Probability Through Caine's Arcade

First day of our probability unit we watched this video.

Day 1: I chose this video, because most of my students are hispanic and I think the biggest thing in our school right now is empathy. We talked about having games of chance like in the video they just watched, what does chance mean? We did our first section of probability and told them they were going to create their own games, just like Caine did. 

We did a 5 question check for understanding and told the students they needed to finish the bottom half of the checklist today.

Here are other great resources including the checklist: http://cainesarcade.com/schools/activitykits/

Students designing their cardboard games.

Day 2: We talked about conditional probability. Did another check for understanding on Kahoot. Then I got lots of cardboard boxes from our recycling bin and had to make a quick pit-stop at Dollar General for more cardboard boxes.

Day 3: I had a substitute teacher this day, but students started creating their boxes.

Day 4: We went over theoretical vs experimental probability. I gave students 7 minutes to finish their cardboard arcade games. Then we went over theoretical probability again. We talked about geometrical probability from Day 1. Students were given rulers and yardsticks and had to find the theoretical probability of successfully completing their arcade game.

Day 5: We finished the material for our probability unit. I gave students 5 minutes to make sure their game is playable and to finish anything on the checklist. Then we went over that I would give them 5 minutes to go play other games to get other groups experimental probability, then the partners would switch and the other partner would go play games.

I thought this unit was much better than the 3D dice activity from last year, this project was more hands-on and did a better job of combining the curriculum and the project together.

License Plate Combinations

When we come back from winter break we normally start our probability and statistics unit. I normally take a week for probability and a week for statistics which normally melts into three weeks. I've always thought nothing of changing it, but during winter break Dan Meyer posted "Plates Without States"  Since we were going over permutations and combinations I thought this would be an excellent way to get students thinking about how many different combinations there are in license plates and why they make them like that.

To start the lesson I had students go through Dan Meyer State-Plate Game.  Students were definitely engaged and loved playing against each other in their groups.

Next we talked about license plates and I separated it from combinations and permutations.

I gave all of the students a blank license plate and a card. The card had a name of a city or state and a population that students had to take in consideration.

Here are some of the license plates that students were working on.

When students were done with their license plates, they took a picture of their license plate and put it on SeeSaw. The last part they had to do was comment on three others the number of different combinations that they had with their license plate.

Here were a few students figuring out and commenting on other students post.

I like this activity much more and students realized how license plates play a role in local governments and how the population of an area can control the different license plates possible.

I posted almost all of them in the back of my room here are a bunch of different ones that are posted.

Children's Books for Algebra 2 Part 2

Children's books are a great way to get students interested in your content. Picking the right book is more difficult for the topic area. Here are three more children's books perfect for Algebra 2 class.

We are Growing by Laurie Keller

This book shows grass growing, yes literally. A theme the book has is that being unique is okay and that everyone is different.

A great math topic for using this book would be introducing unit rates or graphing linear functions. You could have some real grass growing in different stages per day and ask them if grass growing is linear or not? It would be a good exploratory lesson on linear functions.

You can further go into graphing and think about what non-linear grass would look like? How long would it take to cut the grass?

Giraffes Can't Dance by Giles Andreae

The giraffe believes he can't dance, but with words of encouragement he learns that he can dance in his own way.

In the book there are a bunch of different animals dancing. It would be a perfect time to look into transformations, you can look at it in a variety of different ways from linear transformations to parabolic transformations.

It will be good for students to look for similarities and differences. With the book you can even include more social learning skills learning about kindness and encouraging others.



Dragons Love Tacos by Adam Rubin

Dragons love tacos. They love chicken tacos, beef tacos, great big tacos, and teeny tiny tacos. So if you want to lure a bunch of dragons to your party, you should definitely serve tacos. Buckets and buckets of tacos. Unfortunately, where there are tacos, there is also salsa. And if a dragon accidentally eats spicy salsa . . . oh, boy. You're in red-hot trouble.


In the classroom this book would be a great introduction to probability. You could talk about what goes in a taco. What ingredients it would take, alternatives, how many different types of tacos are there?

Project Based Learning

I have been looking at implementing Project-based learning the past year.  I wanted to do a full chapter or section that implemented project based learning, but felt that Algebra 2 is difficult for students, but I think I found the solution.

The project that I have had the past few years is students create their own dice (2 years ago) and 3D print their own dice and find the theoretical and experimental probability (Last year).  I thought this was a good end of the chapter project.  

Now I want to make this my project based learning chapter.

Key Knowledge, Understanding, and Success Skills

I want students to work in groups of 4 and use collaboration skills for them to work on the project together.  The standards that they will cover (using the Nebraska Math Standards):

MA 11.4.1 Representations: Students create displays that represent data.

MA 11.4.2 Analysis and Applications: Students will analyze data to address the situation.

MA 11.4.3 Probability: Students will interpret and apply concepts of probability.

Challenging Problem or Question

The students challenging problem is to create a new dice for a nearby casino and find a dice where the "house" wins over 50% of the time, but not more than 60%. Students are to create a presentation with their dice and their data to a selection of students and teachers. Students will share with other students their presentation and questions.  Students will have a chance to critique and revise before doing their final presentation.

The problem I am having is making their learning public.  How can students take their learning global?

Debates in Math

I have been looking over my Algebra 2 curriculum to find places where I could include debates in the math classroom.  I was trying to find ways of including more formal debates where students take in all of the information.  My goal is to give students a day to find all of the information, that night have them make a poster, meme, or infographic to demonstrate that learning.  The next day students will present their arguments to the class in a fishbowl activity.

1. The first would be about Functions, Equations, and Graphs.  Students would be split into groups of 2 and one would be graphs the other would be equations.  Students would have debate on which is a better demonstration of functions equations or graphs.
• Students would then have to produce a poster or meme.
• Then the next day students would argue about which is better.  A list of questions that I will pose to students to get them talking will be added later.
2. The second debate would be about Quadratic Functions and Equations. Same concept on groups of two but it would it include the best way to solve quadratics.
• This time students will be placed into groups:
• Completing the Square
• Quadratic Formula
• Graphing
3. The last one I will incorporate is probability.  I'm going to go a little off script and give them an article to read and then talk about analyzing data.  Is the article true or not students will have to determine if the samples and survey are sound. 

I will add more as I become more proficient in dealing with debates and keep you posted as we have them in class.

#7: 3D Printing: Weird Dice Part 1

I found this lesson: https://artofmathstudio.wordpress.com/2015/10/09/weird-dice/

By Frederico Chiavlo, he created a lesson called Weird Dice. This is a great way to get new and different dice that the students make for our upcoming statistics unit. Our 3D printer is down at our school, but found a great replacement at DoSpace in Omaha. It was a great place and would be great to take students there.

We used Morphi app to make the 3D dice, it took quite a bit of effort for the students to figure out how to make it they way they wanted. Otherwise the app works great on the iPad.

Some student examples are here: 

The next step is to get students to fill out the form on Chiavlo's website.

Forensics in Math

I have been looking for ways to get students to use math that we learn outside of the classroom and I know that some of my students love mystery books and crime scene investigation shows.  So I have obtained some extra activities for my students to do that includes some forensics work.  Here are some ways you can include forensics in math.

• Probability is the chance of something occurring.  It is calculated by dividing the number of favorable outcomes by the number of possible outcomes.  The theoretical probability of how a coin will land after being tossed 100 times is half. 50/50, if you actually flip a coin a 100 times, you will find the experimental probability, which may be 60 heads and 40 tails, whatever your result.
• Ask students to define probability.  How high does the probability occur for a conviction to occur?
• Regardless of their specialty, scientists use mathematics to help describe the world around them.  Forensic investigations use average growth rates of various structures in the human body, such as hair and fingernails, to decode clues left at a crime scene.  When using average growth rates, it is important to pay close attention to the units of measurement being used.
• To illustrate how blood types are inherited, show a cross between a mother who has blood type O and father who has type AB.  The mother can contribute either an A or a B allele.  So this couple could have children of either blood type A or B.  Point out that the child would have a probability of 1 in 2 of having type A blood.
• Explain how the laws of probability are used in determining the probability that a particular person's blood will match the blood found at a crime scene. 

There will be more activities included in the future.  Right now these are just a few questions to have your students use forensics in these questions.

How could you incorporate this in to your classroom?