A basic set-up leads to a surprisingly complex analysis in this variation on the question of surrounding a central circle with a ring of touching circles. Useful for putting trigonometric functions in a physical context, as well as...

As part of an investigation of transformations of exponential functions, class members use Newton's Law of Cooling as an exponential model to determine temperature based on varying aspects. The resource makes comparisons between...

What function will describe the insect population growth? Pairs or small groups work together to determine which type of function and specific function will model given scenarios. The scenarios differentiate between linear,...

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...

There's a function for that! Scholars examine real-world situations to determine which type of function would best model the data in the 23rd installment of a 35-part module. It involves considering the nature of the data in addition to...

Reflect upon the graphs of quadratic functions. Given a quadratic function to graph, pupils determine whether the graph after a horizontal and vertical reflection is still a function. The final two questions ask scholars to describe a...

Will this be on the test? Learners demonstrate their understanding of trigonometric functions with an end-of-module assessment. They investigate two different real-world situations, one function in pure mathematics, and one...

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...

Trying to find a linear transformation is like finding a needle in a haystack. The second lesson in the series of 32 continues to explore the concept of linearity started in the first lesson. The class explores trigonometric, rational,...

How many intersections can two absolute value functions have? Young scholars consider the question and then develop a set of rules that describe the number of solutions a given system will have. Using the parent function and the standard...

This unit assessment covers the modeling process with linear, quadratic, exponential, and absolute value functions. The modeling is represented as verbal descriptions, tables, graphs, and algebraic expressions. 

Model periodic populations. Here, in the context of foxes and rabbits, pupils look at graphs of the populations of these animals in a national park over a span of 24 months. Groups analyze the graphs and determine trigonometric...

Model the difference between the graphs of discrete and continuous functions. Scholars examine two scenarios and construct graphs to model the situation. They then compare their graphs that illustrate the subtle difference between these...

Wheel the resource right into your classroom. Young mathematicians use given dimensions of a Ferris wheel to write a height versus time function. They use their functions to answer a set of questions about the Ferris wheel.

The structure of an expression is a descriptive feature. Learners build a solid understanding of quadratic functions using an analysis of expressions in different forms. The seventh module in a series of nine includes 12 lessons...

Accumulation functions should behave like other functions. Using content from Unit 5, pupils analyze the first and second derivative to determine the behavior of an accumulation function. Learners find out how to calculate the relative...

Take a functional approach to the national debt. Learners collect information about the national debt by decade and plot the data. They determine whether an exponential curve is a good fit for the data by comparing the percent changes...

No need to be exact every time. Pupils watch an engaging video on approximating function values. They see how to write the equation of a tangent line, use it to calculate approximations, and then determine whether it is an overestimate...

Students examine functions and function notation. They use computer activities to discover how to graph functions, and conduct a vertical line test. Students describe spatial relationships using coordinate geometry.

In this graphing functions worksheet, students solve four problems where they graph given functions, find the sum related to the area under the curve and determine an integral.

In this graphing functions worksheet, students write functions in logarithmic and exponential forms.  They evaluate logarithms and determine the inverse of a function.  Students graph functions.  This six-page worksheet...

In this algebra worksheet, 11th graders graph polynomial functions using quadratics and other exponential functions. They identify the vertex and other properties of a parabola. There are 8 problems with an answer key.

In this algebra worksheet, students evaluate exponential functions using tables and graphs. There are 6 questions with an answer key.

In this algebra worksheet, students rewrite word problems using algebra and relate linear functions to real life scenarios. There are 2 questions with an answer key.