Quadratic Equations & Rockets!

Oh, I wish I could have some of the class pictures here! You should see their smiling faces! You've never seen students so eager to find the vertex of a parabola. This is how it rolled for me:

1) Practice, practice, practice quadratic equations.

2) Practice quadratic story problems about with height, distance, and time.

3) Practice some more and tell your students that they will be building rockets and applying quadratic techniques to discover how high their rockets fly!

I used the Teachers Pay Teachers activity found here. I made some minor adjustments like forgetting about the water bottle rocket. We used a custom PVC launcher with a sprinkler valve and electrical trigger. I also allowed students to design their own rockets as long as the tube was the dimension of the launcher.

The gist is this: based on how long your rocket flies you can determine how high it goes. I did have to disqualify one rocket that "floated" back to the ground so the equation wouldn't have applied there. The winning rocket went over 1100 ft with only 70 lbs of pressure in the launcher! Hint: Make sure students seriously REINFORCE the nose cone if you use this type of rocket.

This activity was amazing. All my classes are now begging to do it.

Sample student rockets. Check out those various designs.

Eagerly awaiting a launch.

Students pressurized the launcher for their own rockets. We used 70 lbs.

Factoring by Grouping

My room was practically silent while students worked on this factoring by grouping activity because there was so much thinking going on. I began by dividing students into pairs. The factors from the problems led to a block letter on the bottom. This was a challenging activity for my class so I allowed them to share answers with each other to be able to complete it in the hour. The activity can be found here.

Absolute Value II

Students loved this project because it involved social media. They had to come up with a question with a numerical answer that people don't know. Ex: What is the average human life span? How old was the oldest sea turtle? How hot is lightning? How many seconds in a year? They then posted that question via Google Forms on social media. They collected the responses and graphed the guess as the independent variable and how far away it was from the actual as the dependent variable. We had amazing absolute value graphs every time! They were surprised. It led to a great discussion. They also had to share pertinent information about the function such as intercepts, translations, domain and range, and the equation of the function.

Math JENGA!

My students are begging to do worksheets. Why? Because they get to play JENGA while doing them. 

I invested in 7 JENGA games this summer (I figured 28 students could be divided into 4 per game). Because I teach high school students I wanted to add some challenge to the game. I divided the blocks into six different colors and created dice with those same colors. 

Here is how it works in my classroom. I print out a worksheet for every group. I then cut the problems into strips. Every group gets a worksheet in the form of strips and put them face down. Individuals in the group take turns picking a problem. Everyone in the group does the problem on a separate piece of paper. Once they confer and agree on an answer the student who picked the problem rolls the dice. If they roll red, then they have to move a red block. And repeat! I collect the papers of work at the end for grading.

My students love this. Especially when I allow 5-10 minutes of free play at the end. If a tower falls, I am always pleasantly surprised when a group rebuilds it so they can keep working on their problems. 

Graphing Absolute Value Functions

Wow my students were rusty with graphing after the summer holiday. At first, they wanted to grab graphing calculators or use a table for every function. With a little guidance, this visual found here really helped my class use transformations of the parent function of the absolute value of x to graph. We also highlighted the domain and range. Interval notation was new to this class so I plan on using it in depth in future lessons as well.

Skittles Absolute Value Function

This activity was originally found at Growing Exponentially. You can visit it at https://growingexponentially.wordpress.com/2013/03/18/absolute-value-project/

There is nothing like a jar full of rainbow candy to get students' attention. Over a period of three days I had students guess how many Skittles were housed in the jar. I allowed them to pick up the jar, shake the jar, and measure the jar. The only thing they couldn't do was dump the candy out and count it. Wow!

Once I had enough data I sat down with my class and asked what they wanted to know about the Skittles activity. I thought the first thing they would ask was "Who was the closest?" I was so wrong. They wanted to know the volume of the jar and the volume of an individual candy. The students wanted to actually calculate the answer! I allowed them to try and they realized they didn't take into account the volume of the empty space between the candies.

Now it was time to lead them where I wanted them. How many candies were there? 1471! How do we determine who was the closest? Should it matter if they guessed above the actual number? Absolutely not! We started calculating by rote how close each individual student was. Well, that's obnoxious so I opened a spreadsheet. I couldn't believe how patient the students were while I populated it in front of them. They loved seeing how much every one guessed.

After creating the spreadsheet I asked the class what they thought a graph of the data would like. EVERY SINGLE STUDENT said it would be a random scatterplot with no pattern. Now to select the data and hit graph. Voila!

Look at that beautiful absolute value function!!!!! The students were shocked! Now for the discussion of why. This will lead into graphing absolute functions tomorrow.

Math Projects & Burritos?

Guess what? IT'S NOT A BURRITO!

One of my favorite times of the school year comes at the end. I give an open-ended math project with the only specifications being 1) It must be math related, and 2) A minimum time requirement of three hours. One of my cute Secondary Mathematics II students made this adorable burrito cake. Yes, cake! The tortilla is fondant, the olives are gumdrops, the peppers are licorice, the cheese is air heads, the lettuce is coconut, and the sour cream is frosting. How freaking adorable? And she turned it in on May 5th, Happy Cinco de Mayo.

So here's the question? Why does this cake-burrito qualify as a Secondary Math project? Let me know what you think.

Descartes' Rule of Signs

My little guy is four years old. He saw me working on my latest doodle notebook page and wanted to help. I think I have a budding mathematician in the house.

That being said, here is a nifty little page that allows you to count and discuss sign changes for f(x) and f(-x). It even has a spot allocated for the  number imaginary numbers if you want to go down that road.

You can find this resource at

https://www.teacherspayteachers.com/Product/Possible-Rational-Zero-Theorem-3779489

Solving Rational Equations

Why are fractions so scary? And then we throw in variables and later factoring and it throws the secondary student for a loop. Today I started with the basics. Method #1: Get a common denominator, simplify, use cross products and solve for x.
Method #2: Find the common denominator for every term in the equation, multiply both sides by that common denominator, distribute and cancel common factors, and solve for x.

What method do you like best?

Geometric Sequences and Series Doodle Journal

I tried these with my Secondary Mathematics III class today and they loved it! They followed along solving the equations and story problems with me. Then they put them in their journals for later us.

This source can be found at https://www.teacherspayteachers.com/Product/Geometric-Sequences-and-Series-Doodle-Notes-3753304.

I'm a believer!

Trying Something New!

Do you ever start on a new project and find that it leads you down a bigger road then you ever expected? Well, that just happened to me.

I have used math journals in my high school math classroom for almost 20 years. While the input varies year by year, it really has been pretty consistent. Because of that fact, I decided to digitize the entries and have them ready for my students...kind-of a hybrid scaffolded note and graphic organizer. My favorite style is doodle notes!

As I created one page, I couldn't wait to create another. I'm an addict. You can find my newest projects at: 

https://www.teacherspayteachers.com/Store/Algebrasaurus. 

I can't wait to see where this journey takes me!