controls a huge bell, often on the order of a tonne in weight. One by one they ring their bells, then switch to a new permutation (a change) and repeat.”
- James Propp plays around with probability: In Praise of Stupid Questions. “The way to find things out is to ask a lot of questions. Ask enough questions, and you’re likely to find a new answer: new to you, and once in a while, new to others.”
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Teaching with Wisdom and Grace
“It can be exhausting to shovel information into our child’s head. We put out a lot of effort without much return, and daily lessons become a struggle of wills. But when we treat a child as a person capable of learning for himself and meet him mind-to-mind, with a focus on understanding big ideas, lessons become a delight.”
—Denise Gaskins
- Dan Finkel concludes that Manipulatives in Math Class Are So Worth It. “When it came to mathematizing — linking equations and the rods — the kids who had previous experience building and free playing with the rods made the connections far more readily. Playing with the rods seems to prime the mind to make connections.”
- JoAnne Growney wonders, Can Poems Affect Students’ Math-Attitudes? “One useful viewpoint is that math need not be treated as an isolated subject . . . it is connected to our lives in VERY MANY ways.”
- Growney also links to two contests your students still have time to enter: Creative Writing — Including Mathematics. For inspiration, consider her poem Like Poetry, Mathematics is Beautiful.
- Cathy Yenca details how to prepare The April Fool’s Day Math Activity Students Never Forget. “I decided I wanted to prank my students, but not the kind of prank that derails a lesson. I wanted something that would make students lean into the math instead of checking out.“
- Jenna Laib discusses Measuring Growth in Mathematical Reasoning: What Mia’s Thinking Reveals. “I confess: sometimes I find wrong answers more interesting than right ones. There can be so many ways to get something wrong!”
- Craig Barton creates interactive tools and games for teachers. “End of lesson treat or whiteboard activity for the whole class. Project a game and play together!”
- The Math is FigureOutAble team highlights Leonhard Euler: The Blind Mathematician Who Saw Everything. “Every student can learn to think like a mathematician. They can persist through challenges, adjust their thinking, and experience the satisfaction of figuring something out. They do not need perfect conditions or special talent. They need instruction that invites sense making and builds confidence over time.”
- David Butler shares More wisdom from the Dodecahedron about the humanity of doing math. “I find that maths is full of emotion. Frustration, curiosity, surprise, satisfaction, pride, sadness, companionship, wonder, silliness, joy — they’re all there, sometimes in quick succession.”
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Giving Credit Where It’s Due
Quotations are from my new book Charlotte Mason’s Living Math. Public domain art is primarily from Wikimedia Commons.
And that rounds up this edition of the Playful Math Education Blog Carnival. I hope you enjoyed the ride.
The next installment of our carnival will open sometime during the 2nd quarter of 2026 at Nature Study Australia. Visit our blog carnival information page for more details.
“The Lesson” by Charles Chaplin, circa 1880. #Activities #AllAges #Games #MTaPPlayfulMathCarnival #Puzzles #Quotations
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