Math

Introduction

Math students are typically introduced to the concept of slope in the 7th grade, learning that slope has to do with steepness.  By the 8th grade many learn how to calculate the slope of a line as the rise divided by the run or rise over run.  If the rise is positive, then the slope is positive (sloping upward).  On the other hand, if the rise is negative, then the slope is negative (sloping downward). If the line is horizontal, then the slope is zero.

Climate change is at the forefront of environmental concerns and it often revolves around atmospheric carbon dioxide concentration and its effect on average surface temperature. However, carbon dioxide concentration is not only rising in the atmosphere but in the ocean as well. The source of this dissolved carbon dioxide is the rising atmospheric carbon dioxide levels we hear so much about, as carbon dioxide is soluble in water.

Introduction to Pi

There is probably no number that has received more interest since ancient times that the number pi, symbolized by the Greek letter π.  Originally defined as the ratio of the circumference of a circle to its diameter, it has been given approximate values including 3.14 and 22/7.  Proven to be an irrational number, supercomputers have computed the value of pi to more than one trillion digits.

Introduction

This lab, featuring Voyager and intelino, designed for junior high math students, will help your students understand the true nature of randomness.  By the time youngsters enter junior high school, they have encountered randomness in a variety of situations.  They have likely seen random ping-pong balls drawn in lotteries.  They have seen coin tosses before the start of football games.  They may have been asked to draw a random card in a card trick.  Perhaps they or their parents have purchased tickets for a raffle.  The list could g

Brownian Motion

Brownian motion can be defined as the random motion of particles in a liquid or gas caused by the bombardment from molecules in the containing medium.  Have you ever looked at dust particles in the sunlight shining through a window?  They appear to move about randomly, even defying gravity.  This is an example of Brownian motion in which the dust particles are bombarded on all sides by gas molecules in the air.  Other examples of Brownian motion include the motion of grains of pollen on the surface of still water, the dif

Introduction to Moment of Inertia

There are numerous analogies when comparing linear and rotational motion.  At the heart of these comparisons lie the concepts of mass on one hand and moment of inertia on the other.  In addition to being a property of any physical object, mass is a measure of the resistance of an object to acceleration when a net force has been applied to the object.  Newton's Second Law of Motion expresses this in the familiar equation F = ma.  By analogy, the moment of inertia of any rigid obj

Introduction to the Physical Pendulum

Mount any rigid body such that it can swing in a vertical plane about an axis passing through the body.  You have constructed what is known as a physical pendulum.  The video below shows an example of such a pendulum.  In this video, a rigid circular body is swinging about an axis very close to the edge of the circle.  The circle was cut from a piece of cardboard.  PocketLab Voyager is resting at the bottom of a ring stand directly below the pivot point of the pendulum.  A tiny magnet has been attached to the bottom of the ci

Introduction to Hysteresis

Hysteresis can be defined as a lag time in the response of a system to forces placed on the system.  The response of the system depends not only on the present magnitude of the force but also on the previous history of the system.  From the point of view of mathematics, the response to the force is a double-valued function.  This means that one value applies when the force is increasing, while another value applies when the force is decreasing.  A graphical plot of force and re

Lissajous Introduction

Lissajous patterns have fascinated physics students for decades.  They are commonly observed on oscilloscopes by applying simple harmonic functions with different frequencies to the vertical and horizontal inputs.  Three examples are shown in Figure 1.  From left to right, the frequency ratios are 1:2, 2:3, and 3:4.  These Lissajous patterns were created by use of the parametric equation section of The Grapher software written by the author of this lesson.  You are welcome to use this softwa

We can create a way to make true random numbers in Scratch using the PocketLab Voyager's light sensor and a lava lamp. Sounds crazy? Not really, there is actually a US patent for such a system! It turns out that on their own, computers are not good at generating true random numbers, therefore to make true random numbers using a computer you need an external source of randomness.