Download Welcome Course: Algebra 1B (Year two of a two year integrated

Welcome
Course:
Teacher:
Contact:
Algebra 1B
(Year two of a two year integrated algebra program)
A. Ferraro
[email protected]
Please feel free to contact me anytime via email. I believe it is the best
means of communication. I check my email often throughout the day.
Course Description
The algebra curriculum has been revised to align with the current New York State Standards of
2008. It has been designed to improve the problem solving abilities of each student while continuing to
develop mathematical skills, concepts, and computation. Critical thinking, organizational skills, and the
ability to communicate effectively are also stressed throughout the year. It is intended that each student
will obtain a better understanding of the material studied and attain the knowledge necessary to
successfully continue in the high school mathematics program.
Throughout the school year, students will study the various topics, outlined below, through the
use of individual, partnered and group work. Students will use various materials and resources in order to
fully understand the covered concepts. It is my hope that all students will have a greater interest and
appreciation for mathematics upon completion of this class.
Supplies
 Pencils
 Paper
 3-ring binder
 5 section dividers labeled:
Warm Ups
Notes
HW
Quizzes
Review
Remember: The more organized you are, the easier it will be to
study for homework quizzes, quizzes, cumulative quizzes, and tests.
Homework – 35%
Homework is a critical part of learning mathematics. Mathematics is not a “spectator sport.”
One must do math in order to learn math. It is crucial that students complete all assigned
homework by the beginning of each class. Homework is assigned for practice after each topic
has been discussed in class. If they pay attention in class, students will be able to complete all
respective assignments. Any questions regarding homework will be addressed during homework
review at the beginning of each class. I strongly believe it is a time for practice and learning.
 There are no late homeworks.
 Every Friday there will be a homework quiz, with the exception of the final
Friday of the month. At the end of each quarter, two of these quiz grades will
be dropped. If you are absent for a homework quiz, it will count as a zero

(that quiz grade can be dropped as one of the two drops). This should
encourage you to ask questions and discourage you from copying homework.
Your overall homework average will be the average of your in class homework
quizzes and your daily homework completion.
Quizzes – 20%
Quizzes are given bi-weekly as a way of monitoring student progress. Cumulative quizzes will
be given at the end of each month. It is our hope that the constant review will help you to feel
more confident and be more prepared for midterms/final exams.
Tests – 45%
Tests will be given at the completion of each unit. Tests will demonstrate students' mastery of
the topics covered.
***Attendance NOTE: If you are absent for a quiz, cumulative quiz or test, you have ONE
WEEK from the date it was given to make it up. If you do not make it up in this time, the
grade will be recorded as a zero.
Course Grade
Since this is a full year course, your course grade is calculated using the following:
Each quarter counts as 2/10 Midterm is 1/10
Final Exam is 1/10
EXTRA HELP
We strongly encourage you to seek extra help when you are struggling or when you do not
understand a concept, however the intent of extra help is not to provide you with an excuse to
pay less attention in class. The purpose of extra help is to assist you in becoming more
independent, not more dependent on us. We do not want to encourage poor habits or enable
you by allowing you to depend on us too much; we want to help you learn how to help
yourself.
Students are expected to be Respectful, Responsible and Prepared
each and every day 
I look forward
successful school year.
can so that you will
potentials. Best wishes
to working with each and every one of you for a very
It is my hope to provide you all with the best opportunities I
have the chance to learn and succeed to your greatest
for a great school year!
~Mrs. Ferraro
In the words of Galileo:
“You can not teach a man (human) anything; you can only help him to
discover it in himself.”
Algebra 1B Curriculum
I. Graphing Linear and Nonlinear Functions (4 weeks)
A. Functions
1. Definition of a function
2. Determine when a relation is a function by examining multiple representations (ordered pairs,
mappings, equations, and graphs)
3. Vertical Line Test
B. Identify and graph linear functions
C. Identify and graph absolute value functions
1. Explore Vertical and Horizontal Shifts
D. Graph linear inequalities
E. Equations of a Line
1. Explain slope as a rate of change between dependent and independent variables. Including:
Calculate rates using appropriate units and solve problems involving conversions within
measurement systems.
2. Determine slope of a line, given the coordinates of two points on a line.
3. Write the equation of a line, given the coordinates of two points on a line.
4. Write an equation of a line, given its slope and the coordinates of a point on the line.
5. Write the equation of a line parallel to the x-axis or y-axis.
6. Determine the slope of a line, given its equation in any form.
7. Determine if two lines are parallel or perpendicular, given their equations in any form.
8. Given an equation of a line, write an equation for a line parallel or perpendicular to the given
equation.
9. Given an equation of a line, determine whether a given point is on a line.
10. Determine whether a given point is in the solution set of a system of linear equalities.
*** Please be advised – graphs must be accompanied by a table of values***
II. Graphing Quadratic Functions (2 weeks)
A. Graphs of Quadratics
1. Identify quadratic graphs
2. Graphing quadratic equations of the form y = ax2, y = ax2 + c, and y = ax2 + bx + c.
(Optional inclusion of a parabola in the vertex form y = (x – h)2 + k)
3. Determine the vertex and axis of symmetry of a parabola given either the equation or the
graph.
4. Investigate how changing the coefficients of a function affects its graph. For example, compare
the graphs of quadratics in the form y = ax2, by changing the sign on a. and the value of a
5. Find the roots of a parabolic function graphically (integral solutions only).
6. Understand the relationship between the roots of a quadratic equation, the factors of a quadratic
expression, and the x-intercepts of the parabola.
III. Systems of Equations (1-2 weeks)
A. Solve systems of linear equations and inequalities with rational coefficients in two variables
graphically.
B. Solve systems of two linear equations in two variables algebraically. (May have already been covered
in semester 1)
C. Solve a system of one linear and one quadratic equation in two variables (the quadratic is a parabola
and the solutions should be integers)
D. Solve systems of linear and quadratic equations graphically (integer solutions only).
IV. Exponential Functions (2 weeks)
A. Exponential Expressions
1. Evaluate exponential expressions
B. Exponential Function Graphs
1. Identify exponential functions
i. y = abx explore what a, b and x represent
2. Graph exponential functions
C. Solving Exponential Functions
1. Solve Exponential Equations with the same base
2. Solve Exponential Equations with powers of the same base.
3. Analyze and solve verbal problems that involve exponential growth and decay.
V. Right Triangles (3 weeks)
A. Radicals
1. Simplify
2. Four arithmetic operations using radicals (leaving answers in simplest radical form)
3. Rationalizing
B. Pythagorean Theorem
C. Special Right Triangles
1. Derivations of the Relationships between the sides of a 45-45-90 and a 30-60-90
D. Right Triangle Trigonometry
1. Find the sine, cosine, and tangent ratios of an angles of a right triangles, given the lengths of
the sides
2. Determine the measure of an angle of a right triangle, given the lengths of any two sides of the
triangle
3. Find the measure of a side of a right triangle, given an acute angle and the length of another
side
4. Right Triangle Trigonometry applications using Angle of Depression and/or Angle of
Elevation.
VI. Statistics (2 weeks)
A. Making Sense of Data
1. Categorize Data as qualitative or quantitative.
2. Determine whether the data to be analyzed is univariate or bivariate.
3. Determine when collected data or display of data may be biased.
4. Evaluate published reports and graphs that are based on data by considering: experimental
sign, appropriateness of the data analysis, and the soundness of the conclusions.
5. Understand the difference between correlation and causation and identify variables that might
have a correlation.
6. Identify and describe sources of bias and its effect
7. Recognize how linear transformations of one-variable data affect the data’s mean, median,
mode, and range.
B. Measures of Central Tendency Vs Measures of Dispersion
1. Mean, Median, Mode and Range –
2. Compare and contrast the appropriateness of difference measure of central tendency or a given
data set.
3. Quartiles and Percentiles
4. The 5 Number Summary – Minimum, Q1, Median (Q2), Q3, and Maximum
C. Graphical Representations - Construct, Analyze, and Interpret
1. Histogram
2. Cumulative Frequency Histogram
3. Box-and-Whisker Plot
4. Scatterplot
a. Construct manually a reasonable line of best fit for a scatterplot and determine the
equation of a line.
b. Using the line of best fit to make a prediction involving interpolation and/or
extrapolation.
VII. Probability (2 weeks)
A. The Counting Principle
1. Use the counting principle to determine the number of possible events
B. Conditional Probability
1. Sample Spaces and Tree Diagrams
2. Determine the number of elements in a sample space and the number of favorable events.
3. Calculate the probability of an event and its complement.
4. Determine empirical probabilities based on specific sample data.
5. Determine, based on calculated probability of a set of events, if:
i. some or all are equally likely to occur
ii. one is more likely to occur than another
iii. whether of not an event is certain to happen or not to happen
6. Calculate the probability of:
i. a series of independent events
ii. a series of dependent events
iii. two mutually exclusive events
iv. two events that are not mutually exclusive
C. Permutations
1. Determine the number of possible arrangements.
2. Calculate Permutations using the notation nPr.