Where should I stand to get the best view? Pupils use inverse trigonometric functions to determine the horizontal distance from an object to get the best view. They round out the lesson by interpreting their answers within context.

Rewrite a quadratic function to easily see the transformations involved. The instructional task takes a general quadratic function and rewrites it into a form that shows the translations and scaling of the parent quadratic function. The...

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...

Not all linear functions are linear transformations, only those that go through the origin. The third lesson in the 32-part unit proves that linear transformations are of the form f(x) = ax. The lesson plan takes another look at examples...

Linear or not linear — that is the question. The lesson plan has class members translate descriptions into algebraic expressions. They take the written expressions and determine whether they are linear or nonlinear based upon the...

This activity guides learners through an exploration of common transformations of the graph of a function. Given the graph of a function f(x), students generate the graphs of f(x + c), f(x) + c, and  cf(x) for...

Learners rewrite a general quadratic function by completing the square to see a new form of the function that more easily identifies the x-coordinate of the vertex and the two roots of the function.

Not all linear functions are linear transformations — show your class the difference. The first lesson in a unit on linear transformations and complex numbers that spans 32 segments introduces the concept of linear transformations and...

Through discussions and journaling, classmates determine methods to associate types of functions with data presented in a table. Small groups then work with examples and exercises to refine their methods and find functions that work...

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

Complex numbers were first represented on the complex plane, now they are being represented using sine and cosine. Introduce the class to the polar form of a complex number with the 13th part of a 32-part series that defines the...

Learners are given a graph of a parabola on a coordinate system, but intercepts and vertex are not labeled. The task is to analyze eight given quadratic functions and determine which ones might possibly be represented by the graph. The...

Eighth graders combine like terms in this properties of variables instructional activity. Using named items (stars, moons and hearts), they combine like terms using variables. They use the distributive property to combine like terms....

Working in small groups and in pairs, classmates build an understanding of what types of relationships can be used to model individual scatter plots. The nonlinear scatter plots in this activity on relationships between two numerical...

When complicated algebraic expressions are involved, it is sometimes easier to use a table or graph to model a context. The exercises in this lesson are designed for business applications and require complex algebraic...

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...

Money, money, money. A complete lesson that makes use of different representations of simple and compound interest, including written scenarios, tables, graphs, and equations to highlight similarities and differences between linear and...

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...

Students discuss compound interest and formulas for compound interest. They listen as the teacher describes continuous compounding and derivations. Students work problems involving compound interest. They compute the effective annual...

Building upon previous knowledge of sequences, collaborative pairs analyze sequences to determine the type and to make predictions of future terms. The exercises build through arithmetic and geometric sequences before introducing...

While creating models from data, pupils make decisions about precision. Exercises are provided that require linear, quadratic, or exponential models based upon the desired precision. 

I got a different answer, are they both correct? While working through modeling problems interpreting graphs, the question of precision is brought into the discussion. Problems are presented in which a precise answer is needed and...

Use proportions to determine the travel distance in a given amount of time. The 10th installment in a series of 33 uses tables and descriptions to determine a person's constant speed. Using the constant speed, pupils write a linear...

Create tables of solutions of linear equations. A lesson has pupils determine solutions for two-variable equations using tables. The class members graph the points on a coordinate graph.