Curated OER
Average Value of Functions
In this integrals and average value worksheet, students problem solve thirty equations or word problems involving average value of functions, volume and integrals.
Curated OER
Trigonometric Functions
In this trigonometric functions worksheet, 11th graders solve and complete 5 different sets of problems. First, they find each angle using angle addition/subtraction formulas as shown. Then, students prove each of the identities provided.
Curated OER
Circular Trigonometric Functions
In this trigonometry/Algebra II learning exercise, students use convert between radian and degree measure, find the value of trigonometric functions, and show that given relationships are true. The three page learning exercise contains...
Virginia Department of Education
Logarithmic Modeling
Explore logarithms and logarithmic regression. Young mathematicians first learn about inverse functions and about the logarithm function family. They take their newfound knowledge to use logarithmic functions to model situations and...
Concord Consortium
You Are What You Drive
Grab the wheel in learning about functions. A short performance task challenges young mathematicians to develop a function that describes the cars eight people drive. They consider whether the inverse of the function exists. If not, they...
West Contra Costa Unified School District
Average Rate of Change
Learners investigate average rates of change for linear functions and connect the concept to slope. They then determine average rates of change in quadratic and exponential functions.
EngageNY
End-of-Module Assessment Task - Algebra 1 (Module 4)
Critical thinking is an important aspect of mathematics — it's time to put your brain to work! Use this assessment to challenge pupils and test their skills. Concepts assessed include function notation, factoring, completing the square,...
EngageNY
Addition and Subtraction Formulas 1
Show budding mathematicans how to find the sine of pi over 12. The third lesson in a series of 16 introduces the addition and subtraction formulas for trigonometric functions. Class members derive the formulas using the distance formula...
EngageNY
End-of-Module Assessment Task: Grade 8 Module 5
Give your class a chance to show how much they've learned in the module with an end-of-module assessment task that covers all topics from the module including linear and non-linear functions and volumes of cones, cylinders, and spheres.
Illustrative Mathematics
As the Wheel Turns
Determine the location of a point on a moving wheel. The task challenges groups to determine the horizontal and vertical locations of a point on the edge of wheel that is moving. Teams first determine a function that will model the...
Virginia Department of Education
Exponential Modeling
Investigate exponential growth and decay. A set of six activities has pupils collecting and researching data in a variety of situations involving exponential relationships. They model these situations with exponential functions and solve...
Concord Consortium
Rising Prices
What will that cost in the future? The scenario provides pupils with a growth as a Consumer Price Index. Learners create functions for a given item to determine future prices and graph them. Class members then compare their functions to...
Achieve
Spread of Disease
Viruses can spread like wildfire, and mathematics can model the speed of infection. Given a function, scholars analyze it to describe the spread of a disease within a stadium. Learners find the initial number infected and the maximum...
Virginia Department of Education
Square Patios
Build a patio from toothpicks and marshmallows to analyze functions! Learners look for patterns in the data as they create different size patios. As they discover patterns, they make connections between the different representations of...
Alabama Learning Exchange
Logarithms: Undo the Exponential
Rumor has it that an exponential can be undone. After playing a rumor game to model exponential growth, pupils learn about undoing exponential functions. They use the definition of the logarithm to convert exponential equations to...
Concord Consortium
It's In the Mail
It's time to check the mail! The task is to determine the most cost-effective way to mail a packet of information. Young scholars write an equation that models the amount of postage as a function of the number of sheets mailed and...
PBL Pathways
Students and Teachers 2
Examine trends in student-to-teacher ratios over time. Building from the first task in the two-part series, classes now explore the pattern of student-to-teacher ratios using a non-linear function. After trying to connect the pattern to...
Concord Consortium
Maintain Your Composition
Compose yourself! Learners first use given graphs of functions f and g to graph the composition function f(g(x)) and identify its value for a specific input. They then consider functions for which f(g(x)) = g(f(x)).
EngageNY
Representations of a Line
Explore how to graph lines from different pieces of information. Scholars learn to graph linear functions when given an equation, given two points that satisfy the function, and when given the initial value and rate of change. They solve...
Mt. San Antonio Collage
Quiz 2: Polynomials
Four questions that get right to the polynomial point. High schoolers list all the attributes of a polynomial function, including finding all complex zeros. The last two questions prompt them to write a function based on the given zeros...
Illustrative Mathematics
Rainfall
Find the how long it has been raining based upon the amount of rainfall. Scholars analyze a table of the amount of rainfall as a function of time. Pupils first determine whether the function is invertible, then they find and interpret...
West Contra Costa Unified School District
Average Rate of Change
The concept of slope gets an approachable, yet theoretical, treatment in a comprehensive algebra instructional activity. The use of functional notation and problem-solving techniques keep the material rigorous, but detailed teaching...
Concord Consortium
Adding the Sines
It's a sign! Scholars analyze sine functions for patterns in their periods. The exploration advances beyond a simple function to the combination of two functions with even and odd coefficients. Their goal is to find a pattern between the...
EngageNY
The Remainder Theorem
Time to put it all together! Building on the concepts learned in the previous lessons in this series, learners apply the Remainder Theorem to finding zeros of a polynomial function. They graph from a function and write a function from...
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