Unit Title: Systems of Linear Equations and Inequalities
Grade Level: 9th
Subject: Algebra 1
Topic: Finding Solutions of Systems of Equations and Inequalities
Designer: Ronald Boutte
Date: April 9th, 2013
STAGE 1. DESIRED RESULTS
Established Goals:
TEKS:
 A4A find specific function values, simplify polynomial expressions, transform and solve equations, and factor as necessary in problem situations
 A8A analyze situations and formulate systems of linear equations in two unknowns to solve problems
 A8B solve systems of linear equations using concrete models, graphs, tables, and algebraic methods
 A8C interpret and determine the reasonableness of solutions to systems of linear equations.
Essential Questions to be Considered:
1. What makes a linear system of equations independent or dependent,
and inconsistent or consistent?
2. How are the solutions to a linear system determined?
3. What are the calculator key strokes that will allow you to solve a linear
system of equations?
4. Explain the different methods of solving a linear system of equations
or inequalities.
Desired Understandings:
Students will understand that…
 Systems of linear equations can have one solution, infinite solutions, or
no solutions,
 Relate the solutions to an intersection of two lines, parallel lines, or
exact or same lines,
 The solution of a linear system can be determined by graphing and
finding the break-even point or solution for real world situations.
 The solution of a linear system can be determined using the
substitution method, elimination method, or by graphing
Knowledge and Skills to be Acquired as a Result of this Unit
Students will know…
Students will be able to…
1. Solve systems of equations using various methods including substitution,
 Vectors and matrices as systems that have some of the properties of
elimination using addition and subtraction, and elimination using
the real-number system
multiplication,
 Properties of, and representations for, the addition and multiplication
2. Use a graphing calculator to solve systems of equations by graphing and
of vectors and matrices
matrices,
 Operations with real numbers, vectors, and matrices, using mental
3. Determine the break-even point in terms of the solution of a linear system
computation or paper and pencil calculations for simple cases and
of equation.
technology for more complicated cases.
 The reasonableness of numerical computations (solutions) and their
results.
STAGE 2: ASSESSMENT EVIDENCE
Performance Tasks*:
 The students will be given a consumers role to determine which phone
company has the best deal. They will determine the equations in terms of
the usage and rates, find the break-even points, describe what occurs
before and after the break-even point, and determine reasonableness of
the break-even point. The idea is to simulate a real situation where they
would have to determine a better deal.
Other Evidence:
 Concept Map- The student will use Multi Media to outline a concept map
that highlights different types of solutions (one, infinite, or no solution)
and give a real life situation to depict their understandings. The students
will use GLOGSTER to create their MM design.
 A series of real situations that would allow for misunderstandings to be
addressed
*Multi-Media Student Centered

Rubric attached for at least one of these.
STAGE 3: LEARNING EXPERIENCES
Numbered key teaching and learning activities in arranged by day with WHERETO elements coded.
The unit plan covers a block schedule which is two days to meet with all students.
MONDAY
TUESDAY

Objectives: Solving
systems by graphing.

Objectives: Solving
systems by graphing
1.
Review Graphing of
linear function (W)
1.
Review Graphing of
linear function(W)
2.
Key Terms – Inconsistent,
Consistent, Dependent,
Independent,
Intersection and, Parallel
(W)
2.
Key Terms –
Inconsistent,
Consistent, Dependent,
Independent,
Intersection and,
Parallel. (W)
WEDNESDAY
THURSDAY
In general, a solution of
a system in two
variables is an ordered
pair that makes BOTH
equations true.
3.
Have students sketch
the three different
examples in their
notebooks and label
each with the
appropriate vocabulary
(H)
4.
KWLA –Exit Ticket (H)
In general, a solution of
a system in two
variables is an ordered
pair that makes BOTH
equations true.
3.
4.
FRIDAY
5.
Have students graph,
find the solutions, and
describe the solutions
to the Systems (Ex)
6.
Have students sketch
the three different
examples in their
notebooks and label
each with the
appropriate
vocabulary(O)
7.
KWLA –Exit Ticket (H)
Have students sketch
the three different
examples in their
notebooks and label
each with the
appropriate vocabulary
(H)
KWLA –Exit Ticket (H)
.
MONDAY
TUESDAY
WEDNESDAY
THURSDAY
FRIDAY
5.
Have students graph,
find the solutions, and
describe the solutions to
the Systems (Ex)
6.
Have students sketch
the three different
examples in their
notebooks and label
each with the
appropriate
vocabulary(O)
7.
KWLA –Exit Ticket (H)


SUBSTITUTION:
Objectives: Solve
systems of equations
using substitution.
8.
KWLA –Exit Ticket
8.
(EV)
SUBSTITUTION:
Objectives: Solve
systems of equations
using substitution.
KWLA –Exit Ticket

12. KWLA –Exit Ticket R.)
13. A series of real
situations that would
allow for
misunderstandings to
be addressed (EV)
ELIMINATION BY
MULTIPLICATION
Objectives: Solve
systems of equations
using elimination and
multiplication.
10. KWLA –Exit Ticket
9. A series of real
situations that would
allow for
misunderstandings to
be addressed (R.)


ELIMINATION BY
MULTIPLICATION
Objectives: Solve
systems of equations
using elimination and
multiplication.
(EV)
9. A series of real
situations that would
allow for
misunderstandings to
be addressed (R.)
11. A series of real
WEDNESDAY
14. Students will want a
copy of the steps to
inputting
a
matrix
system
into
their
calculator and how to
solve it. (T)
THURSDAY
14. F-Students will want a
copy of the steps to
inputting
a
matrix
system
into
their
calculator and how to
solve it. (T)
15. Concept Map (O)
15. Concept Map (O)
16. KWLA –Exit Ticket(R)
16. KWLA –Exit Ticket(R)
.
MONDAY
MATRICES
Objectives: Solve
systems of
equations using
matrices.

TUESDAY
MATRICES
Objectives: Solve
systems of
equations using
matrices.
(EV)
situations that would
allow for
misunderstandings to
be addressed (R)
12. KWLA –Exit Ticket R.)
13. A series of real
situations that would
allow for
misunderstandings to
be addressed (EV)
10. KWLA –Exit Ticket
(EV)
11. A series of real
situations that would
allow for
misunderstandings to
be addressed (R)
FRIDAY
1. Concept Map- Used
to determine whether
students understand
the difference
between inconsistent
systems and
consistent systems.
Used to determine
whether students
understand the
difference of an
intersection, parallel
lines, or same lines
(O)
STAGE 3: LEARNING EXPERIENCES
Key teaching and learning activities numbered and in sequence with WHERETO elements coded.
DAY 1 and
Day2
DAY 1 Introduce idea of what is a system of equations Solve systems of equations by graphing Use graphing calculators & graph paper
Key Vocab: system of equations, consistent, inconsistent, dependent, independent, intersection (W)
DAY 2 Solve systems by substitution Use Algebra Tiles Key Vocab:
Day 3 and
Day 4
DAY 3 Solve systems by elimination using addition or subtraction Key Vocab: Elimination
DAY 4 Solve systems by elimination using multiplication
DAY 5 Solve systems using matrices Use Graphing calculators (Note Taking Guide)
DAY 5 and
Day 6
DAYS 7 and
Day 8
Day 9 and
Day 10
DAY 6 Complete review/ take up review sheet Alg Ch 5 App from TI may be used to help review Quiz *NOTE: Days can be rearranged;
only elimination by addition should be taught before elimination by multiplication
DAY 7 Complete a graphic organizer that demonstrates an understanding character
DAY 8 Complete a graphic organizer that demonstrates an understanding character
DAY 9: Assessment / Ext Tickets (KLWA)
DAY 10 : Assessment/ / Ext Tickets (KLWA