Stake Your Claim

My daughter's 3rd/4th grade class has been working on arrays over the last few weeks. (I recently found out they are using the TERC Investigations curriculum, which seems really strong. Arrays are the first investigation for the 4th grade sequence.)  One of their homework assignments was to find, draw and quantify examples of arrays in their environment at home and at school.  Of course, I love that! 

It reminded me of a game I created for my daughter and I to play in the spring of 2012.  The post about the activity is called Totally Territorial: Cats, Maps, Area & Multiplication.

Essentially, I drew a grid over a map of our fair city and, armed with dice and some pens, we staked out our claim.  It was totally fun and my almost-seven-year-old was completely into it.

Since they are in the middle of a world geography unit (meaning maps!) in addition to their array inquiry I thought it might be fun to formalize the game for the class. I searched for 'maps of imaginary places' and found a bunch at The Explorer's Notebook, created some grids and a game structure and....voila!

The game right now has five maps.  The rules are simple, but I think the narrative context provided by the maps is enough to make this fun:

Purpose of the Game:To capture as much area on your map as possible.

Rules of the Game: 

2 players

Roll one dice to determine who starts the game. 

Roll one dice. First roll determines the number of horizontal squares/length. Second roll determines number of vertical squares/width (include the first horizontal row in your count). 

Outline or highlight your full array in your chosen color. Compute total area (total number of squares) for each turn. 

Game is over when all territory is captured or both players have both had two unsuccessful turns (meaning not being able to find enough area to capture based on their roll). Player with the most territory/area wins although you may want to consider the value of land vs. water in the final value of area claimed. 

They played it today (while I was working with small groups working on half-ness, midpoints, congruence and three-ness with this Sierpinski Triangle activity from The Fractal Foundation).  Their teacher said they were all completely into it for the entire math class.  From what he overheard, it was unclear if the kids had developed any over-arching strategy at this point.  More likely, he thinks, they were simply enjoying rolling the dice, computing the area, and capturing territory. 

I know I'm not on the cutting edge of game design, but the fact that 27 kids were happily engaged in mathematical activity for almost an hour probably says a lot. The teacher and I did discuss upping the difficulty by adding a rule about only being able to add territory attached to previously won territory.  I love the idea, but think you'd need a bigger playing area for that.

Wanna' play? Here are the files! Please do let me know how it goes and what modifications/improvements you made to the execution, or any design suggestions you might have.

Thrifted Math

Here's something you probably don't know about me -- I've got something of a golden touch when I'm out thrifting.  Not always, but I do have a track record that is (to me) quite impressive!  See what you think about these highlights from the last year:

A down jacket, perfect fit, perfect color, just needed a wash and it was brand new again; I paid $4 and am on my second season with it still in great condition

A Leap Frog talking globe, like-new, retailing for $350; I paid $4 and the kid learned her continents and is onto countries, plus she makes up her own dances to the 'music of the world' option.

A sturdy elementary microscope with three lenses and swivel eye piece, like-new, retailing for $160; I paid $5 and, although we haven't really used it much, I just know it'll come in handy at some point.

We also get a lot of great science, social studies, history and art resource books at our library's resale bookstore.  And, just a week or so ago I found two old math games at Goodwill!  The first one is Scan, a "split second matching game" from the 1970's.  I found a comparable version it online offered for $50.  I got it for $1.99 and we've already had a ton of fun with it!!!

When I saw it on the shelf I immediately recognized it as mathematical in some way. There are four categories on each card: color (square, circle, square, circle), position (four black dots on a 4x4 grid), pattern (different combinations of x's and o's) and shape (various irregular purple polygons!). 

Our game didn't come with directions and at first I thought it the point was to match all four categories at once.  I even went so far as to try and analyze and sort the cards so that I could understand how it might work.  Here's one attempt at sorting by grid pattern: 

Ultimately, no pattern emerged and I also determined there were no 4-way matches to be made.  I'm not very good with combinatorics but even I can figure out (albeit after a bit of struggle) that you need more than 26 cards to have a match for every possible combination and permutation.  (Anyone want to figure it out?!  Just kidding.) 

I went online and found the directions and was relieved to find that you only have to match one category on the center card to a card on the table to win the round.  The box said it was for ages 9 to adult, but I decided to try with my 7.5 year old.  Initially I thought maybe I'd have to half-size the deck for the first few games so she'd have a chance to get the hang of it but for some reason I put out the full deck on our first game and, what do you know, she beat the pants off of me! 
 

I found the next game about a week after I found Scan.  It is not branded so I can only describe it with this picture:

Well, actually, as I was editing this post I noticed the company name Garlic Press in the bottom left corner.  Apparently they're still in business and have other similar two-sided 'self-check' math fact puzzles.  Essentially, you piece together this round puzzle by doing your multiplication facts...

...which, incidentally, are not in any particular order around the ring, which is a great feature.  When you've placed all the pieces you flip it over to see if you got them right.  If you did, you have a picture that makes sense.  If you didn't you have a good giggle about the parrot's beak and wing being in the wrong places and try again. 

I'm not that big on drilling math facts, but I thought it'd be interesting to try and a nice addition to our other work even at the sky high thrifting price of $4.99.  What do you know -- the puzzles are fun!  My daughter has only done the 0, 1, 2, 3, 4 and 10 times table puzzles so far but she's motivated to do about one per day.  I mean, who wouldn't want to solve your 8 times tables if you got a cute little tiger cub at the end of it?!

You use the same procedure to solve each puzzle, which makes me optimistic that she'll start developing some reasoning strategies around the skip counting she doesn't already know backward and forward -- like 11 times something is similar to 1 times something.  Or, if I do the 0, 1, 2, 3, 5 and 10 times first in any puzzle, the rest are not hard to figure out. 

The multiplication puzzles might be a little hard to make yourself, but if I knew about Scan and couldn't find the game itself I'd totally make a version myself with my kid or other students!  The Scan cards are just four quadrants with a basic concept and pattern rule for each quadrant.  Also, you need two copies of each card. to play the game.  It's essentially a quick-paced matching game for big kids;  I think upper elementary kids might really enjoy the challenge of making their own versions and variations.

If You Give a Girl a Grid...

...then the girl (newly seven) will want to make a game out of it.

When the girl makes a game out of it she'll be really busy for a few minutes and then make her Papa play the games.

When Papa plays the games, it will be interesting to see how the girl is thinking about math.

And when the girl thinks about math, she'll need a grid to go with it!

(But, in this case I didn't so much give it to her as let her find it and watch her co-opt it for her own uses, just like what happened with her 'divide even numbers' grid game a while back.  And, you do know that this story is jamming off the awesome If You Give a Mouse a Cookie stories by Laura Numeroff, right?)

The reason the grids were out to 'be discovered' is because I'm in the middle of fine tuning a paper quilt-ish activity for my summer arts programming in the city.  It's a really cool project, if I do say so myself, and I'll be sharing the concept and the student work when we're done with the week.  In the mean time, here's what my kid did within a ten minute period, all before 7:00 am, I might add:

The first game she made for her dad was a word search.  Apparently one of her babysitters brought a book of word searches with her one day.  Or something.  In any case, it stuck with her:

In the next game, the question was: "What is similar between geometry and arithmetic?" (Or something along those lines -- my recall is a bit fuzzy.  It was the crack of dawn, if you'll remember.)  If you're wondering what the answer is after looking over everything in the grid, it's that the 'equal' signs are also parallel lines.

In this game she asked her dad to 'make triangles out of a square.'  Hmmm....sounds familiar!  That big dot at the top of the grid is the starting point, she says.

And, finally, this game is a 'number search.'  You're supposed to find the hidden sequence of numerals that can be connected with one line (but not necessarily a straight one).  Hint: It's a sequence of six numerals. 

And that's what happens if you give a girl a grid -- not what you expected, but definitely entertaining!

Sneaky Math: You Know, UNO!

My six-year-old daughter is hip to my game.  You know, that I'm interested in stretching and deepening my personal understanding of what math is and how we make it.  She has become highly sensitive to moments where I might be trying to teach or show her something math related.  She's on to me.  She calls me, accusingly, "Math Mommy!" 

This is an attitude shift, actually.  Back in September, when she had plans to run away with her best friend, she very clearly relied on me to help her learn the math she would need for when they finally headed out into the wilderness. (Or, the elementary school playground, which has a huge field and lots of trees around the edges.  Whichever.)

Now, however, she wants nothing to do with me and my math.  And, after being quite self-motivated and curious about measuring, comparing amounts, comparing sizes, spontaneous chant counting by tens and twos, relationships between numbers, and relationships between shapes the whole summer and fall, her inquiry into all these things has slowed somewhat.

Except, she has become a W-H-I-Z at two person UNO.  We are UNO addicts; we play UNO every day, sometimes twice a day.  UNO perks us up: Having a bad day?  Let's play UNO!  Been in the same argument loop all morning?  Let's play UNO!  And, yes, I know there is math in this game but DON'T TELL HER!!!  Honestly, I have been giddy with glee that I now have an outlet to influence her mathematical thinking and move her math skills forward without her knowing!


Well, I mean, she knows she's adding up points, for example, but she wouldn't do it at all if I just asked her to outright.  She's already shot down my suggestion that maybe, perhaps, we could, let's say put down a 3 and 4 to match that yellow 7 that's on top of the pile?  "Math Mommy!  I just want to play the game!"  So, I've come up with my new 'sneaky math' approach.

What she doesn't know is that, faced with such perceptive resistance, I'm loosing on purpose (sometimes) and I'm quite gleeful about the way that it's working out.  I hand her my handful of lost points and say, "How big a win was it for you?!" giving her an opportunity to be very specific about the magnitude of her victory.  I'll casually say, "How many tens can you find?"  or "What's fifty plus twenty [Wild Draw Four + Skip cards]?"  As a result she's naturally skip counting by tens and sometimes fives, easily finding different combinations of numbers to make ten, adding numbers to sums way past twenty, using her fingers less and less and, in the process, improving her capacity for mental arithmetic.


Examples of different ways to make 'ten'.  I've somehow found my way to guiding her to find as many tens as possible and add those up first, which capitalizes on her love of tens, hundreds, and thousands.  We did get stuck today, though.  She found two 10's but then we were stuck with three 6's.  In the end I got out the paper to show her the 'easy way' to finish up the adding, thus sneaking in a little two digit addition on paper.  She balked a bit, but I said, "How are you going to know if you beat me or not??"  That was motivation enough!  (I'm still not sure, though, when to bring in a calculator.  I'm pretty sure being able to mentally calculate numbers is an important life skill in many ways, so I'll stick with fingers, skip counting and the occasional paper and pencil for now.)

She is quite publicly gleeful herself as she gloats about the magnitude of her victories.  Me? I am secretly thrilled that I've found a way for my incredibly enthusiastic and fiercely independent learner, enigma that she is, to enjoy her math without knowing her mama is enjoying (and influencing) that math along with her. 

For Christmas, since the kid is so into games these days, she's getting Junior Monopoly and the cube version of Quirkle.  Oh, and Mancala, plus some really cool fractal fridge magnets to go with our fridge tangrams.  I've got my sneak on, big time!