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MCSD Mathematics Curriculum
Algebra II
Planned Instruction
Title of Planned Instruction: Algebra II
Subject Area: Mathematics
Grade Level: Grades 9-12
Prerequisites: Algebra I with a grade of A, B,
or C
Course Description:
This course builds on the concepts and skills learned in Algebra
I. Advancements in understanding how to solve equations and graph
functions form the basis for this course. Modeling real life
situations using algebraic techniques allows the students to see
how algebra is applied in today’s ever changing world.
Required Time: 180 days
Major Text(s) and Resources:
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Merrill Algebra 2 with Trigonometry:
Applications and Connections,
Copyright 1992 by Glencoe Macmillan/McGraw-Hill |
| Names of District Subject Area
Curriculum Writing Committee: |
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Daniel F. Bartos, -- Lewistown High School
Sonya D. Curry -- Indian Valley High School
Margaret J. Fisher -- Indian Valley High School
Randy J. Loht -- Lewistown High School |
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Date of Board Approval: July 24, 2003
Major Topics
- Non-linear equations
- Matrices
- Graphing
- Quadratics
- Powers
- Probability
- Systems
- Applications
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Course Objectives and Performance Indicators -----
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Strand: 2.1
Standard: Numbers, Number Systems and Relationships
Course: Algebra II |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
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2.1.11A |
Use algebraic operations. |
Use properties of real
numbers to simplify expressions. Use properties of powers to simplify
powers.
Find the greatest monomial factor of an algebraic expression.
Multiply and divide monomials.
Add, subtract, and multiply polynomials.
Divide polynomials using synthetic division and long division.
Factor polynomials.
Find roots of equations.
Multiply and divide radicals.
Add, subtract, multiply, and divide radical expressions.
Calculate determinants.
Find the sum and product of the roots of the quadratic.
Add, subtract, multiply, and divide complex and imaginary numbers. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.2
Standard: Computation and Estimation
Course: Algebra II |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
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2.2.11A |
Develop and use computation
concepts, operations and procedures with real numbers in problem-solving
situations. |
Perform calculations that
require multiple procedures and operations involving real numbers. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.2.11B |
Use estimation to solve
problems for which an exact answer is not needed. |
Perform multi-step
estimates involving real numbers. Estimate the answer to problems that
contain radicals. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.2.11C |
Construct and apply
mathematical models, including lines and curves of best fit, to estimate
values of related quantities. |
Identify the graphical
representation that best approximates a line of best fit for a given
scatter-plot. Extrapolate an answer from a given scatter-plot.
Interpolate an answer from a given scatter-plot.
Find maximum or minimum values for a given situation using linear
programming techniques. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.2.11D |
Describe and explain the
amount of error that may exist in a computation using estimates. |
Use a prediction equation
derived from a scatter plot to predict a result and then compare it to the
actual data. Use technology (graphing calculator) to find the
correlation coefficient of the regression line and explain what the number
means. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.2.11E |
Recognize that the degree
of precision needed in calculating a number depends on how the results
will be used and the instruments used to generate the measure. |
Compare and contrast the
solution(s) of an equation solved by graphing (hand and graphing
calculator) the related function and solved using other techniques. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.2.11F |
Demonstrate skills for
using scientific and graphing calculators. |
Use scientific and graphing
calculators to answer questions. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.3
Standard: Measurement and Estimation
Course: Algebra II |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
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2.3.11A |
Select and use appropriate
units to measure to the degree of accuracy required in particular
situations. |
Determine reasonable
estimates for multi-step problems that involve conversion of units of
measure. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.4
Standard: Mathematical Reasoning and Connections
Course: Algebra II |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
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2.4.11A |
Use proof by contradiction
to validate conjectures. |
Make conjectures about
graphical transformations and use a graphing calculator to validate or
contradict (e.g., given parent graph f(x) = |x|, guess how graph would
change for 3f(x), f(3x), f(x+3), and f(x)+3). |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.4.11B |
Construct valid arguments
from stated facts. |
Solve algebraic equations
using appropriate techniques. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.4.11E |
Demonstrate mathematical
solutions to problems. |
Use algebraic techniques to
solve problem situations involving formulas used in science (e.g., volume,
distance, business). |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.5
Standard: Mathematical Problem Solving and Communication
Course: Algebra II |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
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2.5.11A |
Select and use appropriate
mathematical concepts and techniques from different areas of mathematics
and apply them to solving non-routine and multi-step problems. |
Select, use, and display
all of the mathematical procedures that are necessary to the solution of a
problem situation and achieve the correct answer. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.5.11B |
Use symbols, mathematical
terminology, standard notation, mathematical rules, graphing and other
types of mathematical representations to communicate observations,
predictions, concepts, procedures, generalizations, ideas and results. |
Communicate all of the
mathematical procedures concepts, conclusions, etc. necessary to the
solution of a problem situation using correct and appropriate mathematical
representations. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.5.11C |
Present mathematical
procedures clearly, systematically, succinctly and correctly. |
Present all of the
procedures important to the solution of a problem in ways that are
understandable. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.5.11D |
Conclude a solution process
with a summary of results and evaluate the degree to which the results
obtained represent an acceptable response to the initial problem and why
the reasoning is valid |
Explain how a problem was
solved and why the chosen procedures were used. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.6
Standard: Statistics and Data Analysis
Course: Algebra II |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
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2.6.11C |
Determine the regression
equation of best fit (e.g., linear, quadratic). |
Find lines of regression
using a graphing calculator or graphing on paper by drawing a scatter
plot. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.7
Standard: Probability and Predictions
Course: Algebra II |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
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2.7.11A |
Compare odds and
probability. |
Compare the odds of an
event and the probability of an event. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.7.11B |
Apply probability and
statistics to perform an experiment involving a sample and generalize its
results to a given population. |
Perform an experiment
involving a sample and apply probability and statistics to describe and
generalize the results to a given population. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.7.11C |
Draw and justify a
conclusion regarding the validity of a probability or statistical
argument. |
Determine a conclusion for
a probability or statistical argument. Justify the validity of the
conclusion for a probability or statistical argument. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.7.11D |
Use experimental and
theoretical probability distributions to make judgments about the
likelihood of various outcomes in uncertain situations. |
Predict outcomes for given
situations using theoretical probability distributions. Predict outcomes
for given situations using information gathered from experimental
probability distributions. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.7.11E |
Solve problems involving
independent simple and compound events. |
Draw diagrams and charts to
help find probability. Solve problems involving simple events.
Solve problems involving compound events. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.8
Standard: Algebra and Functions
Course: Algebra II |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
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2.8.11A |
Analyze a given set of data
for the existence of a pattern and represent the pattern algebraically and
graphically. |
Given a table of values,
find a relationship between two variables. Represent the relationship
between two variables by graphing and by equation. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.8.11B |
Give examples of patterns
that occur in data from other disciplines. |
Find examples of patterns
that occur in data from science, business, or other areas. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.8.11C |
Use patterns to solve
routine and non-routine problems. |
Find the next number in a
sequence. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.8.11D |
Formulate expressions,
equations, inequalities, systems of equations, systems of inequalities and
matrices to model routine and non-routine problem situations. |
Transform word expressions
into algebraic expressions, equations, and inequalities. Write systems
of equations and inequalities given information about a situation. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.8.11E |
Use equations to represent
curves (e.g., lines, parabolas). |
Given a graph of a function
or relation, write the equation. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.8.11F |
Identify whether systems of
equations and inequalities are consistent or inconsistent. |
Graph a system of linear
equations. Indicate the number of solutions to a system.
Classify a system as consistent and independent, consistent and
dependent, or inconsistent.
Classify a system without graphing. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.8.11G |
Analyze and explain systems
of equations, systems of inequalities and matrices. |
Given a real world
situation, write a system of equations and inequalities. Solve a system
of equations by graphing, elimination, substitution, or Cramer’s Rule.
Interpret the solution to a system. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.8.11H |
Select and use an
appropriate strategy to solve systems of equations and inequalities using
graphing calculators. |
Solve a system of linear or
quadratic equations (or inequalities) by graphing. Use both a graphing
calculator and its utilities and graphing by hand to find the solution.
Solve a system of equations by applying Cramer’s Rule.
Solve a system of equations by using algebraic techniques. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.8.11I |
Use matrices to organize
and manipulate data, including matrix addition, subtraction,
multiplication and scalar multiplication. |
Solve a system of equations
in two variables using Cramer’s rule. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.8.11J |
Demonstrate the connections
between algebraic equations and inequalities and the geometry of relations
in the coordinate plane. |
Use equations to help draw
linear, greatest integer, absolute value, and quadratic functions or
relations. Use intercepts to help graph functions or solve related
equations. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.8.11K |
Select, justify and apply
appropriate technique to graph a linear function in two variables,
including slope-intercept, x-and y-intercepts, graphing by transformations
and the use of a graphing calculator. |
Write linear equations in
standard form, and then graph using intercepts. Write equations in
slope-intercept form, and then graph using slope and y-intercept
Use graphing calculators to explore linear transformations.
Graph linear equations by applying concepts of transformations.
Given a linear equation, choose a method to graph and justify the
chosen method. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.8.11L |
Write the equation of a
line when given the graph of the line, two points on the line, or the
slope of the line and a point on the line. |
Given a graph, two points,
one point and the slope, write the equation of the line using point-slope
form and/or slope-intercept form. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.8.11M |
Given a set of data points,
write an equation for a line of best fit. |
Draw a scatter plot and a
line of best fit. Write a prediction equation. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
|
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2.8.11N |
Solve linear, non-linear,
and quadratic equations both symbolically and graphically. |
Solve linear and non-linear
equations by making a table of ordered pairs or by using algebraic
techniques. Solve linear and non-linear equations by graphing the
related function.
Solve a quadratic equation by graphing the related function and/or by
using algebraic techniques. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.8.11O |
Determine the domain and
range of a relation, given a graph or set of ordered pairs. |
State the domain and range
of a relation when given a graph, a set of ordered pairs, or a mapping. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.8.11P |
Analyze a relation to
determine whether a direct or inverse variation exists and represent it
algebraically and graphically. |
Identify the best graphical
representation of a relation of direct or inverse
variation. Represent a relation of direct or inverse variation
using an algebraic equation. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.8.11Q |
Represent functional
relationships in tables, charts and graphs. |
Graph a relation and
determine if the relation is a function. Use a table to identify ordered
pairs for a function.
Write equations for parallel and perpendicular lines.
Determine slope and intercepts from tables, graphs, and equations. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.8.11R |
Create and interpret
functional models. |
Use linear programming
procedures to solve problems. Use graphs to represent real life
situations and to help find solutions to questions about those situations.
Use equations to represent situations and to help find solutions to
questions about those situations.
Collect data from a problem situation, and construct a scatter plot
which can be used to find the equation that represents the data.\ |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.8.11S |
Analyze properties and
relationships of functions. |
Graph linear, quadratic,
absolute value, and greatest integer functions.
Identify distinguishing characteristics of linear and quadratic
functions.
Identify relationships between variables in linear and quadratic
functions. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.8.11T |
Analyze and categorize
functions by their characteristics. |
Given a graph of a
function, identify it as linear, quadratic, absolute value, or greatest
integer. Given an equation, identify it as linear, quadratic, absolute
value, or greatest integer function. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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Strand: 2.11
Standard: Concepts of Calculus
Course: Algebra II |
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Course Objectives |
Performance
Indicators |
Assessment
Options |
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2.11.11A |
Determine maximum and
minimum values of a function over a specified interval. |
Find the maximum and
minimum values of a function defined for a polygonal convex set. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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2.11.11B |
Interpret maximum and
minimum values in problem situations. |
Solve linear programming
problems that involve maximum and minimum values. |
- Observation
- Evaluate written work
- Performance assessments
- Tests, quizzes
- Problem solving journal/activity
- Evaluate oral response
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District Recommended Instructional Approaches For
the Course
To Drive Teacher’s Instructional Activities |
- Whole group instruction
- Small group instruction
- Projects
- Class discussion
- Peer evaluation
- Teacher and peer conferencing
- Oral presentations
- Individual instruction
- Research
- Dramatization
- Role playing
- Independent reading
- Read aloud
- Directed reading-thinking activities
- Modeling process
- Games
- Self-reflection
- Self-evaluation
- Independent study
- Guest speaker
- Guest reading
- Writing activities
- Thematic units
- Study guides
- Notebooks
- Computer technology
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