Scholars first complete an individual assignment using a quadratic equation to model the movement of a bus around a corner. Learners then discuss their solutions with classmates and analyze the provided sample responses.

A five-page worksheet packet guides young mathematicians through solving standard form quadratic equations using the quadratic formula. They can identify the radical sign, the discriminant, and see the three options for finding...

Through a variety of physical and theoretical situations, learners are led through the development of some of the deepest concepts in high school mathematics. Complex numbers, the fundamental theorem of algebra and rational exponents...

Group equations by their solutions. Given six different equations, pupils determine which have the same solutions. Scholars explain why some are the same and some are different.

Math is all about finding solutions and connections you didn't expect! Young mathematicians often first discover nonlinear patterns when graphing quadratic functions. The lesson begins with the vocabulary of a quadratic graph and uses...

How many points are needed to define a unique parabola? Individuals work with data to answer this question. Ultimately, they determine the quadratic model when given three points. The concept is applied to data from a dropped...

Tackle a common misconception using a performance task. Dividing by a variable to eliminate a variable may seem like a good idea, but simplifying the variable eliminates solutions as well. Learners develop algebraic and graphical support...

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...

Use context to explain the importance of the key features of a graph. When context is introduced, the domain and range have meaning, which enhances understanding. Pupils use application questions to explore the key features of the graph...

There is power in spreadsheet formulas and learners use this power to model quadratic data. Given a scatterplot of a parabola, pupils create formulas in a spreadsheet to populate the data. The formulas they use lead to an understanding...

An assessment presents a variety of equations and inequalities. Pupils must find two solutions for each equation or inequality and determine whether there are only two, another finite number, or an infinite number of solutions...

What's in a triangle? Just 180 degrees worth of angles! Young learners use given angle relationships in a triangle to write an algebraic representation. Using a system of equations, they simplify the equation to a linear representation.

One, two, or zero solutions—quadratic systems have a variety of solution possibilities. Using the parent function and the standard form of the function, learners describe the values of a, b, and c that produce each solution type. They...

Need a real scenario to compare functions? This instructional activity has it all! Through application, individuals model using different types of functions. They analyze each in terms of the context using the key features of the...

Nothing better than the original! Help your class understand the relationship of an inverse function to its original function. Learners study the connection between the original function and its inverse through algebraic properties,...

Rewriting expressions in different forms is an essential algebra skill. Support the development of this skill by using a task that asks scholars to begin with a linear, quadratic, and rational expression and then manipulate...

Find the area as it slides. Pupils derive an equation to find the painted area of a section of a trapezoidal-shaped stage The section depends upon the sliding distance the edge of the painted section is from a vertex of the trapezoid....

Through a variety of hands-on activities and physical scenarios, this far-reaching unit leads learners through an exceptionally thorough exploration of circles and parabolas as conic sections. Geometric construction techniques are used...

Read between the curves ... quadratic curves! Young scholars analyze the graphs of two quadratic functions by writing their own function whose outputs are between the two given. They then consider intersecting quadratic functions and...

Writing a general rule to model a specific pattern is a high-level skill. Your classes practice the important skill as they write rules describing the solutions to a system of equations with variable coefficients. As an added challenge,...

It's all in the numbers! Create a mathematical model to analyze a number game and develop a winning strategy. Using a given numerical pattern, scholars write an expression to model the scenario. They then interpret the pattern of the...

An informative module highlights eight polynomial concepts. Learners work with polynomial functions, expressions, and equations through graphing, simplifying, and solving. 

Undo a function to create a new one. The inverse of a function does just that. An inquiry-based lesson examines the result of reversing the variables of a function, beginning with linear patterns and advancing to quadratic and...

We seem to keep missing each other. A short task provides pupils with a quadratic function, as well as a linear function with a missing coefficient. They must determine the value of the coefficient for which the graphs do not intersect.