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Algebra I: Strand 2. Linear Functions; Topic 12. Systems of equations; Topic Notes
STRAND 2: LINEAR FUNCTIONS
TOPIC 2.12: SYSTEMS OF EQUATIONS
Topic Notes
Mathematical focus
The objective of this activity is to have students analyze situations that require the
formulation of systems of linear equations to solve them.
Topic overview
Participants will be presented with several situations involving purchasing tickets. They
will formulate systems of equations using a process column and a table and will find
solutions and make connections between tabular, graphical, and symbolic representations.
This topic contains two tasks:
Task 2.12.1: Donkey Basketball Fundraiser
Task 2.12.2: Susie’s Homework
TExES standards focus
TExES Standard II.006 Patterns and algebra. The teacher understands linear and quadratic
functions, analyzes their algebraic and graphical properties, and uses them to model and solve
problems. The beginning teacher:
(C) Applies techniques of linear and matrix algebra to represent and solve
problems involving linear systems.
(G) Models and solves problems involving linear and quadratic equations and
inequalities using a variety of methods, including technology.
TEKS/TAKS focus
TEKS A.2 Foundations for functions. The student uses the properties and attributes of
functions. The student is expected to:
(B) identify mathematical domains and ranges and determine reasonable domain and
range values for given situations, both continuous and discrete.
TEKS A.3 Foundations for functions. The student understands how algebra can be used to
express generalizations and recognizes and uses the power of symbols to represent situations.
The student is expected to:
(A) use symbols to represent unknowns and variables; and
(B) look for patterns and represent generalizations algebraically.
High School TAKS Objective 2: The student will demonstrate an understanding of the
properties and attributes of functions.
November 22, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at
Austin for the Texas Higher Education Coordinating Board.
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Algebra I: Strand 2. Linear Functions; Topic 12. Systems of equations; Topic Notes
TEKS A.5 Linear functions. The student understands that linear functions can be represented
in different ways and translates among their various representations. The student is expected to:
(B) determine the domain and range for linear functions in given situations; and
(C) use, translate, and make connections among algebraic, tabular, graphical, or verbal
descriptions of linear functions.
TEKS A.6 Linear functions. The student understands the meaning of the slope and intercepts
of the graphs of linear functions and zeros of linear functions and interprets and describes the
effects of changes in parameters of linear functions in real-world and mathematical situations.
The student is expected to:
(B) interpret the meaning of slope and intercepts in situations using data, symbolic
representations, or graphs; and
(E) determines the intercepts of the graphs of linear functions and zeros of linear
functions from graphs, tables, and algebraic representations.
High School TAKS Objective 3: The student will demonstrate an understanding of linear
functions.
TEKS A.7 Linear functions. The student formulates equations and inequalities based on linear
functions, uses a variety of methods to solve them, and analyzes the solutions in terms of the
situation. The student is expected to:
(A) analyze situations involving linear functions and formulate linear equations or
inequalities to solve problems;
(B) investigate methods for solving linear equations and inequalities using concrete
models, graphs, and the properties of equality, select a method, and solve the equations
and inequalities; and
(C) interpret and determine the reasonableness of solutions to linear equations and
inequalities.
TEKS A.8 Linear functions. The student formulates systems of linear equations from problem
situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the
situation. The student is expected to:
(A) analyze situations and formulate systems of linear equations in two unknowns to
solve problems;
(B) solve systems of linear equations using concrete models, graphs, tables and algebraic
methods; and
(C) interpret and determine the reasonableness of solutions to systems of linear
equations.
High School TAKS Objective 4: The student will formulate and use linear equations and
inequalities.
November 22, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at
Austin for the Texas Higher Education Coordinating Board.
3
Algebra I: Strand 2. Linear Functions; Topic 12. Systems of equations; Topic Notes
Materials
Task
Copies of the task “Donkey
Basketball Fund Raiser”
Graphing calculator
Graph paper
Chart paper
#1
#2
x
x
x
x
x
x
x
x
Procedure
After giving each student a copy of the task, break the class into groups of 3 or 4. Give
each group a piece of chart paper. At the end of the first problem, bring the class back
together to make sure that the students have the correct rules. Ask students to complete
the rest of the problems, recording their work on the chart paper. After all have
completed the tasks, post the solutions while letting each group explain their approach for
given questions.
Summary
After completing these tasks, participants will have a better understanding of systems and
their solutions and how they relate to the real world.
Extensions
In TEXTEAMS Algebra I: 2000 and Beyond, Systems of Linear Equations will provide
supplementary materials for participants. In addition, Algebra I Assessments Chapter 8:
Interacting Linear Functions, Linear Systems, also provides extension activities.
Assessment/Transition to the classroom
Participants should complete the Teacher’s Journal, recording their responses and making
any modifications necessary to make the tasks completely classroom ready.
November 22, 2004. Ensuring Teacher Quality: Algebra I, produced by the Charles A. Dana Center at The University of Texas at
Austin for the Texas Higher Education Coordinating Board.