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).

 
50 Lesson(s)
   

Solving Two Variable Inequalities

Algebra I » Unit: Extending Equations
Algebra I » Unit: Extending Equations
James Bialasik
Amherst, NY
Environment: Suburban
 
Big Idea:

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

 
Favorites (14)
 
Resources (22)
 
Reflections (1)
solving two variable inequalities image
   

Ellipses

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

 
Favorites (5)
 
Resources (19)
ellipitcal pool table
   

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
   

An Intersection Point, and What Happens Around It

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

 
Favorites (3)
 
Resources (14)
u5 l12 imperfect graphing
   

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

Algebra I » Unit: The Number Line Project
Algebra I » Unit: The Number Line Project
James Dunseith
Worcester, MA
Environment: Urban
 
Big Idea:

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

 
Favorites (42)
 
Resources (25)
 
Reflections (2)
u1 l16 part 2a setup
   

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
   

Graphing Linear Functions Using Intercepts

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

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

 
Favorites (5)
 
Resources (19)
 
Reflections (1)
intercepts graphing linear image
   

Using Linear Functions for Modeling

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

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

 
Favorites (3)
 
Resources (16)
 
Reflections (1)
modeling slope intercept image
   

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
   

Where Do the Lines Cross?

Algebra I » Unit: Systems of Equations and Inequalities
Algebra I » Unit: Systems of Equations and Inequalities
Amanda Hathaway
Boston, MA
Environment: Urban
 
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.

 
Favorites (2)
 
Resources (16)
 
Reflections (1)
linescross
   

Axis of symmetry and vertex algebraically

8th Grade Math » Unit: QUADRATIC FUNCTIONS
8th Grade Math » Unit: QUADRATIC FUNCTIONS
Jeff Li MTP
New York, NY
Environment: Urban
 
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.

 
Favorites (2)
 
Resources (12)
crying boyfriend resized
   

Explore changing coefficients

8th Grade Math » Unit: QUADRATIC FUNCTIONS
8th Grade Math » Unit: QUADRATIC FUNCTIONS
Jeff Li MTP
New York, NY
Environment: Urban
 
Big Idea:

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

 
Favorites (2)
 
Resources (15)
 
Reflections (1)
graphing calculator image
   

Introduction to a System of Linear Equations

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

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

 
Favorites (16)
 
Resources (12)
 
Reflections (1)
solution
Common Core Math
 
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