Collaborative learners will see the geometric addition of functions by graphing the sum of two graphed curves on the same coordinate plane. This task then naturally flows into giving learners the algebraic representation of the curves...

Introduce your algebra learners to linear and quadratic functions. Learners compare the differences and relate them back to the equations and graphs. Lead your class to discussions on the properties of a function or a constant slope...

Trying to find a linear transformation is like finding a needle in a haystack. The second instructional activity in the series of 32 continues to explore the concept of linearity started in the first instructional activity. The class...

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...

Can you solve an equation graphically? Absolutely! This Algebra II lesson makes the connection between solving an absolute value equation and graphing two functions. Graphing absolute value functions is presented through the process of...

Ready to share the beauty of the inverse function with your classes? This algebra II lesson guides the discovery of an inverse function through a numerical, graphical, and an algebraic approach. Connections are made between the three,...

Your algebra learners explore linear functions concretely using tables of values in a collaborative task. The idea that linear function values change by equal differences over equal intervals, is emphasized. The slope and...

Your algebra learners analyze and interpret the general form and the graph of two functions. The increase of the function due to the multiplicative factor is emphasized.

Learners analyze the difference between the slope intercept and standard forms of a line in this task. Given two general points using letters they explore linear functions and linear equations.

Use equivalent expressions to reveal information about their graphs. Pupils verify that two quadratic functions are equivalent. By comparing the two expressions, they determine the vertex, the zeros, the y-intercept, and the...

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...

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...

Paper folding, flu spreading in a school, bacteria growth, and continuously compounded interest all provide excellent models to study exponential functions. This is a comprehensive resource that looks at many different aspects of...

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 lesson on relationships between two numerical...

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...

A six-day unit for algebra II on exponential and logarithmic functions builds upon Chapter 12 of Merrill Algebra II with Trigonometry; Applications and Connections. The text provides assistance in the depth of instruction...

Connect algebra and geometry on the coordinate plane. The eighth unit in a nine-part integrated course has pupils develop the distance formula from the Pythagorean Theorem. Scholars prove geometric theorems using coordinates...

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

Here you will find a model of a linear relationship between two quantities, the water depth of a channel and the distance across the channel at water level. The cross section of the channel is the shape of an isosceles trapezoid. The...

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.

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. 

Skeeters are used to model linear and exponential population growth in a wonderfully organized lesson plan including teachers' and students' notes, an assignment, graphs, tables, and equations. Filled with constant deep-reaching...

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...

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...