HSA-REI.D.11

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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.

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## 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.*

65 Lesson(s)

### Operations with Polynomials Day 1 of 2

Algebra II »
Unit: Polynomials

Algebra II »
Unit: Polynomials

Big Idea:

#### Students get the opportunity to explore and make conclusions about operations with polynomials using graphing technology.

Standards:

Favorites
(8)

Resources
(20)

Reflections
(1)

### Solving Systems by Graphing

Algebra I »
Unit: Systems of Equations

Algebra I »
Unit: Systems of Equations

Big Idea:

#### As students gain confidence in graphing - and interpreting the intersection points on - systems of equations, we continue to see how this skill relates to guess and check.

Standards:

Favorites
(7)

Resources
(21)

Reflections
(1)

### Review Workshop: Polynomial Functions and Expressions

Algebra II »
Unit: Polynomial Functions and Expressions

Algebra II »
Unit: Polynomial Functions and Expressions

Big Idea:

#### Tomorrow is the unit test on polynomial functions and expressions. In this lesson, we do more practice with word problems, solving equations, graphing parabolas, and rewriting quadratic functions.

Standards:

Favorites
(5)

Resources
(13)

Reflections
(1)

### Quiz and Intro to Graphs of Polynomials

Algebra II »
Unit: Polynomial Theorems and Graphs

Algebra II »
Unit: Polynomial Theorems and Graphs

Big Idea:

#### The graph of a polynomial can look a variety of ways depending on the degree, lead coefficient, and linear factors.

Standards:

Favorites
(3)

Resources
(12)

Reflections
(1)

### Three Ways to Solve a Problem

Algebra I »
Unit: Systems of Equations

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.

Standards:

Favorites
(3)

Resources
(19)

Reflections
(1)

### What's In an Intersection?

Algebra I »
Unit: Systems of Equations

Algebra I »
Unit: Systems of Equations

Big Idea:

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

Standards:

Favorites
(2)

Resources
(16)

Reflections
(1)

### Mastery Session: MP1, 5.1, and 5.2

Algebra I »
Unit: Systems of Equations

Algebra I »
Unit: Systems of Equations

Big Idea:

#### When students are given time to work at their own pace, without the pressure of a "quiz," they can make the most of an opportunity to show what they can do.

Standards:

Favorites
(3)

Resources
(11)

### Another Rational Approach to Solving: Graphing

12th Grade Math »
Unit: Rational Functions and Equations

12th Grade Math »
Unit: Rational Functions and Equations

Big Idea:

#### Students use their knowledge of solving systems to write a system that makes the solution to a rational equation visible.

Standards:

Favorites
(1)

Resources
(13)

Reflections
(1)

### The Best of 2 Cell Phone Plans

Algebra I »
Unit: Systems of Equations

Algebra I »
Unit: Systems of Equations

Big Idea:

#### The purpose of this lesson is for students to understand how to analyze a system of equations to determine when a plan is cheaper, more expensive, or cost the same at certain points on the graph.

Standards:

Favorites
(4)

Resources
(12)

Reflections
(1)

### Non-Linear Systems of Equations

12th Grade Math »
Unit: Conic Sections

12th Grade Math »
Unit: Conic Sections

Big Idea:

#### Students model their solutions to non-linear systems in multiple ways.

Standards:

Favorites
(1)

Resources
(17)

### Creating and Interpreting Equations to Solve Systems

Algebra I »
Unit: Making Informed Decisions with Systems of Equations

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!

Standards:

Favorites
(6)

Resources
(22)

Reflections
(1)

### REALLY BIG IDEAS! Graphing vs. Substitution

Algebra I »
Unit: Systems of Equations

Algebra I »
Unit: Systems of Equations

Big Idea:

#### If you’re going to have a variety a tools, it’s a good idea to have a good idea of what each is good for!

Standards:

Favorites
(3)

Resources
(19)

Reflections
(1)

### Quarters, Dimes and Linear Combinations

Algebra I »
Unit: Systems of Equations

Algebra I »
Unit: Systems of Equations

Big Idea:

#### Students start with a concrete problem as they define constraints and progress to the abstract level of solving using algebraic methods. .

Standards:

Favorites
(3)

Resources
(9)

### From Graphing to Substitution

Algebra I »
Unit: Systems of Equations

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.

Standards:

Favorites
(2)

Resources
(13)

### Solving Equations Involving Exponents

Algebra I »
Unit: Exponential Functions

Algebra I »
Unit: Exponential Functions

Big Idea:

#### Students will use standard A.REI.11 to solve exponential equations without using logarithms.

Standards:

Favorites
(5)

Resources
(16)

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