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,...

Up the difficulty level by solving a system of equations with variable coefficients. Young scholars devise a plan to solve for x and y in terms of a and b. They represent their solutions as expressions and explain their...

What do a line and an ellipse have in common? Maybe zero, one, or two points! Learners consider the equation of an ellipse and a line to determine if their graphs have any shared points. They then write a system of equations, including...

Round and round and round we go. Given a diagram of three circles, two of which share a point with the third circle, learners identify the radius of each circle. Doing so requires setting up and solving a system of equations based on the...

Different equations, same solution. Scholars first find a system with equations y1 and y2 that have a given solution. They then find a different system with equations y3 and y4 that have the same solution. The ultimate goal is to...

Here is a fun project. Sammy observes a chipmunk and a squirrel to see how many holes each needs in order to stash the same number of acorns.  Scholars could find the answer algebraically or create a table to analyze the...

Let's give parameters a second try. Scholars take a second look at a system of linear equations that involve a parameter. Using their knowledge of solutions of systems of linear equations, learners describe the solution to the system as...

Young mathematicians have the hang of graphing with integer coefficients now. Can they generalize what they've learned to equations with variable coefficients? The task asks individuals to verify the solution to the system is (x,y) and...

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...

Explore business problems through mathematical analysis. The task has individuals write and graph a linear system to determine the best business model. They use their models to answer a series of questions that help to make a conclusion.

Turn your classroom into a local cell phone store. Then, have your cell phone agents use linear equations to visually display three cell plans and their advantages. It makes for a great group project. Discuss how to decide which plan is...

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...

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.

Chase the traveling solution. Pupils analyze the solutions to a system of linear equations as the parameter in one equation changes. Scholars then use graphs to illustrate their analyses.

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.

Just between us, this is a pretty cool lesson! Given two functions with the same slope, learners write three new functions whose outputs are all between the given functions. The question is open-ended, allowing pupils to explore the...

How many ways can you make 10? Class members tackle three problems to find all possible ways three numbers add to be 10. The first is with positive integers, secondly with non-negative integers, and finally with real numbers. Pupils also...

This performance task gives the population model of different types of flies and asks scholars to analyze the two populations. After interpreting the functions individually, participants compare the two populations and find the time...

How long does it take alcohol to leave your system? Individuals explore this question by examining a polynomial function. They draw conclusions by analyzing the key features of the given polynomial function.