This makes me wonder what would constitute a good explanation of probability at the grade-school level.
Hmm …
Suppose we put the names of everyone in your school into a hat, and mix them all up, and pull one out, and call that person up and give them a cookie. What’s the chance that the cookie will go to a fifth-grader? (One in five, if your school goes from first to fifth grade and all of the grades have the same number of students.) What’s the chance that the cookie will go to a girl? (One-half, probably.) What’s the chance that it will be a fifth-grader and a girl? Five times two is ten, so it’ll be one in ten. (Multiplication rule for probabilities.)
Suppose that there’s the same number of kids in each grade — but all the first graders are boys, and all the fifth graders are girls. The second through fourth grades are evenly split between boys and girls. If I draw a name out of a hat, and I don’t tell you what grade or gender that person is, how likely is it they’re a fifth grader? (One-fifth.) Suppose I tell you they’re a girl, then how likely do you think it is? (Two-fifths.) Why did your answer change? (New information changes your probabilities.)
I have four chocolate cookies and one gingerbread cookie. I’m going to pick one without looking. If you can guess what kind of cookie it is, I’ll give it to you. Should you guess chocolate or gingerbread? (Chocolate.) How sure are you? (Four-fifths sure.) Why? Because you’ve seen the cookies and you know four out of five are chocolate, but you know there’s a one in five chance I could pick gingerbread even though it’s less likely. If you want to win a cookie, you’re better off picking chocolate. (Probabilities as measurement of uncertainty.)
Oh, sure, I agree pictures and lots more examples would be essential. I was just trying to think of how simple an approach would need to be; not to actually write a probability textbook at the fifth grade level.
This makes me wonder what would constitute a good explanation of probability at the grade-school level.
Hmm …
Suppose we put the names of everyone in your school into a hat, and mix them all up, and pull one out, and call that person up and give them a cookie. What’s the chance that the cookie will go to a fifth-grader? (One in five, if your school goes from first to fifth grade and all of the grades have the same number of students.) What’s the chance that the cookie will go to a girl? (One-half, probably.) What’s the chance that it will be a fifth-grader and a girl? Five times two is ten, so it’ll be one in ten. (Multiplication rule for probabilities.)
Suppose that there’s the same number of kids in each grade — but all the first graders are boys, and all the fifth graders are girls. The second through fourth grades are evenly split between boys and girls. If I draw a name out of a hat, and I don’t tell you what grade or gender that person is, how likely is it they’re a fifth grader? (One-fifth.) Suppose I tell you they’re a girl, then how likely do you think it is? (Two-fifths.) Why did your answer change? (New information changes your probabilities.)
I have four chocolate cookies and one gingerbread cookie. I’m going to pick one without looking. If you can guess what kind of cookie it is, I’ll give it to you. Should you guess chocolate or gingerbread? (Chocolate.) How sure are you? (Four-fifths sure.) Why? Because you’ve seen the cookies and you know four out of five are chocolate, but you know there’s a one in five chance I could pick gingerbread even though it’s less likely. If you want to win a cookie, you’re better off picking chocolate. (Probabilities as measurement of uncertainty.)
For fifth graders you would likely need to do a lot more than just this. For the first case you’d probably need visual aids, and a lot more examples.
Even then, I suspect a lot of kids would have trouble. Probability is tough. Teaching it even to highschool students can be tricky.
Oh, sure, I agree pictures and lots more examples would be essential. I was just trying to think of how simple an approach would need to be; not to actually write a probability textbook at the fifth grade level.