I love probability. I can’t really explain why, but I find it so easy to understand and applicable to real life. My students, on the other hand, don’t seem to really know much about it when we start our probability unit and some of them have never even heard of it. I used to get so surprised when kids didn’t know anything about a topic. Now, I just realize that there is a lot to learn about in the world, and I love the chance to be the one to share something for the first time with them. The probability unit is not only fun, it also uses some concepts that we have focused on this year like proportions and rates.
I use a series of I can statements to introduce this topic and to help us check for progress along the way. Students put the I can statements in their interactive notebooks and refer back to them on a daily basis. This gives students a chance to evaluate their learning and see if they are making progress with the topic. If you want to read more about using I can statements to help keep students on track, you can read this blog post.
What do I want my students to do with simple probability?
Since my 7th graders have not learned about probability before, I make sure that I keep it really simple. Also, we only have a week to learn compound probability, so we don’t get too complicated. We work on the basics and put an emphasis on the vocabulary and the language of probability. The math isn’t too hard, but the language can be an obstacle for many kids. Half of my students are English Language Learners and the other half struggle with academic vocabulary in general.
The fact that they struggle with language means that in a topic like this they need to use a lot of language. They love to learn how to do something and just find the answers. I found out that this wouldn’t work for this topic. So I strategically included some verbs in the I can statements to focus on language. I used words like explain and compare to remind me (and them) of how they would be talking about probability.
Also, when we practice these concepts, I like to have them in centers and doing a lot of math talk. I want them to use the right math terms to describe these patterns. By listening to partner talk I can see how comfortable they’re getting.
Simple probability learning goals
Here’s an overview of the goals we worked through. Laying them out this way helped me chunk out the learning, and it gave students a road map of where we are going.
- I can explain the difference between theoretical and experimental probability.
- I can identify the theoretical probability in a simple situation like rolling dice or flipping a coin.
- I can compare theoretical and experimental probability through trials.
- I can identify what is more likely to happen in simple situations like flipping a coin or rolling a dice.
- I can use experimental probability to make predictions.
Pro Tips: Remember to have these I can statements in students’ notebooks and refer back to them on a daily basis. This can also serve as a time to get them talking about the concept. Help them when they talk by giving them sentence starters and make sure they use precise language.
Want to get a copy of these I Can Statements for probability for your own students? Click the banner below to download a free copy of this and 20+ other middle school concepts, plus a blank template for students to write their own I Can Statements.
Now let’s look closer at each of the goals for this topic.
I can explain the difference between theoretical and experimental probability.
You might think that explaining the difference between theoretical and experimental probability would come easy to students. I know I did. But, it surprised me how many of them got confused and mixed up the words experimental and theoretical. They were very confident while being completely wrong with these two words. I found out about this misconception through an anticipatory set where they had to predict something after doing the experiment. They wrote down their definitions of theoretical and experimental. About half of them had the two definitions written backwards. When we discussed the two types of probability they were legitimately surprised that they were wrong.
This told me that I need to incorporate these words into everything that we do. Students need to use the words over and over in context. That helps me now when I plan for this unit because I can make sure that I have these words attached to everything we do. Furthermore, it inspired me to make a foldable that just identifies the characteristics of these two words.
I can identify the theoretical probability in a simple situation like rolling dice or flipping a coin.
For students to become proficient in this skill they need to be able to find the total possible outcomes and the number of ways the event can happen. I find that students are typically really good at this in simple situations. If you ask them what the probability of flipping a heads on a coin is, they know it is fifty fifty.
When you find something like this that students know you can build on it with the more complicated situations. The flipping of the coin can serve as basis and a reference when you have them find the probability of landing on a red or blue space on the spinner. You just have to keep emphasizing that you are creating a fraction that has the number of ways the event can happen to the number of possible outcomes.
I can compare theoretical and experimental probability through trials.
Comparing theoretical and experimental probably lends itself to lots of hands-on trials. Also, it gives students the chance to distinguish between the two types of probability and draw conclusions about why theoretical probability doesn’t match the experimental. This concept can trip kids up because some of them figure that theoretical probability is pointless because it isn’t right. This gives you the opportunity to show that theoretical is about the chances and that the experimental hardly ever matches the theoretical.
Give students chances to see probability in action. You can do whole class probability experiments, small group, and individual. Show them how probability is used in game shows and carnival games. This concept lends itself to some fun practice examples and experiments.
I can identify what is more likely to happen in simple situations like flipping a coin or rolling a dice.
After students can identify the theoretical probability in simple situations have them compare two situations. This just makes it a little more complex. They have to explain why one situation is more or less likely to happen than another. This acts as a great segue-way to compound probability which students will learn next. It also creates opportunities for students to talk about probability and use the language related to this topic.
Students will compare fractions, so that is a skill to review. Comparing fraction still tricks some 7th graders if they don’t have a great grasp on fractions in general. Overall, this last part just bring more meaning to the probability and extends their understand a little bit.
I can use experimental probability to make predictions.
After conducting an experiment, students needs to be able to show what happened mathematically. This is where proportions come in. Proportions work their way into so many of the 7th grade standards. My students have become very adept at setting up proportions and solving for a missing value. I love it when we get to use this skill again because they are already successful with it.
So, students need to write a ratio that shows how many times something happened over how many trials there were. For example, if the situation is, “Jan rolled the dice 8 times. She rolled a 4 three times,” then students would write the ratio: 3/8.
After they’ve written their ratio, students can use the experimental results to make predictions. So, continuing on in this situation, “Using this data how many times would Jan roll a 4 if she rolled the dice 15 more times?” Students set up a proportion in order to solve as seen below:
When students really “get it”, they are able to read a situation, or actually do an experiment, and represent what is happening in a ratio. Then, they can set up a proportion to predict what is likely to happen in the future based on that data.
Common misconceptions with simple probability
Just like any topic, there are common misconceptions with simple probability. Students confuse theoretical with experimental probability.
Also, the language itself can challenge students. For example, when you ask what the probability of rolling an even number is, there are students who don’t know what that means. Another situation is if you ask the probability of rolling a number larger than 4. Some students don’t know if they should include the 4 or not. The best way to combat these types of misconception is lots of practice. Students need to see a lot of different situations. We practice with spinners, dice, cards, marbles, coins and more. The more experience the better they seem to get at it.
Reading and understanding what word problems are asking is another language challenge for students with this topic. I’ve found it helpful to take extra time annotating questions with students. If they don’t read the questions carefully they will make mistakes. We use C.U.B.E.S. as a way of annotating problems. Click here for a copy of the presentation that I use to introduce this strategy. You can use it with any topic and it lends itself to this topic in particular.
Put it into practice
I chunk the learning through these I can statements when teaching simple probability. There are definitely other statements you could add or maybe you would take away one of the ones I have. The great thing about using the I can statements to plan is that is helps you and your students see what they have done and where they are going. I hope that you can use this information to help plan your instruction and keep you and your students accountable along the way. For your own I Can Statements ready to print and use in students’ interactive notebooks, just click here.
If you are looking for resources to help teach simple probability in a chunked manner like the one explained above then check out this other post about activities for teaching simple probability.
Until next time!
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