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Functions

Graph with downward V-shaped data points.

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

Graph of a quadratic equation with table.

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

Graph showing CO2 emissions per person increase.

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

Tables showing linear, quadratic, and composite functions.

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

Triangle with angle and side measurements chart.

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

Graph and table of exponential function data.

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

Line graph illustrating GDP growth trends.

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

Graph with data table and scatter plot.

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

Mathematical tables with fractions and sums.

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

Tables and graph comparing revenue growth.

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

Graph of functions f(x) and f'(x).

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

Graph showing three intersecting linear functions.

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

Line graph showing y decreasing with x.

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

Graph of a linear function with grid.

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 curve graph with mathematical equations.

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

Mathematical table with parameters and calculations.

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

Transistor count graph with logarithmic scale.

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

Bar graph and data table comparison chart.

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

Bar chart with an orange color scheme.

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 illustrating projectile motion animation.

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

Mathematical table with terms and products.

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 with numerical values displayed.

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

Scatter plot with upward trend line.

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

Scatter plot with upward trend line.

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

Graph depicting distance versus distance data.

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

Parabola graph with plotted data points.

Quadratic Functions

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

Earth's population growth bar graph.

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

Line graph showing total investment growth.

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

Graph of a sine wave function.

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

NASA table of planetary data statistics.

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

Graph of two intersecting linear functions.

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

Mathematical equations and data table chart.

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

Mathematical function table and graph illustration.

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

Graph of two intersecting linear functions.

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

Two empty chessboards with highlighted squares.

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 with grid and table illustration.

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

Mathematical concept with colorful grid patterns.

What is x?

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