Bradley Middle School
Honors Algebra 1
At Bradley, we provide a comprehensive education to all students, in a positive environment, by encouraging each child to reach their fullest potential in all areas."
Instructor: Mr. Santos Reyna II
Textbook: SpringBoard Algebra 1-CollegeBoard
Tutoring Hours: Monday/Friday 7::45 am-8:15 am
Tuesday/Thursday 3:40 pm-4:00 pm
I. Rationale and Course:
This class is designed to develop mathematically literate students. I believe that students can reach their potential and avoid the phobia associated with mathematics. The goal is to teach mathematics using multiple methods to accommodate multiple intelligences. As such, students should expect an incorporation of manipulatives, technology, group interaction, as well as paper and pencil.
II. Course Outcomes:
Specific Learning Outcomes:
By the end of this course, students will:
- Use tables, graphs and expressions to explore linear and nonlinear patterns in real-world situations and how to use those patterns to make predictions.
- Use properties of equality and inverse operations to write and solve linear equations an inequalities in one variable, including multi-step equations.
- Extend the idea of input and output values to the idea of domain and range.
- Relate equations in “y =” form to equations using function notation.
- Explore horizontal and vertical transformations of functions.
- Write explicit formulas for arithmetic and geometric sequences.
- Use explicit formulas to determine specific term values.
- Use recursive formulas for arithmetic and geometric sequences to write sequences.
- Relate arithmetic sequences to linear function.
- Interpret the slope as a rate of change.
- Identify slopes as positive, negative, zero, or undefined.
- Write and use equations in point-slope form
- Write and use equations in standard form.
- Describe the relationship between the slopes and parallel lines.
- Describe the relationships between the slopes and perpendicular lines.
- Use technology to determine regression equations of linear data.
- Interpret equations written in function notation in the context of a problem situation.
- Write, solve, and graph two variable inequalities.
- Solve a system of linear equations using substitution and elimination.
- Use a graph to represent the solution set of a system of linear inequalities.
- Simplify expressions involving exponents.
- Simplify radical expressions.
- Model exponential growth and decay with tables, graphs, and equations.
- Model compound interest and population with exponential functions.
- Use exponential functions to make predictions.
- Add and subtract polynomial expressions.
- Multiply polynomials.
- Determine the greatest common factor of a polynomial expression (GFC)
- Factor trinomials
- Recognize perfect square trinomials.
- Recognize difference of two squares.
- Divide rational expressions when the numerator has a greater degree than the denominator.
- Stretch, compress, and reflect quadratic functions.
- Solve quadratic equations by graphing, factoring, using the square root method, completing the square, and the quadratic formula.
- Interpret key features of quadratic functions in terms of problem situations.
- Model situations with quadratic regression.
I believe strongly that all students are capable of succeeding in mathematics. In order to accomplish this, I have high expectations which include:
- Responsibility for your materials. Bring your book and writing materials to class: paper and PENCIL. Pen is not allowed in my math class.
- Use agenda books daily to write down the learning objective and any homework, if assigned.
- Respect for others. Treat classmates and classroom visitors with courtesy.
- Your best effort. Be responsible for your own learning.
- Listen when others are speaking.
- If you miss class, you are responsible for the material covered.
- Team work: You will spend as much time interacting with others as you will working individually. When you are assigned to work with others, or choose to work with others, work cooperatively.
- Do all required assignments and turn them in on time.
IV. My Assumptions:
I assume the students are able to:
- Find rate of change from data in a table or graph
- Graph proportional relationships from multiple representations, and connect the unit rate to slope
- Represent linear proportional relationships from multiple representations, and connect unit rate to slope.
- Represent linear proportional relationships in various ways, and solve problems involving direct variations.
- Represent linear non-proportional relationships in tables, graphs, equations, and verbal descriptions.
- Given a linear representation, distinguish between proportional and non-proportional relationships
- Develop basic understanding of what a function is.
- Identify functions from tables, graphs, sets of ordered pairs and mappings.
- Identify examples of proportional and non-proportional functions.
- Write, model, and solve one-variable equations with variables on both sides from real-world and mathematical problems.
- Write and match one-variable inequalities with variables on both sides for real-world problems.
- Identify and verify the solution for two graphed linear equations.
- Generalize ratios of corresponding sides of similar shapes and dilations are proportional.
- Compare and contrast attributes of a shape and its dilation on a coordinate plane.
- Use algebraic representations to describe effects of scale factor applied to 2-D figures on a coordinate plane.
- Model the effect on linear and area measurements of dilated 2-D shapes.
- Generalize properties of orientation and congruence of rotations, reflections, and translations.
- Differentiate between transformations that preserve congruence and those that do not.
- Use algebraic representations to explain the effects of translations, rotations, and reflections of 2-D shapes on the coordinate plane.
- Use visual representation to describe relationships between sets and subsets of real numbers.
- Approximate the value of an irrational number and locate its approximation on a number line.
- Order a set of real numbers arising from mathematical and real-world contexts.
- Convert between standard decimal notation and scientific notation.
- Use models and diagrams to explain the Pythagorean Theorem.
- Use the Pythagorean Theorem and its converse to solve problems.
- Determine the distance between two points on a coordinate plane using the Pythagorean Theorem
- Describe the volume formula for a cylinder in terms of base area and height.
- Solve problems involving the volume of cones, cylinders, and spheres.
- Determine solutions for problems involving total and lateral surface area of rectangular prisms, triangular prisms, and cylinders.
- Model the relationships between volume of a cylinder and a cone.
- Contrast bivariate sets of data that suggest a linear relationship with those that do not.
- Use a trend line that approximates the linear relationship between bivariate sets of data to make predictions.
- Construct scatterplots and describe the association of the date.
- Determine the mean absolute deviation of a given data set.
- Calculate and compare simple interest and compound interest earnings.
- Calculate the total cost of repaying a loan.
- Explain how small amount of money invested regularly.
V. Course Requirements:
- Class attendance policy:
MINIMUM ATTENDANCE REQUIREMENTS FOR CREDIT/PROMOTION State law requires that a student may not be given credit for a class unless the student is in attendance for at least 90 percent of the time the class is scheduled to meet. If students are in attendance less than 90 percent of the days the class meets, students will lose credit unless each and every class is made up in an acceptable manner, such as, but not limited to, Saturday School, after school hours, etc. When students' attendance drops below 90 percent but remains at least 75 percent of the days the class is offered, they may earn credit for the class by completing a plan approved by the principal. This plan must provide for students to meet the instructional requirements of the class as determined by the principal. If students fail to successfully complete the plan, or when their attendance drops below 75 percent of the days the class is offered, students and parents/guardians may request award of credit by submitting a written petition to the appropriate attendance committee at the campus. Unusual extenuating circumstances would be a basis for appeal to the attendance review committee. The structure of the review committee, the procedures, and criteria to be considered are available from the campus administration.
- PROCEDURE FOR MAKE-UP WORK FOLLOWING AN ABSENCE:
According to Board Policy, students are required to make up assignments, homework, projects, quizzes and tests missed due to absences. [Board Policy EIAB (Local)]
The District distinguishes absences as excused and unexcused. Make-up work for excused absences will be eligible for full credit. Students shall receive a 20 percent deduction from the total grade earned for any assignment or assessment not made up within the allotted time. A truant absence is an unexcused absence with disciplinary consequences. Make-up work for unexcused absences will be penalized equal to late work. A 20 percent deduction from the total grade earned will be taken on make-up work for unexcused absences.
Students will be allowed reasonable time to make up assignments, homework, projects, quizzes and tests missed due to absences.
- At the secondary school level, reasonable time is defined as one class day per class missed, e.g. students who miss class on Tuesday have until the beginning of class on Thursday to turn in make-up work.
- For extended absences, make-up assignments shall be made available to students after two consecutive class days of absence.
- Teachers will provide the assignments to the students and inform students of the time allotted for completing make-up assignments, homework, projects, quizzes and tests.
- It is the student's responsibility to obtain, complete and submit the missed work in the time allotted.
Students will not be required to take a quiz or test on the day returning to class from an absence if the quiz or test was announced during the student's absence.
After their return to class teachers are required to make arrangements with the student within two class days to take a test/quiz if the test/quiz was announced during the student's absence.
Make-up work and tests for all absences should be of the same rigor, but not necessarily the same format, as the original activity, assignment or test.
Make-up tests or presentations may be scheduled before school, after school, during study hall or during the student's class period, at the teacher's discretion to ensure that new and/or significant content is not missed.
Students should make prior arrangements with teachers for making up missed work when the absence can be anticipated, e.g. a dental appointment, court appearance or appointment, approved school-related activities, etc.
After a prolonged absence, the teacher has the right to exempt a student from some assignments if the teacher determines that doing so will not have a negative impact on the student's ability to master the content or unfairly bias his/her grade.
The District shall not impose a grade penalty for make-up work after an absence because of suspension. [Board Policy EIAB (Local)]
- LATE WORK:
- Late work is defined as any assignment that is not submitted on the due date and class period with the exception of make-up work for absences or approved school activities.
- A 20 percent deduction from the total grade earned will be taken for late assignments.
- Late assignments will be accepted until the material has been assessed summatively or within a three-week grading period.
- Extenuating circumstances may occur that prevent the completion and turning in of assignments on the due date. It is the parent/guardian and/or student’s responsibility to inform the teacher and/or an appropriate administrator of any such circumstances so that an exception to the rule may or may not be granted. The teacher and/or appropriate administrator shall have the authority to render a final decision on the granting of any exceptions.
- #2 Pencils (traditional or mechanical)
- Pencil Erasers
- 1 inch 3 Ring Binder
- Notebook Paper
- Laptop-Provided by the school *Students have an option to bring their own laptop/smartphone/tablet if they choose
- Daily Work/Homework: 30%
2. Quizzes: 30%
3. Tests 40%
Quarter 1 40%
Quarter 2 40%
Semester Exam 20%
Quarter 3 40%
Quarter 4 40%
Semester Exam 20%
VII. Academic Integrity:
Students found to have engaged in academic dishonesty shall be subject to grade penalties on assignments and/or tests and disciplinary penalties in accordance with the Student Code of Conduct and the home campus Academic Honesty Policy. Academic dishonesty includes cheating and/or copying the work of another student, plagiarism, and unauthorized communication between students during an examination. The determination that students have engaged in academic dishonesty shall be based on the judgment of the classroom teacher or another supervising professional employee, taking into consideration written materials, observation, or information from students. [Board Policy EIA (Local)]
VIII. Course of Study: (Order may change to accommodate student needs)
Unit 1: Solving Equations and Inequalities
- Properties of numbers and equality can transform an equation into equivalent equations. This process is used to find solutions.
- Any algebraic equation or inequality can be represented using symbols in an infinite number of ways, where each representation has the same solution.
- One solving method might be better than another for multiple reasons
Unit 2: Rate of Change and Linear Concepts
- Linear relationships have a constant rate of change that is represented as the slope of the line.
- Arithmetic sequences are a form of linear equations.
- Evaluating a function is when a domain value is substituted into the equation for the input.
- The domain of a function is the values of the independent variable and the range of a function is the values of the dependent variable.
- Real world problems have a reasonable domain and range.
Unit 3: Linear Equations and Inequalities
- Linear equations and inequalities can be written in various forms given different conditions about the relationships.
- The graph of a linear function has key features that represent conditions in a real world situation.
- The correlation coefficient describes the strength of a relationship between two variables.
- Arithmetic sequences are a form of linear equations.
- The graph of a linear function has key features that represent the relationship between two variables.
- Linear inequalities have more than one solution.
- Changing the coefficients and constants in the linear parent function have corresponding effects on the graph of the function.
Unit 4: Systems of Linear Equations and Inequalities
- Systems of equations can be used to make good decisions in order to satisfy the conditions of two linear relationships.
- A solution set for a system of inequalities is the overlap of the solution sets for both inequalities.
- A system of linear functions is used to find the value where the function outcomes are equal.
Unit 5: Exponential Functions
- The exponential parent function is in the form y=abx, where a represents the initial amount and b represents the rate of growth or decay.
- Linear functions have a common difference whereas exponential functions have a common ratio.
- Exponential functions have a horizontal asymptote that restricts the range of the function.
- A geometric sequence is defined by a common ratio whereas an arithmetic sequence is defined by a common difference.
- Recursive formulas can be used to show an initial amount and the common ratio in a different format than an explicit formula consisting of the same information.
Unit 6: Polynomials
- The properties of integers apply to polynomials.
- Multiplying and factoring polynomials are inverse operations.
- There are several ways to find the product of two binomials, including models, algebra, and tables.
- Some trinomials of degree 2 can be factored to equivalent forms which are the product of two binomials.
- Polynomials can be divided using steps similar to the long division steps used to divide whole numbers.
- Properties of exponents make it easier to simplify products or quotients of powers with the same base or powers raised to a power.
- The idea of exponents can be extended to include zero and negative exponents.
Unit 7: Graphing and Writing Quadratic Equations
- The family of quadratic functions models certain situations where the rate of change is not constant.
- Quadratic models are necessary to investigate, explain and make mathematical predictions and to determine potential domain and range restrictions.
- Quadratic functions are graphed by a symmetric curve with a highest or lowest point corresponding to a maximum or minimum value.
- The vertex of a parabola will represent the maximum or minimum point of the function, which will help to understand maximum and minimum values in real-life situations.
- For any quadratic function in standard form, the values of a, b, and c provide key information about its graph.
- The parent function f(x)=x2 can transformed in a variety of ways using the values of a, b, c, and d: g(x)=a*f(bx-c)+d
Unit 8: Solving Quadratic Equations
- The use of inverse operations does not always enable one to solve an equation.
- Finding the solutions to quadratic functions yields significant data for many real-world applications.
- To find the zeros of any function, you must set the equation equal to zero.
- Radicals can be used to represent finite and infinite decimals
This syllabus is subject to change at the teacher’s discretion.