Algebra 2 Unit 7 Interactive Notebooks: Probability

This year I’ve committed to posting each unit of both my Algebra 1 and Algebra 2 INBs.

My district is moving to a standards based curriculum, and has identified priority standards for every course. These are the standards we are required to address and assess our students over, so they pretty much form our units.

You can find my Algebra 1 (year long class) INB posts here:

Unit 1 | Unit 2 | Unit 3 | Unit 4 | Unit 5 | Unit 6 | Unit 7

And my Algebra 2 INB posts here:

Unit 1 | Unit 2 | Unit 3 | Unit 4 | Unit 5 | Unit 6

And finally, my posts from a 2nd go around I’m teaching of Algebra 1 here:

Unit 1 | Unit 2 | Unit 3 | Unit 4

The 7th standard I cover in Algebra 1 is not a priority standard, it is one of the “if you have time” standards. I chose to leave the last two priority standards until the last two units of the year, because then they would have covered them closer to taking their final. This standard is one that I really love, and was kind of bummed when it wasn’t chosen as a priority standard, so when I figured out I would have time to do an extra one, I jumped right to it.

S.CP.9: Use permutations and combinations to compute probabilities of compound events and solve problems.

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Skill 1: I can calculate experimental and theoretical probabilities

To kick off this unit, we play a game of BLOCKO! from Sarah Carter, who got it from Natalie Turbiville. I have a Katie Kubes 3D Cube Model set that our industrial tech teacher got from a conference that I never use for the actual 3D modeling but works perfectly for this purpose. As their posts state, you don’t tell the students the rules before they place their cubes the first time, and they get very frustrated when they realize how long it’s going to take for them to remove them all!

We then discussed the difference between theoretical and experimental probability, including us actually flipping a coin – aka one of my students finding ways to bounce it off the wall, ceiling, and tables… I got this notes page from Sarah Carter as well, but I cannot seem to find the post with her file to it at this moment! Then we filled out a chart of theoretical probabilities of rolling two dice (find this file in Sarah’s BLOCKO! post), calculated the probability of each outcome, and then the students placed their blocks again. They noticed that the game was much shorter this time, and made some good changes to their layouts! We tracked the experimental probability of each outcome throughout this game and then discussed the differences.

To close out our intro information, we defined sample space and discussed the fundamental counting principle. I am not entirely convinced that the information I found on possible Social Security numbers is accurate…and my students really wanted me to tell them my Social Security number…nope.

Skill 2: I can calculate permutations in appropriate situations

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To start off our discussion of permutations, I gave my students 5 minutes and the challenge to arrange the numbers 1,2,3, and 4 as many ways as they could. They got very competitive about this challenge and kept asking, “how many are there? Do I have them all?” which, of course, led perfectly into our discussion!

A few of my students got all 24 permutations, which was awesome. We looked at several other examples of permutations, and after we looked at permutations of my name, I had them each find the permutations of their own names. One of them asked if we could do the challenge again with the extra time we had left at the end of class, but with the numbers 1-5. Some of them started listing arrangements, but then someone calculated how many permutations there were for this, and they decided they did not have the patience to write out 120 different arrangements!

Skill 3: I can calculate combinations in appropriate situations

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We also started off this lesson with a challenge: how many different ways are there to choose two letters from A,B,C, and D? “This is easy!” They all exclaimed, thinking of our previous challenge…until I started walking around and pointing out to them that AB and BA were choosing the same letters. They ended up being very unsure about how many possibilities there were here:

We did a few examples of how to find combinations, and then looked at a set of scenarios where they had to decide if it was a permutation or combination needed. This always proves to be an interesting discussion, because my students ALWAYS overthink the situations. The last question on this note page brings them back into the realm of probability, so they can start to see how these skills are related.

Skill 4: I can use probability addition rules

I really like how I started this page with conceptual ideas of mutually exclusive and inclusive, before we got into the probabilities. Students connect pretty strongly with these examples and have good discussions, and this class even started coming up with their own examples when we finished these!

You may notice that in the Venn Diagram I used teachers from my own school…which I will have to change next year because one of them is leaving 😦 😦 😦 You would want to change this to teachers from your school if you use this. My students also called me out on making the numbers up and not using actual overlaps between our classes, so I should probably change the numbers for next time….maybe collect data from my students like I did for a page later in this unit!

Skill 5: I can identify the difference between independent and dependent events

To set up a discussion of independent and dependent events, I spent a lesson playing two games. Probability Bingo is from Sarah Carter – she details her journey of trying to color foam cubes in her post, and I have two large red foam cubes as part of a 3D objects set and did not want to even try coloring them, nor did I really want permanent writing on them in case I wanted to use them for something else later. I ended up changing her colors to shapes – heart, star, and circle – and cutting them out of printer paper and using a glue stick to stick them to the foam. They’ve now lasted two years of this lesson, but I can still peel the shapes off with no damage to the cubes if I want to! I think I want to change the circles to triangles or something next year, because my students keep thinking the circles are zeros when they try to list their possibilities and then getting confused. I’ve played this two ways – once where we play without looking at probabilities first, and once where we start off with the probabilities. The game was enjoyable both ways, so it depends on how much time you have.

We also play Egg Roulette. I’ve seen this on twitter several times where people play with Easter eggs that have confetti inside 3 of them…but I decided to go all in last year and it was GREAT. This is actually the only time all year I hardboil eggs because I don’t like them, so I’m always mildly concerned that I won’t do it right, but they’ve come out ok so far. You boil 9 out of a dozen eggs, and then mix them up in the carton. Bring in a big tupperware container and let your students take turns selecting an egg and smashing it into the tupperware, but BEFORE they smash it, calculate the probability that they will smash a raw one. If they smash a raw egg, they’re out!

Then we discuss the differences between these two activities and how the probabilities worked with in them, using that as a launching point to discuss independent and dependent events. We brainstorm more ideas of both types of event, and then do some sample calculations to compare the difference.

Skill 6: I can calculate conditional probabilities

We begin by conceptually thinking of conditional probabilities: if this thing is already true, what is the probability of this other thing?

Then we move into talking about the formula for calculating conditional probabilities. Every Friday, our opener question is a fun question to help me get to know my students better. One Friday before this lesson, I took the opportunity to use this question to collect some data: I asked my students from all my classes what their favorite fast food restaurant was, and if they’d eaten there in the last week. That’s where this data came from, which made it more interesting for my students to do calculations with, because then they were judging everyone’s fast food preferences.

Last, we used the formula to make calculations when just given probabilities, moving back into more algebraic manipulation.

 

You can find all the files from this post in links (if they are someone else’s) or here (if they’re mine), in Publisher and PDF form.

Author: missmastalio

Math teacher at an alternative high school. Living the best life.

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