STEM – Floating Through Air (Mini-Math Lesson – Algebra 2)

This weeks final STEM activity is also a relatively easy one for students to do on their own. And it is a lot more exciting and realistic to collect your own data and analyze the results than to just use given data. Makes the math more ‘real’. However – as with all the activities this week, there is provided sample data.

Today’s activity has to do with falling objects and how gravity and area have an impact on the resistance and acceleration of that object as it falls. Materials needed are pretty basic – a book of some sort and a piece of paper, measuring tape on a vertical wall, and either a stop watch or a camera (video) to record the fall of the object when dropped from a 6 foot height. Video probably works best because you can slow it down and look at the height frame by frame.  At least two people would work best.

The underlying understandings for this activity have to do with gravity and an object falling towards the surface of earth. If gravity is the only influence acting, then acceleration is always downward and has the same magnitude for all objects. An object falling toward the surface of Earth will fall 32.18 fee per second faster every second (32.18 ft/s^2). Students will explore how area of an object increases the drag, which than impacts the terminal velocity (so parachutes have a lower terminal velocity than say a bullet).

Students will first drop a book and record it’s height as it falls. Then, they will drop a piece of paper from the same height and record it’s height as it falls. They will then fold the paper, and repeat the drop for each fold, which is decreasing the area of the paper and thus should decrease the terminal velocity. They will compare the data by making scatter plots and consider when the falling object might have a constant terminal velocity (speed). They will look at different parts of the graph to see where the data is in a straight line, which indicates when the force of gravity is equal to the air drag force.  It’s a fun little experiment and relevant as well.

This activity is adapted to ClassPad.net from the Fostering STEM In Education with Casio Technology, Casio 2013. The links below include the ClassPad.net version of the activity, the PDF version of the original activity, that includes more description and background information as well as calculator tips and strategies, and then a video overview of the ClassPad.net activity, showing how to create the scatter plots, zoom in and out with the plots to look for when the data is becoming linear.

  1. STEM – Floating Through Air (Scatter Plot, Drag, and Gravity)
  2. STEM Floating Through Air (PDF)
  3. Video Overview – STEM: Floating Through Air (Scatter Plot, Tables, Drag, Gravity)


The tool being used in these mini-math lessons is the FREE web-based math software, ClassPad.net.

Remember – if you want to save and/or modify any of these activities, create a free account.  Some useful links below:

STEM – Conservation Is Not Just About Recycling (Mini-Math Lesson On Energy)(Bouncing Balls, Data & Regression)

Another STEM experiment today that students can easily do with just a few tools/materials:

  • Four different types of balls (so think tennis ball, basketball, ping-pong ball, racket ball, golf ball….)
  • Paper to cover an area of a wall so you can put measures on the wall (or use tape, or tape a measuring tape to a wall vertically).  We are going to be dropping the balls from given heights and record the height of the first bounce, so need to measure vertically.
  • Measuring tape to measure and mark the wall in 1-inch markings up to 6 feet

The idea behind the lesson today is to explore the difference between expected kinetic  energy and observed kinetic energy. Students will record the data of the balls dropped from different heights and their rebound and look at different scatter plots (Drop Height, Rebound) and (Rebound Height, Drop Height), find regression lines and analyze the meaning of the slope in the context of the situation.

There is also an extension activity, where they look at successive rebound heights of a balls bounces when dropped from a given height. This time they will see an exponential relationship (versus linear) and talk about what this means in terms of energy. The whole experiment is exploring the conservation of energy and momentum.

In both parts of the activities, students are encouraged to use their own materials and collect their own data – this obviously makes things a lot more fun and engaging. However, sample data is provided as well if they don’t have the materials. There is even a ball-bounce simulation provided for the second part (successive bounces), using the ability to insert images into ClassPad.net and sliders to control movement.

The activity used is adapted from an exploration in Fostering STEM Education with Casio Technology, Casio 2013. I have made a Classpad.net version here, link provided below, and also provided the PDF of the original activity which goes into more detail and provides some hand-held calculator tips and suggestions. The link to the PDF is also below along with a video overview of the activity in the ClassPad.net version.

  1. STEM-Conservation is NOT Just About Recycling (ClassPad.net Data & Regression)
  2. STEM Conservation Is Not Just About Recycling (PDF)
  3. Video Overview – STEM – Conservation is NOT Just About Recycling (Data Regression Simulation)


The tool being used in these mini-math lessons is the FREE web-based math software, ClassPad.net.

Remember – if you want to save and/or modify any of these activities, create a free account.  Some useful links below:

Mini-Math Lessons – Systems of Equations

(The flowers have nothing to do with the math…just thought we could use a little beauty!!)

Today I am in a sense ‘cheating’ again, as I am using a previously made video and activity to share today. It seemed to fit in well not only with the advanced Algebra focus of the week, but also in light of the current pandemic crisis we are in and importance of our medical experts and workers who are giving so much every day. The activity shared today is an activity called “Not Enough Doctors”, and uses real-world data to explore our future supply-and-demand of doctors. What I like about this activity is that you will experience several different functionalities of ClassPad.net – i.e. data/statistics, graphing, text, equations, tables. It is a nice multiple-representation activity and allows students to see different ways to look at data and display data and answer questions about that data. A really important skill.

Here is the link to the activity and accompanying video:


The tool being used in these mini-math lessons is the FREE web-based math software, ClassPad.net.

Remember – if you want to save and/or modify any of these activities, create a free account.  Some useful links below:

Mini-Math Lessons – Quadratic Equations & Multiple Representations

I am cheating a bit today and using a lesson I created a while ago, along with the accompanying video. You will note that this video support is a bit longer than usual for these mini lessons because I am really using many different aspects of ClassPad.net and going into a bit more depth with them as I talk through this activity. We will explore data, scatter plots, fitting curves, using the connected functionality of ClassPad.net to do column calculations quickly. There’s graphing, equations, calculations, curve fitting and exploring of real-world context, i.e. finding the dimensions of a garden, which means thinking about dimensions. This lesson has a lot!

Here are the links to the activity itself as well as the support video:

  1. Quadratic Functions – Area of A Garden
  2. Video Overview of Quadratic Functions – Area of A Garden

 


The tool being used in these mini-math lessons is the FREE web-based math software, ClassPad.net.

Remember – if you want to save and/or modify any of these activities, create a free account.  Some useful links below: