Functions

Absolute Value Functions

﻿The absolute value (ABS) function is the positive value of a number or quantity. Its graph has a very peculiar shape, a V. Since absolute… Continue

Absolute Value Polynomials

What would you guess the absolute value of a polynomial function would look like? Try some here. I think you will be very surprised. Can… Continue

CO2 Growth

Spreadsheets offer us a nearly unlimited ability to develop and learn from case studies using real world data. We will focus mainly on climate change… Continue

Composition of Functions

One of the most powerful aspects of the mathematics of functions is our ability to treat them as abstract quantities (essentially numbers) and then combine… Continue

Exploring Triangles

Create, manipulate, and explore triangles in this live interactive spreadsheet. On the surface, a triangle is being drawn on a graph, but the real magic… Continue

Exponential Functions

What if you created a function where the exponent is a variable? As you might expect, this would be called an exponential function. When you… Continue

GDP

The GDP or Gross Domestic Product of a country is one measure of its wealth. What can this data tell us about the U.S. economy?… Continue

Graphing

Graphs as we know them were first invented by Galileo. They are powerful images of functions. I will introduce you to graphs by letting you… Continue

Hindu Algebra Problem

This problem is typical of the earliest algebra problems that likely came out of India. It is interesting historically, and it is the kind of… Continue

Interest

Which form of interest, simple or compound, is the fairest? If you were buying a house or a car which would you rather have, which… Continue

Inverse of a Function

Spreadsheets make it very easy to switch axes and add graphs. They enable students to play with what may have been difficult and abstract concepts… Continue

Inverse of Linear Functions

What does a linear function look like when we interchange the inputs and outputs, that is make the x-axis the y-axis and vice versa. Continue

Inverse Variation

The variables in most of the functions we are used to working with vary directly, as one goes up the other goes up. What do… Continue

Linear Functions

Linear functions are the most important family of functions. They pervade our everyday lives and our work. Their graph is a line, and their general… Continue

Lissajous Figures

We often see Lissajous figures in old sci-fi movies because they are so cool. As you play with them I think you will find them… Continue

Magic Number (Infinite Series)

What if you made a series of unit fractions with the odd numbers as their denominator, added the first two together, subtracted the next one,… Continue

Moore’s Law

It was one of the most amazing visions of the future ever made. In 1965 Gordon Moore, one of the founders of Intel, proposed a… Continue

Motion Problems

George is in New York and Martha is in Washington. They leave at the same time and follow the same road to meet each other… Continue

Normal Distribution

Most museums with math exhibits have a Pascal’s triangle made up of pegs with balls falling down between them and bouncing off of them. One… Continue

Parametric Equations

Parametric equations are powerful tools to model projectile motions and to graph things that are not functions like circle or ellipses. The x and y… Continue

Parentheses and Pi

Parentheses are very important in spreadsheets because like all programming, spreadsheet formulas have to be very specific. A big formula, especially one like Viete’s approximation… Continue

Pascal’s Triangle

Another famous pattern, Pascal’s triangle, is easy to construct and explore on spreadsheets. Create a formula for any cell that adds the two cells in… Continue

Polynomial Functions

Polynomial functions are not limited to the highest term and while that term is most important in determining the shape of its graph, additional terms… Continue

Power Functions

Adding an exponent, sometimes referred to as a ‘power’, to the input variable of a linear function that passes through the origin creates a power… Continue

Projectile Motion

Let’s do a little target practice with this spreadsheet projectile simulator, which will map out the flight path of an arrow shooting toward a target. Continue

What does each of the coefficients do? How does it change the graph of the parabola. What does a do, what does c do and… Continue

Rate of Growth

We look at world population over the past 60+ years and ask whether the earth’s population is growing faster or slower today. Is it out… Continue

Rule of 72

The rule of 72 is an old banker’s rule of thumb to find out how long it will take to double your money at different… Continue

Sine Function

Spreadsheets are not limited to algebraic functions, they can also display trigonometric functions. We are modeling the sine function, but you can try any of… Continue

Solar System

When I was young I loved to play with planetary data, to explore their patterns, to learn more about astronomy, and to deal with large… Continue

Solving Equations

Typical algebra courses start with equations and solving equations and then move to graphing and functions. We start with functions and use them to solve… Continue

Solving Equations Digitally

This Lab introduces a method for solving or estimating the solution to an equation digitally that can be applied to many types of equations. This… Continue

Syracuse Problem

I built a Lab for you to play with the Syracuse Problem and to learn to use spreadsheets to play with like problems in fun… Continue

Systems of Equations

Solving systems of equations sometimes called simultaneous equations with graphs is simply a matter of finding out where they intersect. One of the most valuable… Continue

The Chessboard

We take that great old problem of the inventor of chess and the ruler of India and use it to see how powers of 2… Continue

Triangular Numbers

1, 3, 6, 10… are called the triangular numbers because they can be stacked up to form a triangle. They are very interesting numbers, and… Continue

What is x?

What is “x”? Or how do we represent variables and functions on spreadsheets? Continue