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UNIT TEMPLATE
Unit Title: Systems of Equations
Content Area/Grade Level(s): _______Algebra 1/9________________
Implementation Time Frame: ______10 days____________
Stage 1 – Desired Results
Established Goals:
A.REI.5: Prove that, given a system of linear equations in two variables, replacing one equation by the sum of that equation and a multiple of the
other produces a system with the same solutions.
A.REI.6: Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
A.REI.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).
A.REI.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.
A.REI.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.
A.CED.1: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic
functions, and simple rational and exponential functions.
A.CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels
and scales.
A.CED.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or
nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of
different foods.
A.CED.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's
law V=IR to highlight resistance R.
Understandings
A system of equations can have one solution, no solution, or infinitely
many solutions and can be determined by examining the slope and
intercept of the equations.
Solutions to equations are represented by each point on the line that is
created by graphing the equation. If 2 lines cross, they share a common
Essential Questions:
What is a solution to a system of equations and how do I know if I’ve
found it?
What are the advantages and disadvantages of solving a system of linear
equations graphically versus algebraically?
How can a system of equations be used to represent and solve real world
solution at the point where they cross. If two inequalities solutions are
shared the solution set can be found in the overlapping shaded region.
Solutions to equations can be found by graphing, substitution or
elimination.
Real world situations can be modeled by systems of equations or
inequalities. These systems can be used to solve problems.
Students will know….
That the slope and the y intercept can be examined to determine if there
is one solution, no solution or infinitely many solutions to a pair of
linear equations.
…that the intersecting point in a system of equations is a solution to
both equations.
…that any point in the shaded region of a linear inequality represents a
solution to that inequality.
Performance Tasks:
Formative assessment – substitution (Pearson)
Formative assessment – elimination (Pearson)
Formative assessment – graphing systems of inequalities
Date
Monday
1-4
problems?
How do I find and represent the solution set to a linear inequality?
How do I find and represent the shared solution set to a system of linear
inequalities?
Students will be able to…….
Find the solution to a system of linear equations by graphing,
substitution and by elimination.
…create a system of equations which models a real world situation.
…graph linear inequalities and systems of inequalities.
…explain that the solution to a system of equations is also a solution to
each equation.
Stage 2 – Assessment Evidence
Other Evidence:
In class assessment – white board, closures, activities
Stage 3 – Learning Plan
Learning Activities & Assessments
Graphing calculator activity-solve by graphing. What is a solution to a system?
Tues.
1-5
Systems of equations – what’s in the box activity
http://mathtalesfromthespring.blogspot.com/2012/12/introducing-systems.html
Wed.
1-6
Solve by substitution – journal activity with instructions, real world examples.
Homework
Thursday Substitution activity – Speed dial
1-7
Friday
1-8
Graphing calculator How Many Solutions – Activity
https://education.ti.com/en/84activitycentral/us
/detail?id=1E982C9CA9794FF98592CFF74F21B612&t=83717EEE82D04244ADB249FEFAC26C30
Monday
1-11
Review Substitution, teach elimination. White board SHOWDOWN choosing between
substitution or elimination
Reflections
Tuesday
1-12
Solving with review
Wed.
1-13
Systems of Inequalities: Notes for journals
Thurs.
1-14
Choose your method review (whiteboard and ppt.) inequalities with colors
Fri.
1-15
Journal notes and application
Monday
1-18
No School – MLK
Tuesday
1-19
Systems of inequalities and dating project (mathalicious – half+7)
Wed.
1-20
Test #1 unit 5