Download Algebra_2_files/Scope and Sequence Alg 2A 2013-14

Scope and Sequence – Algebra 2A
2013-14
Course
Algebra 2A (.5 credits)
Instructor(s)
Sue Harvey, Paul Huggins, Theresa Kahl, Dave Hauser
Text
Prentice Hall - - Algebra 2 - - 2004
Prerequisite
Grade
Course
Description
Geometry or Informal Geometry
11th and 12th
This course emphasizes the study of algebraic forms of linear expressions. It includes solving
systems of equations and inequalities. Graphing calculators will be used extensively in this
course to help tie in the relationship between these functions and real world situations. This
course places emphasis on applications and meets the college minimum requirement for an
Algebra II course
Units
Unit 1 ( 2.5 weeks): Equations and Inequalities
Common Core State Standards Covered (Codes only):
A.REI.1
A.REI.3
A.CED.1 A.REI.11
Unit 2 ( 2 weeks): Linear Equations and Functions
Common Core State Standards Covered (Codes only):
A.REI.10 A.REI.12 F.IF.1 F.IF.2 G.GPE.L.5 F.LE.2
Unit 3 ( 2 weeks): Liner Applications
Common Core State Standards Covered (Codes only):
A.CED.2 S.ID.6 S.ID.7 S.ID.8 S.ID.9 A.CED.3 F.IF.5
Unit 4 ( 2 weeks): Systems of Equations
Common Core State Standards Covered (Codes only):
A.REI.5 A.REI.6 A.REI.10 A.REI.12
(1 week): Oaks Review and Testing
EA
Opportunities
CRLE
Opportunities
F.IF.6
F.IF.9
Unit 1:
Equations and Inequalities
Time Frame 2.5 weeks
Summary of
 Algebraic expressions and models
Unit
 Solving linear equations
 Solving linear inequalities
 Applications using distance, rate and time
 Geometry applications
 Solving two-sided equations with a graphing calculator
CCSS
Code
A.REI.1
A.REI.3
A.CED.1
A.REI.11
Common Core State Standard
Explain each step in solving a simple equation as following from the equality of numbers
asserted at the previous step, starting from the assumption that the original equation
has a solution. Construct a viable argument to justify a solution method
Solve linear equations and inequalities in one variable, including equations with
coefficients represented by letters.
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.
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.★
Major
Assignments/
Learning
Activities
Work Sample
Unit Test
Learning
Targets
I can explain why equivalent expressions are equivalent.
I can write the equation or inequality that best models the problem.
I can solve an equation or inequality
I can interpret the solution in the context of the problem.
I can infer that the x-coordinate of the points of intersection for y = f(x) and y = g(x) are also
solutions for f(x) = g(x).
Essential
Questions
Academic
Vocabulary
Performance
Tasks or
Work
Samples
Expressions, terms, factors, coefficients, simplify, solve, equations, inequality, rate
Distance = rate x time work sample
Unit 2:
Linear Equations and Functions
Time Frame 2 weeks
Summary of
 Functions and their graphs
Unit
 Slope
 Writing equations of lines
 Parallel and perpendicular lines
 Solving two variable inequalities
 Graphing inequalities
CCSS
Code
A.REI.10
A.REI.12
F.IF.1
F.IF.2
G.GPE.5
F.LE.2
Common Core State Standard
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).
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.
Understand that a function from one set (called the domain) to another set (called the
range) assigns to each element of the domain exactly one element of the range. If f is a
function and x is an element of its domain, then f(x) denotes the output of f
corresponding to the input x. The graph of f is the graph of the equation y = f(x).
Use function notation, evaluate functions for inputs in their domains, and interpret
statements that use function notation in terms of a context.
Prove the slope criteria for parallel and perpendicular lines and use them to solve
geometric problems (e.g., find the equation of a line parallel or perpendicular to a given
line that passes through a given point).
Construct linear and exponential functions, including arithmetic and geometric
sequences, given a graph, a description of a relationship, or two input-output pairs
(include reading these from a table).
Major
Assignments/
Learning
Activities
Unit Test
Learning
Targets
I can explain that every point on the graph of an equation represents values x and y that make
the equation true.
I can graph a linear inequality on a coordinate plane resulting in a boundary line (solid or
dashed) and a shaded half-plane.
I can define a function as a relation in which each input (domain) has exactly one output
(range).
I can analyze the input and output values of a function based on a problem situation.
I determine if lines are parallel/perpendicular using their slopes.
I can write an equation for a line that is parallel/perpendicular to a given line that passes
through a given point.
I can construct a linear function from an arithmetic sequence, graph, table of values, or a
description of relationships.
I can identify the variables and quantities represented in a real-world problem
I can interpret solutions in the context of the situation modeled and decide if they are
reasonable.
I can state the appropriate domain of a function that represents a problem situation, defend my
choice, and explain why other numbers might be excluded from the domain.
I can interpret the meaning of the average rate of change (using units) as it relates to a realworld problem.
I can compare properties of two functions when represented in different ways (algebraically,
graphically, numerically in tables, or by verbal descriptions)
Essential
Questions
Academic
Vocabulary
For 2014-15
Performance
Tasks or
Work
Samples
None for this unit.
Parallel, Perpendicular, half-plane, boundary line, function, relation, domain, range,
Unit 3:
Linear Applications
Time Frame 2 weeks
Summary of
 Application of Linear situations
Unit
 Scatterplots
 Linear regression
 Problem solving, real world situations, using linear regression
CCSS
Code
A.CED.2
S.ID.6
Create equations in two or more variables to represent relationships between
quantities; graph equations on coordinate axes with labels and scales.
Represent data on two quantitative variables on a scatter plot, and describe how the
variables are related.
a. Fit a function to the data; use functions fitted to data to solve problems
in the context of the data. Use given functions or choose a function
suggested by the context. Emphasize linear and exponential models.
b. Informally assess the fit of a function by plotting and analyzing
residuals.
c. Fit a linear function for a scatter plot that suggests a linear association.
S.ID.7
Interpret the slope (rate of change) and the intercept (constant term) of a linear model
in the context of the data.
S.ID.8
Compute (using technology) and interpret the correlation coefficient of a linear fit.
S.ID.9
A.CED.3
Distinguish between correlation and causation.
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
Relate the domain of a function to its graph and, where applicable, to the quantitative
relationship it describes. For example, if the function h(n) gives the number of personhours it takes to assemble n engines in a factory, then the positive integers would be an
appropriate domain for the function.★
F.IF.5
Major
Assignments/
Common Core State Standard
F.IF.6
Calculate and interpret the average rate of change of a function (presented symbolically
or as a table) over a specified interval. Estimate the rate of change from a graph.★
F.IF.9
Compare properties of two functions each represented in a different way (algebraically,
graphically, numerically in tables, or by verbal descriptions). For example, given a graph
of one quadratic function and an algebraic expression for another, say which has the
larger maximum.
Linear Regression Project
Work Sample
Learning
Activities
Unit Test
Learning
Targets
I can graph equations on coordinate axis with appropriate labels and scales.
I can identify the dependent and independent variable and describe the relationship.
I can construct a scatterplot with appropriate scales
I can write the equation of the line of best fit (y = mx + b) using technology or by using two
points (by hand) on the best-fit line.
I can interpret the meaning of the slope and the y-intercept in terms of the units used in the data.
I can use the correlation coefficient to determine if a linear model is a good fit for the data.
I can recognize that correlation does not imply causation and that causation is not illustrated on
a scatter plot.
Essential
Questions
Academic
Vocabulary
For 2014-15
Performance
Tasks or
Work
Samples
Regression Work Sample
Scatterplot, dependent, independent, line of best fit, correlation, causation,
Unit 4:
Systems of Equations
Time Frame 2 Weeks
Summary of
 Solving systems of equations by graphing
Unit
 Solving systems of equations by the substitution method
 Solving systems of equations by the elimination method
 Solving systems of inequalities by graphing
 Writing to justify why solutions work
CCSS
Code
Common Core State Standard
A.REI.5
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.
Solve systems of linear equations exactly and approximately (e.g., with graphs),
focusing on pairs of linear equations in two variables.
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).
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.REI.6
A.REI.10
A.REI.12
Major
Assignments/
Learning
Activities
Work Sample
Unit Test
Learning
Targets
I can solve systems of linear equations graphically and algebraically.
I can solve a system of two equations in two variables by elimination.
I can solve a system of two equations in two variables by substitution.
I can demonstrate that replacing one equation with the sum of that equation and a multiple of the
other creates a system with the same solutions as the original system.
I can explain why some linear systems have no solutions and identify linear systems that have no
solutions.
I can explain why some linear systems have infinitely many solutions and identify linear systems that
have infinitely many solutions.
I can define linear inequality, half-plane, and boundary.
I can graph a linear inequality on a coordinate plane, resulting in a boundary line (solid or dashed) and
shaded half-plane
I can explain that the solution set for a system of linear inequalities is the intersection of the shaded
regions (half-plains) of both inequalities
Essential
Questions
Academic
Vocabulary
For 2014-15
Performance
Tasks or
Work
Samples
Systems Work Sample
Solution, substitution, elimination,