Lesson Plan for Projectile Motion and predicting where objects will land. Student lab sheet (includes how to find uncertainties in the predicted landing spot).
Projectile motion is studied in most physics classes, since projectiles are so common in our lives. The idea that the parabolic trajectory of a thrown or kicked ball is due to the combination of a horizontal motion of constant velocity with a vertical motion of constant acceleration (free fall) can be eye-opening for anyone who has wondered why things move along those curves in the first place!
For those who want a more detailed explanation of the math behind projectile motion, check here. A second video looks at the change in trajectory when air friction is added.
For those who have access to the Internet and want computer simulations, check this PhET simulation you can experiment with.
Lab sheet for students for Radioactive Half-lives (for introductory class) More advanced lab sheet for Radioactive Half-lives
Radioactivity is one of those words that largely scares people. It isn't always a bad thing, in fact our own bodies have radioactive materials in them! This term refers to the process of certain atomic nuclei spontaneously and randomly breaking down, where the parent nucleus decays/splits apart into other pieces. The 'stuff' that comes out of that decay process is radiation. Most radioactive processes result in one of three types of radiation being emitted from the material: alpha, beta, and gamma particles.
Alpha particles consist of 2 protons and 2 neutrons (a helium nucleus). Beta particles/rays are electrons coming from the nucleus, as a result of a neutron decaying into a proton and electron (yes, neutrons are radioactive). Gamma rays are high-energy photons coming from the nucleus.
One of the key properties of radioactive materials is their half-life. This is the time it takes an initial sample of a radioactive material to have half of that material decay. So if a half-life is 1 year, a 10 kilogram sample of the material will decay and about 5 kilograms will remain. In another year, only around 2.5 kilograms will remain. In another year, only around 1.25 kilograms will remain, and so on. Half lives can ranges from fractions of seconds to over a billion years!
This lesson requires any large number of 2-sided items, such as coins or even a deck or two of playing cards. If you have certain candies available, such as M&Ms or Skittles, those can be used and students can eat them once done. Each time you have a cup-full of the items (it is ideal to have around 100 items for a small group of students to use as their 'radioactive sample'), that would represent one decay cycle over a half-life period. One side of the coins or candies represent an atom that decayed, and the other side means the atom is still 'alive.' Students count and keep the alive atoms, spill them again, and repeat until all atoms have decayed/died. Graphing the number of alive atoms to the spill number (i.e. how many half lives have gone by), students get the curve scientists use to determine how old certain fossils and other items are when they find them. It is an interesting procedure and method for doing this type of work!
Lesson plan for Extracting your own DNA with simple supplies Video showing how to extract your DNA
Every cell in our body has DNA, the molecule with our genetic information. This is at the heart of the study of genetics, and determines to a large degree who we are and what we look like. Because it is a central topic in any biology class, having a way for students to physically experience it and literally see their own DNA can be not just informative but also inspirational and one of those moments they will remember about their schooling! If you have the materials to do this, it is worth it!
If your students have access to the Internet, this is possible. Video series explaining and showing what mathematical modeling is.
Open-ended problems are real-world, complex problems that do NOT have a SINGLE correct solution. Instead, these are problems that require a mathematical model (a set of equations) that address a more complex situation than what we normally would give students, and must use assumptions relevant to the problem in order to begin developing the model. These are like the actual problems professional applied mathematicians develop. Depending on the assumptions one starts with, viable solutions will be different from person to person.
There is a competition that allows students to have a chance to try this process, and attempt to develop a possible solution to open-ended problems. This site has all sorts of resources, including an Archives page that has numerous examples of this type of problem AND the top six solution papers for each problem; and a Resources page with booklets, videos, teaching guidelines, and examples of what math modeling is and how to approach it.
For high school/secondary aged students, these types of complex problems and the process of developing mathematical models based on assumptions, data and other evidence, can expose students to actual real-world problems that can only be approached in this manner, and allow students to apply what they've learned in STEM classes over the years in a more practical way.
Lesson plan for using a pendulum to determine acceleration of gravity, g, and Mass of the Earth. Example of lab sheet for students.
A pendulum is one of the simplest devices to build and use in an experimental activity. And the main property of a pendulum we can measure and use is its period, or the time it takes a pendulum mass to be released, swing across, and then back to where it started. It turns out that by knowing the length and period of a pendulum, one can calculate the acceleration due to gravity, g. For Earth this is g = 9.8 m/s^2 at its surface. This value is also the measure of the strength of the gravitational field of the Earth.
A bonus calculation one can do once we have a value or g is to determine the mass of the Earth! This is because the gravitational acceleration depends on the mass of the planet, g = GM/R^2, where M is the mass of the earth, G is the gravitational constant, and R is the radius of the earth. These values are provided in the lesson plan.
It is a fascinating idea that the mass of an entire planet can be determined using, effectively, a piece of string!
Link to lesson plan for measuring densities.
Density is a property of materials which can be vital in determining an unknown material. This is because each material has its own unique density value.
Density is defined as the amount of mass packed into a given volume of space, or Density = Mass/Volume, D = M/V. This is therefore a relatively easy value to determine in the laboratory, if one has a balance or scale to measure mass, and containers such as beakers or graduated cylinders for measuring the volume of displaced water when an object is put into the water. Here is an example of a table of elements, arranged from lowest density to highest density. Here is a extensive list of densities for different materials.
It can be fun to have students to take some small number of objects, determine their densities, and then find the closest match on these lists to see if they can identify what the object of made of!
