Download Adel DeSoto Minburn (ADM) High School Algebra I Instructor: Mr

Adel DeSoto Minburn (ADM) High School
Algebra I
Instructor: Mr. David Zwank
Email: [email protected]
Room 202
I.
Course Description. Algebra I is designed to give students a solid foundation in
algebra concepts and skills. The course covers laws of mathematics, operations with signed
numbers, concepts of sets, solutions of equations and inequalities, factoring, functions, and
real numbers. The course spends a great deal of time on various types of word problems.
Algebra I is recommended for students who plan to attend college.
II. Rationale. Mathematical skills and concepts stress the ability to read for
comprehension, pay attention to detail, follow directions and think abstractly. It is
impossible to know what future occupations and responsibilities high school age students
will have. The ability to analyze information, apply rules that govern outcomes and look for
answers is essential not matter what role in life someone takes. Mathematics is a language
that explains the world around us. Algebra is just one stepping-stone to furthering this
understanding and being able to communicate it to others.
III.
Textbook and class resources.
a. Textbook. Charles, Randall I. Algebra 1: Common Core. Boston, MA: Pearson, 2012.
Print.
b. Notes. Each student will be provided a Student Companion as a supplement to the
textbook. This resource is a guided note-taking tool. Students will be expected to bring it
to class every day unless told otherwise. At the end of each unit it will be graded as a daily
assignment grade.
c. Calculators. Calculators are an acceptable resource to use in the process of
answering mathematical questions. Remember, the calculator is only a tool. It is not
required for the course but is recommended. A scientific calculator such as the Texas
Instruments TI-30X will provide all of the necessary capabilities. (This is not an
endorsement of any specific product. It is unnecessary to spend a lot of money for
whatever choice is made.) To avoid issues with violation of school rules or other conflicts,
the use of smartphones and other devices is discouraged and can be completely prohibited
should circumstances warrant it based on the discretion of the teacher.
d. Students should bring the text, student companion, a notebook, writing utensils
(both a pencil and a pen) every day unless told otherwise.
IV.
Course objectives and outcomes.
a. This course and its material promote the student outcomes that have been
established for the ADM Community School District.
b. This course is aligned with the Common Core State Standards for Mathematical
Content.
Number and Quantity
The Real Number System
Extend the properties of exponents to rational exponents.
N.RN.1
Explain how the definition of the meaning of rational exponents follows from extending the
properties of integer exponents to those values, allowing for a notation for radicals in terms of
rational exponents.
N.RN.2
Rewrite expressions involving radicals and rational exponents using the properties of
exponents.
Use properties of rational and irrational numbers.
N.RN.3
Explain why the sum or product of two rational numbers is rational; that the sum of a rational
number and an irrational number is irrational; and that the product of a nonzero rational
number and an irrational number is irrational.
Quantities
Reason quantitatively and use units to solve problems.
N.Q.1
N.Q.2
N.Q.3
Use units as a way to understand problems and to guide the solution of multi-step problems;
choose and interpret units consistently in formulas; choose and interpret the scale and the
origin in graphs and data displays.
Define appropriate quantities for the purpose of descriptive modeling.
Choose a level of accuracy appropriate to limitations on measurement when reporting
quantities.
Algebra
Seeing Structure in Expressions
Interpret the structure of expressions
A.SSE.1
A.SSE.2
Interpret expressions that represent a quantity in terms of its context.
a. Interpret parts of an expression, such as terms, factors, and coefficients.
b. Interpret complicated expressions by viewing one or more of their parts as a single entity.
Use the structure of an expression to identify ways to rewrite it.
Write expressions in equivalent forms to solve problems
A.SSE.3
Choose and produce an equivalent form of an expression to reveal and explain properties of the
quantity represented by the expression.★
a. Factor a quadratic expression to reveal the zeros of the function it defines.
b. Complete the square in a quadratic expression to reveal the maximum or minimum value
of the function it defines.
c. Use the properties of exponents to transform expressions for exponential functions.
Arithmetic with Polynomials and Rational Expressions
Perform arithmetic operations on polynomials
A.APR.1
Understand that polynomials form a system analogous to the integers, namely, they are closed
under the operations of addition, subtraction, and multiplication; add, subtract, and multiply
polynomials.
Algebra I, p.2
Understand the relationship between zeros and factors of polynomials
A.APR.3
Identify zeros of polynomials when suitable factorizations are available, and use the zeros to
construct a rough graph of the function defined by the polynomial.
Rewrite rational expressions
A. APR.6
Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) +
r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the
degree of b(x), using inspection, long division, or, for the more complicated examples, a
computer algebra system.
A. APR.7 Understand that rational expressions form a system analogous to the rational numbers, closed
under addition, subtraction, multiplication, and division by a nonzero rational expression; add,
subtract, multiply, and divide rational expressions.
Creating Equations
Create equations that describe numbers or relationships
A.CED.1
Create equations and inequalities in one variable and use them to solve problems.
A.CED.2
Create equations in two or more variables to represent relationships between quantities; graph
equations on coordinate axes with labels and scales.
A.CED.3
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.
A.CED.4
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving
equations.
Reasoning with Equations and Inequalities
Understand solving equations as a process of reasoning and explain the reasoning
A.REI.1
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.
A.REI.2
Solve simple rational and radical equations in one variable, and give examples showing how
extraneous solutions may arise.
Solve equations and inequalities in one variable
A.REI.3
Solve linear equations and inequalities in one variable, including equations with coefficients
represented by letters.
A.REI.4
Solve quadratic equations in one variable.
a. Use the method of completing the square to transform any quadratic equation in x into an
equation of the form (x – p)2 = q that has the same solutions. Derive the quadratic formula
from this form.
b. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing
the square, the quadratic formula and factoring, as appropriate to the initial form of the
equation. Recognize when the quadratic formula gives complex solutions and write them
as a ± bi for real numbers a and b.
Solve systems of equations
A.REI.5
A.REI.6
A.REI.7
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.
Solve a simple system consisting of a linear equation and a quadratic equation in two variables
algebraically and graphically.
Algebra I, p.3
Represent and solve equations and inequalities graphically
A.REI.10
A.REI.11
A.REI.12
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).
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.
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.
Functions
Building Functions
Build a function that models a relationship between two quantities
F.BF.1
Write a function that describes a relationship between two quantities.
F.BF.2
Write arithmetic and geometric sequences both recursively and with an explicit formula, use
them to model situations, and translate between the two forms.★
Build new functions from existing functions
F.BF.3
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific
values of k (both positive and negative); find the value of k given the graphs. Experiment with
cases and illustrate an explanation of the effects on the graph using technology.
F.BF.4
Find inverse functions.
a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write
an expression for the inverse.
Linear, Quadratic, and Exponential Models
Construct and compare linear, quadratic, and exponential models and solve problems
F.LE.1
F.LE.2
F.LE.3
Distinguish between situations that can be modeled with linear functions and with exponential
functions.
a. Prove that linear functions grow by equal differences over equal intervals, and that
exponential functions grow by equal factors over equal intervals.
b. Recognize situations in which one quantity changes at a constant rate per unit interval
relative to another.
c. Recognize situations in which a quantity grows or decays by a constant percent rate per
unit interval relative to another.
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).
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a
quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
Algebra I, p.4
Interpret expressions for functions in terms of the situation they model
F.LE.5
Interpret the parameters in a linear or exponential function in terms of a context.
Geometry
Similarity, Right Triangles, and Trigonometry
Define trigonometric ratios and solve problems involving right triangles
G.SRT.6
Understand that by similarity, side ratios in right triangles are properties of the angles in the
triangle, leading to definitions of trigonometric ratios for acute angles.
G.SRT.8
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied
problems.
Expressing Geometric Properties with Equations
Use coordinates to prove simple geometric theorems algebraically
G.GPE.5
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).
Statistics and Probability
Interpreting Categorical and Quantitative Data
Summarize, represent, and interpret data on a single count or measurement variable
S.ID.1
Represent data with plots on the real number line (dot plots, histograms, and box plots).
S.ID.2
Use statistics appropriate to the shape of the data distribution to compare center (median,
mean) and spread (interquartile range, standard deviation) of two or more different data sets.
S.ID.3
Interpret differences in shape, center, and spread in the context of the data sets, accounting for
possible effects of extreme data points (outliers).
Summarize, represent, and interpret data on two categorical and quantitative variables
S.ID.5
Summarize categorical data for two categories in two-way frequency tables. Interpret relative
frequencies in the context of the data (including joint, marginal, and conditional relative
frequencies). Recognize possible associations and trends in the data.
S.ID.6
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.
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.
Interpret linear models
S.ID.7
S.ID.8
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the
context of the data.
Compute (using technology) and interpret the correlation coefficient of a linear fit.
Algebra I, p.5
S.ID.9
Distinguish between correlation and causation.
Making Inferences and Justifying Conclusions
Make inferences and justify conclusions from sample surveys, experiments, and observational
studies
S.IC.3
Recognize the purposes of and differences among sample surveys, experiments, and
observational studies; explain how randomization relates to each.
S.IC.5
Use data from a randomized experiment to compare two treatments; use simulations to decide
if differences between parameters are significant.
Conditional Probability and the Rules of Probability
Understand independence and conditional probability and use them to interpret data
S.CP.1
Describe events as subsets of a sample space (the set of outcomes) using characteristics (or
categories) of the outcomes, or as unions, intersections, or complements of other events ("or,"
"and," "not").
S.CP.2
Understand that two events A and B are independent if the probability of A and B occurring
together is the product of their probabilities, and use this characterization to determine if they
are independent.
S.CP.3
Understand the conditional probability of A given B as P(A and B)/P(B), and interpret
independence of A and B as saying that the conditional probability of A given B is the same as
the probability of A, and the conditional probability of B given A is the same as the probability
of B.
S.CP.4
Construct and interpret two-way frequency tables of data when two categories are associated
with each object being classified. Use the two-way table as a sample space to decide if events
are independent and to approximate conditional probabilities.
S.CP.5
Recognize and explain the concepts of conditional probability and independence in everyday
language and everyday situations.
Use the rules of probability to compute probabilities of compound events in a uniform probability
model
S.CP.7
Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms
of the model.
S.CP.8
Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) =
P(B)P(A|B), and interpret the answer in terms of the model.
c. In addition to these curriculum standards, this class will stress attention to detail,
following directions and double-checking work, in addition to other life skills. These skills
are not always blatantly obvious to the high school student. Honestly, this and other things
can frustrate both the students and the teacher. Together we will work to make
connections and deepen the understanding of everyone in the classroom.
V.
Methods of instruction.
a. There will be multiple methods of instruction and forms of assessment used during
the course of the year. Students can expect to be engaged in small group work, individual
work, writing assignments, lectures, group quizzes, and tests.
b. All of these opportunities and exercises are meant to create the opportunity for the
student to construct meaning and attach new experiences to prior learning. It is inherent
in the learning process for each individual to actively think about the material.
Algebra I, p.6
VI.
Evaluation methods and grade assignment.
a. Daily assignments. Expect to get related problems to work on nearly every day of
the school year. These assignments are a critical opportunity to practice the concepts
discussed in class. While they provide less of the course grade than tests and quizzes do,
these assignments will present the opportunity to practice and develop the understanding
of course skills and concepts. The grading is intended to allow for mistakes and errors at
this point in the learning. In fact, mistakes and errors are expected the first time material is
covered.
b. Testing. Testing provides the greatest percentage of the course grade. Each unit
will include a mid-unit quiz and an end of unit test. The teacher will structure each testing
situation and will inform the class of the expectations.
c. Retakes. After each test students that score less than 85% are allowed to retake the
test. In order to retake the test the student is required to come into the classroom to work
on the missed problems from the test. The student is allowed to use textbook and notes as
resources to correctly identify how they missed problems on the test. This is a great
opportunity to get individual help. Once the problems have been satisfactorily answered
the student will be given a retake form of the test. This procedure is required to take place
during the timeframe designated by the teacher. Most frequently this will be a 5-day
period of time.
d. This course marks a transition from the previous practices of repetitive testing.
Students will be accountable for the level of achievement they maintain quicker than
previously has been done.
VII. Classroom policies.
a. Students are expected to adhere to the policies and procedures included in the ADM
HS Student Handbook.
b. Come prepared every day.
c. Demonstrate respect to all people in the room.
d. Have fun.
Algebra I, p.7
You can expect the teacher to…
1. Promote a learning environment that is safe, engaging and intellectually challenging
2. Communicate expectations and requirements
3. Provide meaningful feedback
4. Present information in a clear and detailed manner
5. Provide assistance when subject matter is unclear
6. Work hard and diligently to help students
7. Challenge you
Each student is expected to…
1. Demonstrate socially acceptable behavior toward the teacher and other students
2. Complete assigned work according to the deadlines and manner assigned by the
teacher
3. Be accountable and responsible for learning and standing with the course grading
4. Interact in classroom discussions and activities
5. Ask questions when something is unclear
6. Put in extra effort and time when making up work, trying to understand difficult
material and/or going through the test retake process
7. At some point the material will frustrate you
Algebra I, p.8