What are the chances your students will forget what they learn about probability? It’s an uncomfortable truth that they often forget things that they’ve studied in class. But they are much more likely to forget if they don’t build schema and connections with this concept. I’m excited to share with you my favorite way to do just that. Discovery labs give you one way that help your students to build background and ultimately remember what they learn (wanna read more how I got started with discovery labs? Read that story here.)

Now, many times in my teaching career I have taken what looks like the easier road and just given kids information. After all, there’s so much to go over and so little time. So I would give them notes with all the information they needed, and students would write them in their notebooks. It was a very controlled activity and the students are attentive. But I realized that as teachers, when we just keep doing this over and over, it almost seems like we are hoping they can remember all the steps to 30-50 concepts. Fingers crossed! Obviously, they can’t keep that all straight. And as for the kids who can remember that much information, well, they actually don’t need very much help from their teacher.

Discovery labs helped me break up that teaching routine. They make a great start to the teaching unit. Instead of starting with a data dump, I start with a few guided questions. Then, students explore the math and look for patterns. They build a framework to understand the more explicit instruction that still comes, it just comes a bit later.

**Discovering compound probability**

For compound probability we move into it straight from simple probability, so students already have probability on the brain. The difference with discovering compound probability has to do with the fact that they have to perform a math operation. They will multiply fractions. If you just tell them to multiply the fractions from the simple probability you are missing out on an incredible opportunity to discover something cool.

**The compound probability discovery lab consists of:**

- a simple probability background building activity
- an opportunity for students to try to figure out the probability of a compound event
- a second opportunity with a compound event in a tree diagram and a table
- writing a conclusion

After you complete this discovery lab then your students are primed for taking notes and practicing this concept. We took notes in our interactive notebook after we finished and then moved into a practice activity in a scaffolded manner. My students were so much more prepared for tackling a topic when they had discovered some aspect of that concept.

**Step 1-Building background**

Students began with a building background activity designed so that students should be able to complete it without a lot of outside help. This activity activated their prior knowledge. In this case for us, the prior knowledge was only from the week prior. That doesn’t always happen, but with this topic we had just completed simple probability before moving into compound probability. Students were given different scenarios and some fractions written as a probability (“1 out of 2”). Then, they had to match the scenario with the probability.

My students flew through this part. It was very easy for them, which is a good thing! This let me know that they could handle the next part of the discovery lab. Sometimes they don’t understand the building background part of the discovery lab and you have to take a few minutes to help remind them of what they have forgotten. But not this time! This was probably the easiest building background activity that we have done this year.

**Step 2-Observations**

Moving into the “discovery” part of this lab, there were two main parts. In the first part I gave students a compound event and asked them to try to find the probability. I wanted to see if they could figure out how to find the probability. This was not easy. Some students came up with ways to show the possible outcomes. Many students were a little stumped. I like to guide students a little bit, but not too much. In this case I did start hinting that they might want to dry a picture or use some sort of graphic organizer.

I will be honest that my students really struggled with this part of the lab. As long as it is productive struggle, that is okay. When it starts to spiral into comments about how “this is impossible” and “I’m just not good at math”, then I know that I should intervene.

There was one group who figured out several parts of solving these types of problems. They figured out the probability of the individual events. Then, they knew they had to do an operation to combine those two numbers. They decided to add them together. Throughout the process, the students in this group had also done a fair amount of talking about it, trying to figure out how to reach a solution. While their answer wasn’t correct, their attempt showed the math thinking that they were doing. They tackled an unknown problem and used what they knew to try to figure it out! So very cool to see!!!

** With some added support**

After trying to solve the first compound probability problem, I gave them a bit more support. I gave students a tree diagram and a table to use. Students tried to figure out how to use the tree diagram or the table to organize the information for 5 minutes or so while I stepped back. Some kids were coming up with ideas to make it work and others were stuck. This is pretty typical with a discovery lab. The key is to not swoop in too quickly to save them. There should be some struggle (again, the key is *productive *struggle).

I gave them a few hints without giving it all away:

- How many columns are there in the table? What could match that?
- Remember these are graphic organizer that represent the possible outcomes.
- The diagram and the table are two ways to represent the same information.
- What do you notice about the tree diagram and the table that is similar?

Some partnerships figured a lot out with just a couple of pointers and some were still lost. I went over the first example with them and let them continue with the second example. By the time the second example was finished most of them were seeing the pattern. It was amazing to see because they had the opportunity to draw connections without me just telling them how to do it.

**Drawing conclusions**

I love reading my students’ conclusions at the end of a discovery lab. It shows me what they understand and what they have figured out through the experience. I usually give them a good 10 minutes to write their conclusions. We focus on making our writing academic. I usually tell them to not write like a cavemen. It’s extra fund to channel your inner Tarzan and give them examples of caveman speak. Seriously, you should try it!

Example of caveman conclusions(modeled in a caveman voice):

- I learn stuff
- Probability good
- Me no understand
- Tree diagram good
- Me finished

Kids get a good laugh out of this and they understand that they have to write meaningful statements. And when they finish in less than a minute, I make them go back and add more.

**Student conclusions**

I gave them very little direction on what to write in their conclusions. Often, for students who are not strong writers, I do offer sentence stems.

In this discovery lab students talked about using tree diagrams or tables as a way of organizing information. Some even drew a picture to show what they were talking about. Overall, most of the students showed an understanding of tree diagrams and tables as a way to represent compound probability.

In this activity I could see that students understood the reasons why we would use a tree diagram or table. This is an effective introduction lesson, but it doesn’t make students experts on this topic. It sets the stage for our notes and formal instruction (you can see how I chunk out the learning for this whole unit here), and then into practice with compound probability (read about 12 practice activities for compound probability here.)

**Try this in your classroom**

You can find this compound probability discovery lab in our TpT store, or you can use the same principles and make your own activity. If you have never done a discovery activity before then you are in for a treat. If you have done many discovery activities then I hope you have seen the value of them in your class. It can be hard to believe that students can learn in this way, but I challenge you to give it a try. I think you’ll be surprised by the results. Thanks for reading! Until next time 🙂

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