Illustrative Mathematics
Invertible or Not?
What determines whether a function has an inverse? Learners investigate that criteria when they examine values in a partially completed input-output table for two different functions. The task is to complete the table so that one of the...
Illustrative Mathematics
Rainfall
Ideal for use as an introduction to the idea of inverse functions, this activity investigates rainfall as a function of time. Learners use the data displayed in a table of values to analyze the function and its inverse, including why the...
Curated OER
Get a Half Life!: Student Worksheet
Upper elementary or middle schoolers will explore non-linear functions, graphing, and the curve of best fit through real-life data collection and trial analysis. They explore the concept of half-life and radioactive decay using M&Ms,...
Inside Mathematics
Printing Tickets
Determine the better deal. Pupils write the equation for the cost of printing tickets from different printers. They compare the costs graphically and algebraicaly to determine which printer has the best deal based upon the quantity of...
Curated OER
The Viewing Tube
Looking for an excellent lesson that incorporates math, science, and technology? Groups of three students use a viewing tube to perform an experiment, and discover how to organize their data into an Excel spreadsheet. This is a...
Illustrative Mathematics
Average Cost
Here is an activity that presents a good example of a function modeling a relationship between two quantities. John is making DVDs of his friend's favorite shows and needs to know how much to charge his friend to cover the cost of making...
Curated OER
Exponential Growth versus Polynomial Growth
Your algebra learners explore the values of two types of functions in order to compare growth rates in this short cooperative task. Two types of solutions are given, using a table of values and an abstract argument.
Curated OER
US Population 1790-1860
Your young population scientists analyze a table of values, write a model to represent the real life data, finish the table of data and predict future populations in a collaborative, real-life activity.
EngageNY
Polynomial, Rational, and Radical Relationships
This assessment pair goes way beyond simple graphing, factoring and solving polynomial equations, really forcing learners to investigate the math ideas behind the calculations. Short and to-the-point questions build on one another,...
Noyce Foundation
Toy Trains
Scholars identify and continue the numerical pattern for the number of wheels on a train. Using the established pattern and its inverse, they determine whether a number of wheels is possible. Pupils finish...
Curated OER
Extending the Definitions of Exponents, Variation 2
Introduce the concept of exponential functions with an activity that extends the definition of exponents to include rational values. Start with a doubling function at integer values of time, then expand table to include frational time...
Curated OER
The Customers
Exploring functions not represented by an expression is this task's secret. As your learners organize business customers in a database, they explore the definition of what it is to be a function.
Curated OER
Sandia Aerial Tram
Your learners analyze a table of real-life data in order to write an equation that best models the information. Exponential, quadratic, and linear rates of changes are all possibilities in this task.
Ohio Department of Education
I Can Do This! Systems of Equations
Use tables, graphs, and substitution to solve systems of linear equations. An envelope of sample problems is passed around the classroom, and each learner has the opportunity to solve the system in the envelope. This is a great way to...
Curated OER
US Population 1982-1988
Your algebra learners make predictions using the concepts of a linear model from real-life data given in table form. Learners analyze and discuss solutions without having to write a linear equation.
Curated OER
The Canoe Trip, Variation 2
The behavior of a rational function near a vertical asymptote is the focus around this trip up a river. Specifically, numerical and graphical understanding is studied. The canoe context pushes the variables as numbers, rather than as...
Illustrative Mathematics
Flu on Campus
An outbreak of the swine flu on a school campus has caused an increase in the number of boxes of tissues sold by the school store. In a real-world-modeling activity, pupils use composition of functions to determine how the number of...
Agile Mind
Rabbit populations
For this real-world problem about the rapid growth of rabbit populations, students must analyze two different scenarios and create mathematical models to represent them. They use their exponential models to answer questions about the...
Curated OER
In the Billions and Exponential Modeling
Modeling population growth gives learners an opportunity to experiment with real data. Comparing the growth rates in this real-life task strengthens learners' understanding that exponential functions change by equal factors over equal...
Curated OER
Exponential Growth Versus Linear Growth I
Your algebra learners will discover how quickly an exponential function value grows compared to a linear function's value. Making a table of values helps in this comparison, set in the context of making a wage for raking leaves.
Curated OER
Basketball Bounces, Assessment Variation 1
This highly scaffolded, summative assessment tasks learners to choose the model that represents the height of a bouncing basketball given the data in graph and table form. Learners then use the model to answer questions about the...
Stats Monkey
Everything I Ever Needed to Learn about AP Statistics I Learned from a Bag of M and M's®
Candy is always a good motivator! Use this collection of M&M's® experiments to introduce statistics topics, including mean, standard deviation, nonlinear transformation, and many more. The use of a hands-on model with...
EngageNY
The Most Important Property of Logarithms
Won't the other properties be sad to learn that they're not the most important? The 11th installment of a 35-part module is essentially a continuation of the previous lesson, using logarithm tables to develop properties. Scholars...
Curated OER
US Households
Learners construct and use inverse functions to model a real-world context. They use the inverse function to interpolate a data point.