A few years ago I viewed “The Hundred Languages of Children,” a travelling exhibit about the Reggio Emilia approach to early childhood education. If you’re not familiar with this approach it, among other things, considers the environment (of the classroom and other spaces) as a “third teacher”.
Of course, I was drawn to the part of the exhibit that focused on movement and dance as one of the “hundred languages” with which children express themselves. There was a video that showed the children’s first experiences with an old factory space – a huge room empty except for two rows of large, white columns. The children were running around and between the columns, peeking around them, and interacting with their friends, all movements and ideas that eventually turned into a formal piece of choreography.
At the time I was just starting to think about creating a math/dance program for preschoolers and my biggest question was how could I encourage that kind of exploration? It seemed unlikely I would be able to find an empty factory or other interesting environment and get a bunch of preschoolers there on a weekly basis. And then it hit me – I could create an environment out of tape. I could define three-dimensional space using two-dimensional lines and colors.
After experimenting with my daughter’s preschool class, I came up with some starting points for parents and teachers who are interested in employing tape in the interest of math and kinesthetic exploration of space.
A simple straight line taped down a hallway becomes a pathway. It also divides the space in two, and provides a chance to walk on it or jump over it. Best of all, one can march (or walk, or skip, or slide, etc.) rhythmically down it singing “As I was marching down the street, down the street, down the street…” Or, tape two or more parallel lines down a space and see what happens when you sing “Down by the banks of the hankey pankey, when the bullfrogs jump from bank to bankey…”
A simple alteration of a child’s environment can deepen their experience and exploration of the space around them. When my daughter was three her teachers put down a straight line of tape to help the class ‘line up’ before leaving the classroom. It was a simple, visual learning strategy that appeared to work as envisioned by the teachers. Later in the year though, I saw pictures of what else the kids had done with the line. They had used their large blocks to build a wall the length of the tape and then lined up their animals and cars alongside it.
A simple taped perimeter can highlight empty space, as in “Find an empty spot inside the tape and make a shape.” Floor tape can define and redefine the space it’s in. Large open spaces encourage a lot of endless running. The minute you create a large rectangular box on the floor, with corners, you now have enough visual cues to focus a preschooler’s attention to IN (the box), OUT (of the box), AROUND (the sides of the box), CORNERS, and ACROSS, all age-appropriate math terminology.
Ultimately, I would love if every parent or preschool teacher would put down taped lines in their living and learning spaces then stand back to observe how the children interact with them.
Start with one straight line and go from there but don’t bring attention to it. Let your kids find it and interact with it on their own volition and let us know what you observe!
p.s. FYI, when I talk about ‘floor tape’ I am referring to two different products, both of them sticky. First, there’s painters tape which is blue and low tack so it can come up easily off both hard surfaces and carpet. There is also the floor tape that P.E. teachers use, which comes in lots of fabulous colors, the better to design with, my dear.
Finding math patterns or cute meanings in dates is a popular pastime. We celebrate Pi Day on March 14th, because 3.14 are the first three digits of that number. Star Wars day is on May 4th, from the pun on the Jedi blessing, “May the Force be with you!” It’s also neat to have dates like 12/12/12.
David Coffey started a meme on making every day mathematically special. Try it with your kids! Ask them for their favorite numbers, and celebrate when those days come up.
You can use a sign generator, or simply write on paper and put that sign up in your house. I made a few signs for upcoming dates, using some of my favorite math tidbits: composite numbers, Fibonacci sequence and plain old multiplication.
What objects can you add, and what do you get as a result? I will re-post this game once in a while, as we find more good examples. Check out what Moebius Noodles readers submitted:
- 1+1=7 One square plus one pentagon equals to seven diagonals (JJ Rodríguez)
- 1+1=1 One car traveling east plus one car traveling west equals to one crash! (David)
- 1+1=45 One mother plus one daughter equals forty-five years old (Pei Lee)
Here is an example that makes me go “awww” – found via Arithmetic Village:
Moby Snoodles says: “Add your own example!”
These are examples we have so far. It takes about five minutes for your answer to appear here. Wait and then reload the page to see.
My name is Marie, and I am ten years old. Since I was six years old, I have attended a math circle. Last year I started to help out with the class for little kids. This year, I decided that I could start teaching a math circle on my own. Now, I am teaching a Pre-K math circle for little kids that are about four or five years old. The kids are used to me now, and I am really enjoying the teaching experience.
This is what I observed during one of the classes; it’s very funny. When I told the kids that the problem they were solving was a game, even if it was a just an ordinary problem, the kids started getting much more involved in it, because they thought that they weren’t actually solving a problem, but that they were playing a game! An example of when this happened was when we were using the board and pieces of the game, “Othello” (we weren’t actually playing the game though). The kids were reluctantly solving geometric problems using Othello pieces, until I told them that we were playing a game. “A game? Let’s play!” yelled the kids, excitedly going back to the exact same problems they were solving before.
Kids are much more involved in the class when:
- The problems involve them
- They get to choose what the problems are about, or at least change the details of the problems
- The problems involve real-life situations, especially if they have to do with their life
- The problem has a fairy tale, or some other kind of story woven into it.
For example, when the class was doing Venn diagrams, I made the diagrams about who in the class had sisters, brothers, or both. The kids were delighted with the very idea that they would be inside a mathematical problem!
I observed that warm-ups and easy problems that kids can solve on their own, correctly, help the kids relax and build more confidence in themselves, when encountering harder problems later in the lesson. Discussions and introductory examples to the topic are a good way to start a lesson. DO NOT start a lesson with a game! Kids will lose their attention, become over-excited, and be unable to return to the topic.
Teaching a math circle turned out being much more fun and interesting than I expected. I enjoy listening to the kids’ ideas and thoughts, and observing how they react. The kids consider me adult enough that they listen to me, but they see that I am still a child, so they are not afraid to share their ideas, and make mistakes.
If you would like to see the lessons of the math circle, and more details, please visit my blog at:
This is the game my son and I are calling “Gummy Bear Go!” even though most of the time we play it with paperclips instead of treats. I got this game from the Russian mathematician Alexander Zvonkin’s book “Math from Three to Seven: The Story of a Mathematical Circle for Preschoolers“.
To play the game all you need is a piece of paper with a grid drawn on it, a pair of dice, and some counters. The grid has 7 rows and 15 columns, although you can certainly make more rows for a longer game. Each cell in the bottom row is numbered 1 through 15.
Decide how many counters each player will have. The first few rounds we played, we each had 3 counters (make sure you can tell your counters apart from the other player’s). Place the counters on the numbered cells. Make sure to not put more than one counter in each cell. Now, roll the dice, add up the dots, find the counter with the cell number corresponding to the rolled sum and move the counter up one row. Repeat until one of the counters reaches the top row. The first to reach the top row wins the game.
When we first played the game, my son placed his first counter on 6, but his other counter – on 1 and his third counter – on 15. If this happens when you try this game, don’t rush to correct your little one. Instead, play along and let him learn from experience. If your child, like mine, doesn’t do well with loosing a game, you can level the field a bit by placing your counters on “impossible” (1, 13, 14, 15) or unlikely to win numbers (2, 3, 11, 12).
Rolling two dice means that there’s a lot of addition work in this game. Which is great, but keep in mind that practicing additions is not the main goal of the game. I didn’t want to give the answers to my son, but he did need help with the larger sums. So I gave him a ruler that he used as a number line.
Of course, since there were just the two of us playing with a total of 6 counters in the game, most of the numbers were left open. When we happened to roll a sum equal to an unoccupied number, I’d make sure to say things like “ah, too bad neither one of us had a counter on 7″ or “hey, 9 again?! I just might play it in the next round!”
At the end of each round we’d stop to survey the game board and note which counters didn’t move at all and which ones “put up a good fight”. I had the idea to mark each round’s winning number.
After the first round, my son’s choice of numbers to place counters on became much more interesting. He clearly understood that his best chance at winning was on the middle numbers – 5, 6, 7, 8, 9. He abandoned the impossibles and after one or two games moved away from the marginal 2, 11 and 12.
Finally, after playing this game for a few days on and off, we played one last round that I called “the grand parade”. We put one counter in EACH cell in the bottom row. This way, every time we rolled the dice, something moved. And once the game was over, we surveyed the battle field.
And then we filled out this little table of all the possible roll combinations. That’s a whole lot of additions which gets pretty boring. So instead I suggested to look for patterns. My son quickly noticed the horizontal and vertical patterns.
Finally, I suggested we try to figure out what’s the most likely winning number. To do that, I asked my son to find the smallest sum in the table, 2. Which explained why placing a counter on 1 was a waste of time. Then I asked him to find the largest sum, 12. Which ruled out 13, 14 and 15 once and forever.
Next, we started counting how many of each sum we had in the table. The 2 and the 12 were easy-peasy. It was interesting to see that although he noticed the horizontal and vertical patterns right away, he failed to see the diagonals. But after finding and counting all the 3s and 4s, he noticed the diagonals and after that counting was a breeze. But the best part was that once we were done counting all the different outcomes, he knew right away which three numbers were the likeliest to win. It was so awesome to see him go through the “Aha!” moment! Plus we got to have gummy bears and mini-marshmallows to celebrate!
What are you more willing to buy for your child, a toy or a board game? Personally, while I cringe and say “no” every time my son asks me for a toy, I would happily indulge him if he asked me to buy him Monopoly Jr or Life or Four in a Row. Well, he doesn’t ask, so I end up buying them anyway and now we have a growing collection of card and board games. My excuse, of course, is that playing games helps my son to learn math (here’s an article about using games for teaching math and here’s a great list of board games that build math skills). Which it does, at least until we lose game pieces or a few cards or go on a road trip. What if there were (or we could invent) board games that would be portable, DIY-able, cheap (better yet, free), and full of interesting math?
Once you start looking for something, you find it everywhere. Once I asked myself this “what if…” question, I started coming across just such games. And then I was lucky to meet Daniel Solis, who asked what if there were tabletop games that lasted thousands of years? What would those games be like? (I particularly appreciated the longevity angle since a few days before I met Daniel I bought UNO and some of the cards were already missing or bent).
Turns out, Daniel, who himself is a game designer, did more than just ask. Back in 2011 he actually created and ran The Thousand-Year Game Design Challenge. (You can also watch Daniel’s presentation about the project here). Participants were asked to
Create a game. The game can be of any theme or genre you desire, but there is one restriction: You’re creating a “new classic,” like Chess, Tag or card games. So, create a game to be enjoyed by generations of players for a thousand years.
The original Thousand-Year Game Design post has links to each month’s submissions. One of the games Daniel mentioned was Numeria. You can make it in less than 5 minutes if you have a chess board and a set of tiles numbered 1 through 36 (numbered pieces of paper will do). I haven’t played this game yet, but it sounds like a cross between a connect-four and a mathematical Scrabble.
For Daniel himself, Numeria was one of the few entries that actually made him want to create or buy a set for himself. At the same time, since the game is based on the ability to build and recognize number patterns, Daniel noted that “there are some problems if players have different levels of knowledge of mathematical tropes.”
I think Numeria is a rather tough game to play with the little ones. But you can try playing a Function Machine game. If you are interested in reading more about how playing board games helps children with math, check out this article. If you need some ideas on commercially available games, LivingMath.net has a nice list of board, dice and card games for learning math, strategy and logic.
Which table games do you play with your children? Do you invent your own games?
Image source: Nara J via Flickr!
It’s been a little while since I did the original post about the hundred chart I put together for my son and his reaction to it. Finally, I have a professionally done (thank you, Ever!) chart you can download, play with, explore and, if framed, admire (it has a certain beauty to it, don’t you think). The chart prints to 1 letter page. Additionally, you can print individual cards and play with those.
Download the low-res PDF hundred chart (leave password blank)
Download individual cards to print (leave password blank)
Download full size high resolution chart. It prints to a 30×60 poster (leave password blank)
As you might know, Maria collects Hundred Charts like the one she shared in our newsletter. So now I’m curious to see other charts in her collection. Have you come across different versions of the good ol’ Hundred Chart? Please let us know!
And if you are looking for games to play with the chart, check out Let’s Play Math post about 20+ things to do with a hundred chart.