Put together the pieces and model a parabola. Learners work through several examples to develop an understanding of a parabola graphically and algebraically. 

Augment a unit on parabolas with an instructive math activity. Pupils graph parabolas by examining the relationship between the focus and directrix. 

Congruence and similarity apply to functions as well as polygons. Learners examine the effects of transformations on the shape of parabolas. They determine the transformation(s) that produce similar and congruent functions.

Time for pupils to use their imagination! Learners examine the relationship between a system with no real solution and its graph. They then verify their discoveries with algebra. 

Working with imaginary numbers — this is where it gets complex! After exploring the graph of complex numbers, learners simplify them using addition, subtraction, and multiplication. 

Quadratic solutions come in all shapes and sizes, so help your classes find the right one! Learners use the quadratic formula to find solutions for quadratic equations. Solutions vary from one, two, and complex. 

A solution will work one way or another: find solutions, or use solutions to find the function. Learners use polynomial identities to factor polynomials with complex solutions. They then use solutions and the Zero Product Property to...

The greater the degree, the more solutions to find! Individuals find the real solutions from a graph and use the Fundamental Theorem of Algebra to find the remaining factors. 

A series of assessment tasks require learners to process information and communicate solutions. Topics include graphing parabolas, solving linear-quadratic systems, factoring polynomials, and solving polynomial equations. 

Collaborative groups utilize their knowledge of parent functions and transformations to determine the equations associated with graphs. The graph is then related to the scenario it represents. 

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,...

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...

Collaborative pairs develop functions that model a graph from a context using the modeling cycle. They then analyze their function models in order to answer questions about the scenario.

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. 

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...

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

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. 

What does math have to do with the behavior of the earth and sun? Learn how the movement of celestial bodies has influenced the development of trigonometry. Scholars connects the details in mathematics to their...

Round and round we go! Pupils use reference angles to evaluate common sine and cosine values of angles greater than 360 degrees. Once they have mastered the reference angle, learners repeat the process with negative angles.

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...

Can you use triangles to create a circle? Learners develop the unit circle using right triangle trigonometry. They then use the unit circle to evaluate common sine and cosine values.

Turn your class upside down as they explore the reciprocal functions. Scholars use the unit circle to develop the definition of the secant and cosecant functions. They analyze the domain, range, and end behavior of each function.

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...