If you're like most Americans, you and your children spend a lot of time on the road. There are plenty of ways for kids to pass the time on car trips, whether of 5 minutes or 500 miles. Several of them I'm quite sure you know:
Screaming "She's on MYYYY side!!!! Mom, make her get off of MYYYY side!"
Asking as often as possible, "Are we there yet?"
Threatening to throw up.
Singing vaguely risque songs like "The boys and girls are kissing in the D-R-A-K, D-R-A-K, D-R-A-K, Dark!"
Singing "George Washington Bridge." OH MY EARS QUICK RINSE THEM OUT WITH RUBBING ALCOHOL (George Washington Bridge, for those of you not in the know, repeats the lyrics "George Washington Bridge" again and again and again to an essentially unmelodic melody. My sister pulled this one on a 5-hour car ride between Chicago and La Crosse, Wisconsin, many years ago, and when she was finally told she could NO LONGER sing "George Washington Bridge" she said "Okay, then I will sing 'Adobe Bricks.' 'Adobe Bricks,' as it turns out, is 10 times worse. We eventually threw her out of the car)
But those days are over, for here is a list of WONDERFUL MATH ACTIVITIES that you can do in the car. (Assuming that your children can actually see out the windows.)
1. LICENSE PLATES. In New York State, most (not all) plates are of the form AAA 1111--three letters, then four numbers. Have kids hunt for license plates withe certain characteristics. Who can find one that has four even digits? Four odd digits? Four digits that are ascending (like 4689)? Descending (say, 8521)? Two digits that are the same? Three digits that are the same? If you're stuck at a stoplight, ask your child to add the four digits on the license plate of the vehicle in front of you--which two are best to add first? What shortcuts can your child find? (To add 6364, kids might start with 6+6=12, a "doubles fact," or with the "ten-friends" fact that 6+4=10.) Estimate by looking if the sum will be greater than or less than 20. Then check. Whoops, green light--better move on...
2. STOPLIGHTS. How many stoplights do you think there will be between here and the mall/camp/Grandma's house? Let's keep track. Will they mostly be green when we get to them, or red? You count the red ones, I'll count the green ones. Do you think it'll be about the same on the way back, or will it be different? Let's find out. For a route you drive frequently, choose a couple of lights and keep track of whether they're red or green over a period of 8-10 days. These are exercises in counting; they also ask kids to gather, use, and interpret data. More than half of the lights are green? Why do you think that might be?...That light where we cross Route 55 is almost always red when we get there--how come?
3. VROOM, VROOM. On a 4-lane highway, have kids count the cars you pass and the cars that pass you. Make this an exercise in counting forwards and backwards: start with a score of 10, add one for every car you pass, subtract one for every car that passes you. Or, start with 50 or even 100. Try not to give in to your children's pleadings to do whatever it takes to avoid being passed by that in-your-face Oldsmobile or to overtake that weirdly painted appliance truck. Does it matter who's driving?...why yes, yes, it might. (And can we correlate that with speeding tickets received? Why yes, yes, we can...)
4. NUMBERS ON SIGNS. There are lots of these running around the roads: speed limits, mileage markers, route numbers, distances to upcoming cities. We call Route 376 "route three-seventy-six," but what's its "proper" name? (Three hundred seventy-six. Yes, I know it isn't *really* a number, because it doesn't indicate three hundred seventy-six of anything...) Who can find a two-digit number on a road sign? A three-digit number? An odd number? The sign tells how many miles to Montreal and how many to Buffalo. Which is further away from us right now? How do you know?
5. MENTAL ARITHMETIC. We're at milepost 27--look, there's the sign. What milepost will we pass in five miles? Ten miles? (Careful--are we driving towards milepost 0 or away from it?) How many more miles till milepost 40? (See above.) The sign says Albany is 65 miles away. Our speed is, guess what, 65 miles per hour. About how long till we're in Albany? (Only use easy numbers for this kind of question!) The car can be a good place to go over basic facts as well: "7 + 2." "9!" "Tell me two ways to make 10." "Um--"
6. MAPS and DIRECTIONS. Have children direct you to a location they've visited many times before. Ask them to tell you where to go straight and where to turn, and whether you should go left or right when you turn. Obviously, don't break any traffic laws--you are still the captain of the ship! As for maps: Print out a map showing your route to a (relatively) nearby place. Go over the map with your child before you leave. Have your child hold the map and try to track your position along the route as you drive. Try using a road map for longer distances: Find a long thick blue line with a shield and the number 84. That's the road we're on now. We're heading west...which way is west? Can you find a city called Middletown? Excellent--we're just a little bit west of that right now. What's the next town you see? Some third and fourth graders can become quite good at navigating. Just be sure that the "road" they're having you follow isn't just a marmalade stain on the map (this happened once to Paddington Brown and his family, I believe).
As always, these are ideas, nothing more; you can come up with others yourself. Be sure not to push too hard. REPEAT: BE SURE NOT TO PUSH TOO HARD. If you find you're suddenly more invested in these activities than the kids are, cut the games short and do something else: talk, sing, tell jokes, look at scenery. But if people start yelling about siblings being on theirrrrr side, it helps to have games like find-a-license-plate-with-4-odd-digits in your back pocket; and if you can find the right combination of math activities for the car ride on any given day, you will NEVER EVER EVER have to put up with anybody singing George Washington Bridge, and that will make any hardship worthwhile.
Tuesday, August 4, 2009
My Heart's in the Heartland
A cool map for you geography geeks out there:
http://strangemaps.wordpress.com/2009/07/27/402-homeland-is-where-the-heartland-is/#comments
Note that some of the sizes are a bit off. Also, something seems to have happened to Dutchess County. STILL!
http://strangemaps.wordpress.com/2009/07/27/402-homeland-is-where-the-heartland-is/#comments
Note that some of the sizes are a bit off. Also, something seems to have happened to Dutchess County. STILL!
More Rabbit News
--> NEWS FLASH <--
THE MATH GUY'S RABBIT CAN MULTIPLY!!!!
(Technically, this is NOT the Math Guy's rabbit. It belongs to his daughter, who purchased it from a pet store a couple of years ago and then hid it in the garage for three days while she worked up the nerve to tell us what she'd done. However, now that she's away at school, guess who does the bulk of caretaking for Miss Rabbit? --That's right.)
Anyway. The other day I was communing with the rabbit and asked it a question, offhandedly:
"Rabbit!" I said. "What is 3 x 5?"
And darned if she didn't woffle her nose 15 times.
"Remarkable!" I said. "And, Rabbit, what is 2 x 4?"
I counted eight woffles.
"Such a mathematical rabbit!" I crowed, and took her through several more examples: 6 x 2, 4 x 4, and 2 x 10. Woffle, woffle, woffle, and she was right on the money EVERY TIME.
My family seems suspicious of her awesome abilities. They seem to believe that I am cheating or perhaps misinterpreting her responses, but I swear she woffles the correct number of times. Anyhow, who cares what they say. I'm considering taking her on the talk show circuit--your thoughts?
THE MATH GUY'S RABBIT CAN MULTIPLY!!!!
(Technically, this is NOT the Math Guy's rabbit. It belongs to his daughter, who purchased it from a pet store a couple of years ago and then hid it in the garage for three days while she worked up the nerve to tell us what she'd done. However, now that she's away at school, guess who does the bulk of caretaking for Miss Rabbit? --That's right.)
Anyway. The other day I was communing with the rabbit and asked it a question, offhandedly:
"Rabbit!" I said. "What is 3 x 5?"
And darned if she didn't woffle her nose 15 times.
"Remarkable!" I said. "And, Rabbit, what is 2 x 4?"
I counted eight woffles.
"Such a mathematical rabbit!" I crowed, and took her through several more examples: 6 x 2, 4 x 4, and 2 x 10. Woffle, woffle, woffle, and she was right on the money EVERY TIME.
My family seems suspicious of her awesome abilities. They seem to believe that I am cheating or perhaps misinterpreting her responses, but I swear she woffles the correct number of times. Anyhow, who cares what they say. I'm considering taking her on the talk show circuit--your thoughts?
Tuesday, July 21, 2009
Of Rabbits and Math Guys
Several years ago, early in my incarnation as Math Guy, I walked into Sue's third and fourth grade classroom ready to present a lesson. I was surprised to see that a bunch of rabbits had replaced the children that day.
The class had been reading a novel about rabbits or rabbitlike creatures, Sue explained, and several children had come up with the idea of dressing like rabbits one day, and the idea had met with approval from basically everybody.
Some had done just the basics--a few face-paint whiskers, a kush ball for a tail. Others had added a carefully-stapled set of ears made from construction paper. A few had gone whole hog (whole bunny?) and dressed all in white or brown or black with socks and slippers and even gloves. They looked...different. They looked...creative.
"Greetings, rabbits," I said, and asked them to take their seats so we could begin the math instruction for the day. For rabbits, they did reasonably well sitting still, and they did an even better job of listening (must've been the big ears).
My planned lesson was on what kids often like to call "timesing." We began by reviewing some basic multiplication facts and then moved on to multiplication strategies and the link between multiplication and addition, and just before I sent them to the tables to do some independent work, it suddenly occurred to me that I was--
--that's right--
--teaching rabbits to multiply.
Bada-bing!
True story, too.
The class had been reading a novel about rabbits or rabbitlike creatures, Sue explained, and several children had come up with the idea of dressing like rabbits one day, and the idea had met with approval from basically everybody.
Some had done just the basics--a few face-paint whiskers, a kush ball for a tail. Others had added a carefully-stapled set of ears made from construction paper. A few had gone whole hog (whole bunny?) and dressed all in white or brown or black with socks and slippers and even gloves. They looked...different. They looked...creative.
"Greetings, rabbits," I said, and asked them to take their seats so we could begin the math instruction for the day. For rabbits, they did reasonably well sitting still, and they did an even better job of listening (must've been the big ears).
My planned lesson was on what kids often like to call "timesing." We began by reviewing some basic multiplication facts and then moved on to multiplication strategies and the link between multiplication and addition, and just before I sent them to the tables to do some independent work, it suddenly occurred to me that I was--
--that's right--
--teaching rabbits to multiply.
Bada-bing!
True story, too.
Thursday, July 16, 2009
SummerMath, Part 3: The Bikepath, the Ballpark, and Beyond
My family went to the ballgame the other day, attracted by among other things a "Henry Hudson Bobblehead" giveaway (see picture). My son is quite eager to show off his Hudson Valley roots with this, um, iconic image when he heads west for his next college semester, and as for the rest of us, well, how could we pass up such a quality and historic freebie??
(Ol' Henry)
Anyhow, the game put me in my mind of Sports and Math. I spent most of my childhood free time engaged in one of five activities:
1) eating
2) reading the classics, mainly the Hardy Boys books
3) writing short stories with meandering plots and lots of unnecessary characters
4) playing board games and card games (see SummerMath Parts 1 and 2)
and
5) playing, watching, reading about, or thinking about baseball.
Baseball and math are closely linked, and in fact I learned quite a lot about math from my interest in baseball. My 1972 Sports Illustrated baseball board game (see 4 and 5 above) helped inform me about probability. I can remember the power I felt when I realized that I could use what (little) I knew about ratios to compare teams' won-lost records in my head--was it better to be 38-37 or 37-36, and how could I prove it? And I developed some facility with division, if not comprehension of WHY it worked, by virtue of calculating my batting average every day back when I was ten or so. (My batting average was very good. I counted it as a hit, of course, if someone muffed a ball I'd put in play. Or if the umpire mistakenly called me out when I was CLEARLY safe at first--don't laugh, it happened all the time. Or if I hit a line drive or a deep fly ball that somebody managed to corral, but which clearly SHOULD'VE been a hit--why should I be penalized just because my opponents had good hands? That was in addition to the occasional, you know, REAL hits I got. As I said, my batting average was very good.)
In any case, there are lots of ways to combine math with sports, for those of you whose children like to watch baseball, play soccer, ride bikes, or mess around with balls and such in the back yard after dinner. Here are some ideas of questions you can ask and projects you can do:
*Counting and estimating. "I wonder how many pitches the pitcher will throw this inning. Do you think it'll be more than 15 or less than 15?" "Take ten shots on goal from right here. Let's see how many go in...Now let's move you back a few feet. How many do you think will go into the net now?" "Good job! We just did 6 throws back and forth in a row without dropping a single one. Think we can beat that record? Let's keep track."
*Adding and subtracting, multiplying and dividing. "The scoreboard says the Renegades are winning 7 to 2. How many runs are they winning by?" "That's your third basket. Each basket is worth 2 points. How many points do you have so far?" I'll just add that I have taught many primary graders who could count rapidly by twos, fives, and tens when they came to my class, and a few who could rattle off threes, fours, and nines; but the only one I ever had who could count fluently by sevens was the one who lived and died with the NY Giants. Sevens...football...hmm!
*Measuring. "You sure hit that one a long way! I wonder how far it went.." You can measure with "nonstandard units," such as steps or rake lengths, which tends to be a little more meaningful for younger children, or with standard units--feet, yards, meters. "14 rake lengths--that's a lot. Whoa, that one went even further! Would you say 15, or 20, or even more?" How long does it take to run around the yard or the perimeter of the park? Time your child; let your child time you. Write it down. Try it again another day. Look at the map of one of the local bike paths. "It's 10 and a half miles long! How far do you think we'll get before I'll be ready to turn around?...I see another mileage marker up ahead--4 miles and still going!"
*Graphing. These take a little more time and energy, but they're great for kids who really love sports, especially team spectator sports. Work with your child to make a bar graph showing his or her favorite team's wins and losses.
(A sample bar graph)
Update it daily; use the internet or the newspaper to get the scores.
Or, make a line graph showing the number of runs your team scores on a daily basis. Look how the line moves around. What has the trend been? More runs over time, or fewer or about the same? How could you show the number of runs they gave up each day on the same graph?
(A sample line graph)
Can you make a graph showing how many times you go swimming/bicycling/hiking this month? We'll write the words down here; put up a blue sticker for the water whenever we swim, a red sticker for the color of your bike to show each time you go for a ride, a green sticker for the color of the leaves to stand for a hike.
(A sample picture graph)
Which has the most so far? The fewest? How many more bike rides have you taken than hikes?
Of course, I don't mean to reduce sports and physical activity to numbers. Nor is the point for kids to quantify their outside play. Be sure that timing and measuring are just for fun, a nice way of bringing a little math into children's lives, not an opportunity for frustration and embarrassment because they can't seem to beat their old record; be sure that a graph is a cute little add-on, not another chore that has to be done or the sole reason for taking a bike ride or going out for a hike. Sports are their own reward. Though, now that I think about, the ability to hit .658 (and calculate it properly!) might be its own reward, too...
(Ol' Henry)Anyhow, the game put me in my mind of Sports and Math. I spent most of my childhood free time engaged in one of five activities:
1) eating
2) reading the classics, mainly the Hardy Boys books
3) writing short stories with meandering plots and lots of unnecessary characters
4) playing board games and card games (see SummerMath Parts 1 and 2)
and
5) playing, watching, reading about, or thinking about baseball.
Baseball and math are closely linked, and in fact I learned quite a lot about math from my interest in baseball. My 1972 Sports Illustrated baseball board game (see 4 and 5 above) helped inform me about probability. I can remember the power I felt when I realized that I could use what (little) I knew about ratios to compare teams' won-lost records in my head--was it better to be 38-37 or 37-36, and how could I prove it? And I developed some facility with division, if not comprehension of WHY it worked, by virtue of calculating my batting average every day back when I was ten or so. (My batting average was very good. I counted it as a hit, of course, if someone muffed a ball I'd put in play. Or if the umpire mistakenly called me out when I was CLEARLY safe at first--don't laugh, it happened all the time. Or if I hit a line drive or a deep fly ball that somebody managed to corral, but which clearly SHOULD'VE been a hit--why should I be penalized just because my opponents had good hands? That was in addition to the occasional, you know, REAL hits I got. As I said, my batting average was very good.)
In any case, there are lots of ways to combine math with sports, for those of you whose children like to watch baseball, play soccer, ride bikes, or mess around with balls and such in the back yard after dinner. Here are some ideas of questions you can ask and projects you can do:
*Counting and estimating. "I wonder how many pitches the pitcher will throw this inning. Do you think it'll be more than 15 or less than 15?" "Take ten shots on goal from right here. Let's see how many go in...Now let's move you back a few feet. How many do you think will go into the net now?" "Good job! We just did 6 throws back and forth in a row without dropping a single one. Think we can beat that record? Let's keep track."
*Adding and subtracting, multiplying and dividing. "The scoreboard says the Renegades are winning 7 to 2. How many runs are they winning by?" "That's your third basket. Each basket is worth 2 points. How many points do you have so far?" I'll just add that I have taught many primary graders who could count rapidly by twos, fives, and tens when they came to my class, and a few who could rattle off threes, fours, and nines; but the only one I ever had who could count fluently by sevens was the one who lived and died with the NY Giants. Sevens...football...hmm!
*Measuring. "You sure hit that one a long way! I wonder how far it went.." You can measure with "nonstandard units," such as steps or rake lengths, which tends to be a little more meaningful for younger children, or with standard units--feet, yards, meters. "14 rake lengths--that's a lot. Whoa, that one went even further! Would you say 15, or 20, or even more?" How long does it take to run around the yard or the perimeter of the park? Time your child; let your child time you. Write it down. Try it again another day. Look at the map of one of the local bike paths. "It's 10 and a half miles long! How far do you think we'll get before I'll be ready to turn around?...I see another mileage marker up ahead--4 miles and still going!"
*Graphing. These take a little more time and energy, but they're great for kids who really love sports, especially team spectator sports. Work with your child to make a bar graph showing his or her favorite team's wins and losses.
(A sample bar graph)Update it daily; use the internet or the newspaper to get the scores.
Or, make a line graph showing the number of runs your team scores on a daily basis. Look how the line moves around. What has the trend been? More runs over time, or fewer or about the same? How could you show the number of runs they gave up each day on the same graph?
(A sample line graph)Can you make a graph showing how many times you go swimming/bicycling/hiking this month? We'll write the words down here; put up a blue sticker for the water whenever we swim, a red sticker for the color of your bike to show each time you go for a ride, a green sticker for the color of the leaves to stand for a hike.
(A sample picture graph)
Which has the most so far? The fewest? How many more bike rides have you taken than hikes?
Of course, I don't mean to reduce sports and physical activity to numbers. Nor is the point for kids to quantify their outside play. Be sure that timing and measuring are just for fun, a nice way of bringing a little math into children's lives, not an opportunity for frustration and embarrassment because they can't seem to beat their old record; be sure that a graph is a cute little add-on, not another chore that has to be done or the sole reason for taking a bike ride or going out for a hike. Sports are their own reward. Though, now that I think about, the ability to hit .658 (and calculate it properly!) might be its own reward, too...
Tuesday, July 14, 2009
A Games-in-Education Site
This one is intended mainly for teachers who want to make better use of games of all kinds in their classrooms (and I'll be passing on the link to lower school teachers, of course), but parents should be able to benefit from it too. I recommend it!
http://www.gamesforeducators.com
Happy July 14, by the way. In, let's see, 12 years this will be a special date of its own: 7/14/21. No prizes for guessing the pattern, but you might try it out on your third grader.
http://www.gamesforeducators.com
Happy July 14, by the way. In, let's see, 12 years this will be a special date of its own: 7/14/21. No prizes for guessing the pattern, but you might try it out on your third grader.
Tuesday, July 7, 2009
SummerMath, Part 2: Card Games
I wrote a few days ago about board games. Now it's the card games' turn. What can I say? They whined and groaned until I HAD to include them...
Card games are if anything even more math-y than board games. In fact, cards themselves are pretty solidly mathematical. Consider: There are 4 suits with 13 cards in each; there are 4 seasons in the year, with 13 weeks (give or take a day here and there) in each. Coincidence? Nah!
Many of you know the game Crazy Eights, a version of which is marketed under the trade name UNO. This is a great game for getting kids to think about attributes--the different categories that cards fit into. On a seven of diamonds, for instance, you can play any diamond or any seven. Young children often scan their hands and then say with disappointment "I don't have any cards that will work." "You don't have any diamonds?" I'll ask. "No," they'll say. "And no sevens either?" "No--oh, wait!" The ability to keep two attributes (such as suit AND rank) in mind at the same time is extremely useful in math. In geometry, for instance, kids will need to know that a square is a kind of a rhombus and a kind of a quadrilateral (and on and on); in numbers, kids should recognize that 44, say, is divisible by both 2 and 11 (not to mention 4 and 22). So a hand of Crazy Eights before dinner is a nice painless way to encourage mathematical thinking--and knock off a few of those prerequisites for geometry, division, and more.
Okay, okay, the game War is exceedingly dull and involves no strategy whatever. I get that (boy, do I ever). But your 4-7-year-old is busy practicing concepts of greater than and less than while playing, which ALMOST makes up for the boredom issue. Ask questions as the game goes on, too. (And it DOES go on...okay, enough carping.) "Your 9 beats my 2...by a little, or by a lot?" "I'm going to put my card down first--oh, a 3. Do you think I will probably win with a 3? Let's check your prediction."
There are any number of variations on rummy. These games are especially good for third grade and up. Basically, players try to get groups of three (or more) cards that are all the same rank (as in three queens) or same suit and in a run (as in 4, 5, 6, 7 of spades). You pick up and discard various cards in an attempt to make these groups. We're talking strategic thinking and probability in addition to attributes and sequencing. Scoring requires adding the values of cards, too.
Then there are the approximately one zillion forms of solitaire. Many of these games deal with attributes, or with addition, or with sequencing; all of them are good for strategic thinking. The game Spit was extremely popular as a snacktime/rainyday activity for third and fourth graders last year; despite its unsavory name it helps develop sequencing skills, both backwards and forwards, and encourages kids to know what's one less or one more than a given number automatically. Concentration isn't much of a math game, but you can make it one by playing only with cards A-9 and having the object be to draw 2 cards that have a sum of 10. (Instead of matching two 8s, say, you match an 8 and a 2.) The same principle applies to Go Fish, another not-very-mathy-game, which becomes "Tens Go Fish" when you ask for a card that goes with one of your own to make 10.
A little more purely mathematical, but still fun: For younger kids you can try Close to 10 or Close to 20. For Close to 10, deal out 3 cards after removing the face cards from the deck. Focus only on the rank (ace = 1). Choose two cards with a sum that is as close to 10 as possible. How close are you? That's your score. Record it. Play 5 rounds. High score loses. You can play this cooperatively or competitively, which each player having a different set of cards. For Close to 20, use five cards and choose three, or try some other variation. This game is great for estimation, for practicing addition strategies, and again for strategic thinking.
Then there are various betting games. "Can we play Cash Cab poker?" one of Ellen's fourth graders used to ask me almost every day last year, and though the answer was usually "Not today," kids ages 7 and up very much enjoy the mixture of skill and luck in --> HIGH STAKES <-- card games. I don't advise using actual money, but counters work just fine. Here's a basic template, which permits a whole mess of variations:
*Remove the face cards (and sometimes the tens). Remind players that ace counts as 1.
*Deal each player a card face up. High card bets (or folds). Other players follow (or fold). (I generally don't do raises, but you can if you like.)
*Next, deal a second card face down. High card showing bets again; others follow.
*Finally, deal a third card face down. High card showing bets again; others follow.
Who gets the dough? Here are some possible ways to do it.
*Multiplication practice. Choose two of your three cards. Find the product (what you get when you multiply them). Greatest product wins the pot. Alternatively, play high/low in which players who have low cards still can win. Before revealing their cards, players announce whether they're going for high or going for low. Those who announce they're going for high reveal their products; highest product gets half the pot. Those who announce they're going for low do the same; lowest product gets the other half the pot. Sneaky, huh?
*Greatest 3-digit number. Or greatest 2-digit number chosen from the 3 cards. Or high/low. Which way should you order 4, 7, and 2 if you're going for high? Which way for low? Which gives you a better chance of winning?
*Greatest sum. Make a 2-digit number and a 1-digit number (so if your cards are 4, 7, 2 you can do 47 and 2, or 24 and 7, or...). Add them, mentally or with paper and pencil. Greatest sum wins; or do high/low...
*Make it 5 cards instead of 3. Your goal is to have the 5 cards that add to a total nearer 25 than anyone else. This one's especially interesting because what looks like a "good" hand early on may prove to be a "bad" hand as those nines and tens don't stop coming
Or other variations that you and your children come up with.
As before, these games should be considered an opportunity for some fun rather than a chore. They're games, after all. Be aware of when your child starts to squirm, or when the brain begins to turn off, or when the beautiful day outside is becoming more appealing than the king of hearts. But if you don't overdo it and play your cards right (hardy-har-har), these games can be great ways to help your child have fun--and practice a little math in the bargain.
Card games are if anything even more math-y than board games. In fact, cards themselves are pretty solidly mathematical. Consider: There are 4 suits with 13 cards in each; there are 4 seasons in the year, with 13 weeks (give or take a day here and there) in each. Coincidence? Nah!
Many of you know the game Crazy Eights, a version of which is marketed under the trade name UNO. This is a great game for getting kids to think about attributes--the different categories that cards fit into. On a seven of diamonds, for instance, you can play any diamond or any seven. Young children often scan their hands and then say with disappointment "I don't have any cards that will work." "You don't have any diamonds?" I'll ask. "No," they'll say. "And no sevens either?" "No--oh, wait!" The ability to keep two attributes (such as suit AND rank) in mind at the same time is extremely useful in math. In geometry, for instance, kids will need to know that a square is a kind of a rhombus and a kind of a quadrilateral (and on and on); in numbers, kids should recognize that 44, say, is divisible by both 2 and 11 (not to mention 4 and 22). So a hand of Crazy Eights before dinner is a nice painless way to encourage mathematical thinking--and knock off a few of those prerequisites for geometry, division, and more.
Okay, okay, the game War is exceedingly dull and involves no strategy whatever. I get that (boy, do I ever). But your 4-7-year-old is busy practicing concepts of greater than and less than while playing, which ALMOST makes up for the boredom issue. Ask questions as the game goes on, too. (And it DOES go on...okay, enough carping.) "Your 9 beats my 2...by a little, or by a lot?" "I'm going to put my card down first--oh, a 3. Do you think I will probably win with a 3? Let's check your prediction."
There are any number of variations on rummy. These games are especially good for third grade and up. Basically, players try to get groups of three (or more) cards that are all the same rank (as in three queens) or same suit and in a run (as in 4, 5, 6, 7 of spades). You pick up and discard various cards in an attempt to make these groups. We're talking strategic thinking and probability in addition to attributes and sequencing. Scoring requires adding the values of cards, too.
Then there are the approximately one zillion forms of solitaire. Many of these games deal with attributes, or with addition, or with sequencing; all of them are good for strategic thinking. The game Spit was extremely popular as a snacktime/rainyday activity for third and fourth graders last year; despite its unsavory name it helps develop sequencing skills, both backwards and forwards, and encourages kids to know what's one less or one more than a given number automatically. Concentration isn't much of a math game, but you can make it one by playing only with cards A-9 and having the object be to draw 2 cards that have a sum of 10. (Instead of matching two 8s, say, you match an 8 and a 2.) The same principle applies to Go Fish, another not-very-mathy-game, which becomes "Tens Go Fish" when you ask for a card that goes with one of your own to make 10.
A little more purely mathematical, but still fun: For younger kids you can try Close to 10 or Close to 20. For Close to 10, deal out 3 cards after removing the face cards from the deck. Focus only on the rank (ace = 1). Choose two cards with a sum that is as close to 10 as possible. How close are you? That's your score. Record it. Play 5 rounds. High score loses. You can play this cooperatively or competitively, which each player having a different set of cards. For Close to 20, use five cards and choose three, or try some other variation. This game is great for estimation, for practicing addition strategies, and again for strategic thinking.
Then there are various betting games. "Can we play Cash Cab poker?" one of Ellen's fourth graders used to ask me almost every day last year, and though the answer was usually "Not today," kids ages 7 and up very much enjoy the mixture of skill and luck in --> HIGH STAKES <-- card games. I don't advise using actual money, but counters work just fine. Here's a basic template, which permits a whole mess of variations:
*Remove the face cards (and sometimes the tens). Remind players that ace counts as 1.
*Deal each player a card face up. High card bets (or folds). Other players follow (or fold). (I generally don't do raises, but you can if you like.)
*Next, deal a second card face down. High card showing bets again; others follow.
*Finally, deal a third card face down. High card showing bets again; others follow.
Who gets the dough? Here are some possible ways to do it.
*Multiplication practice. Choose two of your three cards. Find the product (what you get when you multiply them). Greatest product wins the pot. Alternatively, play high/low in which players who have low cards still can win. Before revealing their cards, players announce whether they're going for high or going for low. Those who announce they're going for high reveal their products; highest product gets half the pot. Those who announce they're going for low do the same; lowest product gets the other half the pot. Sneaky, huh?
*Greatest 3-digit number. Or greatest 2-digit number chosen from the 3 cards. Or high/low. Which way should you order 4, 7, and 2 if you're going for high? Which way for low? Which gives you a better chance of winning?
*Greatest sum. Make a 2-digit number and a 1-digit number (so if your cards are 4, 7, 2 you can do 47 and 2, or 24 and 7, or...). Add them, mentally or with paper and pencil. Greatest sum wins; or do high/low...
*Make it 5 cards instead of 3. Your goal is to have the 5 cards that add to a total nearer 25 than anyone else. This one's especially interesting because what looks like a "good" hand early on may prove to be a "bad" hand as those nines and tens don't stop coming
Or other variations that you and your children come up with.
As before, these games should be considered an opportunity for some fun rather than a chore. They're games, after all. Be aware of when your child starts to squirm, or when the brain begins to turn off, or when the beautiful day outside is becoming more appealing than the king of hearts. But if you don't overdo it and play your cards right (hardy-har-har), these games can be great ways to help your child have fun--and practice a little math in the bargain.
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