High School Curriculum Map Algebra 1

Transcription

1 High School Curriculum Map Algebra 1 Marking Period 1 Topic Chapters Number of Blocks Dates Expressions, Equations and Functions /9 9/24 PRE-TEST 1 9/25 Linear Equations /26-10/15 Linear Functions /16 11/4 MP 1 ASSESSMENT Chapters /6 Marking Period 2 Topic Chapters Number of Blocks Dates Equations of Linear Functions /11-11/27 Linear Inequalities / Systems of Linear Equations and /2-1/22 Inequalities MP 2 ASSESSMENT Chapters /23 Marking Period 3 Topic Chapters Number of Blocks Dates Exponents and Exponential Functions /24-2/12 Quadratic Expressions and Equations /20-3/12 Solving Quadratic Equations by using the /13-4/3 Quadratic Formula MP 3 ASSESSMENT Chapters /4

2 Marking Period 4 Topic Chapters Number of Blocks Dates Radical Functions and Geometry /7 4/30 Rational Functions and Equations /1 5/21 Statistics and Probability /22 6/11 MP 4 ASSESSMENT Chapters /12

3 Unit Overview Content Area: Math Unit Title: Expressions, Equations, and Functions Target Course/Grade Level: Algebra I Duration: 12 blocks Description: In this unit, students learn how to write and evaluate expressions using exponents and the order of operations, check solutions to equations and inequalities, use verbal and algebraic models to represent real-life situations, and use tables and graphs to organize data and to represent functions. They translate and calculate expressions that model real-life situations and write equations for real-life functions. Students are evaluated by a unit test, quizzes, notebook, class participation, along with other alternate assessments throughout the unit. Concepts Concepts & Understandings Understandings Identify functions and create input/output tables. Write and evaluate expressions. Check solutions to equations and inequalities. Identify and use the properties of real numbers. Use verbal and algebraic models to represent reallife situations. Organize data and represent functions. CPI Codes Learning Targets A-SSE.HS.01 A-SSE.HS.02 A-REI.HS.10 A-CED.HS.01 F-IF.HS.01 F-IF.HS.02 F-IF.HS.04 N-Q.HS.01 Math Practices See Addendum 21 st Century Themes and Skills See addendum

4 Guiding Questions How do we evaluate an expression? In what order do we perform mathematical operations? Why is the order important? What are grouping symbols? What steps do you follow when you see them? What is a solution? What properties are needed to evaluate the expression,? What is the hardest part in solving a word problem? What can we look for that would make them easier? What tools do we have to help us solve real-life problems? When looking at a graph, what key pieces should we identify? Why is an input-output table important? What skills are necessary to be able to write a real-life problem? Students will... Unit Results Students will be able to write verbal expressions for algebraic expressions and vice versa. Students will be able to evaluate numerical and algebraic expressions by using the order of operations. Students will be able to evaluate expressions containing exponents and to also use exponents in real-life problems. Students will use the order of operations to evaluate algebraic expressions. Students will also use the order of operations to evaluate real-life problems that require a calculator. Students will recognize the properties of equality, identity, Commutative and Associative properties. Students will be able to use the distributive property to evaluate and simplify expressions. Students will check solutions to equations and inequalities, translate verbal statements into math statements, and solve real-life problems using formulas. Students will translate verbal phrases into algebraic expression and use models to write and solve real-life applications algebraically. Students will be able to interpret the data presented in various forms of tables and graphs relating to real-life situations. Students will be able to indentify functions, make input-output tables for functions, and to apply reallife situations as functions. Students will be assessed on their comprehension of the material and their ability to apply it to solving problems. The goal of this activity is to assess the students' ability to create and solve word problems. Suggested Activities The following activities can be incorporated into the daily lessons: Evaluate the following expressions: 1. 2x2x2x2x2 2. 4x4x4x4x4x4x4 Evaluate expressions containing exponents. Simplify expressions using the order of operations.

5 Read the log to the class. Write down a list of what you did this morning in the exact order. Identify the properties of real numbers that can be found. Use the distributive property to combine like terms and evaluate expressions. Brainstorm ideas for solving simple equations and inequalities in groups of four. Share ideas for solving equations with other members of the class the board. Solve simple equations and inequalities using mental math. Complete activity quiz. Create a chart showing verbal phrases and their algebraic equivalents. Translate verbal phrases into algebraic expressions. Simplify expressions using the order of operations. Brainstorm ideas for solving simple equations and inequalities in groups of four. Share ideas for solving equations with other members of the class the board. Create a chart showing verbal phrases and their algebraic equivalents. Evaluate expressions containing exponents. Interpret tables and graphs to draw conclusions about situations. Students will evaluate functions with given domains in groups Chapter Test. Unit Overview Content Area: Math Unit Title: Linear Equations Target Course/Grade Level: Algebra 1 Duration: 13 blocks Description: The primary goal of this unit is for the students to solve linear equations in one variable. They will solve one-step, multi-step, variable on each side, and decimal equations. As well as rewriting formulas, functions, and applying these skills to the application of solving real-life problems. Finally, students will be solving ratio, rate and percent problems. Students are evaluated by a unit test, quizzes, notebook, homework, class participation along with other alternate assessments throughout the unit. Concepts: Concepts & Understandings Understandings: Writing equations Solving one-step and multi-step equations Variables on both sides of the equation Solving using absolute value Ratios and proportions Solving single and multi-step linear equations using arithmetic operations. Use linear equations to solve real life situations. Draw diagrams and use tables and graphs to

6 Percent of Change understand real life problems. Find the exact and approximate solutions of equations with decimals. Solve formulas for one variable. Solve problems using rates and ratios. CPI Codes Learning Targets A-CED.HS.01 A-CED.HS.04 A-REI.HS.01 A-REI.HS.03 N-Q.HS.01 F-IF.HS.02 Math Practices See Addendum 21 st Century Themes and Skills See addendum Guiding Questions What are linear equations? How do I solve a linear equation? What are inverse operations? What are the rules for solving equations? How do we solve an equation when our variable has a fraction in front of it? What does combining like terms mean? What tells us to use the distributive property? What do I do first; Combine like terms or Inverse Operations? What should we do when the variable appears on each side of the equation? What does it mean when there is no solution or many solutions? When do we draw a diagram? How do I visualize a problem? What is the importance of making tables and graphs? How do I manipulate a formula for a particular variable? What are the formulas for Interest, Distance, Temperature Conversion Formula, and Area? What is the difference between a rate and a ratio? What is a unit rate? What is a proportion? What are the steps for solving an equation?

7 How can we calculate percent increase and percent decrease? What does the absolute value of a number represent? What steps should be carried out in order to calculate a weighted average? Students will... Unit Results Students will be able to translate sentences into equations. Students will be able to solve linear equations using addition and subtraction. Students will be able to solve equations using multiplication and division. Students will be able to solve multi-step equations. Students will be able to solve equations with the same variable on both sides. Students will be able to solve linear equations and solve real-life problems. Students will be able to evaluate absolute value expressions. Students will be able to solve absolute value equations. Students will be able to solve decimal equations. Students will be able to rewrite formulas and functions to isolate one variable. Students will be able to find rates, ratios, and percents involving real-life situations. Students will be able to find and solve problems involving the percent of change. Students will be able to mixture and uniform motion problems. Suggested Activities The following activities can be incorporated into the daily lessons: Produce transformations that result in equivalent equations. Model Real life problem with an expression Multiply each side of the by the reciprocal. Use the distributive property and distribute the negative Solve Real-Life problems using a known formula d=rt or I=Prt. Solve for the rate when given distance and time. Solve for the time when given Interest, Principal and the rate. Solve Problems with similar triangles using proportions. Interpreting solutions Solving complicated equations, by using the distributive property first, then simplifying and doing inverse operations Solving word problems by drawing a diagram and a verbal model Problem solving using tables and graphs. Changing Decimals into integers before solving equations Solve real-life problems containing decimal amounts. Solving a temperature Conversion formula. Rewriting an equation in function form. Apply unit analysis to problems Calculate the slugging average for several major league baseball players.

8 Unit Overview Content Area: Math Unit Title: Linear Functions Target Course/Grade Level: Algebra 1 Duration: 14 blocks Description The primary goal of this unit is for the students to write and use linear equations. They write the equation of a line when given a graph, the slope and a point on a line, or two points from the line. The standard form, point-slope form and slope-intercept forms of linear equations are all explored including equations for horizontal, vertical as well as parallel and perpendicular lines. Ultimately, students write equations of real-life situations and find possible linear correlations from a set of data points. Students are evaluated by a unit test, quizzes, notebook, homework, class participation along with other alternate assessments throughout the unit. Concepts Concepts & Understandings Understandings Graphing linear equations Solving by graphing Rate of change and slope Direct Variation Arithmetic sequences Proportional relationships The graph of any linear equation will be a line on the coordinate plane. The relationship between any two real life situations can be represented as a linear equation in two variables. What it means for a relationship to be a function. CPI Codes Learning Targets A-CED.HS.02 A-CED.HS.10 F-BF.HS.02 F-IF.HS.06 F-IF.HS.07 F-LE.HS.01a F-LE.HS.01 F.LE.HS.02 Math Practices See Addendum

9 21 st Century Themes and Skills See Addendum Guiding Questions Describe the domain, range, intercepts, and any maximum or minimum points for a given graph. What are linear equations? How many points are needed to determine a straight line? What is the difference between horizontal and vertical lines? What are intercepts? How do we apply the intercepts when graphing? Where does the intercept appear? What is a slope? How can we analyze the slope? Is there a negative slope? When you hear the term rate of change, what other term should automatically pop into your head? What two pieces of information are needed to order to create the graph of a linear equation? What is Direct Variation? Where does direct variation apply? What information is gained by solving an equation algebraically? What does it mean for a relationship to be a function? How can we a function on a calculator? Students will... Unit Results Students will be able to identify linear equations, intercepts, and zeros. Students will be able to graph linear equations. Students will be able to solve linear equations by graphing. Students will be able estimate solutions to a linear equation by graphing Students will be able to use rate of change to solve problems. Students will be able to find the slope of a line. Students will be able to write and graph direct variation equations. Students will be able to solve problems involving direct variation. Students will be able to recognize arithmetic sequences. Students will be able to relate arithmetic sequences to linear functions. Students will be able to write an equation for a proportional relationship. Students will be able to write an equation for a non-proportional relationship. Suggested Activities The following activities can be incorporated into the daily lessons: Plot points in a coordinate plane.

10 Describing patterns from a scatter plot. Create a scatter plot. Graph Equations of horizontal and vertical lines. Graph equations Verify solutions to various equations. Make a Quick Graph using 2 points to form a line. Solve the equation by substituting 0 for x and then 0 for y. Find the intercepts of a line Draw appropriate scales, graphs should represent the data accurately. Draw a line with a positive, negative, and no slope. Slope of a vertical line is undefined. Explain rise over run where the run is 0. Interpret slope as a rate of change. Rate of change compares two different quantities that are changing. Create the equation of the line whose y-intercept is -4 and slope is. Analyze graphs various direct variation models. List properties of graphs of direct variation. Write a direct variation equation Use a graphing calculator. Approximate real-life solutions. Chapter Test Unit Overview Content Area: Math Unit Title- Equations of Linear Functions Target Course/Grade Level- Algebra 1 Duration: 13 blocks Description The primary goal of this unit is for the students to write and use linear equations. They write the equation of a line when given a graph, the slope and a point on a line, or two points from the line. The standard form, point-slope form and slope-intercept forms of linear equations are all explored including equations for horizontal, vertical as well as parallel and perpendicular lines. Ultimately, students write equations of real-life situations and find possible linear correlations from a set of data points. Students are evaluated by a unit test, quizzes, notebook, homework, class participation along with other alternate assessments throughout the unit. Concepts & Understandings Concepts Understandings Graphing equations in slope intercept form The forms of the linear equations. Writing equations in slope intercept form Interpreting graphs of linear equations. Writing equations in point-slope form Understanding slope and intercepts.

11 Parallel and Perpendicular lines Scatter plots Lines of Best fit Regression and Median-fit lines Inverse Linear Functions Finding a "best fit" line. Interpolation/extrapolation. Finding inverse functions. CPI Codes Learning Targets A-CED.HS.02 A-CED.HS.03 F-BF.HS.01 F-BF.HS.04 F-IF.HS.02 F-IF.HS.07 F-LE.HS.02 S-ID.HS.01 S-ID.HS.06 S-ID.HS.07 S-ID.HS.08 Math Practices See Addendum 21 st Century Themes and Skills See Addendum Guiding Questions When can I use the coordinate system? What is a Quadrant? What are the difference between positive, negative, and no correlation? How do we make a scatter plot? What is slope? What is the y-intercept? What do we need in order to write the slope-intercept equation? How can we find the missing value? What is special about lines being parallel? What is needed to write the slope-intercept equation? What can we find knowing two points? What does it mean if two lines are perpendicular? If the slope-intercept form needs m and b, what does the point-slope form need?

12 What do we know if we have 2 points? How can we get to the slope-intercept form? What values are missing from the standard form? If we don't know A, B, C, what should we do to write the equation? What does extrapolate mean? (prefix "extra") What does interpolate mean? (prefix "inter") What are the forms of an equation that we can write? Unit Results Students will... Students will be able to write and graph linear equations in slope-intercept form. Students will be able to model real-world data with equations in slope-intercept form. Students will be able to write an equation of a line in slope-intercept form given the slope and one point. Students will be able to write an equation of a line in slope-intercept form given two points. Students will be able to write equations of lines in point slope form. Students will be able to write linear equations in different forms. Students will be able to write an equation of the line that passes through a point, parallel to a given point. Students will be able to write an equation of the line that passes through a given point, perpendicular to a given line. Investigate relationships between quantities by using points on a scatter plot. Students will be able to use lines of best fit to make and evaluate predictions. Students will be able to write equations of best-fit lines using linear regression. Students will be able to write equations of median-fit lines. Students will be able to find the inverses of a relation. Students will be able to find the inverses of a linear function. Assess students' comprehension of the material and their ability to apply it to the solving of problems in a unit test. Suggested Activities The following activities can be incorporated into the daily lessons: Write equation when given a graph. Write equation given slope (m) and y-intercept (b). Substitute and solve for the intercept (b) when given the slope (m) and one point (x, y). When given a graph, find the y-intercept to write the slope-intercept equation. Find the equation of a parallel line given one line. Write the slope-intercept equation when given two points When given a graph, write the slope-intercept equation. Find the equation of a line that is perpendicular to a given line. Use a graph to write the point-slope equation. Write point-slope equation when given two points. Rewrite point-slope equation into slope-intercept form. Write equations when given a point and slope. Write equations when given two points. Write equations for vertical/horizontal lines

13 Use correlations to determine appropriateness. Use a best fit line to interpolate/extrapolate Find a "best fit" line and write an equation Unit Overview Content Area: Math Unit Title- Solving and Graphing Linear Inequalities Target Course/Grade- Algebra 1 Duration: 15 blocks Description Students write, solve and graph linear inequalities in one variable including compound inequalities. They solve absolute value equations and inequalities and graph linear inequalities in two variables. Students are evaluated by a unit test, quizzes, notebook, homework, class participation along with other alternate assessments throughout the unit. Concepts Concepts & Understandings Understandings Solving inequalities by addition and subtraction. Solving inequalities by multiplication and division. Solving multi-step inequalities. Solving compound inequalities. Inequalities involving absolute value. Graphing inequalities in two variables. How to solve and graph inequalities. How to solve and graph absolute value equations and inequalities. CPI Codes Learning Targets A-CED.HS.01 A-CED.HS.03 A-REI.HS.03 A-REI.HS.12 S-ID.HS.01 Math Practices See Addendum

14 21 st Century Themes and Skills See Addendum Guiding Questions What is a linear inequality? What does the solution to a linear inequality look like? How do you solve a one-step linear inequality? How do you graph the solution to a linear inequality? How do you solve multi-step linear inequalities? How do you model a real-life problem using linear inequalities? How do you solve real-life problems using linear inequalities? What does compound mean? In set notatation what is the difference between an "and" and "or? What is meant by absolute-value? Why is absolute-value always positive? How many solutions does an absolute-value have? What methods do we have for graphing equations on a plane? How do you show the solutions when graphing an inequality? Students will... Unit Results Solve linear inequalities by using addition. Solve linear inequalities by using subtraction. Solve linear inequalities by using multiplication. Solve linear inequalities by using division. Solve linear inequalities involving more than one operation. Solve linear inequalities involving the Distributive Property. Solve compound inequalities containing the word and, and graph their solution set. Solve compound inequalities containing the word or, and graph their solution set. Solve and graph absolute value inequalities (<) and (>). Graph linear inequalities on the coordinate plane. Solve inequalities by graphing. Suggested Activities The following activities can be incorporated into the daily lessons: Identify a solution to a linear inequality. Solve one-step linear inequalities Graph the solution of a linear inequality. Solve multi-step linear inequalities.

15 Model and solve a real-life problem using linear inequalities. Solve and graph the solutions to an "and" and or compound inequality Review and solve an absolute-value equation and inequality. Graph a linear inequality in two variables. Model a real-life scenario using a linear inequality in two variables. Unit Overview Content Area: Math Unit Title- Systems of Linear Equations and Inequalities Target Course/Grade Level Algebra 1 Duration: 3 weeks Description This unit introduces systems of linear equations and systems of inequalities. Students solve a system of two linear equations by using graphing, substitution, linear combination and the graphing calculator. The choice of method for solving a particular system is considered and linear systems that have one solution, no solution, or infinitely many solutions are identified. Systems of linear inequalities are solved by graphing. Throughout this unit, real-life problems are modeled using linear systems. Students are evaluated by a unit test, quizzes, notebook, homework, class participation, along with other alternate assessments throughout the unit. Concepts & Understandings Concepts Understandings Graphing systems of equations The solution to a linear system is the point of Substitution intersection of the graphs. Elimination using addition and subtraction Solutions to linear systems can be found in a Elimination using multiplication variety of ways special solutions sometimes Applying systems of linear equations occur and need to be identified solutions to Systems of Inequalities inequalities are intersecting areas. CPI Codes Learning Targets A-CED.HS.02 A-CED.HS.03 A-REI.HS.05 A-REI.HS.06 A-REI.HS.11 A-REI.HS.12

16 Math Practices See Addendum Garfield High School 21 st Century Themes and Skills See Addendum Guiding Questions How can you determine the number of solutions a system of equations will have? How do we check a solution? How do we graph equations? What does substitution mean? How do we rewrite and equation? What does combining mean in math? What property allows us to multiply an equation? What methods do we have to solve a linear system? What should we look for when choosing a method? If a solution to a system is an intersection point, what problems might exist with finding a solution? How does the intersection idea relate to graphing systems of inequalities? Students will... Unit Results Determine the number of solutions a system of linear equations has. Solve systems of linear equations by graphing. Solve systems of equations by using substitution. Solve real-world problems involving systems of equations by using substitution. Solve systems of equations by using elimination with addition. Solve systems of equations by using elimination with subtraction. Solve systems of equations by using elimination with multiplication. Solve real-world problems involving systems of equations. Determine the best method for solving systems of equations. Apply systems of equations. Solve systems of linear inequalities by graphing. Apply systems of linear inequalities. Suggested Activities The following activities can be incorporated into the daily lessons: Check solutions to systems and find them graphically. Solve by direct substitution.

17 Solve by rewriting first, then substituting. Solve by combining directly. Solve by multiplying then combining Solve by rewriting then multiplying before combining. Unit Overview Content Area: Math Unit Title- Exponents and Exponential Functions Target Course/Grade Level Algebra 1 Duration: 14 blocks Description In this unit, students learn how to multiply and divide expressions with exponents, including zero and negative exponents. They use scientific notation to represent real numbers and solve inter-curricular problems. They graph exponential functions and use these functions to solve real-life problems involving exponential growth and decay. Students also learn how to use technology to find a best fitting exponential growth or decay model. Students are evaluated by a unit test, quizzes, notebook, homework, class participation along with other alternate assessments throughout the unit. Concepts & Understandings Concepts Understandings Multiplication properties of exponents How to multiply and divide expressions with Division properties of exponents exponents. Rational exponents How to use scientific notation in problem Scientific notation solving. Exponential Functions How to use exponential growth and decay Growth and Decay models to solve real-life problems. Geometric Sequences as Exponential Finding the nth term of a geometric Functions. sequences. Recursive Formulas Complete sequences using the recursive formulas. CPI Codes Learning Targets A-APR.HS.01 A-SSE.HS.01 A-SSE.HS.02 A-SSE.HS.03 F-BF.HS.02 F-IF.HS.03

18 F-IF.HS.07 F-IF.HS.08 F-LE.HS.01 Math Practices See Addendum 21 st Century Themes and Skills See addendum Guiding Questions How do you multiply two numbers with exponents? What happens when you take a power of a power? How do you find the power of a product? How do you simplify exponential expressions? What do you get when you put any number to the zero power? How do you use negative exponents? How do you simplify exponential expressions with negative exponents? How do you divide numbers with exponents? How do you find a power of a quotient? How do you simplify exponential expressions with quotients? What are the two ways to write very large or very small numbers? Where should the decimal point always appear? How can you model a situation of rapid growth using an exponental function? How do you graph an exponential growth function? What is exponential decay? How can you model a situation of rapid decay using an exponential function? How do you graph an exponential decay function? What is a recursive formula? How can a recursive formula help us find the nth term in a sequence? Students will... Unit Results Multiply monomials using the properties of exponents. Simplify expressions using the multiplication properties of exponents. Divide monomials using the properties of exponents. Simplify expressions containing negative and zero exponents. Evaluate and rewrite expressions involving rational exponents. Solve equations involving expressions with rational exponents. Express numbers of in scientific notation. Find products and quotients of numbers expressed in scientific notation. Graph exponential functions. Identify data that displays exponential behavior.

19 Solve problems involving exponential growth. Solve problems involving exponential decay. Identify and generate geometric sequences. Relate geometric sequences to exponential functions. Use a recursive formula to list terms in a sequence. Write recursive formulas for arithmetic and geometric sequences. Suggested Activities The following activities can be incorporated into the daily lessons: Use powers to model real-life problems, such as finding the area of crop irrigation circles. Evaluate powers that have zero and negative exponents. Graph exponential factors. Use the division property of exponents to find a probability of tossing 5 heads. Use scientific notation to describe real-life situations like the price of land in Alaska per acre. Write, use and graph models of exponential growth and decay. Use a recursive formula to find the nth term in an arithmetic or geometric sequence. Write a recursive formula. Translate between recursive and explicit formulas. Unit Overview Content Area: Math Unit Title - Quadratic Expressions and Equations Target Course/Grade Level Algebra 1 Duration: 15 blocks Description - The primary goal of this unit is to have students identify, perform operations with, and factor polynomial expressions. They will add, subtract, and multiply, utilizing patterns when present, polynomial expressions. Later in this unit, students will learn to factor polynomial expressions by using factors, patterns, GCF's, and the Distributive Property. They will use their factoring skills to solve quadratic equations and apply this understanding to real-life situations. Students are evaluated by a unit test, quizzes, notebook, homework, class participation along with other alternate assessments throughout the unit. Concepts & Understandings Concepts Understandings Adding and subtracting polynomials Add, subtract, and multiply polynomials Multiplying a polynomial by a monomial Factoring trinomials Multiplying polynomials Factor differences of squares Special products Graph quadratic functions Using the distributive property. Solve quadratic equations Solving

20 Solving Difference of Squares Perfect Squares CPI Codes A-APR.HS.01 A-REI.HS.01 A-REI.HS.04 A-SSE.HS.01 A-SSE.HS.02 A-SSE.HS.03 Learning Targets Math Practices See Addendum 21 st Century Themes and Skills See Addendum Guiding Questions What do you think a polynomial is? What might one look like? What do you think is indicated by the terms: monomial, binomial, trinomial, and polynomial? How do you add and subtract polynomials? In general, how does the distributive property work? How can it be extended to binomial products? Can it be extended to binomial products? Have you noticed any patterns when you applied the FOIL method? What are those patterns? Do we have the tools to solve an equation that looks like (x + a)(x b) = 0? Could we solve ab = 0? How does the FOIL method work? Do you think it can be reversed? What should we be looking for? Name the steps that need to be taken in order to solve a trinomial that is in the form Students will... Unit Results Write polynomials in standard form. Add and subtract polynomials. Multiply a polynomial by a monomial. Solve equations involving the products of monomials and polynomials.

21 Multiply binomials by using the FOIL method. Multiply binomials by using the Distributive Property. Find squares of sums and differences. Find the product of a sum and difference. Use the distributive property to factor polynomials. Solve equations of the form Factor trinomials of the form Solve equations in the form Factor trinomials of the form Solve equations in the form Factor binomials that are the difference of squares. Use the difference of squares to solve equations. Factor perfect square trinomials. Solve equations involving perfect squares. Suggested Activities The following activities can be incorporated into the daily lessons: The glass portion of a window has a height to width ratio of 3:2. The framework adds 6 inches to the width and 10 inches to the height. Write a polynomial expression that represents the total area of the window, including the framework. (3x + 10)(2x + 6) 6x^2 + 38x Use the sum and difference pattern to multiply two binomials. Use the square of a binomial pattern to find the product of a binomial squared. Relate x-intercepts and factors to graph a quadratic function. Solve a factored quadratic equation using the zero-product property. Solve a factored cubic equation using the zero-product property. Solve a factored cubic equation using the zero-product property. Solve a quadratic equation by factoring. Factor a trinomial in the form Unit Overview Content Area: Math Unit Title - Quadratic Equations and Functions Target Course/Grade Level- Algebra 1 Duration: 16 blocks Description - Students approximate and evaluate square roots and simplify radicals. They use these skills to solve quadratic equations by finding square roots and using the Quadratic formula. Students graph quadratic functions and inequalities using the x-intercepts of the graph to solve the related quadratic equation. Students explore the relationships between the discriminate and the number of solutions in a quadratic equation. The unit concludes with an exploration of choosing a linear, quadratic or exponential model that best fits a collection of data. Students are evaluated by a unit test, quizzes, notebook, homework, class participation along with other

22 alternate assessments throughout the unit. Concepts & Understandings Concepts Understandings Graphing quadratic functions Solve quadratic equations by graphing, Solving quadratic equations by graphing completing the square, and using the Transformations of quadratic functions quadratic formula. Solving quadratic equations by completing the square Analyze functions with successive difference and ratios. Solving quadratic equations using the quadratic formula Identify and graph special functions. Analyzing functions with successive differences Special functions CPI Codes Learning Targets A-REI.HS.04 A-SSE.HS.03 A-SSE.HS.04 F-IF.HS.04 F-IF.HS.06 F-IF.HS.07 F-IF.HS.08 F-LE.HS.01 Math Practices See Addendum 21 st Century Themes and Skills See Addendum Guiding Questions How do we find a square root? How many square roots do all positive real numbers have? What is a radical? How do we evaluate radical expressions? How do we solve quadratic equations with square roots? How do you determine the square root of a product? How do you calculate the square root of a quotient? How do you simplify radicals using the product property? How do you simplify radicals using the quotient property?

23 What is the standard form of a quadratic equation? What is the vertex form of a quadratic equation? How do you know if the parabola opens up or down? What is the formula for determing the vertex of a quadratic function? How do you evaluate a quadratic equation? What do the zeros of a quadratic function represent? What does a double root represent? How do we solve a quadratic equation by graphing? How do you use a formula? What is the quadratic formula? How do you use the quadratic formula in a real-life setting? What is the discriminate? How can you determine the number of solutions of a quadratic equation? How can you use the discriminate the find the number of x-intercepts? What steps do you need to take to graph a quadratic equation? What needs to be remembered when graphing an inequality on a plane? How does the graph of a linear function compare to an exponential or quadratic function? How do you know which model is the most appropriate given a set of data? How do you write a model? Unit Results Students will... Analyze the characteristics of graphs of quadratic functions. Graph quadratics functions. Solve quadratic equations by graphing. Estimate solutions of quadratic equations by graphing. Apply translations to quadratic functions. Apply dilations and reflections to quadratic functions. Complete the square to write perfect square trinomials. Solve quadratic equations by completing the square. Solve quadratic equations by using the quadratic formula. Use the discriminant to determine the number of solutions of a quadratic equation. Identify linear, quadratic, and exponential functions from given data. Write equations that model data. Identify and graph step functions. Identify and graph absolute value and piecewise defined functions. Suggested Activities The following activities can be incorporated into the daily lessons: Find and evaluate square roots. Evaluate radical expression. Simplify radical expressions. Real life application 'Boat Racing." Solve a quadratic equation graphically through the related equation. Solve motion problems for dropped and thrown objects. Use the discriminate to find the number of solutions to a quadratic equation. Sketch the graph of a quadratic inequality. Choose an appropriate model for given data.

24 Unit Overview Content Area: Math Unit Title - Rational Equations and Functions Target Course/Grade Level - Algebra 1 Duration: 10 blocks Description - The primary goal for this unit is for students to work with polynomial and rational expressions. They will solve proportions containing polynomials as well as percent problems. Direct variation will be reviewed as inverse variation is introduced. Students will simplify, multiply, divide, add, and subtract rational expressions. Later in the unit, students will perform polynomial division. Finally, students will solve rational equations by cross multiplying or applying LCD's and connecting to the related graphs. Students are evaluated by a unit test, quizzes, notebook, homework, class participation along with other alternate assessments throughout the unit. Concepts & Understandings Concepts Understandings Square root functions Graph and transform radical functions. Simplifying radical expressions Simplify, add, subtract, and multiply radical Operations with radical expressions expressions. Radical equations Solve radical equations. The Pythagorean theorem Use the Pythagorean Theorem Trigonometric ratios Find trigonometric ratios CPI Codes Learning Targets A-CED.HS.02 A-REI.HS.04 F-IF.HS.04 F-IF.HS.07 G-SRT.HS.08 N-RN.HS.02 Math Practices See Addendum 21 st Century Themes and Skills See Addendum Guiding Questions

25 What is a ratio? What is a proportion? Where can you use proportions in real life? What key ideas help us set up percent problems? What do you know about the concept of direct variation? What does it mean for two quantities to vary directly? To vary inversely? What is a rational number? What is a rational expression? How do we simplify fractions? What is the formula for finding a simple probability? What is a rational expression? What are the rules for multiplying fractions? What rule do we follow when dividing fractions? Where do we use rational expression in real life? What is necessary in order to add or subtract two fractions? What is the rule when there is a common denominator? What steps do we take when there is not a common denominator? How is long division set up with real numbers? What are the steps used in performing long division? How should polynomial long division be set up? How do you solve a proportion? What technique allows us eliminate fractions from an equation? What graphing method will help us graph y = ax+b/cx+d? What is the Pythagorean Theorem? How can the Pythagorean Theorem be helpful when determining the lengths of the sides of a triangle? When can t the Pythagorean Theorem be used? What are the three trigonometric ratios? Students will... Unit Results Graph and analyze dilations of radical functions. Graph and analyze reflections and translations of radical functions. Simplify radical expressions by using the property product of square roots. Simplify radical expressions by using the quotient property of square roots. Add and subtract radical expressions. Multiply radical expressions. Solve radical expressions. Solve radical equations with extraneous solutions. Solve problems by using the Pythagorean Theorem. Determine whether a triangle is a right triangle. Find trigonometric ratios of angles. Use trigonometry to solve triangles. Suggested Activities

26 The following activities can be incorporated into the daily lessons: Find the dilation of a square root function. Find the reflection of a square root function. Translate and transform square root functions. Simplify radical expressions. Multiply radical expressions. Simplify radical expressions with variables raised to an exponent. Add and subtract like and unlike radicands. Solving radicand expressions. Find the length of the missing side of a right triangle. Determine whether the given side lengths from a right triangle. Find sine, cosine, and tangent ratios for the given right triangle. Use trigonometric ratios to solve right triangles. Unit Overview Content Area: Math Unit Title Rational Functions and Equations Target Course/Grade Level- Algebra 1 Duration: 15 Blocks Description The students will investigate and graph square-root functions. They will simplify expressions involving radicals and will solve radical equations by factoring, or by completing the square. Students will study and use the Pythagorean theorem and its converse. They will be introduced to the midpoint and distance formulas. They will also use similar triangles to explore trigonometric ratios. Concepts & Understandings Concepts Understandings Inverse variation Identify and graph inverse variations. Rational functions Identify excluded values of rational functions. Simplifying rational expressions Multiply, divide, and add rational expressions. Multiplying and dividing rational expressions Divide polynomials. Dividing polynomials Solve rational equations. Adding and subtracting rational expression Mixed expressions and complex fractions Rational equations Learning Targets CPI Codes A-APR.HS.01 A-CED.HS.02 A-REI.HS.02

27 A-REI.HS.04 F-IF.HS.07 G-SRT.HS.08 Math Practices See Addendum 21 st Century Themes and Skills See Addendum Guiding Questions How do we evaluate a function? What are the definitions of the domain and range of a function? What are like terms? How do we combine like terms? What is the order of the steps we use to solve and equation? How do we remove a square root? What is the order of the steps we use to solve and equation? How do we remove a square root? How can we add or subtract rational expressions with unlike denominators? Students will... Unit Results Identify and use inverse variation. Graph inverse variations. Identify excluded values. Identify and use asymptotes to graph rational functions. Identify values excluded from the domain of a rational expression Simplify rational expressions. Multiply rational expressions. Divide rational expressions. Divide a polynomial by a monomial. Divide a polynomial by a binomial. Add and subtract rational expressions with like denominators. Add and subtract rational expressions with unlike denominators. Simplify mixed expressions. Simplify complex fractions. Solve rational expressions. Use rational equations to solve problems. Suggested Activities

28 The following activities can be incorporated into the daily lessons: Identify inverse and direct variations. Write an inverse variation. Solve for x and y. Find excluded values. Graph real-life rational functions. Use the GCF to simplify an expression. Use rational expressions. Simplify rational functions. Multiply expression involving monomials. Divide by rational expressions. Divide by polynomial by monomials. Use long division to divide polynomials. Add and subtract rational expressions with like and unlike denominators. Use complex fractions to solve problems. Change mixed expressions to rational expressions. Use cross products to solve equations. Determine extraneous solutions. Unit Overview Content Area: Math Unit Title: Statistics and Probability Target Course/Grade Level: Algebra I Duration: 14 blocks Description: In this unit, students will investigate the basics of statistics and probability. They will describe and analyze several different types of data display (such as bell curves, histograms, and box and whisker plots). Students will study the difference between combinations, permutations, compound and simple events. Students are evaluated by a unit test, quizzes, notebook, class participation, along with other alternate assessments throughout the unit. Concepts Samples and studies Statistics and probability Distributions of data Comparing sets of data Simulation Permutations and combinations Probability of compound events Probability distributions Concepts & Understandings Understandings Design surveys and evaluate results. Use permutations and combinations. Find probabilities of compound events. Design and use simulations.

29 CPI Codes Learning Targets S-CP.HS.02 S-IC.HS.04 S-ID.HS.02 S-ID.HS.03 Math Practices See Addendum 21 st Century Themes and Skills See Addendum Guiding Questions Is it better to have a large of small sample size? Why? What is a population parameter? How many different ways can a bell curve be shaped? Describe their forms. What is the difference between mean absolute deviation and standard deviation? What kind of information can be displayed in a histogram? A box-and-whisker plot? Describe a linear transformation. Describe the difference between theoretical and experimental probability. What is a permutation? What is a combination? Describe the difference between simple and compound events. Students will... Unit Results Classify and analyze samples and studies. Identify sample statistics and population parameters. Analyze data sets using statistics. Describe the shape of a distribution. Use the shapes of distributions to select appropriate statistics. Determine the effect that transformations of data have on measures of central tendency and variation. Compare data using measures of central tendency and variation. Calculate experimental probabilities. Design simulations and summarize data from simulations. Use permutations and combinations. Find probabilities of independent and dependent events. Find probabilities of mutually exclusive events.

30 Find probabilities by using random variables. Find the expected value of a probability distribution. Suggested Activities The following activities can be incorporated into the daily lessons: Classify random samples Determine the difference between biased and unbiased samples. Classify the different types of study techniques. Find the standard deviation of the given data set. Compare two sets of data using their standard deviation. Create a histogram. Create a box-and-whisker plot. Choose the appropriate data display to visually display different types of data sets. Transformations using addition and multiplication. Determine the theoretical and experimental probability of flipping a coin and it landing on a tails when tossed 20 different times. Design a probability simulation. Use factorials as permutations. Use the permutation formula to determine how many different ways there are to place 6 books on a bookshelf. Use the combination formula to determine how many pizzas can be made when given 5 different topping choices. Find the probability of independent and dependent events. Describe a mutually exclusive event. Create a probability distribution. Find the expected value of an event when given a probability distribution.

31 Addendum Math Practices 1. CCSS.Math.Practice.MP1 Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, Does this make sense? They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. 2. CCSS.Math.Practice.MP2 Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

32 3. CCSS.Math.Practice.MP3 Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and if there is a flaw in an argument explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. 4. CCSS.Math.Practice.MP4 Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.