# Nim - A Devilishly Difficult Game

Years ago, a teacher friend sent me an online version of the game Nim. "Try it out!" they said innocently enough, "See if you can figure out the strategy!"

The game seemed simple enough, basically just a set of three rows of objects. So I gave it a shot, and I lost. And then I lost again, and again. I finally walked away from my computer, a broken man.

In the years since then, I've moved cities and schools, had three kids, and STILL CANNOT BEAT THIS GAME.

In preparation for this newsletter, I finally gave in and looked up the solution. And having seen a lovely explanation from one of my favorite mathematicians, James Tanton, I think I can provide a way to turn this maddening little game into a meaningful mathematical exploration for you and your child.

# Connect 4 - Add to 10 Variation

Do you have a Sharpie handy? I hope so, because today we are going to be defacing a classic game, Connect 4!

Connect 4 doesn't need any improvement, honestly. The game is great for young kids developing their fine motor skills and their spatial reasoning. But I found a lovely little variation from Catherine Reed at Brown Bag Teacher and I just had to try it with my son.

# Ultimate Tic Tac Toe

Periodically I pull out a math game in my 8th grade classes, usually when I have 20 minutes or so to kill after a field trip or standardized test.

In the past I've shared Magic Squares and The 100 Game, both of which I really enjoy introducing to my students. But I know how to beat both of those games, so I don't enjoy them as a participant in the same way that I enjoy games like chess or Blokus.

But there is one game I use with my students that captures my full attention: tic tac toe. But not the boring, solved version that you learned to beat when you were 6. I'm talking about Ultimate Tic Tac Toe.

# Manifold - An Origami Puzzle Game

I picked up Manifold at a game shop shortly before a flight I took recently. It turned out to be one of the most addictive puzzle games I've ever played. As soon as I solved one puzzle, I stuffed it in the front pocket of my backpack and tore off the next one.

By the time the plane landed, my backpack was practically brimming with folded puzzles. I had solved over half the puzzles and was feeling very accomplished (I had to skip #39, but I don't want to talk about it and I'm not mad.)

This game is aimed at older kids (10+) than most of the games I review for this newsletter. It's also one of the most engaging and unique puzzle-solving experiences I've ever had. I simply had to share it with you.

# War (and variants)

My greatest parenting regret is that I taught my son how to play War.

Don't get me wrong, he loves the game. In fact, that's precisely the problem. For weeks after I taught him the rules, War was the only game he let us play, and it got old fast.

If you haven't played War, it's a ridiculously simple card game. You deal the whole deck out to two players, and then both players flip over the top card. Highest card wins. If the cards are the same rank, both players put three cards face down and then flip over the fourth card. Again, the highest card wins the whole pile. The game continues until one person has all the cards.

The game is entirely driven by luck, and it can drag on for twenty or thirty minutes as one player, deck spilling over with forty-something cards, tries to win those last few pesky cards from their opponent.

To stave off the boredom, I started looking up some variants on War. As it turns out, some of these are really fun! Most importantly, they create opportunities for you and your kid to have a little math talk while playing.

# Laser Maze

I walked into the playroom holding a board game, which is a pretty routine occurrence in our household. "Hey J, do you want to play a game?"

"No."

"It has lasers..."

"OK!"

Since I showed my son this game, he has introduced it to his little sister, his cousins at the beach, and two different friends who have come over on playdates. He has also wandered our house, finding new mirrors he can use to bounce lasers onto furniture, framed photos, and annoyed family members.

In short, Laser Maze is a hit in the Haines household. J definitely doesn't think of Laser Maze as a math game, but I can already see him learning new concepts about angles of reflection and spatial relationships.

Occasionally he even lets me play, which is really fun because, again, there are lasers.

# One Dollar Words

I truly believe that one reason I was a strong math student is that, when my mind wandered, it wandered in a mathematical direction. I noticed patterns, I developed strategies and shortcuts, and I generally became fluent at basic calculations, all without drilling my times tables.

My hope is that when you introduce your kids to little math games like One Dollar Words, their minds will start to wander mathematically as well.

# Race to the Treasure

The first five years of your child's life are the most developmentally important years, and the foundation they build through play and exploration will form the basis of their learning for years and years to come.

That's why I am a big proponent of the Tammany Hall approach to the first five years: Math Early and Math Often.

So when I found Race to the Treasure, I knew I had to share it with my kids, and with you! If you're looking for your child's first board game, you could hardly do better.

# Fifteen

Sometimes, your kids have finished the maze and the crossword on the kids' menu and have started arguing about who is on whose side of the booth. Or maybe they are asking you when dinner will be ready in alternating 20-second intervals.

In either case, you just need a quick, simple game to occupy their minds. Something that doesn't involve a bunch of pieces or instructions.

If you find yourself in that situation, I'd like to recommend Fifteen.

# Yahtzee

Can a three-year-old play Yahtzee? Well, no, not exactly. The rules are simply too complex.

But can a three-year-old have a rich mathematical experience while playing a modified version of Yahtzee, or by helping their parent or sibling play? Of course!

You may have noticed that I am pretty liberal with my age recommendations for games. This is intentional; I believe that kids can gain mathematical ideas and insights from a game, even if they don't have the attention or skill to complete the game in its original form.

Once you know how to play a game, you can modify it to meet the needs of your children. To illustrate what I mean, let's talk about Yahtzee.

# How Many?

It's no secret that I love the work of Christopher Danielson. His website, Talking Math With Your Kids, was the inspiration for this newsletter, and I've already shared one of his books, Which One Doesn't Belong?, in a previous edition.

Christopher is out with a new book, How Many?, that I honestly believe should be in any child's book collection. If you invite my kid to your kid's birthday party, you already know what present they're getting.

# Mastermind

My wife really shouldn't let me go to Target. Every time, she sends me to get one simple item, and every time I show up at home with a new board game. I keep telling her "It's helping the kids learn!" but honestly they'd probably learn plenty from the other 28 board games we have...

But you, dear reader, get to benefit from my game addiction! A few weeks ago, I spied a game in retro packaging that I'd never seen before. I eagerly snapped it up and brought it home.

Within minutes of playing the game, I couldn't wait to see what my own students could do with the mathematical implications of the game. It's a great game for a 3rd or 4th grader, but the mathematical ideas that the game uses are taught in high school and college courses on discrete mathematics. Not that your kid will know that! To them, they're just guessing which colors match your secret code.

# Magic Square

I really, really dislike state testing. The kids get stressed, the teachers get practically crazed, and in the end I have a great deal of skepticism about the validity of our particular tests.

The silver lining of state tests is that my principal asks that we decrease the workload on that week so that kids are fresh and ready on each testing day. I take that as an excuse to pull out some of my favorite math puzzles and problems, in order to keep my students' brains working without overwhelming them with new math material.

One of my favorite puzzles is the Magic Square.

# Peg Solitaire

When I was a kid, my parents bought me a triangular peg solitaire game from a Cracker Barrel, and I never could figure it out. No matter how hard I tried, I couldn't end the game with one peg. I always ended the game with two or three pegs, no matter how hard I tried.

Well, I am happy to announce that I dug this game out of the closet recently, inspired to finally conquer my old nemesis. And I did it! At long last, this deceptively challenging game of pegs and holes was within my grasp.

# Table Talk Math

I started this newsletter because I believe that games are the easiest, most consistently entertaining way to introduce math ideas to your kids. Despite this, I know that games are far from the only way to get your kids talking about and exploring math. As a parent, I have many other tools in my toolkit for provoking an interesting conversation. Many of those tools I cribbed directly from Table Talk Math.

# The Between Game

I went on a trip with my son this past week, so I invented this game for those moments when even the iPad couldn't hold his attention any longer.

The goal of the Between Game is simple: yell out the same number at the same time. The only constraint is that you must each choose a number that is between the two previous numbers. That way, the range of numbers shrinks and shrinks until both players think of the same number.

# Othello

When playing a game with your child, should you let them win? This is a common dilemma for any parent who routinely plays games with their kids. On one hand, you don't want to beat your kid at Go Fish or Battleship or chess every time; they'd get sick of losing and quit playing with you eventually. On the other hand, you don't want your child to get so accustomed to winning that they can't handle a loss.

# Dragonbox Numbers

I have a skeptical outlook on the value of screen time. It's probably not hurting my kids too much, but it's probably not helping either. And the math apps I've found have mostly been underwhelming. Mostly, these apps focus on repetitive practice of math facts, which doesn't exactly sound like a rich mathematical experience.

But Dragonbox Numbers is a different sort of math app. I was skeptical at first, but the game won me over with its well-designed activities that get kids thinking about the relationships between numbers, rather than simply drilling math facts.

# Pyramid Solitaire

I firmly believe that our kids learn best when they have casual, patient conversations about math with an adult that cares about them. But my new baby has been a stark reminder that I am not going to have time to talk deeply about math with each of my kids every day. Fortunately, I have some back-up plans.

Pyramid solitaire is a game my own parents taught me when I was in early elementary school, and I happily played it for years afterward. It's quick, it's tough to win, and all you need is a deck of cards.