Algebra I Pacing Guide Days Units Notes 9 Chapter 1 ( , )

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1 Algebra I Pacing Guide Days Units Notes 9 Chapter 1 ( , ) Expressions, Equations and Functions Differentiate between and write expressions, equations and inequalities as well as applying order of operations. Word problems will be incorporated 8 Chapter 2 ( ) 14 Chapter 3 ( ) 14 Chapter 4 ( ) 14 Chapter 5 ( ) 14 Chapter 6 ( ) 11 Chapter 7A ( ) in several of the different sections. Properties of Real Numbers Add, Subtract, Multiply, Divide and apply the Square Root function as well as classify and differentiate between different types of numbers. Word problems will be incorporated in many of the different sections. Solving Linear Equations Progress through solving equations, including onestep equations, two-step equations, multi-step equations, equations with variables on both sides of the equation, ratios and proportions and percents. Word problems will be incorporated in each individual section. Graphing Linear Equations and Functions Students will learn about graphing points as well as linear equations (lines). During this time we will investigate topics like slope, rate of change and different forms of equations and methods of graphing. Students will also use the graphing calculator to estimate what a line would look like when given specific data. End of 1 st Nine Weeks Writing Linear Equations Students will learn how to write equations that will produce graphs similar to those in the previous chapter. They will investigate many different ways of writing equations and determine which method is most appropriate in certain situations. Also, parallel and perpendicular lines will be discussed. Solving and Graphing Linear Inequalities Students will investigate the graphs of inequalities, including greater than, less than, greater than or equal to and less than or equal to. Absolute value equations and inequalities will also be discussed in this chapter. Students will also write and solve word problems in this chapter. Systems of Equations Students will explore the different methods for 1

2 5 Chapter 7B (7.5 & 7.6) 12 Chapter 8 ( ) 12 Chapter 11 ( ) 10 Chapter 9A ( ) 13 Chapter 9B ( ) 12 Chapter 10A ( ) solving two equations at the same time. Methods that will be explored include graphing, substitution and adding or subtracting. End of 2 nd Nine Weeks End of 1 st Semester Systems of Inequalities and Special Systems of Equations Students will learn about special cases of systems of equations (no solution and infinite solutions) as well as discover how to graph systems of inequalities. Students will also write and solve word problems. Exponents and Exponential Functions Students will learn rules for working with exponents in Algebra. They will also learn several properties, use scientific notation and explore exponential growth and decay. Word problems will be used often in this chapter. Simplifying and Solving Square Root Expressions and Equations, Pythagorean Theorem Students will simplify radical expressions exactly (rather than estimate), they will learn to solve radical equations and apply the Pythagorean Theorem. Word problems will be used in much of this chapter. Simplifying Polynomials Students will learn to simplify polynomials through addition, subtraction and multiplication, as well as distribution. Students will also begin to learn how to solve equations involving polynomials with equations that have already been factored. Factoring Polynomials Students will learn to factor polynomials on their own through many different methods. They will also learn to solve equations with unfactored polynomials. Word problems and writing about their answers can be expected in this and the previous unit. End of 3 rd Nine Weeks Graphing Quadratic Equations and Solving by Factoring Students will graph quadratic equations and solve them through interpreting the graphs. Use of calculators and graphing by hand will both be implemented. 2

3 7 Chapter 10B (10.6 & 10.7) 14 Chapter 13 ( ) Solving Quadratic Equations by Quadratic Formula Students will solve quadratic equations through the use of the quadratic formula and will be able to find the number of real roots by using the discriminant. Probability and Statistics Students will begin to investigate the world of probability and statistics, including an investigation of permutations and combinations, simple probability, compound probability and critique of samples and surveys. End of 4 th Nine Weeks End of 2 nd Semester 3

4 Algebra I Learning Targets Chapter 1: Expressions, Equations and Functions Evaluate Expressions and Write Expressions 1. Define a variable and an expression. 2. Translate an expression into a word sentence and vice versa. 3. Use proper terminology with respect to exponents, bases and powers. 1.2 Order of Operations 1. Correctly use the order of operations to simplify expressions without a calculator. 2. Check their answers with a calculator and look for mistakes that may have been made. 1.4 Write Equations and Inequalities 1.6 Represent Functions as Rules and Tables 1.7 Represent Functions as Graphs 1. Differentiate between an expression, equation and inequality. 2. Correctly identify inequality symbols (less than, greater than, less than or equal to, greater than or equal to). 3. Begin to identify solutions to an equation through checking possible solutions. 4. Write and solve word problems. 1. Define function, domain, range, independent variable and dependent variable. 2. Identify a function. 3. Make a table and a rule for a function, including real-life applications. 1. Identify the X and Y axes on a coordinate plane. 2. Graph ordered pairs on a coordinate plane. 3. Write a rule for a function from a graph translate from a graph to a table or rule. 4

5 Chapter 2: Properties of Real Numbers 2.1 Using Integers and Rational Numbers 2.2 & 2.3 Add and Subtract Real Numbers 2.4 Multiply Real Numbers 2.5 Apply Distributive Property 2.6 Divide Real Numbers 2.7 Find Square Roots and Compare with Real Numbers 1. Graph positive and negative numbers on a number line. 2. Compare positive and negative numbers. 3. Compare (differentiate between) whole numbers, integers and rational numbers. 1. Add and subtract positive and negative numbers. 2. Use number sense to solve and write word problems. 3. Add and subtract decimals and fractions with and without a calculator. 1. Multiply real numbers with and without a calculator. 2. Substitute values for variables and simplify expressions. 1. Determine when to apply the distributive property. 2. Apply the distributive property when appropriate. 3. Use the distributive property to help write and solve word problems. 1. Divide real numbers with and without a calculator. 2. Divide by fractions and decimals. 3. Understand and correctly use the terminology associated with division (quotient, reciprocal, etc.). 1. Find approximate values of square roots and order them with other numbers. 2. Classify numbers as real, rational, irrational or integers. 3. Use square roots to write and solve word problems. 5

6 Chapter 3: Solving Linear Equations 3.1 Solving One-Step Equations 3.2 Solve Two-Step Equations 3.3 Solve Multi-Step Equations 3.4 Solving Equations with Variables on Both Sides 3.5 & 3.6 Write Ratios and Proportions 3.7 Solve Percent Problems 3.8 Rewrite Equations and Formulas 1. Solve one-step equations using addition, subtraction, multiplication and division. 2. Solve equations that have decimals and fractions. 3. Solve equations with the variable on either side of the equation. 1. Solve two-step equations using addition, subtraction, multiplication and division. 2. Differentiate a one-step equation from a two-step equation. 3. Solve equations with the variable(s) on either side of the equation. 1. Differentiate between one-step, two-step and multi-step equations. 2. Solve multi-step equations with decimals and fractions. 3. Apply the distributive property and use correctly to solve multi-step equations. 1. Differentiate between an equation with variables on both sides and a multi-step equation or two-step equation. 2. Combine like terms appropriately by moving the correct variable or number. 3. Apply the distributive property if necessary. 4. Write and solve real-world word problems. 1. Differentiate between a ratio and a proportion. 2. Set up ratios and proportions. 3. Solve proportions using the cross multiply method. Correctly apply distribution if necessary. 4. Write and solve word problems. 1. Apply number sense to remember that a percent is a number out of Solve percent problems by writing a proportion or using the percent equation. 3. Write and solve real-world word problems involving percents. 1. Successfully manipulate equations to solve for a variable instead of a number. 2. Solve problems using the manipulation of an equation. 6

7 Chapter 4: Graphing Linear Equations and Functions 4.1 Plot Points in a 1. Plot points when given coordinates. Coordinate Plane 4.2 Graph Linear Equations 4.3 Graph Using Intercepts 4.4 Find Slope and Rate of Change 4.5 Graph Using Slope Intercept Form 4.6 Model Direct Variation 4.7 Graph Linear Functions 2. Give coordinates when points have been plotted. 1. Recognize a vertical and horizontal line by their equation. 2. Write an equation in standard form. 3. Graph an equation by using a table. 1. Understand the concept of X- and Y-Intercepts. 2. Use the intercepts to find an equation. 3. Use a graph to find the intercepts. 1. Differentiate between positive, negative, 0 and no slopes. 2. Use the formula to find slope of lines. 3. Relate Rate of Change to Slope. 1. Recognize Slope-Intercept Form (in equation form). 2. Identify different parts of the equation (Slope & Intercept). 3. Graph using slope intercept form. 1. Graph direct variation equations. 2. Write direct variation equations. 1. Apply earlier knowledge of Standard and Slope- Intercept Forms to graph functions. 2. Find values when given a function. 7

8 Chapter 5: Writing Linear Equations 5.1 Write Linear Equations in Slope- Intercept form 5.2 Use Linear Equations in Slope- Intercept Form 5.3 Write Linear Equations in Point- Slope Form 5.4 Write Linear Equations in Standard Form 5.5 Write Equations of Parallel and Perpendicular Lines 1. Write an equation of a line when given two points. 2. Use slope and y-intercept to write an equation. 1. Write equations when given the slope and y- intercept. 2. Recall information from section 5.1 and apply it to real world situations. 1. Recognize difference between slope-intercept, standard and point-slope forms. 2. Write equations using point-slope forms. 1. Transfer between slope-intercept, standard and point-slope forms. 1. Differentiate between parallel and perpendicular lines. 2. Recognize parallel and perpendicular lines based on their slopes. 3. Determine whether lines are parallel or perpendicular. 5.6 Fit a Line to Data 1. Discuss correlation and differentiate between positive, negative and no correlation. 2. Sketch a line of best fit. 5.7 Predict with Linear Models 1. Find a linear equation that represents the data well. 2. Make an estimate for given values. 8

9 Chapter 6: Solving and Graphing Linear Inequalities 6.1 Solve Inequalities using Addition and Subtraction 6.2 Solve Inequalities using Multiplication and Division 6.3 Solve Multi-Step Inequalities 6.4 Solving Compound Inequalities 6.5 Solve Absolute Value Equations 6.6 Solve Absolute Value Inequalities 6.7 Graph Linear Inequalities in Two Variables 1. Write and graph basic inequalities. 2. Solve and graph an inequality using addition or subtraction. 3. Differentiate between inequality signs. 1. Solve and graph inequalities using multiplication and division. 2. Differentiate between dividing by and negative number and simply dividing a negative number. 1. Solve and graph inequalities that require more than one step. 2. Recognize both no solution and infinite solution inequalities. 1. Differentiate between compound inequalities from simple inequalities. 2. Differentiate between or and and compound inequalities. 3. Write and graph both types of compound inequalities. 1. Understand and apply the absolute value concept. 2. Solve one-, two- and multi-step equations with absolute values. 3. Graph absolute value equations. 1. Understand the difference between or and and inequalities. 2. Solve and graph absolute value inequalities. 1. Manipulate inequalities to graph them more easily (slope-intercept form). 2. Graph two variable inequalities with proper shading and line type. 9

10 Chapter 7A: Solving Systems of Equations 7.1 Solving Linear Systems by Graphing 7.2 Solve Linear Systems by Substitution 7.3 Solve Linear Systems by Elimination (Adding and Subtracting) 7.4 Solve Linear Systems by Multiplying First 1. Identify a linear system of equations. 2. Graph two linear equations on the same coordinate plane. 3. Estimate and identify exactly the solution of a linear system. 1. Solve an equation for an identified variable. 2. Substitute and solve an equation for a variable. 3. Solve word problems by using substitution. 1. Re-order equations to place variables in the same order. 2. Determine whether to use addition or subtraction to eliminate a variable. 3. Solve word problems using elimination. 1. Determine when multiplication is necessary. 2. Decide whether one or both equations must be multiplied. 3. Solve using elimination as in section 7.3 Chapter 7B: Solving Systems of Inequalities 7.5 Solve Special Types of Linear Systems 7.6 Solving Systems of Linear Inequalities 1. Solve systems of equations through graphing, elimination or substitution, whichever is easiest. 2. Recognize a system of equations with one solution, infinite solutions or no solution 1. Solve and graph multiple (2 or 3) linear inequalities on the same coordinate plane. 2. Shade appropriately for each individual inequality and for the overall system of inequalities. 3. Identify systems with no solution as well as limited solutions. 10

11 Chapter 8: Exponents and Exponential Functions 8.1 Apply Exponent Properties Involving Products 8.2 Apply Exponent Properties Involving Quotients 8.3 Define and Use Zero and Negative Exponents 8.4 Using Scientific Notation 8.5 Write and Graph Exponential Growth Functions 8.6 Write and Graph Exponential Decay Functions 1. Understand and apply the Product of Powers Property, the Power of a Power Property and the Power of a Product Property. 2. Differentiate between all three properties. 3. Write and solve word problems. 1. Understand and apply the Quotient of Powers Property and the Power of a Quotient Property. 2. Combine knowledge of section 8.1 properties with section 8.2 properties. 1. Understand and apply the Zero Exponent and Negative Exponent Properties. 2. Combine knowledge of section 8.1 and 8.2 properties with section 8.3 properties. 1. Recognize and differentiate between standard form and scientific notation. 2. Move between standard form and scientific notation in both directions. 3. Order numbers from least to greatest in both standard form and scientific notation. 4. Compute with numbers in scientific notation. 1. Recognize an exponential function as compared to a linear function. 2. Graph an exponential function. 3. Use formulas to solve exponential growth word problems. 1. Recognize and write a rule for an exponential function. 2. Graph exponential functions. 3. Differentiate between exponential growth and exponential decay. 11

12 Chapter 11: Square Roots Continued 11.2 Simplifying Radical Expressions 11.3 Solve Radical Equations 11.4 Apply the Pythagorean Theorem and Its Converse 1. Multiply radicals. 2. Divide radicals 3. Add and subtract radicals 4. Rationalize the denominator of a fraction. 1. Recognize a radical equation. 2. Simplify radical equations. 3. Solve radical equations by squaring both sides. 1. Plug numbers into the Pythagorean Theorem and determine whether they are in fact a Pythagorean Triple or not. 2. Solve for missing sides of right triangles. 3. Use the Pythagorean Theorem to solve word problems. 12

13 Chapter 9A: Simplifying Polynomials 9.1 Add and Subtract Polynomials 9.2 Multiply Polynomials 9.3 Find Special Products of Polynomials 9.4 Solve Polynomial Equations in Factored Form 1. Determine the degree of a monomial. 2. Determine the degree of a polynomial. 3. Differentiate between monomials, binomials, trinomials and polynomials. 4. Simplify polynomials by adding and subtracting. 1. Multiply a polynomial by a monomial. 2. Multiply a binomial by a binomial. 3. Multiply a polynomial by a polynomial. 4. Simplify after multiplication using skills from section Recognize special products. 2. Simplify special products with and without using the FOIL method. 1. Find the solutions (roots) of a polynomial equation. 2. Solve equations by factoring out a Greatest Common Factor (GCF). 3. Solve word problems using factoring. Chapter 9B: Factoring Polynomials 9.5 Factor Trinomials 1. Understand and apply the pattern of signs. 2. Determine whether the solutions will be positive or negative without solving problems. 3. Factor a trinomial into two binomials and solve for roots. 9.6 Factor Trinomials with Leading Coefficients 9.7 Factoring Special Products 9.8 Factor Polynomials Completely 1. Recognize differences between problems in section 9.5 and in this section. 2. Solve problems using guess and check method. 1. Recognize perfect square trinomials. 2. Factor a difference of two squares both before and after factoring out a greatest common factor. 1. Factor out a GCF or common binomial. 2. Factor by grouping. 3. Find all solutions to a polynomial with a degree of 2 or higher. 13

14 Chapter 10A: Solving and Graphing Quadratics 10.1 Graphing Quadratic Equations 10.2 Graph Quadratic Equations 10.3 Solving Quadratic Equations by Graphing 10.4 Use Square Roots to Solve Quadratic Equations 10.5 Solve Quadratic Equations by Completing the Square 1. Find the vertex and axis of symmetry of a parabola. 2. Use the vertex and axis of symmetry to graph parabolas. 3. Graph using a table of values. 1. Find the vertex and axis of symmetry of a parabola that is not at the origin. 2. Use the vertex and axis of symmetry to graph parabolas not at the center of the coordinate plane. 3. Graph using a table of values. 1. Find whole number solutions for quadratic equations by graphing. 2. Recognize when a graph will have two solutions, one solution and no solution. 1. Solve quadratic equations algebraically through manipulation of numbers and variables. 2. Use the square root in order to remove squared terms. 1. Understand and apply the steps of forming a perfect square trinomial using guided notes and example problems. Chapter 10B: Solving Quadratics using the Quadratic Formula 10.6 Solve Quadratic Equations by the Quadratic Formula 10.7 Interpret the Discriminant 1. Recognize different portions of a quadratic equation (a, b and c). 2. Memorize and recall the quadratic formula. 3. Successfully substitute numbers for letters in the formula and solve to find solutions. 1. Memorize and recall the formula necessary to use the discriminant. 2. Find the number of solutions without actually finding the actual solutions. 3. Recognize no solution problems by using the discriminant. 14

15 Chapter 13: Probability and Statistics 13.1 Find Probabilities and Odds 13.2 Find Probabilities Using Permutations 13.3 Find Probabilities Using Combinations 13.4 Find Probabilities of Compound Events 13.5 Analyze Surveys and Samples 13.6 Use Measures of Central Tendency 13.7 Interpret Stem and Leaf Plots and Histograms 13.8 Interpret Box and Whisker Plots 1. Define terms often used in probability (event, outcome, sample space, etc.). 2. Use simple division to find the probability of events. 1. Recognize and define permutations. 2. Memorize, recall and substitute into permutation formula. 1. Recognize and define combinations. 2. Memorize, recall and substitute into combination formula. 1. Recognize differences between simple and compound events. 2. Define independent and dependent events. 3. Define mutually exclusive events and understand events that are counted twice. 1. Define different types of samples and classify examples of different types as one of the methods. 2. Identify biased samples and suggest potentially more appropriate samples. 1. Define measures of center (measures of central tendency), including mean, median and mode. 2. Use appropriate skills to find the measures of center. 3. Compare measures of center and determine which is best. 1. Understand construction of both types of graphs and interpret their meaning. 2. Determine which type of plot may be most appropriate for different types of data. 3. Construct a stem and leaf plot and histogram. 1. Understand construction of and interpret meaning of a box and whisker plot. 2. Define key terms, including quartiles, median, minimum and maximum. 3. Construct a box and whisker plot. 15

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