Whitman-Hanson Regional High School provides all students with a high- quality education in order to develop reflective, concerned citizens and contributing members of the global community. Course Number 420 Title Algebra I Honors Grade 9 # of Days 60 Course Description This accelerated course completes the Algebra I course started in grade 8. Topics will include exponents and powers, quadratic equations and square roots, polynomials, linear systems, factoring, and functions. Symbolism is used to express abstract ideas. Real life applications will be included for all topics. Students achieving Honor Roll grades should continue on into Algebra II Honors, Trig/Precal Honors, and Advanced Placement math courses. This course addresses Whitman-Hanson Student Learning Expectations 1-6. Instructional Strategies Instructional Strategies include but may not be limited to the following: 1. Whole class instruction 2. Individual work: homework, classwork, assessments 3. Group work: activities, problem solving 4. Experiments, demonstrations, investigations 5. Video presentations 6. Use of technology (graphing calculators and computers) 7. Projects Student Learning Expectations 1. Read, write and communicate effectively. 2. Utilize technologies appropriately and effectively. 3. Apply critical thinking skills. 4. Explore and express ideas creatively. 5. Participate in learning both individually and collaboratively. 6. Demonstrate personal, social, and civic responsibility. 1
Part A Linear Equations and Their Graphs - Chapter 6 Rate of Change and Slope Definitions Define rate of change, slope, positive slope, negative slope, zero slope, undefined slope Calculating Slope Find the rate of change using a table Find the rate of change using two points on a graph Find the slope using two given points or two points on a graph Find the slope of a horizontal line using two points or memorization State the slope of a vertical line is undefined Write an equation in slope-intercept form given the slope and the y-interce Slope-Intercept Form Definitions Define y-intercept, slope-intercept form y-intercept Find the y-intercept by looking at a graph Slope-Intercept Form Find the slope and y-intercept by looking at the equation y = mx + b Write an equation in slope-intercept form from a graph Graph an equation in slope-intercept form Standard Form Definitions Define standard form of a linear equation, x-intercept x and y-intercepts Find x-intercept by making y=0 and solving for x Find y-intercept by making x=0 and solving for y Graph a line using the x and y-intercepts Graph a horizontal line by keeping the y value constant Graph a vertical line by keeping the x value constant Transform an equation in slope-intercept form to standard form through algebra Point-Slope From and Writing Linear Equations Definitions Point-Slope Form Define point-slope form Graph a line in point-slope form Write the equation of a line in point-slope form given a point and a slope Write the equation of a line in point-slope form given two points Write the equation of a line in point-slope form given a table of data Parallel & Perpendicular Lines Definitions Define parallel lines, perpendicular lines, negative reciprocal slope, right angle Parallel Lines Determine whether two lines are parallel given any form of the linear equations 2
Scatter Plots & Equations of Lines Perpendicular Lines Definitions Trend Lines or Lines of Best Fit Write the equation of a line through a given point, parallel to another line Find the slope of a line perpendicular to a given line Write the equation of a line through a given point, perpendicular to a given line Define line of best fit, correlation coefficient Draw a trend line (line of best fit) from a scatter plot Use points on the trend line to estimate the equation of the line Use a graphing calculator to find the equation of a line of best fit Use a graphing calculator to find the correlation coefficient, r Absolute Value Equations Definitions Define absolute value equation, translation Absolute Value Equations Graph the absolute value equation with a vertical translation Graph the absolute value equation with a horizontal translation Write the equation of an absolute value function using horizontal and/or vertical translations to y = x Systems of Equations and Inequalities - Chapter 7 Solving Systems by Graphing Definitions Define system of equations, solution of a system of equations Solving Systems by Graphing Manually graph two lines and find any points of intersection Use Technology to graph two lines and find any points of intersection Identify a system with one solution Identify a system with no solution Identify a system with an infinite number of solutions Solving Systems Using Substitution Substitution Method Use the Substitution Method to find any solutions when the coefficient whe you substitute is 1 Use the Substitution Method to find any solutions when the coefficient whe you substitute is not 1 Solving Systems Using Elimination Elimination Method Use the Elimination Method and addition to solve a system where one pai like terms are opposites. Use the Elimination Method and subtraction to solve a system where one of like terms are the same. Use the Elimination Method after multiplying one equation to get a pair of opposites. 3
Use the Elimination Method after multiplying two equations to get a pair of opposites. Applications of Linear Systems Writing Systems of Linear Equations Write a system of linear equations from a verbal description and solve Linear Inequalities Definitions Define linear inequality, solutions of an inequality Graphing Linear Inequalities Use dotted or solid lines and shading to represent the solution to a linear inequality Transform the given inequality if necessary to facilitate graphing Check a point on the graph to verify the solution Systems of Linear Inequalities Solving by Graphing Graph the linear inequalities on the same coordinate plane and indicate an solution Writing Systems of Linear Inequalities Write a system of linear inequalities from a verbal description and solve by graphing Part C Exponents and Exponential Functions - Chapter 8 Types of Exponents Zero Exponent Know that every nonzero number raised to the zero power is one ex: a 0 = Negative Exponent Scientific Notation Know that every nonzero number raised to a negative exponent is one ove that number raised to the positive of that exponent ex: a -n = (1/a n ) Simplify expressions involving exponents Recognize scientific notation Manually Convert between scientific notation and standard notation Order numbers written in scientific notation Properties of Exponents Multiplication Properties of Exponents Multiply two numbers with the same base ex: a m a n = a n+m Division Properties of Exponents Raise a number with an exponent to a power ex: (a m ) n = a m n Raise a product to a power ex: (ab) m = a m b m Divide powers with the same base ex: (a m /a n ) = a m-n Raise a quotient to a power ex: (a/b) m = (a m /b m ) Geometric Sequences Definition Calculate the common ratio of a geometric sequence Determine whether a sequence is arithmetic, geometric or neither Rules Determine the first term, common ratio, and term number of a rule Create a rule given a geometric sequence: A(n) = a r n-1 Exponential Functions Definition Identify that an exponential function is in the form y = a b x 4
Graphing Exponential Growth Exponential Decay 5 Generate tabular data from exponential functions Graph exponential functions utilizing tabular data Identify exponential growth functions in the form y = a b x when a>0 and b Identify the growth factor from the function (b) Use functions to reflect compound interest with varying interest periods Identify exponential decay functions in the form y = a b x when a>0 and 0<b<1 Identify the decay factor from the function (b) Polynomials and Factoring - Chapter 9 Adding/Subtracting Polynomials Definitions Identify and differentiate between a mono-, bi-, tri-, and poly-nomials Determine degrees of polynomials Write polynomials in Standard Form Adding and Subtracting Polynomials Simplify polynomials by combining like terms Multiplying Polynomials Multiplying a Monomial and a Trinomial Multiply polynomials using the Distributive Property Multiplying a Binomial and a Trinomial Multiply polynomials using the vertical or horizontal method Multiplying a Binomial and a Binomial Multiply using the Distributive Property Multiply using First Outside Inside Last (FOIL) method Identifying special cases with squares and differences of squares Alternative Methods of Multiplying Polynomials Multiply polynomials using the area model Multiply polynomials using algebra tiles Factoring Polynomials Finding the Greatest Common Factor (GCF) Find GCF using prime factorization or common factors Factoring out a Monomial Use the GCF to factor out a monomial from a polynomial Factoring ax 2 + bx + c where a = 1 Factor a trinomial into two binomials Factoring ax 2 + bx + c where a 1 Factor a trinomial into two binomials Identify perfect square polynomials and factor them ex: a 2 + 2ab + b 2 = (a + b) 2 and a 2 2ab + b 2 = (a b) 2 3rd Degree Polynomials with Four Terms Factor four term polynomials by grouping Quadratic Equations and Functions - Chapter 10 Square Roots Working with Square Roots State the square root of a number (and whether it is rational or irrational) Know the perfect squares from 0-400 Standard Form Quadratic Function Convert quadratic functions into Standard Form ex: y = ax 2 + bx + c
Quadratic Equation Convert quadratic equations into Standard Form ex: ax 2 + bx + c = 0 Graphing Quadratic Equations Definitions Define and label a parabola, axis of symmetry, vertex, and the maximum o minimum point of a parabola Creating Coordinate Tables Finding the Axis of Symmetry Create a table of values to graph a parabola from a quadratic equation Use x= b/2a to find the axis of symmetry of a parabola Solving Quadratic Equations Various Methods to Solve Quadratic Equations Solve quadratic equations by graphing (creating parabolas) Solve quadratic equations by using algebra and square roots Solve quadratic equations by factoring polynomials Solve quadratic equations by completing the square Solve quadratic equations by using the Quadratic Formula Utilize the discriminant to determine whether there are two, one or no solutions to a quadratic equation Linear, Quadratic and Exponential Models Choosing a Model from Graphs, Data and Verbal Descriptions Identify and differentiate between the following types of functions: Linear, Quadratic and Exponential Radical Expressions and Equations- Chapter 11 Simplifying Radicals Simplifying Radicals in products and quotients Apply the Multiplication Property of Square Roots Apply the Division Property of Square Roots Simplify radicals The Pythagorean Theorem Parts of the right triangle Identify parts of a right triangle a^2 + b^2 = c^2 Solve for a missing side of a right triangle using the Pythagorean Theorem Use side of a triangle to prove the triangle is a right triangle The Distance & Midpoint Distance formula Find the distance between 2 points using the Distance Formula Formulas Midpoint Formula Find the midpoint between 2 points using the Midpoint Formula Use the Midpoint Formula to find the center of a circle from the diameter Special Right Triangles Recognize 30-60-90 and 45-45-90 right triangles Solve for missing sides of a special right triangle using the ratio of side lengths Operations with Radical Computation with like and unlike radicals Add and subtract like radicals Expressions Multiply monomial and binomial radical expressions Rationalize denominators using conjagates Solving Radical Equations Solving Radical Equations Solve by isolating the radical and then raising the equation to a power 6
Graphing Square Root Functions Solve equations with radicals on both sides by squaring both sides of the equation Find extraneous solutions Graphing by hand using translations Use y = sqrt(x) to graph y = sqrt(x+c) and y = sqrt(x) +c Apply right triangle trig in angle of elevation/angle of depression problems Find the domain of the sqrt function Trigonometric Ratios Sine, Cosine and Tangent of right triangles Use trig ratios to find missing sides and angles in triangles Rationall Expressions and Functions- Chapter 12 Simplifying Rational Expressions Factored Form Factor the rational expression and simplify by diving out common factors Multiplying and Dividing Multiplication Apply rules for multiplying fractions to algebraic expressions Rational Expressions Multiply and put final answers in simple form Division Apply rules for dividing fractions to algebraic expressions Divide and put final answers in simple form Simplify complex fractions Dividing Polynomials Long division Divide a polynomial by a monomial Divide a polynomial by a binomial 7
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