EngageNY
The Height and Co-Height Functions of a Ferris Wheel
Show learners the power of mathematics as they model real-life designs. Pupils graph a periodic function by comparing the degree of rotation to the height of a ferris wheel.
EngageNY
Four Interesting Transformations of Functions (Part 1)
Understanding how functions transform is a key concept in mathematics. This introductory instructional activity makes a strong connection between the function, table, and graph when exploring transformations. While the resource uses...
EngageNY
Comparing Quadratic, Square Root, and Cube Root Functions Represented in Different Ways
Need a real scenario to compare functions? This lesson has it all! Through application, individuals model using different types of functions. They analyze each in terms of the context using the key features of the graphs.
EngageNY
Transformations of the Quadratic Parent Function
Efficiently graph a quadratic function using transformations! Pupils graph quadratic equations by completing the square to determine the transformations. They locate the vertex and determine more points from a stretch or shrink and...
EngageNY
Four Interesting Transformations of Functions (Part 2)
What happens to a function whose graph is translated horizontally? Groups find out as they investigate the effects of addition and subtraction within a function. This nineteenth lesson in a 26-part series focuses on horizontal...
Curated OER
Building a Quadratic Function Form
Comparing the movement of graphs geometrically when small changes are made to the parent function motivates this collaborative discussion on the transformations of functions to their various forms. Vertical and horizontal shifts due to...
EngageNY
End Behavior of Rational Functions
Connect end behavior to previous learning. Pupils connect finding the end behavior of rational functions to finding end behavior of polynomial functions. The 13th segment in a 23-part unit starts with finding the end behavior or power...
EngageNY
Inverses of Logarithmic and Exponential Functions
Revisit the relationship between logarithms and exponentials. Learners review the notion of logarithms as the way to solve exponential equations in the 21st segment in a Pre-calculus series of 23. Pupils use the knowledge to prove that...
Mathematics Assessment Project
Representing Trigonometric Functions
Discover the classic example of periodicity: Ferris wheels. Young mathematicians learn about trigonometric functions through Ferris wheels. They match functions to their graphs and relate the functions to the context.
Mathematics Assessment Project
Representing Quadratic Functions Graphically
Sometimes being different is an advantage. An engaging activity has scholars match cards with quadratic functions in various forms. Along the way, they learn about how each form highlights key features of quadratic functions.
Chicago Teachers Union Quest Center
Factored Form of a Quadratic Function
Build upon linear functions to learn about quadratics. The lesson introduces the concept of zeros for quadratic functions and makes the connection to the linear factors of the function. It presents quadratics in both graphical and...
EngageNY
Comparing Linear and Exponential Models Again
Making connections between a function, table, graph, and context is an essential skill in mathematics. Focused on comparing linear and exponential relationships in all these aspects, this resource equips pupils to recognize and interpret...
Illustrative Mathematics
Points on a Graph
Learners practice using their knowledge of how to interpret a function and use function notation. The activity includes two questions. Given an input of a function and its output, the first question asks learners to write the ordered...
EngageNY
Why Call It Tangent?
Discover the relationship between tangent lines and the tangent function. Class members develop the idea of the tangent function using the unit circle. They create tables of values and explore the domain, range, and end behavior of the...
EngageNY
Modeling a Context from Data (part 2)
Forgive me, I regress. Building upon previous modeling activities, the class examines models using the regression function on a graphing calculator. They use the modeling process to interpret the context and to make predictions based...
Virginia Department of Education
Functions 1
Scholars learn what it means for a relation to be a function and see various representations of functions. After learning the definition, they participate in a card sorting activity classifying relations as functions or not.
Kenan Fellows
Dinner Party: Using Pattern Trains to Demonstrate Linear Functions
Nothing fancy here ... just your run-of-the-mill Algebra party! Learners explore the patterns of linear functions while designing seating arrangements for a dinner party. Comparing the number of tables to the perimeter of the combined...
Curated OER
Yam in the Oven
Your vegetable eaters will practice function notation statement interpretation in this short task. These few exercises will bring out misconceptions high schoolers may have about function notation as well.
Illustrative Mathematics
Chicken and Steak, Variation 2
Many organizations put on barbecues in order to make money. In a real-world math problem, the money allotted to purchase steak and chicken at this barbecue is only one hundred dollars. It is up to your potential chefs to figure out how...
West Contra Costa Unified School District
Comparing Rational Functions and Simplified Functions
What kind of functions have holes in their graphs? Here, the teacher guides the class on how to use the simplified function of a rational function to aid in the graphing of the original rational function. T-tables are used in order to...
Virginia Department of Education
Functions 2
Demonstrate linear and quadratic functions through contextual modeling. Young mathematicians explore both types of functions by analyzing their key features. They then relate these key features to the contextual relationship the function...
Curated OER
Algebra I: Linear Functions
Using rates from a rental car company, young mathematicians graph data, explore linear relationships, and discuss the role of slope and the y-intercept. This lesson allows for the discussion of independent and dependent variables, as...
EngageNY
Graphs of Exponential Functions
What does an exponential pattern look like in real life? After viewing a video of the population growth of bacteria, learners use the real-life scenario to collect data and graph the result. Their conclusion should be a new type of graph...
EngageNY
Graphs of Quadratic Functions
How high is too high for a belly flop? Learners analyze data to model the world record belly flop using a quadratic equation. They create a graph and analyze the key features and apply them to the context of the video.