Illustrative Mathematics
Cell Phone Plans
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...
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A Linear System
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...
Illustrative Mathematics
Sammy's Chipmunk and Squirrel Observations
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...
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Parameters and Clusters II
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...
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"Equal" Equations
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...
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Systematic Solution I
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,...
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Parameters and Clusters I
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.
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The Line and the Ellipse
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...
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Systematic Solution II
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...
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Intersections II
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...
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Betweenness I
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...
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Look but Do Not Touch
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.
Balanced Assessment
Bagels or Donuts
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.
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In a Triangle
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.