Do you wonder what to do with your child, when the subject of math arises? It's Friday. No subject is sexier than math. I mean that sincerely. Here are some of the best ideas I encountered in my teaching career.
-The spinner. You can manufacture a spinner at home. Cut out a small paper circle. Poke a hole through the center with the edge of a paper clip. Then, stick a tiny tube of straw down the stick-out part of the paper clip. Lastly, overlay a second circle--this one divided into sections. (For example, you could divide the circle into fourths, and label each part with a 1, 2, 3, or 4.) On the "base" circle, draw a long line extending from the center to one spot on the circumference. This is a spinner! The straw tube removes the issue of friction. (A little bit of science thrown in!) Ask your kid: "If I spin, am I most likely to land on 1, 2, 3, or 4?" Ask for a rationale. (It's fascinating that many small children won't intuit each outcome is equally likely, and fascinating to watch children grope for words to explain their thinking.) You can make multiple spinners: some where the outcome will almost certainly be 1 or 2, some where the outcome will be more up-in-the-air. You keep the paper clip affixed to the base circle with a small piece of tape. Beautiful, simple lesson--and you can reproduce it with materials from your house.
-"Pig." This is a game where you take two dice and try to reach one hundred. You keep track of your sums with each roll. If you get any double that is not "snake eyes," you lose all your new points and your turn. If you get snake eyes, you actually go back to ground zero. You can stop rolling and give up your turn at any point. The temptation is to keep rolling and rolling, but of course, if you do this, you are more and more likely to get a double. You can have children analyze varying strategies--"go for broke," "play it cautious," "play it cautious only for the first three turns"--and then test their predictions. They're practicing sums, studying probability, and learning to observe and draw conclusions from the world. Do you see how working with small kids can be an art?
-"The Likely/Unlikely Book." When kids are introduced to probability, the terms "likely" and "unlikely" are new. So you can read "Cloudy with a Chance of Meatballs" and divide the events into "likely" and "unlikely" categories. (It's likely that the sun will come up in the morning. It's unlikely that cottage cheese will drop down from the clouds.) Then kids can make their own booklets, in which they manufacture their own likely/unlikely events. ("It's likely I'll have lunch. It's unlikely I'll meet a flying dragon.") Marilyn Burns is a great fan of student-generated books, and another one she enjoys is "The Book of Skip-Counting." That's a way for you to introduce multiplication. You ask, How many people are in this park? I just gave a set of chopsticks to each of them. How many chopsticks in all? Chopsticks always come in twos. What is something that comes in threes? In fours? In fives? And you have a book. Or: Page one. There are some barn animals here, and there is a total of twenty-three feet. Draw the animals. (The great trick is that a slug counts as "one foot.") Page two. A total of thirty feet. How would you make that? And so on. You're counting, and it's likely you're skip-counting, since you may want to use two cows, or three wasps, to move things along.
-The Game of Circles and Stars. So easy and addictive. I roll my first die. That's the number of circles I draw. I roll again. That's the number of stars per circle. So, a six and a four, and I've generated twenty-four stars. And so on. You're racing your kid to rack up the highest numbers, but also, you're getting your kid to practice multiplication facts (in the most subversive and enjoyable way).
-And then some quick tricks. "A Cloak for the Dreamer" is a story in which an absent-minded student makes a cloak of circles, with large holes where the sides aren't touching. You can ask your kid to turn the cloak into something functional--which invites a discussion about the difference between a circle and a polygon, and the way that polygons can lock together to make one large shape. You can give a kid a cut-out set of four equilateral triangles and have him or her construct varying larger shapes with the cut-outs (a mega-triangle, a parallelogram, and so on). You can work with "conservation of space." Take a square paper, divide it into thirds, convert one of the thirds into three triangles, and you suddenly have a rocket. Kids won't believe that the rocket came from the square because, of course, it seems to be a different size. So you challenge the kids to reproduce the rocket, without wasting even one square inch of the original mega-square. This is wonderfully easy for some students and nearly impossible for others, and it's often students who aren't fast with conventional measures of academic success (e.g. spelling tests) who nevertheless seem to kick ass with the rocket challenge. (I love this.) I have a sense that any one of these lessons would have rocked my world in childhood, when I was taught poorly year after year, and when math was a source of anxiety or tedium or sometimes both, in the span of just a thirty-minute lesson. Just an observation. Math is thinking. What is more exciting than using your brain, and pushing to achieve something now that was inconceivable just yesterday, or the day before?
-The spinner. You can manufacture a spinner at home. Cut out a small paper circle. Poke a hole through the center with the edge of a paper clip. Then, stick a tiny tube of straw down the stick-out part of the paper clip. Lastly, overlay a second circle--this one divided into sections. (For example, you could divide the circle into fourths, and label each part with a 1, 2, 3, or 4.) On the "base" circle, draw a long line extending from the center to one spot on the circumference. This is a spinner! The straw tube removes the issue of friction. (A little bit of science thrown in!) Ask your kid: "If I spin, am I most likely to land on 1, 2, 3, or 4?" Ask for a rationale. (It's fascinating that many small children won't intuit each outcome is equally likely, and fascinating to watch children grope for words to explain their thinking.) You can make multiple spinners: some where the outcome will almost certainly be 1 or 2, some where the outcome will be more up-in-the-air. You keep the paper clip affixed to the base circle with a small piece of tape. Beautiful, simple lesson--and you can reproduce it with materials from your house.
-"Pig." This is a game where you take two dice and try to reach one hundred. You keep track of your sums with each roll. If you get any double that is not "snake eyes," you lose all your new points and your turn. If you get snake eyes, you actually go back to ground zero. You can stop rolling and give up your turn at any point. The temptation is to keep rolling and rolling, but of course, if you do this, you are more and more likely to get a double. You can have children analyze varying strategies--"go for broke," "play it cautious," "play it cautious only for the first three turns"--and then test their predictions. They're practicing sums, studying probability, and learning to observe and draw conclusions from the world. Do you see how working with small kids can be an art?
-"The Likely/Unlikely Book." When kids are introduced to probability, the terms "likely" and "unlikely" are new. So you can read "Cloudy with a Chance of Meatballs" and divide the events into "likely" and "unlikely" categories. (It's likely that the sun will come up in the morning. It's unlikely that cottage cheese will drop down from the clouds.) Then kids can make their own booklets, in which they manufacture their own likely/unlikely events. ("It's likely I'll have lunch. It's unlikely I'll meet a flying dragon.") Marilyn Burns is a great fan of student-generated books, and another one she enjoys is "The Book of Skip-Counting." That's a way for you to introduce multiplication. You ask, How many people are in this park? I just gave a set of chopsticks to each of them. How many chopsticks in all? Chopsticks always come in twos. What is something that comes in threes? In fours? In fives? And you have a book. Or: Page one. There are some barn animals here, and there is a total of twenty-three feet. Draw the animals. (The great trick is that a slug counts as "one foot.") Page two. A total of thirty feet. How would you make that? And so on. You're counting, and it's likely you're skip-counting, since you may want to use two cows, or three wasps, to move things along.
-The Game of Circles and Stars. So easy and addictive. I roll my first die. That's the number of circles I draw. I roll again. That's the number of stars per circle. So, a six and a four, and I've generated twenty-four stars. And so on. You're racing your kid to rack up the highest numbers, but also, you're getting your kid to practice multiplication facts (in the most subversive and enjoyable way).
-And then some quick tricks. "A Cloak for the Dreamer" is a story in which an absent-minded student makes a cloak of circles, with large holes where the sides aren't touching. You can ask your kid to turn the cloak into something functional--which invites a discussion about the difference between a circle and a polygon, and the way that polygons can lock together to make one large shape. You can give a kid a cut-out set of four equilateral triangles and have him or her construct varying larger shapes with the cut-outs (a mega-triangle, a parallelogram, and so on). You can work with "conservation of space." Take a square paper, divide it into thirds, convert one of the thirds into three triangles, and you suddenly have a rocket. Kids won't believe that the rocket came from the square because, of course, it seems to be a different size. So you challenge the kids to reproduce the rocket, without wasting even one square inch of the original mega-square. This is wonderfully easy for some students and nearly impossible for others, and it's often students who aren't fast with conventional measures of academic success (e.g. spelling tests) who nevertheless seem to kick ass with the rocket challenge. (I love this.) I have a sense that any one of these lessons would have rocked my world in childhood, when I was taught poorly year after year, and when math was a source of anxiety or tedium or sometimes both, in the span of just a thirty-minute lesson. Just an observation. Math is thinking. What is more exciting than using your brain, and pushing to achieve something now that was inconceivable just yesterday, or the day before?
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