This week, I told my son that I had a mystery for him to solve. I put 20 game tokens into our "Probability Pouch" and it was his job to try to figure out how many of each color was in the pouch. I didn't tell him what colors I'd used...only that 20 tokens were in the pouch.
- Probability Pouch (if you don't have one, either use a paper bag or find a large sock and fit a small yogurt container tightly into the bottom of it...this works great to draw from)
- felt markers
We talked about how important it was to shake the bag and to put the game markers back in the bag after each draw. Once, he ended up with 3 markers on the table. I asked what would happen if he kept doing that. He grinned and agreed that we'd know what was in the bag based on what was on the table. He took away the data for those 3 draws, put the markers back in the bag, and redrew.
After about every 10th draw, I asked him to stop, look at the data he'd collected so far, and predict what he might get over the next ten draws. Which colors would he draw least? Which most? How many of each did he think he'd get?
He quickly recognized that he was consistently drawing the most red, the least yellow, and blue somewhere in the middle. As he considered what he might draw in the next 10, he made predictions like: 5 red, 4 blue, 1 yellow, and later, 6 red, 3 blue, 1 yellow. He kept a running total of what he'd drawn so far. After 40 draws, he'd gotten 25 red, 12 blue, and 3 yellow.
I asked him if it was possible that there was another color in the bag. He said yes, that there could be one green that he just hadn't drawn yet.
I asked, "What do you think the bag contains? Why?" Initially, he guessed the numbers based solely on the fact that he "drew the most red then blue then yellow." (He had the most red, followed by blue, then by yellow, BUT he didn't have any particular reason for the number of each color he selected as long as they were in that particular order.) I asked him to look at his data again (25 red, 12 blue, and 3 yellow) to see if there was any pattern to it. For instance, about how many more red did he have than blue? His eyes lit up. I gave him the option to change his prediction if he wanted to. (I did not push this.)
He altered his response to 12 red, 6 blue, 2 yellow. When I asked, "Why did you pick these numbers?" he responded, "I got lots of red and half blue and I got a 1/4 of yellow than blue."
Last question..."If we made more draws would it help you decide what is in the bag?" He said yes. Although he didn't use this vocabulary, he seemed to understand the concept of theoretical probability vs. experimental probability.
I asked if he wanted to know what was in the bag. Um, YES! He dumped it out, quickly counted and GLOWED. His response? "I got it EXACTLY!" (See answer pictured below.) While an exact answer was not my goal, it was fun to see his excitement. ;)
I love teaching probability. I'm sure it stems from the fact that lessons* are high interest, creating incredible "AH HA" moments in kids.
[*Note: The lesson that I did with my son taps from Bridges. I modified it to fit our needs.]
Kids LOVE probability! Funny thing is...I don't remember EVER doing a lesson on probability when I was a student. Do you?
I asked one group of students to brainstorm a list of all the ways that probability is used in daily life. Their list was huge. Probability has so many implications for daily life. Perhaps you'll consider generating your own list with your kiddos and submitting it as a comment?
Resources to check out:
- ProTeacher Collection (several ideas here)
- Tootsie Pop Pull (might need a bigger bag!)
- Bridges Breakout: Math With a Sock--Probability and Fractions
(or see economy version)...also love the tie dye probability containers
- If you need help coming up with color combinations, here is a page of probability clipart that might give you some ideas on what to put in the bag.
- And here is a nice introduction to probability.
- Children's Books on Probability, Data Analysis, Graphs:
- Do You Wanna Bet? Your Chance to Find Out About Probability, Jean Cushman (chapter bk)
- Pigs at Odds, Amy Axelrod
- Probably Pistachio, Stuart J. Murphy
- Socrates and the Three Little Pigs, Mitsumasa Anno
- A Very Improbable Story, Edward Einhorn
What is the probability that your family will have fun with a lesson like this? :)
P.S. Don't forget to enter to win your own "Probability Pouch!"