Mathematics
Curriculum Documentfor Algebra 2
Unit Title: Systems and Quadratics / Time Frame: 12 blocksSix Weeks:2nd / Unit Number: 2 and 3
Curriculum
Enduring Understandings (Big Ideas):
- Representing a situation in a variety of ways increases understanding.
- Choosing the right tools to solve a problem makes you more efficient.
- A “right” answer is not the same as a “reasonable” answer.
- Graphs provide a visual representation of how the parts are related to the whole.
- No one mathematical representation is best for all situations.
- Changing one parameter of a situation affects the whole.
- Systems include two or more equations/inequalities
- What the solution(s) to a system of equations/inequalities represents
- Matrices can be used to represent data or systems
- There are four different methods to solving systems (substitution, elimination, graphing, and matrices)
- Different forms of quadratic functions (standard, vertex, and intercept forms)
- Graphs of quadratic functions are parabolas
- x-intercepts of a parabola are roots/solutions/zeros of the equation
- Solve systems of linear equations/inequalities graphically
- Solve systems of linear equations/inequalities using tables
- Solve systems of linear equations algebraically
- Use systems of linear equations/inequalities to represent real-life models
- Interpret and determine the reasonableness of a solution to a system of linear equations for given contexts
- Formulate and analyze systems of more than two variable equations/inequalities
- Solve systems of equations/inequalities with more than two variables
- Solve systems of linear equations using matrices
- Identify and sketch the quadratic parent function
- Identify characteristics of a parabola including vertex, axis of symmetry, x-intercept, y-intercept
- Translate the quadratic function using a (stretch), h (horizontal) , and k (vertical)
- Identify the domain and range of quadratic functions
- Relate multiple representations of quadratic functions (table, graph, equation, and verbal)
- Determine and graph a quadratic function from its roots
- Convert from standard form to intercept form to graph the function
- Graph quadratic inequalities
- Solve systems of quadratic equations/inequalities graphically
Essential Questions:
- How do we know a relationship exists?
- How do we compare real life situations mathematically?
- How do we know which method is most efficient?
- What is a solution and what does it represent?
- How do you know you have the correct solution?
- Why is it important to approach a problem from more than one perspective?
- How do we visually represent mathematical ideas?
- How is the whole picture affected when one aspect is altered?
- Why is it useful to represent mathematical ideas in different ways?
Student Understanding (student friendly TEKS):
- I can solve systems of linear equations/inequalities graphically. (taken from 2A.3B)
- I can solve systems of linear equations/inequalities using tables. (taken from 2A.3B)
- I can solve systems of linear equations algebraically. (taken from 2A.3B)
- I can use systems of linear equations/inequalities to represent real-life models. (taken from 2A.3A)
- I can interpret and determine the reasonableness of a solution to a system of linear equations for given contexts (taken from 2A.3C)
- I can write and analyze systems of more than two variable equations/inequalities. (taken from 2A.3A)
- I can solve systems of equations/inequalities with more than two variables. (taken from 2A.3B)
- I can solve systems of linear equations using matrices. (taken from 2A.3B)
- I can identify and sketch the quadratic parent function. (taken from 2A.4A)
- I can identify characteristics of a parabola including vertex, axis of symmetry, x-intercept, y-intercept. (taken from 2A.7A)
- I can translate the quadratic function using a (stretch), h (horizontal) , and k (vertical). (taken from 2A.7B and 2A.4B)
- I can describe the effects of parameter changes on the quadratic function. (taken from 2A.4B and 2A.7B)
- I can identify the domain and range of quadratic functions. (taken from 2A.6A)
- I can relate multiple representations of quadratic functions (table, graph, equation, and verbal). (taken from 2A.6B)
- I can determine and graph a quadratic function from its roots. (taken from 2A.6C)
- I can convert from standard form to intercept form to graph the function. (taken from 2A.2A and 2A.6C)
- I can graph quadratic inequalities. (taken from 2A.6A)
- I can solve systems of quadratic equations/inequalities graphically. (taken from 2A.3B)
TEKS:
(A2.3)Foundations for functions. The student formulates systems of equations and inequalities from problem situations, uses a variety of methods to solve them, and analyzes the solutions in terms of the situations. The student is expected to:
(A)analyze situations and formulate systems of equations in two or more unknowns or inequalities in two unknowns to solve problems;
(B)use algebraic methods, graphs, tables, or matrices, to solve systems of equations or inequalities; and
(C)interpret and determine the reasonableness of solutions to systems of equations or inequalities for given contexts.
(A2.4)Algebra and geometry. The student connects algebraic and geometric representations of functions. The student is expected to:
(A)identify and sketch graphs of parent functions, including linear (f (x) = x),
quadratic (f (x) = x2), exponential (f (x) = ax), and logarithmic (f (x) = logax) functions, absolute value of x (f (x) = |x|), square root of x (f (x) = x), and reciprocal of x (f (x) = 1/x);
(B)extend parent functions with parameters such as a in f (x) = a/x and describe the effects of the parameter changes on the graph of parent functions; and
(A2.6)Quadratic and square root functions. The student understands that quadratic functions can be represented in different ways and translates among their various representations. The student is expected to:
(A)determine the reasonable domain and range values of quadratic functions, as well as interpret and determine the reasonableness of solutions to quadratic equations and inequalities;
(B)relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions; and
(C)determine a quadratic function from its roots (real and complex) or a graph.
(A2.7)Quadratic and square root functions. The student interprets and describes the effects of changes in the parameters of quadratic functions in applied and mathematical situations. The student is expected to:
(A)use characteristics of the quadratic parent function to sketch the related graphs and connect between
the y = ax2 + bx + c and the y = a (x - h)2 + k symbolic representations of quadratic functions; and
(B)use the parent function to investigate, describe, and predict the effects of changes in a, h, and k on the graphs of
y = a (x - h)2 + k form of a function in applied and purely mathematical situations.
Targeted College Readiness Standards:
- IC1, IIB1, IIC1, IIC2, IID1, IID2, VIIB1, VIIB2, VIIC1, VIIC2, VIIIA1, VIIIA2, VIIIA3, VIIIA4, VIIIA5, VIIIB1, VIIIB2, VIIIC1, VIIIC2, VIIIC3, IXA1, IXA2, IXA3, IXB1, IXB2, IXC1, IXC2, IXC3, XA1, XA2, XB1, XB2, XB3
Targeted ELPs:
- 1A, 1C, 1D, 1E, 1F, 1H, 2C, 2E, 2G, 2I, 3D, 3E, 3F, 3G, 3H, 3J, 4C, 4D
Academic Vocabulary:
- Matrix
- Axis of symmetry
- Maximum
- Minimum
- Parabola
- Roots
- vertex
- Zeros
elimination
point of intersection
slope
substitution
systems
y-intercept
domain
inequalities
intercept form/factored form
quadratic
range
solutions
standard form
systems
transformations
vertex form
x-intercepts
y-intercepts
Instruction
Instructional Resources:
Textbook:
- Chapter 3
- Chapter 4
Technology:
Graphing calculator / Career Connections/Real Life Application:
Exemplar Lessons: / Research Based Instructional Strategies:
Interactive Lecture
Assessment
Student self-assessment & reflection: / Acceptable evidence or artifacts:
Chapter 3.1-3.4 test
Chapter 3.5-3.8 test
Chapter 4.1-4.4 test
TIMELINE
Date / Lesson / HomeworkSept 30,Oct 3 / 3.2 Solve Linear Systems Algebraically / Workbook 3.2
4,5 / 3.4 Solve Systems of Linear Equations in Three Variables / Workbook 3.4
6,7 / 3.3 Graph Systems of Linear Inequalities / Workbook 3.3
11,12 / Review systems from 3.1-3.4 / Review Worksheet
13,14 / Test / Review PSAT booklet
17,18 / PSAT
19,20 / 3.5 Perform Basic Matrix Operations
3.6 Multiply Matrices / Workbook 3.5
Workbook 3.6
21,24 / 3.7 Evaluate Determinants and Solve Systems with the calculator
3.8 Evaluate Inverses of matrices / Workbook 3.7
Workbook 3.8
25,26 / Review matrices from 3.5-3.8 / Review Worksheet
27,28 / Test
31, Nov 1 / 4.1 Graph Quadratic Functions in Standard Form
4.2 Graph Quadratic Functions in Vertex Form / Workbook 4.1
Workbook 4.2
2,3 / 4.3 Factoring using GCF, trinomials and Difference of Squares methods / Workbook 4.4
Unit Title: Systems Unit Number 2Page 1 of 6