St. Mary's College High School Algebra 1-2 The Language of Algebra What is a variable? A. Identify and translate variables and expressions. The following apply to all the skills How is a variable used in a sentence and in an expression? What are the identity, equality, distributive, and the commutative and associative properties used for? What if there were no Order of Operations? Determining what a variable is, gives students an understanding that variables represent the unknown. Understanding what variables are, leads to the use of the various properties. By evaluating expressions, students learn the importance of the Order of Operations. B Simplify and evaluate both numerical and algebraic expressions using order of operations. C. Recognize and use the identity and equality properties. D. Use the distributive property to simplify and evaluate expressions. E1. Understand and identify the commutative and associative properties. E2. Use the commutative and associative properties to simplify expressions. F. Interpret and draw graphs and functions. G. Analyze data given in tables and graphs, and determine whether graphs are misleading. worksheet. class. Nightly homework, which is reviewed. Comprehensive chapter exam. Real Numbers What is the real number system? What are primary subsets of real number? A1. Graph Rational numbers on a Number Line A2. Find absolute value of rational numbers In-class examples, practice and class. 1 of 8
B. Add and subtract integers and What is an irrational number? rational numbers. Review nightly homework. What is absolute value? What is the number line, and what is it used for? The understanding of real numbers and its subsets establishes the foundation for solving balanced equations. The number line establishes the basis for adding positive and negative numbers. Solving Linear Equations What is a balanced equation? What is a solution to an algebraic equation? What is percent, and how is it applied? Solving balanced equations demonstrates how to find the unknown, by utilizing the four operations of addition, subtraction, multiplication and division. Calculating percents allows students see how taxes and discounts work. C. Multiply integers and rational numbers D. Dividing integers and rational numbers E. Explain and interpret statistics, by analyzing and displaying data F. Find and classify square roots and real numbers A. Write and solve equations using addition, subtraction, multiplication, and division. B1. Solve problems by working backwards B2. Solve equations involving more that one operation C. Solve equations with the variable on each side, and by involving grouping symbols D. Compare ratios and proportions. E. Solve problems involving taxes and discounts F. Solve equations for given variables Timed math test without calculators Jeopardy math for chapter Comprehensive chapter exams. 2 of 8
Analyzing Linear Equations What is slope, and how is it calculated? How does slope determine change? What are parallel and perpendicular lines, and how are they determined? Understand that slope is a constant rate of change, and that it determines how a line is graphed. Calculating slope using the slope formula, and understanding what the slope-intercept equation represents. Using parallel and perpendicular lines to find related linear equations. A. Find the slope of a line, and distinguish the various types of slope. B1. Restate and apply the slopeintercept form of the linear equation. B2. Write and graph linear equations in slope-intercept form. C. Write equations of a line given the slope and one point on a line, and given two points on a line. D1. Rewrite linear equations in the point-slope form. D2. Write linear equations in different forms E1. Interpret and compare parallel and perpendicular lines. E2. Write linear equations involving parallel and perpendicular lines. Review nightly homework. class. Comprehensive chapter exam. Solving Linear Inequalities What is a linear inequality, and how is it different form an equation involving an equals sign? A. Solving linear inequalities by using addition, subtraction, multiplication, and division. B. Solving compound inequalities by using the words and, and or, In-class examples, practice and 3 of 8
What is a compound inequality, and being able to graph their class understanding and homework and how is it solved? solution sets. How are absolute value equations and inequalities solved? How are linear inequalities with two variables graphed? Solving linear inequalities using the four operations. Solving compound inequalities, and inequality equations with absolute value. Being able to graph two linear inequalites to determine their solution. C. Solving absolute value equations and inequalities. D1. Graphing inequalities on the coordinate plane. D2. Solving real-world problems involving linear inequalities. Evaluate student notebooks. Cumulative Final Exam of chapters 1-6. Solving Systems of Equations What is a system of equations, and how are they solved? How can the system of inequalities be determined by graphing? Understand that solving systems A1. Determine whether a system of equations has one, none or infinitely many solutions. A2. Solve systems of equations by graphing. B. Solve systems of equations by using substitution. C. Solve systems of equations by using addition and subtraction. class understanding, and homework Play a review game to prepare for chapter 6 test. 4 of 8
of equations is finding the one and only answer to two unknowns by a variety of methods. D1. Solve systems of equations by using multiplication. D2. Determine the best method for solving systems of equations. E.Solve systems of inequalities by graphing. Polynomials What is a monomial and what is a polynomial? How to multiply and divide monomials and polynomials? What is FOIL, and how is it used? What does it mean to simplify? Understanding that there are accepted methods, such as FOIL to use when multiplying and dividing monomials and polynomials. A. Multiply monomials and simplify expressions involving powers of monomials B. Divide monomials simplify expressions containing negative exponents C. Express numbers in scientific and standard notation D. Find the degree of monomials and polynomials E. Add and Subtract polynomials F. Solve equations involving polynomials G. Multiply two polynomials by using the distributive property, and FOIL H. Find squares of sums and differences. class understanding and homework Factoring 5 of 8
Essential Questions: What is a prime number, and how does it help find the greatest common factor? What is factoring, and how does it help solve quadratic equations? How do the number of terms in an equation determine which factoring method to use? Big Ideas: Learn how to factor by being able to determine the Greatest Common Factor. Understand the zero product property rule, and how to apply it to solve equations. Learn all the factoring methods, and know when to use them. A. Find prime factorization and greatest common factors B1. Factor polynomials using the distributive property. B2. Solve quadratic equations using the zero product property rule. C. Factor and solve trinomials in quadratic equation form. D. Factor and solve binomials that are differences of squares, and perfect squares. class understanding and homework Quadratic and Exponential Functions Essential Questions: What form does a quadratic equation take when graphed on a coordinate plane? How can graphing be used to find solutions to a quadratic equations? What is completing the square, A1. Graph quadratic functions. A2. Find the equation of the axis of symmetry and the coordinates of the vertex of a parabola. B. Solve quadratic equations by graphing. C. Solve quadratic equations by finding the square root, and by completing the square. class understanding and homework 6 of 8
and how can it be used to solve a quadratic equation? What is the quadratic formula, and how can it be used to solve a quadratic equation? What is a Geometric Sequence? Big Ideas: Learn how to graph a quadratic equation on a coordinate plane, and how to locate the solution when the graph crosses the x-axis. Learn how to complete the square, and use it to solve a quadratic equation. Learn the quadratic formula, and how to apply it to solve a quadratic equation. D. Solve quadratic equations by using the Quadratic Formula, and using the Discriminant to determine the number, and type of roots. E. Recognize and extend geometric sequences. Radical Expressions and Triangles Essential Questions: What is a radical expression, and how can it be simplified? How can radical equations be solved? What is the Pythagorean Theorem, and how is it used? What is the distance formula, and how is it applied? A. Simplify radical expressions using the product and quotient properties of square roots. B. Add, subtract and multiply radical expressions. C. Solve radical expressions, and check for extraneous solutions. D1. Solve problems using the Pythagorean Theorem. D2. Determine whether a triangle is a right triangle. worsheets. class understanding and homework Cryptography project presentation and written report. Review and evaluate student 7 of 8
Big Ideas: E. Use the distance formula to find notebooks. the distance between two points on a coordinate plane. Learn to simplify all radical expressions and apply mathematical operations. Use the Pythagorean Theorem to find missing values of a right triangle, and apply this to real-life problems. Understand how and when to apply the distance formula. Cumulative semester final exam(skilss/critical thinking/problem solving) 8 of 8