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 – Pendulum Exploration – Mini-Math Lesson (PreCalculus)

Today’s STEM lesson is at a PreCalculus level, where we are exploring the graph of a a pendulum swing. The image to the right is a short GIF of a pendulum swinging. It’s hard to tell because this is a short GIF, but the pendulum will swing because of gravity, over the center point and, if there were no air resistance friction, this swing would continue indefinitely. The motion of a pendulum has been traced before by others, and forms a regular periodic curve, and because of the damped motion (slowed by friction), the motion of the damped pendulum can be modeled by a sine function with a decreasing amplitude over time.

The activity today explores the proportion that the amplitude is decreasing, given by an exponential function. Students will graph the function and explore the position of the pendulum at given times. They will explore the swing positions of the pendulum using the graph and ratio of the changes in the peaks.

We will explore a bit more with pendulum and force in tomorrow’s STEM lesson as well, with a focus more on the force of a pendulum pushing on an object as it hits it.

Here is the link to the activity and also the 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:

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:

Mini-Math Lessons – Middle School Equivalent Expressions and Exponential Expressions

If we are thinking about equity and getting technology in the hands of students, scientific calculators are powerful tools that can support math discovery and exploration (except graph, though the fx-991EX even does that!) and are really inexpensive (between $10 – $20). This week I am going to be showing some of the capabilities of scientific calculators that I don’t think many people realize they can do – i.e. equations, expressions, inequalities, and statistics.

Today I am going to share two  activities that utilize the fx-300ESPlus2, though you could use these with any scientific calculator from Casio (or graphing for that matter). Both these activities focus on expressions with a goal of understanding what expressions are, equivalent expressions, the role of variables. The first activity, It’s All the Same, is about using properties of operations (associative, commutative, distributive) to explore equivalent expressions. The calculator is used as a verification tool, where students use stored values for given variables that then allow them to check that different expressions yield the same result. The second activity, The Variable Game, focuses on exponential expressions, and helping students apply properties and write exponential expressions with given parameters. They use the calculator to store variable values and then use these as either the base or the exponent to try to create expressions that fit specific criteria. This allows them to get a better understanding about exponential rules and working with whole number exponents and bases. Both activities, as you will see, include standards, warm-up exploration questions, suggestions for student discussion and ways to extend. Each activity has an application and then some practice problems.

Here are the links to the two activities and a video overview that goes through some of the functionality of the fx-300ESPlus2 that is needed in the activities.

  1. It’s All the Same
  2. The Variable Game


Be sure to visit Casio Cares: https://www.casioeducation.com/remote-learning

Here are quick links:

Mini-Math Lesson – Proportional Reasoning: Juggling Peppers (Scale, Distance, Application)

We’ve been focused on proportional reasoning all week. Hopefully you have noticed that rarely were any of the activities the ‘process’ of solving proportions – i.e. ‘cross-multiply then divide’. While that may have come up at some point to help answer a question, the activities really were about using ratios and proportional comparisons in real situations to make decisions or model a situation. Today’s lesson is more of the same, and I would say fits in the category of an application. It’s not straight forward – instead, students have to use their understanding of proportion and scaling to come up with their own scale for a situation.

The image in this activity is a fun one – a chef juggling peppers. For those of you who think this is unrealistic, I will tell you that my husband (an amateur chef for sure) juggles whatever produce he can find, be it eggs, vegetables or utensils (thankfully not knives). The activity starts with an image on a coordinate grid and the first thing students are asked to do is come up with reference points that would help them make an estimate of realistic distance from chef’s shoulders to his head. This involves so much more than just looking – i.e. where on the head? Do you include the hat? Where on the shoulders? What is an average distance? Would I need to measure people around me to get a more realistic measurement? Once they determine this realistic distance, then they look at the y-axis and determine what an appropriate scale would be (i.e. how many inches does each mark on the y-axis represent?). The cool thing about this is different students will have different interpretations, so you are not going to get the same answer, which leads to amazing discussions about reasonableness and approximations and proportion.

After students determine there scale, then they actually look at the peppers and determine the height each pepper is above the chef’s hands. This again is more involved than it looks. Where do they place the points on each pepper so that they are consistent? What distance are we measuring? Where on his hands are we measuring from? How does the scale enter in to our calculations?

It’s a fun problem and there is no one ‘right’ answer, which to me is the beauty of this because students are forced to justify their choices and work based on their own understandings and interpretations of the situation.

Here is the link to the activity and also the video overview of the activity.


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: