Welcome to the 97th edition of the Math Teachers At Play math education blog carnival: a monthly smorgasbord of links to bloggers all around the internet who have great ideas for learning, teaching, and playing around with math from preschool to pre-college.
A few articles were submitted by their authors, but most were drawn from the immense backlog in my rss reader. If you’d like to see your blog post featured next month, be sure to send it in yourself. Our hosts are busy parents and teachers who have limited time to scour the Internet for goodies.
To add a bit of color, I’ve thrown in several favorites from my newly updated Math with Living Books pages. Some (affiliate) links go to Amazon.com, where you can read descriptions and reviews — but there’s no need to buy. Most of these books should be available through your local library.
Table of Contents
If you’d like to skip directly to your area of interest, click here:
- Talking Math with Kids
- Elementary Exploration and Middle School Mastery
- Adventures in Basic Algebra and Geometry
- Advanced Mathematical Endeavors
- Puzzling Recreations
- Teaching Tips
Please: If you enjoy the carnival, would you consider volunteering to host sometime this year? Classroom teachers, homeschoolers, unschoolers, or anyone who likes to play around with math (even if the only person you “teach” is yourself) — if you would like to take a turn, please speak up!
And now, let the mathematical fun begin!
When the queen of her bugs demands that her army march in even lines, Private Joe divides the marchers into more and more lines so that he will not be left out of the parade.
Talking Math with Kids
- Tracy Zager (@TracyZager) and her daughter are Talking Math in Ghirardelli Square: “Wait! It’s the same thing again! It’s going to go on forever!”
- David Wees (@DavidWees) and his son explore Inductive Reasoning: “You know, Dad. There are an infinite number of solutions…”
- Joshua Greene (@JoshuaGreene19) writes Ode to a bead string (a non-poem poem): “One of the cool things about open play with math manipulatives is that it provides a lot of easy entry points into short math chats.”
- Dan Finkel (@MathforLove) explains How to help your kids fall in love with math: a guide for grown-ups: “Think out loud. Your child is imitating everything you do, and the more you can narrate your thoughts, the better a model of thinking you can be.”
- Crystal Wagner (@Tri_Learning) shares several Math Games to Play in the Car: “Or maybe you are waiting in line at the grocery store or doctor’s appointment. Turn these times of waiting into learning opportunities.”
- Caroline Mukisa (@MathsInsider) lists 11 Award Winning Math Books to Share With Your Child: “Whether you want to introduce a young child to their very first math concepts or supplement an older child’s math curriculum, this list is for you.”
- Christopher Danielson (@Trianglemancsd) shows how The sequence machine can launch math conversations with older students: “Now you can generate number sequences, without being distracted by the multiplication facts.”
Help inspire your kids to try writing their own unique problems. Includes a wide range of math topics and concepts: money and time, fractions, percentages, geometry, logic, and multi-step problem solving.
Elementary Exploration And Middle School Mastery
- Jamie Duncan (@JamieDunc3) presides over First Grade Math Fight… Fractions, Proportional Reasoning, and Algebra, Oh my!: “The uproar was on the border of out of control, but it’s in the name of math, so…”
- Joe Schwartz (@JSchwartz10a) goes Dot Crazy investigating number patterns with third-graders: “It was like we had turned on a fire hose. Math started gushing out all over the place.”
- Mike Jacobs (@MsbJacobs) uncovers an unexpected misconception in Measuring Up: “They see something like length as a count and not a measure.”
- John Stevens (@Jstevens009) wants kids to justify their decisions in Would You Rather…?: “Ask them what they would rather have that many of? Dollars? Shoes? Pimples?”
- For my own contribution to the carnival, I’ve refined my explanation of multiplication in Multiplication Is Not Repeated Addition: Update: “A strange, new concept sits at the heart of multiplication, something students have never seen before.”
- Erick Lee (@HRSBMathematics) crosses a piece of rope with a tangram and gets Fraction Talks Clothesline: “This was a really fun activity and there was lots of engagement.”
- Margie Pearse (@Pearse_Margie) wonders How Do I Teach Numeracy in My Class… Tomorrow?: “Now write another fraction that is closer to 1 than the first one you picked. Explain how you know this fraction is even closer to one.”
This collection of puzzles, games and activities is designed to stimulate and challenge people of all ages who enjoy puzzles with a mathematical flavour. Many of the puzzles have a long history, while others are original.
Adventures in Basic Algebra & Geometry
- Paula Beardell Krieg (@PaulaKrieg) creates a beautiful Puffy Pentagon Box template: “It was simple to do, delightful, and just the sort of hands-on relief I needed. But then I got to thinking…”
- “Area v. Perimeter” is just one of the goodies in the Des-Blog’s (@Desmos) Friday Five for April 22: “What happens when you turn Dan Meyer loose…?”
- Patrick Vennebush (@Pvennebush) and sons apply mental algebra in All Systems Go: “Why can’t these poor boys look at a pizza menu without perceiving it as a system of equations?”
- Lisa Bejarano (@LisaBej_Manitou) is Analyzing Triangle Congruence with AngLegs: “Wait! I made two different triangles with all three angles the same and one side the same. Does this count? Look!”
- Elizabeth Statmore (@Cheesemonkeysf) is dumbfounded by Volume of a Pyramid: Proof by Play-Doh: “This is the best idea I never had.”
- Michael Pershan (@Mpershan) harnesses the power of a non-specific question in Cognitive Load Theory and Why Students Are Answer-Obsessed: “Attention is a zero-sum game. There’s only so much that a person can notice. A person focused on finding the solution is unable to focus on much else.”
- Jo Morgan (@MathsJem) links to a great Sum of Exterior Angles demonstration and other treats in Gem Awards 2016: “I’ve never thought of doing this lovely paper demonstration.”
- Keith Devlin (@ProfKeithDevlin) dips into math history in Algebraic roots – Part 1: “Instead of algebra being a codification of human logical thinking that emerges from within, it becomes a set of externally imposed, and often arbitrary-seeming rules to be mastered by repetitive practice. The natural, relevant, and empowering becomes the artificial, pointless, and tedious.”
Renowned mathematician Ian Stewart gives math buffs and non-technical readers the perfect guide to today’s mathematics. He shows us not only that math can be explained in everyday language, but that it can be downright fun as well.
Advanced Mathematical Endeavors
- Matt Vaudrey (@MrVaudrey) performs an Algebra 2 Math Makeover: Spencer’s Soccer Ball: “It’s often the students who don’t know how to start that get stuck, and something like that will offer a low door for entry.”
- Bryan Anderson (@Anderson02B) poses a Matrix Multiplication — Open Middle Problem: “Using the digits 1-9, each only once, fill in the blanks to create the smallest possible value…”
- And check out Gironda’s calculus lesson Volumes Performance Task: A Love Story: “I left it totally open ended and they all took a different approach — but every group nailed it!”
- Dan MacKinnon (@MathRecreation) investigates dividing polynomials: the backwards reverse tabular method: “If you are intrigued by the possibility of polynomial explosions, read on; for others: you’ve been warned.”
- Caitlyn Gironda (@Caitlyn_Gironda) challenges her students with Logarithm Clothesline: “They actually had to think about a logarithm having a value — something which is usually a struggle for them.”
- Dave Richeson (@DivByZero) shares A Geometry Theorem Looking for a Geometric Proof: “The heptagon is noteworthy because it is the regular polygon with the fewest number of sides that cannot be constructed with compass and straightedge alone.”
- And don’t miss the 133rd Carnival of Mathematics.
Puzzle-lovers of all ages will gobble up this smorgasbord of riddles, mysteries, and logic problems. When Smullyan tells stories, fun and wonderment ensue.
- Recreational math is not just for the big kids. Sonya Post (@NoMathFears) helps four- and five-year-old children take on the Hundred Face Challenge: “This exercise has caught on and now it’s a ‘thing’. You know an internet ‘thing’. Not like the ice-bucket challenge or bullet-proof coffee, but we’ll get there.”
- Rodi Steinig’s math circle students play with Parity #1: NIM, Sums, and Conjectures (see also meetings #2 and #3): “The students made predictions, some accurate and some not-so-accurate, then used a jumprope as the river and tested their conjectures.”
- Kate Owens (@KateMath) shares several activity links in her Fun with Paper Folding workshop: “The scalene triangle puzzle stuck with me for several hours one day and I was almost unable to function in any capacity until I figured it out.”
- Ben Orlin (@BenOrlin) poses The Accidental Fraction Brainbuster: “Sometimes you accidentally write a problem six times harder than you meant to.”
- A good recreational math puzzle is one that spawns new ideas every time you look at it — like the painted blocks. Sam Shah (@samjshah) looks at A New Insight on the Famous Painted Block Problem: “When I finally figured it out, my mind was blown. So simple and elegant, yet so unintuitive for me.”
- David Butler (@DavidKButlerUoA) explores 100 ways to Quarter the Cross: “Along the way I’ve learned a few brand new things; I’ve relearned a few things I’d forgotten; I’ve seen things I knew with new eyes and understood them better; and I’ve made brand new maths (for me anyway).”
- Tanya Khovanova mourns the ruin of a great puzzle in The Battle I am Losing: “In the simplified adapted video, there are no longer any discoveries. There is no joy. People consume the solution, without realizing why this puzzle is beautiful and counterintuitive.”
- Mike Lawler (@MikeAndAllie) throws down A challenge / plea to math folks: “This problem provides a great opportunity for people to see how people in math think, and, importantly, that the path to the solution of a problem isn’t always a straight line.”
The daughter of mathematician Theon, Hypatia grew up on the northern tip of Egypt in the great city of Alexandria in the 4th century A.D. Records of her fame as a teacher can be found in the writings of Socrates.
- Jo Boaler (@JoBoaler) announced the opening of YouCubed’s free Visual Math Network, which includes research links, activities, and a discussion forum: “We know that the very best learning comes from teachers discussing and sharing ideas with each other.”
- Malke Rosenfeld (@mathinyourfeet) shares Some thoughts on “hands on” math learning: “Students need active and interactive experiences with math ideas in multiple learning modes to make sense of math.”
- Will Richardson (@WillRich45) examines 9 Elephants in the (Class)Room That Should “Unsettle” Us: “We ourselves have forgotten the vast majority of what we supposedly learned in school. Yet we continue to focus our efforts primarily on content knowledge.”
- Katrina Schwartz (@Kschwart) explores How ‘Productive Failure’ In Math Class Helps Make Lessons Stick: “But turning the difficult experience of failure into a positive isn’t as easy as telling students to change their mindsets.”
- Dan Meyer (@ddMeyer) shares Beyond Relevance & Real World: Stronger Strategies for Student Engagement: “A very natural follow-up to the famous ‘Math class needs a makeover’ talk.”
- Marcus du Sautoy (@MarcusduSautoy) tries to change the public perception of math in Reckon you were born without a brain for maths? Highly unlikely: “You might have trouble with your multiplication tables but actually be a great mathematician.”
- Jamie Duncan (@JamieDunc3) demonstrates that Teachers [Are Greater Than] Curriculum: “This is where most, if not nearly all, of the publishers’ curriculum gets it wrong.”
- And finally, you may be interested in my new Frequently Asked Questions blog post series. Check out Let’s Play Math FAQs: Introduction and my latest FAQ: Lifelong Learning for Parents: “When you struggle with a math concept and conquer it, it will make you free. You don’t have to be afraid of it anymore.”
More than thirty authors share their math enthusiasm with stories about their communities, families, or students. After every chapter is a puzzle, game, or activity to get you and your kids playing with math, too.
- “97” photo by Steve Bowbrick via Flickr. (CC BY 2.0)
- Book links are from my Math with Living Books pages.
And that rounds up this edition of the Math Teachers at Play carnival. I hope you enjoyed the ride.
The May 2016 installment of our carnival will open sometime during the week of May 23-27 at Math Misery? blog. If you would like to contribute, please use this handy submission form. Posts must be relevant to students or teachers of preK-12 mathematics. Old posts are welcome, as long as they haven’t been published in past editions of this carnival.
Past posts and future hosts can be found on our blog carnival information page. Or browse all the past editions of the Math Teachers at Play blog carnival on Pinterest.
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