Illustrative Mathematics
Temperatures in degrees Fahrenheit and Celsius
Learners investigate the relationship between the Fahrenheit and Celsius temperature scales. Given two data points, they construct a linear function to describe the relationship, find the inverse of the function, and make observations...
Illustrative Mathematics
Throwing Baseballs
This is a wonderful exercise for learners to apply their critical thinking skills along with their knowledge of quadratic functions and parabolas. Young mathematicians investigate a real-world scenario about the height a baseball reaches...
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.
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
Sum of Even and Odd
Your algebra learners will make use of structure and manipulate expressions involving function notation using the definition of odd and even functions. They then advance even further to analyze the structure in a system of two equations.
Illustrative Mathematics
Medieval Archer
This activity presents a problem about a computer game which uses functions to simulate the path of an arrow fired by an archer. Learners use the given function to determine where the archer must stand in order to fire an arrow that will...
Illustrative Mathematics
The High School Gym
Learners apply critical thinking skills as they analyze data about the temperature inside a gymnasium during a school assembly. The focus is on representing temperature as a function of time and interpreting input and output values...
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...
Curated OER
Model Air Plane Acrobatics
Your young airplane enthusiasts will enjoy this collaborative task of graphing an airplane's distance from the ground as it flies in a perfect circle. They will discover that they have graphed a sinusoidal function that comes from the...
Curated OER
Domains
Your algebra learners work to address the order of operations applied to an expression's input variable and the limitations that may be created because of it. This simple task of a few very well-chosen exercises is elegant in it's way of...
Curated OER
Find Parabolas through Two Points
Your learners will write quadratic functions whose graphs include specific points and explore how these graphs are related to each other.
Curated OER
A Saturating Exponential
Your learners analyze the familiar model of a cold beverage warming when it is taken out of the refrigerator. The general form of the equation and its graph are presented. Learners learn about the specific pieces of the function by...
EngageNY
Are All Parabolas Similar?
Congruence and similarity apply to functions as well as polygons. Learners examine the effects of transformations on the shape of parabolas. They determine the transformation(s) that produce similar and congruent functions.
EngageNY
Factoring Extended to the Complex Realm
A solution will work one way or another: find solutions, or use solutions to find the function. Learners use polynomial identities to factor polynomials with complex solutions. They then use solutions and the Zero Product Property to...
Curated OER
Buying Cars/Financing Cars Compound Interest
Provide a real world context in which exponential functions are used to determine a eal world phenomena such as compound interest and exponential growth. This lesson should be taught after students have mastered the laws of exponents and...
Curated OER
Radical Expressions and Rational Numbers as Exponents
In this radical expressions worksheet, students find the function value of given functions. They identify the domain of functions. Students write functions without fractional exponents. This three-page worksheet contains 55 problems.
Mathematics Assessment Project
Representing Polynomials
Use this complete and very detailed lesson plan to assess your students' understanding of two important behaviors of polynomials. The first is the relationship between the zeros of a polynomial function and the function's graph, and the...
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...
Illustrative Mathematics
Exponentials and Logarithms II
Learners are given a logarithmic function and its inverse exponential function. The task, which is to graph both compositions of the two functions, uses the inverse nature of exponents and logarithms to generalize about the properties of...
Curated OER
The Canoe Trip, Variation 1
Your river sportsmen will explore an example of paddling upstream as they build functions modeling speed and time in terms of the speed of the current. They then use their algebraic models to interpret features of the function related to...
Curated OER
Who am I? Find A Polynomial From Its Roots
High schoolers generate the equation of a polynomial given its roots and the end behavior of the function. They need to apply theorems concerning the multiplicity of roots, conjugates of irrational or imaginary roots to find 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...
HHS Math
Group Worksheet 1F - Graphing and Finding Zero
Graph quadratic functions and find the zero in this worksheet. Twelve problems range from those that could be quickly factored and graphed, to those that require use of the quadratic formula and their graphs approximated. Solutions...
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.
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