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
Amelia Jamison
Caldwell, ID
Environment: Rural
 
Big Idea:

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

 
Favorites (6)
 
Resources (20)
 
Reflections (1)
image operations with polynomial functions
   

Solving Systems by Graphing

Algebra I » Unit: Systems of Equations
Algebra I » Unit: Systems of Equations
James Dunseith
Worcester, MA
Environment: Urban
 
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.

 
Favorites (6)
 
Resources (21)
 
Reflections (1)
u5 l4 key elements of a graph
   

Review Workshop: Polynomial Functions and Expressions

Algebra II » Unit: Polynomial Functions and Expressions
Algebra II » Unit: Polynomial Functions and Expressions
Colleen Werner
Ipswich, MA
Environment: Suburban
 
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.

 
Favorites (5)
 
Resources (13)
 
Reflections (1)
unit checklist
   

Quiz and Intro to Graphs of Polynomials

Algebra II » Unit: Polynomial Theorems and Graphs
Algebra II » Unit: Polynomial Theorems and Graphs
Colleen Werner
Ipswich, MA
Environment: Suburban
 
Big Idea:

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

 
Favorites (3)
 
Resources (12)
 
Reflections (1)
quartic
   

What's In an Intersection?

Algebra I » Unit: Systems of Equations
Algebra I » Unit: Systems of Equations
James Dunseith
Worcester, MA
Environment: Urban
 
Big Idea:

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

 
Favorites (2)
 
Resources (16)
 
Reflections (1)
u5 l3 desmos sketch on board first
   

Three Ways to Solve a Problem

Algebra I » Unit: Systems of Equations
Algebra I » Unit: Systems of Equations
James Dunseith
Worcester, MA
Environment: Urban
 
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.

 
Favorites (3)
 
Resources (19)
 
Reflections (1)
u5 l9 connect dots and intersection
   

Mastery Session: MP1, 5.1, and 5.2

Algebra I » Unit: Systems of Equations
Algebra I » Unit: Systems of Equations
James Dunseith
Worcester, MA
Environment: Urban
 
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.

 
Favorites (2)
 
Resources (11)
knight v dragon
   

Another Rational Approach to Solving: Graphing

12th Grade Math » Unit: Rational Functions and Equations
12th Grade Math » Unit: Rational Functions and Equations
Tiffany Dawdy
Phoenix, AZ
Environment: Urban
 
Big Idea:

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

 
Favorites (1)
 
Resources (13)
 
Reflections (1)
solv rational eqn graphing
   

The Best of 2 Cell Phone Plans

Algebra I » Unit: Systems of Equations
Algebra I » Unit: Systems of Equations
Rhonda Leichliter
Rogers, AR
Environment: Rural
 
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.

 
Favorites (4)
 
Resources (12)
 
Reflections (1)
cell phone plan
   

Non-Linear Systems of Equations

12th Grade Math » Unit: Conic Sections
12th Grade Math » Unit: Conic Sections
Tiffany Dawdy
Phoenix, AZ
Environment: Urban
 
Big Idea:

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

 
Favorites (1)
 
Resources (17)
nonlinear system image
   

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
Jason Colombino
Salem, MA
Environment: Urban
 
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!

 
Favorites (6)
 
Resources (22)
 
Reflections (1)
creating and int image resized
   

Quarters, Dimes and Linear Combinations

Algebra I » Unit: Systems of Equations
Algebra I » Unit: Systems of Equations
Rhonda Leichliter
Rogers, AR
Environment: Rural
 
Big Idea:

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

 
Favorites (3)
 
Resources (9)
quarters and dimes
   

From Graphing to Substitution

Algebra I » Unit: Systems of Equations
Algebra I » Unit: Systems of Equations
James Dunseith
Worcester, MA
Environment: Urban
 
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.

 
Favorites (2)
 
Resources (13)
u5 l10 mastery of slt 502
   

Solving Equations Involving Exponents

Algebra I » Unit: Exponential Functions
Algebra I » Unit: Exponential Functions
James Bialasik
Amherst, NY
Environment: Suburban
 
Big Idea:

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

 
Favorites (4)
 
Resources (16)
solving exponential equations image
   

Algebraic Nuts and Bolts: Solving Systems

Algebra I » Unit: Systems of Equations
Algebra I » Unit: Systems of Equations
James Dunseith
Worcester, MA
Environment: Urban
 
Big Idea:

It's a pretty straightforward practice session, of the sort that kids actually look forward to after days of problem solving.

 
Favorites (3)
 
Resources (12)
u5 l13 working
Common Core Math
 
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