HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK

Transcription

1 HUDSONVILLE HIGH SCHOOL COURSE FRAMEWORK COURSE/SUBJECT Algebra I A KEY COURSE OBJECTIVES/ENDURING UNDERSTANDINGS Important ideas and core processes OVERARCHING/ESSENTIAL SKILLS OR QUESTIONS Ideas/skills that transcend discipline-specific learning SOLVE EQUATIONS AND UNDERSTANDING PERCENTS LINEAR FUNCTIONS FUNCTIONS SOLVING SYSTEMS INEQUALITIES EXPONENTS & POLYNOMIALS Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.

2 UNIT PACING LESSON # STANDARD UNIT LEARNING TARGETS Examples Key Names of units and By the end of the unit, Concept approximate pacing students will be able to... SOLVING 1.1 A.CED.1 solve multi-step equations with variables Solve 9x + 2 = 21 Equation, solution, EQUATIONS AND A.REI.1 on both sides of the equation properties of equality UNDERSTANDING A.REI.3 Solve 3x = including: addition, PERCENTS 2(x + 2) subtraction, multiplication, & division SOLVING EQUATIONS AND UNDERSTANDING PERCENTS 1.2 A.CED.4 A.REI.3 solve an equation for another variable solve linear equations for a given variable with coefficients represented by letters Solve 9 F = C + 32 for 5 C. Formulas SOLVING 1.3 N.Q.1 solve problems involving rates Rates EQUATIONS AND convert units Convert 52 ft per Conversions UNDERSTANDING hour to inches per PERCENTS second. SOLVING EQUATIONS AND UNDERSTANDING PERCENTS 1.4 N.Q.1.. solve problems involving ratios and proportions g Solve = 5 4 RST ~ BCD, find x. Cross products

3 UNIT PACING LESSON # STANDARD UNIT LEARNING TARGETS Examples Key Names of units and By the end of the unit, Concept approximate pacing students will be able to... SOLVING 1.5 F.IF.7 solve absolute value equations Solve x 5 = 10. EQUATIONS AND A.REI.11 UNDERSTANDING PERCENTS SOLVING 1.6 understand percents If 8000 people go EQUATIONS AND to the game and UNDERSTANDING 52% are male, how PERCENTS many people are male? SOLVING 1.7 understand discounts, commissions, sales If the jacket costs EQUATIONS AND tax, and tip $54.99 and it is UNDERSTANDING 30% off, what is PERCENTS the sale price?

4 UNIT PACING LESSON # STANDARD UNIT LEARNING TARGETS Examples Key Names of units and By the end of the unit, Concept approximate pacing students will be able to... LINEAR FUNCTIONS 2.1 A.CED.2 A.SSE.1 graph equations on coordinate axes can use x and y intercepts to interpret meaning in real world problems interpret intercepts in a graph x and y intercepts F.IF.4 LINEAR FUNCTIONS 2.2 F.IF.6 A.SSE.1 estimate rate of change interpret rate of change/slope use slope to interpret meaning in real world problems Rate of change Slope LINEAR FUNCTIONS 2.3 A.CED.2 A.SSE.1 create linear equations in point slope form in two variables and graph Graph the equation 1 y 3 = (x + 2) 2 Point-slope form LINEAR FUNCTIONS 2.4 A.CED.2 A.SSE.1 create linear equations in slope intercept form in two variables and graph Write an equation in slope-intercept form for a line passing through (-3,6) and (-2,-8) Slope-intercept form

5 UNIT PACING Names of units and approximate pacing LESSON # STANDARD UNIT LEARNING TARGETS By the end of the unit, students will be able to... Examples Key Concept LINEAR FUNCTIONS 2.5 A.CED.2 A.SSE.1 students will be able to write equations for parallel and perpendicular lines in slope intercept and point slope form Write an equation for a line parallel to y = 2x 3 passing Parallel and perpendicular lines through (-4, 2) in point-slope form

6 UNIT PACING Names of units and approximate pacing LESSON # STANDARD UNIT LEARNING TARGETS By the end of the unit, students will be able to... Examples Key Concept FUNCTIONS 3.1 N.Q.1 choose and understand the scales & origins for graphic display Discrete and continuous graphs F.IF.4 sketch & interpret key features in a graph (increasing,decreasing, etc.) FUNCTIONS 3.2 F.IF.1 F.IF.2 identify domain and range understand 1 to 1 correspondence. determine if given data is a function. Domain and range FUNCTIONS 3.3 F.IF.2 F.IF.3 F.IF.5 A.CED.2 understand function notation. evaluate functions for inputs in the domains. recognize that sequences are function. interpret function in applications. give a reasonable domain and range. create equations in two or more variables to represent relationships between quantities. Function notation

7 UNIT PACING Names of units and approximate pacing LESSON # STANDARD UNIT LEARNING TARGETS By the end of the unit, students will be able to... Examples Key Concept FUNCTIONS 3.4 A.CED.2 F.IF.1 create linear equations in two variables and graph understand that the graph represents the equation. FUNCTIONS 3.5 S.ID.8 S.ID.9 S.ID.5 S.ID.6 compute(using technology) and interpret the line of regression. understand positive, negative and no correlation. recognize trends in data represent data on a scatterplot. fit a linear function for a scatter plot that suggest a linear association Linear regression lines FUNCTIONS 3.6 F.IF.7.b explore different graphs including absolute value functions, cubic functions, parabolas, hyperbolas, inverse square curves, etc. 3 Graph y =. x

8 UNIT PACING Names of units and approximate pacing LESSON # STANDARD UNIT LEARNING TARGETS By the end of the unit, students will be able to... Examples Key Concept SOLVING SYSTEMS 4.1 A.CED.3 interpret solutions for linear systems of equations. Solve the system by graphing; Solving systems by graphing A.REI.6 A.REI.11 approximate the solution to a linear system by graphing. locate the solution for two linear equations through graphing and examining a table. y = 2x + 5 y = 3x 10 SOLVING SYSTEMS 4.2 N.Q.2 identify the variables and quantities in linear system word problems. A.CED.3 A.REI.6 interpret solutions for linear systems of equations. find exact solutions for a linear system. Solve the system with substitution: 3x 4y = 12 y = 2x 7 Write a system and solve. The length of a rectangle is 3 times larger than its width. The perimeter of the rectangle is 30 cm. Find the length and the width. Writing and solving systems with substitution

9 UNIT PACING Names of units and approximate pacing LESSON # STANDARD UNIT LEARNING TARGETS By the end of the unit, students will be able to... Examples Key Concept SOLVING SYSTEMS 4.3 N.Q.2 identify the variables and quantities in linear system word problems. A.CED.3 A.REI.5 A.REI.6 interpret solutions for linear systems of equations. solve a system using elimination. find exact solutions for a linear system. Solve the system with elimination: 2x 3y = 50 7x + 8y = 10 Write a system and solve. Bill bought 5 french fries and 3 hamburgers for $ Betty bought 6 french fries and 8 hamburgers for $ Find the cost of a hamburger. Writing and solving systems with elimination

10 UNIT PACING LESSON # STANDARD UNIT LEARNING TARGETS Examples Key Names of units and By the end of the unit, Concept approximate pacing students will be able to... INEQUALITIES 5.1 A.CED.I create linear inequalities in two variable. solve linear inequalities in two variable. INEQUALITIES 5.2 A.REI.12 graph the solutions to linear inequalities in two variables. Solve and graph 2(x 3) < 5 (2x 8) Write an inequality to represent the situation. Binders cost $1.99 and Sarah has $12. Write, solve, and graph in inequality to represent the situation. Graph the inequality: y > 3x + 6 Write and solve inequalities. Graph each inequality. INEQUALITIES 5.3 A.CED.3 A.REI.12 create linear inequalities in one variable. solve linear inequalities in one variable. Determine the feasible region for a system of linear inequalities. Solving systems of linear inequalities Graph the solutions to a system of linear inequalities in two variables. INEQUALITIES 5.4 solve & graph compound inequalities. Solve and graph 12 < 2x Solve and graph 3x 1 < 14 or 2x 18 Graph, write, and solve compound inequalities including intersection and union INEQUALITIES 5.5 A.REI.11 solve absolute value inequalities Solve 3x 4 > 8

11 UNIT PACING LESSON # STANDARD UNIT LEARNING TARGETS Examples Key Names of units and By the end of the unit, Concept approximate pacing students will be able to... EXPONENTS AND POLYNOMIALS 6.1 N.RN.1 simplify expressions containing zero and negative exponents. 3 0 = 1, ( 5) 0 = 1 4m 5 4 p 6 = p 6 m 5 Integer Exponents EXPONENTS AND 6.2 N.RN.2 multiply properties of exponents to evaluate m 4 n 3 m 8 = m 12 n 3 POLYNOMIALS and simplify expression. divide properties of exponents to evaluate and (x 3 ) 4 = x 12 simplify expressions. 4m 9 = 4m 5 m 4 Multiplication Properties of Exponents Division Properties of Exponents EXPONENTS AND POLYNOMIALS 6.3 scientific notation classify polynomials according to their degree and number of terms. 5x 9 + 4x 3 2x 8 3x 2 = 2x 8 + 4x 3 3x 2 + 5x 9 4x 2 2x + 5 is a quadratic trinomial Polynomials

12 UNIT PACING Names of units and approximate pacing LESSON # STANDARD UNIT LEARNING TARGETS By the end of the unit, students will be able to... Examples Key Concept EXPONENTS AND POLYNOMIALS 6.4 A.SSE.2 A.APR.1 simplify expressions and write in standard form. add and subtract polynomials and simplify. ( 3x 2 + 2x 7) + (5x 2 8x +1) = 2x 2 6x 6 ( 3x 4 + 2x 2 +5) ( 2x 4 + 7x 2 3) = 1x 4 5x Adding and Subtracting Polynomials EXPONENTS AND POLYNOMIALS 6.5 A.SSE.2 A.APR.1 multiply polynomials and simplify. (x 7)(x + 4) = x 2 3x 28 Multiplying Polynomials (2x 3)(2x + 3) = 4x 2 9