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:

STEM – Newton Knew Forces (F=ma) (Mini-Math Lesson Algebra/Algebra2)

Yesterday’s lesson was related to the motion of a pendulum and it’s graph as its swing was impacted by friction. Today we are looking at force, using a pendulum as the push (force) on an object (scooter). This is a fun little experiment that you could do with students, and in this time of home-schooling, it would be a relatively easy experiment for parents to set up with their kids. You just need some rope, a bucket full of water or even a jug of water to use as your pendulum, a door frame to swing the ‘pendulum’ from, and then a scooter or something with wheels that can move when pushed (so a wagon or a skateboard). You will also need a measuring tape, some weights to add to the scooter (three different weights), and something to mark start lines and height release for pendulum.

If it’s already sounding like too much work, don’t worry!! There is sample data in the activity, so you can still explore the mathematics if you don’t have the time to set up!!

The idea is to set up the pendulum so that it hangs from a door-frame/beam at the height of the scooter (so place scooters back end directly at where the pendulums lowest point so that the pendulum will hit the scooter and push it). Measure the weight of the pendulum bob (bucket/jug of water) before you begin. Measure the weight of the empty scooter. You then decide on a release height for the pendulum (will be the same height for each release). Mark the start position of the scooter (back end), position the scooter (empty) and release the pendulum from the designated height. It should hit the scooter and push the scooter. You then measure the distance the scooter traveled after it was hit (so from the start position) to where it ends (be sure to measure at the back of the scooter, to be consistent with the start position). The next step is to add some weight to the scooter (make sure it is secured on so it doesn’t fall off when pushed!). Repeat the experiment, record the distances and weights.  Do this for at least five different weights of the scooter – empty to heavier. (Don’t worry – I have included the PDF as well with all the detailed instructions).

Once data has been collected,then you will graph the data and look at how force and mass impacted acceleration. The goal of this experiment is to show that the rate of change of momentum of an object is proportional to the resultant force acting on the object and in the same direction.  Students will explore their table of data, make scatter plots, look at the relationships. The experiment has to do with Newtons’s 2nd Law, where Force=mass x acceleration. There are a couple things to keep in mind:

  • The pendulum weight represents the force (because you don’t change the drop height)
  • The scooter weight is proportional to the mass (because gravity is constant through the experiment)
  • The average distance the scooter moves is proportional to the acceleration
  • Weight is used in the experiment instead of mass, but for this experiment it is acceptable to deal with weight because the force of acceleration is constant throughout the activity. The weight in this activity is always proportional to the mass.

This activity comes from Fostering STEM Education with Casio Technology, Casio 2013. I have converted part of the activity (the pendulum component) to a ClassPad.net activity, which is shared in the link below and also overviewed in the video below. I have attached the complete activity, which includes a wagon-pushing activity. The PDF is the whole activity with a lot of description and calculator suggestions, as well as sample data.

  1. STEM – Newton Knew Forces (F=ma) ClassPad.net Activity
  2. STEM Newton Knew Forces (F=ma) (PDF)
  3. Video Overview – STEM Newton Knew Forces (F=ma) Mini-Math Lesson (Data & Regression)

 


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 – Inertia, Force and Velocity – Newton Knew Inertia (Mini-Math Lesson)

I wanted to focus on some STEM lessons this week, using ClassPad.net, since it is so great for collecting data, showing statistical plots, and it’s ability to quickly change things to see the impact and more importantly, to do everything in the one activity (i.e. calculations, data collection, graphs, and explanations). So, I am going to share a different STEM focused lesson each day this week.

STEM is an acronym that stands for Science, Technology, Engineering, and Mathematics. It’s really about ensuring educational experiences that blend these four areas, so that learning is not in isolation, but rather a connected learning on real-world concepts, that require students to problem-solve, collect data and analyze results, and communicate their findings and use critical thinking. There are many definitions and reasoning behind the push for STEM in education – here is one article that I think gives a good overview if you feel you need more information.

For me, STEM means learning and problems that are real-world, that students can actually do or experiment or relate to, that require them to use science, math, technology and engineering in realistic ways or situations. It’s looking for and collecting evidence, and then modeling this information, and applying understandings of the subjects to make sense or make decisions. The activities I am going to focus on this week come from Fostering STEM Education with Casio Technology, Casio 2013. It is a resource with some really great real-world problems and explorations, and these can be done by students or there is also sample data provided if you don’t have the materials needed to do the experiments yourself. So you can make these activities as hands-on as you want, but if not possible, still have the great discovery and conversations and critical-thinking experiences needed for deep learning and application of STEM concepts.

Today’s activity is one that you could very easily do with students (and it even adheres to social distancing rules!).  In the image above, you will see it involves six students – five to stand at designated and one to push the object in a straight path.  This activity explores how the amount of push impacts inertia and acceleration. There is an object that starts from static position (so a disc (like a frisbee) or ball), and then a student pushes it in a same line with as much consistent push as possible, and as it passes student at the set up positions, they time when the object passes.  The force is changed for three trials and then students compare the data in several ways. So, a fun activity, but, if you are unable to do this with all the materials, or students, then you can use the sample data provided.

Here is the link to the activity, both the ClassPad.net version and the PDF that can be used and a video overview:


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:

Women in STEM – Celebrating Women’s History Month

Yesterday it was announced that mathematician Karen Uhlenbeck . from the University of Texas at Austin, had been awarded the Abel Prize 2019 “for her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics.” Impressive in itself, but more impressive because she is the first woman ever to be awarded the prize (The Abel Prize was established on 1 January 2002. The purpose is to award the Abel Prize for outstanding scientific work in the field of mathematics. The prize amount is 6 million NOK (about 750,000 Euro) and was awarded for the first time on 3 June 2003).  A fitting tribute and accomplishment during this month, which happens to be Women’s History Month, which celebrates women’s’ contributions to society and history.

Seems only appropriate to dedicate this post to other significant women and their contributions to STEM, especially as there is still such a need for more women in the STEM fields of science, technology, engineering and mathematics. The more young girls and women see what others have done, the more they are inspired to pursue futures in these fields. I’ve done a little research and pulled together a few names to share in this post. By no means is this an exhaustive list, rather a list of women that sparked my interest, particularly in mathematics, since this has been my personal passion for most of my life. There are many more out there, but the idea of celebrating Women’s History Month is to realize how important, and often unknown/hidden, women have been in many of our STEM advances and historical events.

  1. Marie Curie the only woman to have received TWO Nobel Prizes (one for Physics and one for Chemistry).
  2. Gertrude B. Elion another Nobel Prize winner in Physiology, whose work contributed to many new drugs, including AZT, the aides drug
  3. Augusta Ada King-Noel, Countess of Lovelace – credited with being the first computer programmer!!  Very cool.
  4. Barbara McClintock – Nobel Prize winner in Physiology, credited with showing that genes turn certain physical attributes on and off.
  5. Rachel Carson – credited with creating the EPA (Environmental Protection Agency) as a result of her writings and work.
  6. Radia Perlman – commonly referred to as ‘the Mother of the Internet” for her algorithm (STP) that basically allows the Ethernet to handle massive networks
  7. Rear Admiral Grace Hopper – credited with creating the programming language C.O.B.A.L
  8. Lisa Meitner – part of the duo that discovered nuclear fission (fascinating history here about her being ignored in the awarding of the Nobel Prize)
  9. Katherine Johnson – her mathematical computations influenced every major NASA space project – wow!! (See the movie Hidden Figures)
  10. Florence Nightingale – helped pioneer the field of applied statistics and created a version of a pie chart called the ‘coxcomb‘. Totally new information for me!!

I could go on and on – it is amazing once you start looking, how many women have been pioneers, ‘firsts’, and influencers/contributors to math, science, engineering and technology. It’s exciting that so many are finally being recognized. Inspirational. There are lots of interesting articles and synopses out there that can spark student interest and maybe inspire some of our youth as well. Maybe spend some of this Women’s History Month exploring with your students or just on your own. I know I have been really surprised and amazed and plan to keep researching.