3 Act Task: Bacteria Growth

Act 1:

How many bacteria are there in 300 minutes?

Act 2:

• Pause the video at 0:00 time frame. There is 1 bacteria at 0 minutes.

• Pause the video again at 0:01 time frame, when there is 2 bacteria at 38 minutes.

• Pause the video again at 0:04 time frame, when there is 4 bacteria at 88 minutes.

• Lastly, pause or show a screen shot at 0:05 time frame, when there is 8 bacteria at 114 minutes.

Act 3:

There are a total of 471 bacteria in 300 minutes.

Extensions:

• When does the number of minutes and bacteria the same?
• How many bacteria would there be in 500 minutes?
• When will there be 1,000,000 bacteria?
• How else could we represent this information?

Exponential Growth through TAG

After a great day of teaching exponential growth and decay, I felt like my students really knew the topic forwards and backwards. We did this Desmos activity as some students were finish up their MAP test.

It was a great Desmos activity, almost all the students wanted 100$ at the beginning and very insightful finishing questions at the end and I was pleased overall. Later that day I began to wonder if students would notice if something was exponential or not exponential if I gave it to them. I thought to myself how could I find a question that I could do that would model exponential growth or decay.

Then I found this game: 

I wanted an activity that got students out of the classroom. Since I have two periods at the beginning of the day we did inside in the gym, but the last time we went outside and played it on the Football field.

If you didn't watch the video, it is a simple game where one person is a shark, they yell "Minnows come out to play." the minnows job is to make it to the other side without getting tagged. The sharks job is to tag people, once a minnow is tagged they become a shark.

Here comes the math:

I had them start out with one shark, I made all the others line up and asked them how easy it was going to be this time down. All of them were confident that they could make it down without any real sweat, then I asked them what about the 5th time down? I was surprised how most of them thought it was still going to be easy, thinking of it linearly instead of exponential. We played it through the first time here are the pictures and the charts we did at the end.

Here is one of the charts that I made after each run down and back.

After all the students were tagged on the 4th down and back with ease. I asked them to estimate how many would get tagged on the fourth time back. Then I asked about the whole school, how many down and backs would there be playing with 576 students?

We came back after playing 2-3 more times. Then asked them how you could write an equation to model the graph. We did a short mini-lesson on finding equations of a exponential graph.

Children's Books for Algebra 2

Children's books are are a great way of introducing concepts and to help build a classroom community.  Students love sitting together on the floor and listen to a teacher read aloud a picture book. Letting a picture book and prior knowledge give them a hook into the curriculum.

Here are three great books to help teach some Algebra 2 concepts.

Follow the Line
by Laura Ljungkvist

This picture book goes from the city to farms. Each scene contains questions designed to get children counting, thinking, and observing.  Children would count 5-6 times on each page.

In Algebra 2 class I am going to read aloud the book, but instead of going over the questions in the book I am going to ask different questions.

What types of lines do you see?
Which ones of these are functions?
Which of these are not functions?
What type of slope do some of these lines have?

The Man Who Walked Between the Towers
by Mordicai Gerstein

This picture book is about Philippe Petit who tightrope walked across from one World Trade Center tower to the other. He performed tricks, walking, and dancing for an hour. The book has great and different types of numbers you could number talk during the read aloud.

The way that I am going to use the book in Algebra 2 is to get students use to the idea that mathematical models illustrate the behavior of real world situations.

During the talk I am going to ask the students at specific times to model different situations in the book and ask them about the math being used.




Lifetime: Amazing Numbers in Animal Lives
by Lola M. Schaefer

This book talks about the different animals what can happen in their entire lifetime.

An example, in one lifetime an alligator will build 22 nests and lay 550 eggs.

In Algebra 2 we are going to use this book to introduce students to exponential expressions and how they can be written in different ways.  We are going to talk about If one alligator lays 550 eggs, and then one of those alligators lays 550 eggs. How many alligators in twenty generations?

Financial Literacy in Math

Financial literacy is the ability to understand how money works in the world: how someone manages to earn or make it, how that person manages it, how he/she invests it, and how that person donates it to help others.

I believe that my past Algebra 2 students understand the material.  I don't think that they could go out and apply those concepts (for example in a job environment.)

Looking at exponential functions, for example, students can look at the depreciation of a new or their old car in terms of re-sale value.  Students can enter the data and draw a scatter plot on a sheet of graph paper.

If students didn't have a car they could search for one.  For example I searched my wife's car a 2015 Chevy Cruze.

The MSRP is $16,170

After the first year it depreciates: $7,904
After the second year: $1,200
After the third year: $1,000
After the fourth year: $875
After the fifth year: $675

Students could then plot this and look for the exponential line of best fit through that data on Desmos. You could then prompt follow up questions, what will the value be 8 years from now? Is $8,456 a good price now for a 2015 Chevy Cruze?

For slope and finding slope of a line, give them real-world data to extrapolate.  This data below came from the Nebraska Department of Roads.

What is the slope of each year from January to May?  What is the slope of each year from May to December?  What causes this?

What do you expect June to look like? Can we determine what the price will be December?

Having students know the concepts is one thing.  Having them use the concepts beyond the classroom is what we are looking for as math teacher.