Classical Conversations Week 20 Combinations

I've posted my lab sheet for this lab on CC Connected (user name lb_oliver). My thoughts here will dovetail with that approach. You can also see my suggestions for ways to expand on this topic in my post here.

Welcome back to week 2 of CC’s statistics-based labs! Here are my thoughts about presenting these topics in class (for what it’s worth!) . . .

Remember to spend a minute or two reviewing last week’s lab and last week’s grammar (probability, outcome). Revisiting those terms and definitions will just help them stick in the kids’ minds. Plus, this week we’re setting aside those topics and picking up a new one, but we’ll be coming back to probability and outcome in future weeks, so it’s to everyone’s benefit to work on getting really comfortable with those terms.

Like last week, let’s begin with the end in mind. What’s the point of this particular lab? In my opinion, for our Classical Conversations Foundations students, it’s twofold:

1. Grammar: To teach some basic statistics grammar (Combination) and to see that term in action.
2. Dialectic: To begin teaching children to think about how adding “just one more” option exponentially changes the number of combinations that are possible. In other words, adding ONE additional option does NOT result in just ONE more possible combination. How many more combinations are possible? Well, it would depend on how that new option could be used.

In my mind, we’ve got to set a couple of ground rules in this particular lab – We’ll assume that every pizza has to have a crust, sauce (they’ll all have it, so we won’t make it an option), and at least one topping (no plain pizzas here!).

So, if you’re teaching a group of YOUNGER STUDENTS, you’ll want to focus on the grammar and you may need to keep the options more limited. Work up slowly! One crust option and two possible pizza toppings results in how may combinations? Three. Show them how this works, either by drawing it on the board or by using some sort of manipulative – paper, paper plates, or felt. Personally, I like felt and it’s pretty cheap. It’s fun for kids to see and handle something different, and since a parent could easily create something similar at home, I believe this is in keeping with CC’s simple approach.

Once you’ve shown them how it works with two toppings, let them try three. Ask them to think first about how many combinations that would result in. Will one more topping mean only one more possible combination? No. It will mean four additional possible combinations! Wow!

Like last week, I’d suggest that children do this lab in pairs with a parent assigned to each pair to be the record-keeper (if necessary) and auditor (someone to keep up with “have we already recorded that combination?”).

If you’re teaching a group of OLDER STUDENTS, you’ll move through the warm-up quickly, and then you can let them have a turn at one crust and three toppings on their own or in teams of two. Even students of this age will enjoy working in teams usually, and it gives them someone to bounce ideas off of. If they’re still at an age where having a visual will help (or you just want to liven up the lab), you can print out these pizza toppings to match the toppings on my Lab Sheets on CC Connected. You can cut out circles from two different colors of brown construction paper. I bought a pack like this and cut out circles the size of a mason jar lid, but you could just as easily use paper plates. Write “Thick” and “Thin” on them. It doesn’t have to be complicated.

Once they’ve worked through that set of options, they’ll be ready to move to the next step – adding another pizza crust option! What happens then? At this point, they’ll probably be able to guess that it means a lot more than just one more possible combination. But will any of them guess that it actually DOUBLES the possible combinations? (That’s 14 in total) Wow!

And if that is something they can work through, then try adding “just one more” option and going for 4 toppings. What do you end up with? 22 possible combinations, by my calculation! Amazing!

What should you emphasize? For every additional option we add, the combinations grow much larger than “just one more” and that would continue to happen as long as we added more possible options.

For ADULTS/PARENTS– I gave an overview in my post last week of why we do these labs in general. But, why did we do THIS lab? What was the point?

This lab, like all of the others during this 6 weeks is related to the science of origins. One way the math of combinations relates to the science of origins is through DNA. I’m not a scientist nor am I a mathematician, but a scientist would tell you that your DNA contains 23 chromosomes. Scientists are still investigating how many genes make up those chromosomes, but the current ballpark number is 20,000. Based on what I’ve read, the possible combinations of children resulting from a single couple’s DNA is 70,368,744,177,664. This is fascinating and goes a long way toward explaining how all human beings (black-skinned, white-skinned, blue-eyed, brown-eyed, etc.) could have descended from a single original couple created by an amazing (and very creative!) God.

Again, just as I said last week, gathering data, analyzing data and drawing conclusions are very much a part of many explanations of the origins of the universe. Eventually, our children will need to be able to draw their own conclusions from data that is presented to them. These labs are a great introduction to early critical thinking skills.