Welcome to the Playful Math Blog Carnival #132
It's time for my yearly Playful Math Blog Carnival post. It's where I gather all kinds of great math blog posts from around the internet and share them with you. The Playful Math Blog Carnival was started by Denise Gaskins author of Let's Play Math (are you detecting a theme?).
September's Blog Carnival was hosted by Iva Sallay over at Find The Factors. Iva's blog is full Find the Factors puzzles and a whole lot of play (just trying to stick to the theme).
Playing Around with #132
It's tradition to start the carnival with some interesting facts about the carnival number. So let's talk #132.
Sometimes there isn't much to say about a number other than it's odd and it's prime. But 132 has some pretty interesting characteristics.
First, it's a pronic number. What's a pronic number? Yeah, I didn't know either.
It is the product of two consecutive numbers - in this case 11 and 12. If we want to write that algebraically we'd write it as n (n + 1).
Pronic numbers can't be square numbers, but they can be triangle numbers.
132 is also a Catalan number. Catalan numbers show up in combinitorics - like how many ways can you can divide a polygon into triangles. Also, the number of ways in which parentheses can be placed in a sequence of numbers to be multiplied - two at a time. I find it interesting that these number patterns appear all over the place.
132 has 12 divisors. And since 132 is divisible by 12 (the number of it's divisors), it is a refactorable number. Six is divisible by 1, 2, 3, and 6. It has 4 divisors. 6 is not divisible by 4, therefore it is not a refactorable number.
If you take the sum of all 2 digit numbers that can be made with 1, 3 and 2, it is equal to 132: 12 + 13 + 21 + 23 + 31 + 32 = 132. It is the first number with this property.
132 is a self number. This means that there isn't a number that can be added to the sum of it's digits to come up with 132. For example if we take 15 and add its digits to it like this: 15 + 1 + 5, we get 21. Therefore, 21 is not a self number. 16 + 1 + 6 = 23, so 23 is not a self-number. There is no such number that equals 132.
Playful Math Carnival - The Point Is PLAY
This came in my inbox this week:
M. - Frustrated Mom
My kids grasp things very quickly when they find the subject interesting but so far they have found the curriculums I’ve used too boring and when they aren’t engaged it’s like hitting my head against a wall to get them to learn.
I know a lot of parents and teachers who struggle to play math with their kids and students. Given that, I've decided the theme of this carnival is books and games that will help us learn to relax and just play math.
This is in no way a comprehensive list. There are a ton of great math educators and thinkers right now. I'm sharing the ones that I've found most helpful and tried to find others who share my opinion.
- Let's get down to business and go straight for the motherlode of mathy non-textbook - books. The Living Math site has books listed by concepts. You aren't going to find a more comprehensive list than this one anywhere on the internet. The number of books that she has categorized is simply amazing - compliling this list was a lot of work. Have fun reading about all kinds of mathy goodness.
- Picture Books are an excellent way to teach concepts. Melissa Taylor from Imagination Soup has compiled a much smaller list of math picture books which covers arithmetic, geometry, telling time, number sense, plus sorting and patterns.
- Jason Gipson-Nahman over at Geek Dad reviewed the book Moebius Noodles published by Maria Droujkova at Natural Math. This book is full of fun activies that allow youngest children to explore complex math ideas. Every parent of a preschool to early elementary child needs this book in their library. It's going to help you focus on the right stuff from the very beginning. Here's short lecture given by Dr. Droujkova about how 5-year olds can learn calculus. And Laura Grace Weldon interviews Maria about Moebius Noodles.
Since we are on the subject of Dr. Droujkova, you might as well go check out her site Natural Math. You can't go wrong with any of the books there - Avoid Hard Work by James Tanton get it - I have a strong math crush on Dr. Tanton. They are going to help you step out of the curriculum mentality and into math love and play. Spend some time looking around.
- You also can't go wrong with anything written by Denise Gaskins. "Let's Play Math" is my go to recommendation for parents who are having a hard time getting their kids on board with math (she's the one who started this blog carnival of math play). One of the things I've learned since starting my blog is that kids usually don't have math issues, they have issues with poor teaching/curriculum. This book is going to help parents/teachers step out of the poor math teaching. For moms - it's going to save lots of tears and frustration. Denise is going to take you by the hand and help you shift your thinking when it comes to math education. I also love her book '70 Things to Do With A 100 Chart'. You can check out this Place Value Fish game she shared.
- Cuisenaire Rods: From Early Years to Adult written by Mike Ollerton, Helen Williams and Simon Gregg is another favorite that's published by ATM. I just happen to love Cuisenaire Rods. This book is full of ideas. It's not comprehensive by any means, but it is going to get you started no matter what grade you are teaching. These three are amazing math educators and it would be worth it to cyber stalk them to find out what they are doing with students. I conviently linked to their twitter feeds above.
- Also published by the ATM is Little People Big Maths. I'm using this book along with Moebius Noodles this year for my kindergarden/1st grade co-op math class this year. While you are there, you should check out all of their other books. There are too many to mention here by some of the best ones I've found are: Functioning Mathematically (also by Ollerton), Enjoying Mathematics with Oragami, Mathmatical Journey's (a collection of starting points -love starting points), Thinkers and Thinking for Ourselves.
- Martin Gardner was an author and popularizer of mathematics. I've heard more than one interview with someone who became a mathematician because of Gardner. Ronald Graham said of Gardner, "Martin has turned thousands of children into mathematicians, and thousands of mathematicians into children."
At Martin-Gardner.org they compiled a list of the 10 best books he wrote for children. Mike Lawler gave his kids an introduction to machine learning via the game 'hexapawn' found in Gardner's Colossal Book of Mathematics. And let's not forget Vi Hart's popularization of hexaflexagons.
Math Games Pre-K to Early Elementary
There are two types of math games/activities. The first type of game is primarily for practicing math facts. It's my least favorite math game but we do play them. Most can be made more interesting with a little creativity. The other type of math game develops mathematical thinking and maybe students practice math facts as part of the game. Those are my favorite. They are the kind of game/activity that makes everyone want to play.
- Tangrams are an excellent activity not just for elementary students but for students of all ages. Students explore rotation, reflection, and translation. They develop spatial reasoning and problem solving skills as well. Additionally, tangrams make for a gentle and interesting introduction to basic geometry. Mathwire tangrams page is chock-full of links on how to make your own tangrams, tangram picture books (a repeat from Melissa Taylor's list), unit studies, tangrams and fractions, and lots and lots of puzzles.
- Tiny Polka Dot is a lovely set of cards with dots and numbers on them and provides rules for 10 games to play and explore numbers. The cards are heavy and attractive to adults and children. If you get Denise's book, mentioned above, you will find additional ways to use these cards in your math time. Kent Haines reviews Tiny Polka Dot over at The Process Column.
- Pattern Blocks are a staple in most schools and many homeschools. Unfortunately, we adults usually put these away after early elementary, but there is so much to explore. The Young Mathematcians site shared this post on pattern block puzzles. If you click the link you'll find several PDF's of activities and links to books for further exploration. At the Mathy Moments blog they used pattern blocks in their mirror books. Directions and ideas for playing with mirror books can be found in the book Moebius Noodles above. At Jessica's Corner of Cyberspace you can find a ton of FREE pattern block resources including patterns for all seasons.
- Math Geek Mama has a great list of 20 card games for practicing math. She divided the list up by concept so it's easy to find what you need like sorting and counting, addition and subtraction, multiplication, prime numbers, plus fractions and decimals. She's right, board games are great, but decks of cards are super easy to get out.
- Greg Tang is both a math author (you'll find his books like 'The Grapes of Math' reviewed in the links above) and math game creator. Tang's Home Kit Jr. includes the games Kakooma, Numtanga, and Numskill. Students develop fluency with numbers by using numbers bonds, different representations and solve reasoning puzzles. These games allow kids to develop the skills that make other math games a lot more fun. He also has a kit for older students.
- Box Cars and One Eyed Jacks is a huge site full of math card and dice games and the largest selection of dice I've ever seen. The games on this site are pretty straight-forward way of practicing math facts. Think gamified worksheets. They aren't bad, but they aren't as challenging as some of the other games listed. Here's a few of their k-2 dice games and games for grades 3-5. You can buy sets for home and classroom.
Games For The Whole Family
These games aren't just excuses for practicing math facts. They are games that develop mathematical thinking and require strategy. This makes them fun for everyone.
- Henri Picciotta shares a bunch of pattern block and tangram resources for middle and high school students on his mathed page.
- Calli from the Mind Research Blog posted this big list of board games that inspire mathematical thinking - a lot of these were new to me.
- Box Cars and One Eyed Jacks also has games (and dice) for upper elementary grades through about grade 10. This includes decimals, basic algebra, statistics and probability, exponents, and linear equations. Here's a 39 page training manual and sample of some of their games from Singapore Math Training.
Mathino is one of our favorite math games. Based on the card game casino, kids practice their math facts over and over again. They learn that 3 isn't just 3. It is 1 + 2, the square root of 9, 15 divided by 5 and so on. This game grows with your students and it's fun for the whole family. Michael Hartley reviews Mathino over at Dr. Mike's Math Games for Kids.
- SET Game is another family favorite. Players collect sets of three cards based on rules that apply to color, shape, number and shading. Players must apply the rules to the spatial array of patterns at the same time. The player with the most sets at the end of the game wins. SET can be just as challenging for pre-k kids as it is for university students and mothers like me. This game will enhance cognitive and spatial reasoning skills, visual perception, plus math skills in the areas of counting, algebra, set theory, and discrete mathematics. Bob Hazen from Algebra for Kids talks about the game of SET and at Wonder in Mathematics Hugh Kerns talks about the Joy of SET. You can pick-up a PDF that the SET folks put out on how to use SET in the classroom.
- Muggins is a strategy game that will have your kids practicing the 4 basic operations (addition, subtraction, multiplication, and division), developing symbol and number sense, problem solving skills and much more. As one of the winners of the 2002 Mensa Mind Games select, you can rest assured this is not just a game for practicing math facts and will keep the whole family engaged. It also won the 2003 Major Fun Award - the first educational game to do so. This means you won't be just 'doin math'.
- Blokus is a shapes game that will have everyone practicing spatial reasoning, rotation, and reflexion while trying to get rid of all their game pieces. This is a go to game when company comes and is generally enjoyed by everyone. It's also very addictive. Reviewing Blokus for us is The Games Journal.
- Prime Climb is an excellent game that requires some strategy but is mostly a roll and play game. The best part about prime climb is the way it visualizes math and how numbers work - think Cuisenaire towers for my followers. Kids needs to memorize less if they get how numbers work. Engaged Family Gaming reviewed Prime Climb. But this video review by Edo is my favorite. He gets Prime Climb.
How Do We Make Math Education More Like Play and Less Like Torture?
Well, it seems like the answer to that is to just play. There are enough resources in this blog carnival to start anyone on the journey to making math playful and engaging. This is just to get you started. Once you go down this road, there is really no turning back. Why would you?
Books and math puzzles are a way to teach concept without needing a textbook. There are lots of games to practice math facts as well as games to get kids thinking. I give you permission to ditch the math drill. Seriously. Do it. Go play math.