Level: 8th grade or 9th (Freshman)
Prerequisites: Teacher Recommendation
Credit: Year; 1 unit
Description: The properties of real numbers and the solutions of equations and inequalities will be studied in detail. Through word problems and graphing, algebraic principles will be applied to physical/real life situations.
Algebra provides the foundation for all future studies in mathematics. Since Algebra is the language of all mathematics, Algebra skills are vital to any detailed study of computer programming, the physical sciences, or advanced mathematics.
It is intended that students come to appreciate the need for painstaking accuracy in dealing with data and formulas. Through practice and some memorization, the student will come to approach difficult problems with the confidence that he can find solutions by thinking, reading, and working carefully, by applying methodically the skills they have learned in class. It is intended that the student come to appreciate and acquire self-discipline by doing homework daily.
I. At the end of the first semester each student should be able to:
1. Translate verbal/written expressions and sentences into mathematical expressions and equations.
2. Use the order of operations and properties of real numbers to simplify expressions.
3. Graph integers, rational numbers, solutions sets, and inequalities, on a number line.
4. Add, subtract, multiply, divide, compare, and order integers and rational numbers.
5. Use various strategies to solve equations such as addition, subtraction, multiplication, division, and working backwards.
6. Solve equations that involve more than one operation, variables on both sides of the equation, equations with grouping symbols, fractions, decimals, and more than one variable.
7. Solve work problems involving the use of a chart or table including mixture and distance.
8. Solve simple and compound inequalities involving one or more operations by using addition, subtraction, multiplication, division, and graphing.
9. Graph ordered pairs on a coordinate plane and identify the domain and range.
10. Show relations as sets of ordered pairs and mappings, and determine whether a relation is a function.
11. Solve and graph linear equations, graph inequalities, and write an equation to represent a relation given a chart of values.
II. At the end of second semester each student should be able to:
1. Solve systems of equations by various methods including graphing, and be able to predict how many solutions each system has.
2. Find the degree of a polynomial, arrange the terms of a polynomial so that the powers of a certain variable are in ascending or descending order, add, subtract, and multiply monomials and polynomials, and multiply two polynomials using FOIL and the distributive property.
3. Express numbers in scientific and decimal notation.
4. Find the greatest common factor (GCF) and prime factorizations of a set of integers or set of monomials.
5. Factor polynomials and solve equations by applying various methods of factoring.
6. Divide polynomials by binomials and simplify mixed expressions and complex fractions.
7. Simplify square roots, and find approximate values for rational square roots.
8. Simplify radical expressions and solve radical equations.
9. Solve quadratic equations by using the quadratic formula and write a quadratic equation when given its roots.
10. Display and interpret data on line plots, stem-and-leaf plots, box-and-whisker plots, and scatter plots. (Optional: As time allows)
11. Calculate and interpret the mean, median, mode, range, quartiles, and interquartile range of a set of data. (Optional: As time allows)