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- HSA-REI.D.10Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
- HSA-REI.D.11Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.*
- HSA-REI.D.12Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

Solving Two Variable Inequalities

Algebra I

» Unit:

Extending Equations

Big Idea:See how to use test points to determine how to determine the solution to a two-variable inequality.

Ellipses

12th Grade Math

» Unit:

Conic Sections

Big Idea:After learning to write the equation of an ellipse, students design an elliptical pool table that would guarantee that even the worst player can always make a shot.

Three Ways to Solve a Problem

Algebra I

» Unit:

Systems of Equations

Big Idea:Over the course of today’s lesson, students will beg for an algebraic solution, understand on their own why it’s great that algebra was invented, and see the beauty of an elegant solution.

What's In an Intersection?

Algebra I

» Unit:

Systems of Equations

Big Idea:The "closeness" of one graph to another matches the accuracy of a guess and a check.

An Intersection Point, and What Happens Around It

Algebra I

» Unit:

Systems of Equations

Big Idea:Often the truest solution to a problem is that "it depends". Substitution is an efficient method for finding the precise intersection of two lines; a graph makes it clear what happens on either side of that point.

The Number Line Project, Part 2: Two Dimensional Number Lines

Algebra I

» Unit:

The Number Line Project

Big Idea:The mathematical structures we build today will be used to justify many algebraic ideas in the coming months.

Non-Linear Systems of Equations

12th Grade Math

» Unit:

Conic Sections

Big Idea:Students model their solutions to non-linear systems in multiple ways.

Creating and Interpreting Equations to Solve Systems

Algebra I

» Unit:

Making Informed Decisions with Systems of Equations

Big Idea:Students create systems of equations and attempt to solve them as an introduction to the relevance of solving systems of equations and inequalities!

Graphing Linear Functions Using Intercepts

Algebra I

» Unit:

Linear Functions

Big Idea:Finding the intercepts of a function can be a useful way to determine some coordinates that satisfy the equation of that function.

Using Linear Functions for Modeling

Algebra I

» Unit:

Linear Functions

Big Idea:Students can construct meaningful interpretations of slope and y-intercept by seeing both in a real-world context.

From Graphing to Substitution

Algebra I

» Unit:

Systems of Equations

Big Idea:It’s amazing to get to the point where students truly understand how useful and beautiful algebra can be. Transitioning from graphing systems to solving by substitution is an opportunity to get kids there.

Where Do the Lines Cross?

Algebra I

» Unit:

Systems of Equations and Inequalities

Big Idea:How can we figure out the exact value of x and y when two lines cross? Students learn the importance of solving systems of equations using algebraic methods.

Axis of symmetry and vertex algebraically

8th Grade Math

» Unit:

QUADRATIC FUNCTIONS

Big Idea:Don't be so negative, b! Get over 2a. Show students a funny and memorable way to remember the formula for the axis of symmetry.

Explore changing coefficients

8th Grade Math

» Unit:

QUADRATIC FUNCTIONS

Big Idea:Use the graphing calculator to explore how changing a and c change a quadratic function.

Introduction to a System of Linear Equations

Algebra I

» Unit:

Systems of Equations

Big Idea:Students need to be able to meaningfully describe the solution to a system of linear equations.

HSA-REI.D.10

Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

HSA-REI.D.11

Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.*

HSA-REI.D.12

Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.