Grade/Course: Algebra I (Second Semester)
Instructional Unit 6: Linear Equations and Inequalities in Two Variables
Instructional Schedule: Third Nine Weeks (suggested for 15 days)
Adapted from Timothy Kanold Scope-and-Sequence documents
Standards:
(BA/PASS 2.2d) Create equations in
two or more variables to represent
relationships between quantities;
graph equations on coordinate axes
with labels and scales.
(BA 2.4a) Represent constraints by
equations or inequalities, and by
systems of equations and
inequalities, and interpret solutions
as viable or non-viable options in a
modeling context.
(BA 2.4b) Prove that, given a system
of two 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.
Evidence Of Standard:
(student should be able to…)
Prerequisite Knowledge:
(standards linked to content taught
in previous grades)
Create equations that describe numbers or relationships. (key content)
-Use appropriate labels and scale
factors on coordinate axes to graph
linear equations of two variables.
-Recognize the relationship between
quantities and create equations of
two variables to represent the
relationship.
-Represent solution constraints by
equations or inequalities.
-Represent solution constraints by
systems of equations and/or
inequalities.-Determine which
solutions are appropriate for the
context of a given real-world
problem.
Solve systems of equations. (additional content)
-Show that when an equation is
multiplied by the same quantity on
both sides of the equals sign, an
equivalent equation results.
-Use the resulting multiple equation
to substitute the original equation
from the two variable system of
equations.
-Demonstrate that the sum of the
other original equation and the new
substituted multiple equation will
result in the same solution as
combining both original equations.
Assessment Tools:
(formative assessments, quizzes,
mastery tasks/activities)
(BA/PASS 2.4) Solve systems of linear
equations exactly and approximately
(e.g., with graphs), focusing on pairs
of linear equations in two variables.
-Solve systems of linear equations in
two variables exactly and
approximately, either algebraically or
graphically.
Represent and solve equations and inequalities graphically. (key content)
(BA/PASS 2.2a) Understand that the
-Understand that the graph of an
graph of an equation in two variables equation in two variables is the set of
is the set of all its solutions plotted in all its solutions plotted in the
the coordinate plane, often forming a coordinate plane (as represented by
curve (which could be a line).
point variables x, y).
(BA/PASS 2.3a) Graph the solutions to -Graph the solutions to a linear
a linear inequality in two variables as inequality in two variables as a halfa half-plane (excluding the boundary plane (excluding the boundary in the
in the case of a strict inequality), and case of a strict inequality).
graph the solution set to a system of -Graph the solution set to a system of
linear inequalities in two variables as linear inequalities in two variables as
the intersection of the corresponding the intersection of the corresponding
half-planes.
half-planes.
Note: Any italicized text denotes portions of a given standard that do not apply to identified standard content in this unit.
Resources/Exemplar Tasks:
( list possible task/activities students could engage in within this unit)
Standards for Mathematical Practice:
(highlight practice standards to be emphasized in the instructional unit)
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of instruction.
8. Look for and express regularity in repeated reasoning.
( BA: Broken Arrow rigor standard; PASS: Priority Academic Student Skills standard; BA/PASS: Combination standard )