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Algebra I Pacing Guide Days 9 Units Chapter 1 (1.1-1.4, 1.6-1.7) 8 Chapter 2 (2.1-2.7) 14 Chapter 3 (3.1-3.8) 14 Chapter 4 (4.1-4.7) 14 Chapter 5 (5.1-5.7) 14 Chapter 6 (6.1-6.7) 11 Chapter 7A (7.1-7.4) Notes Expressions, Equations and Functions Differentiate between and write expressions, equations and inequalities as well as applying order of operations. Word problems will be incorporated 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 1st 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 5 Chapter 7B (7.5 & 7.6) 12 Chapter 8 (8.1-8.6) 12 Chapter 11 (11.2-11.4) 10 Chapter 9A (9.1-9.4) 13 Chapter 9B (9.5-9.8) 12 Chapter 10A (10.1-10.5) 7 Chapter 10B (10.6 & 10.7) solving two equations at the same time. Methods that will be explored include graphing, substitution and adding or subtracting. End of 2nd Nine Weeks End of 1st 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 3rd 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. Solving Quadratic Equations by Quadratic Formula Students will solve quadratic equations through the use of the quadratic formula and will be able to find 14 Chapter 13 (13.1-13.8) 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 4th Nine Weeks End of 2nd Semester Algebra I Learning Targets Section 1.1 1.3 1.2 1.4 1.6 1.7 Chapter 1: Expressions, Equations and Functions Section Title Learning Target(s) I can… Evaluate 1. Define a variable and an expression. Expressions and 2. Translate an expression into a word sentence and Write Expressions vice versa. 3. Use proper terminology with respect to exponents, bases and powers. 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. Write Equations 1. Differentiate between an expression, equation and and Inequalities 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. Represent 1. Define function, domain, range, independent Functions as Rules variable and dependent variable. and Tables 2. Identify a function. 3. Make a table and a rule for a function, including real-life applications. Represent 1. Identify the X and Y axes on a coordinate plane. Functions as 2. Graph ordered pairs on a coordinate plane. Graphs 3. Write a rule for a function from a graph…translate from a graph to a table or rule. Section 2.1 2.2 & 2.3 2.4 2.5 2.6 2.7 Chapter 2: Properties of Real Numbers Section Title Learning Target(s) I can… Using Integers and 1. Graph positive and negative numbers on a Rational Numbers number line. 2. Compare positive and negative numbers. 3. Compare (differentiate between) whole numbers, integers and rational numbers. Add and Subtract 1. Add and subtract positive and negative numbers. Real Numbers 2. Use number sense to solve and write word problems. 3. Add and subtract decimals and fractions with and without a calculator. Multiply Real 1. Multiply real numbers with and without a Numbers calculator. 2. Substitute values for variables and simplify expressions. Apply Distributive 1. Determine when to apply the distributive Property property. 2. Apply the distributive property when appropriate. 3. Use the distributive property to help write and solve word problems. Divide Real 1. Divide real numbers with and without a Numbers calculator. 2. Divide by fractions and decimals. 3. Understand and correctly use the terminology associated with division (quotient, reciprocal, etc.). Find Square Roots 1. Find approximate values of square roots and and Compare with order them with other numbers. Real Numbers 2. Classify numbers as real, rational, irrational or integers. 3. Use square roots to write and solve word problems. Section 3.1 3.2 3.3 3.4 3.5 & 3.6 3.7 3.8 Chapter 3: Solving Linear Equations Section Title Learning Target(s) I can… Solving One-Step 1. Solve one-step equations using addition, Equations subtraction, multiplication and division. 2. Solve equations that have decimals and fractions. 3. Solve equations with the variable on either side of the equation. Solve Two-Step 1. Solve two-step equations using addition, Equations 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. Solve Multi-Step 1. Differentiate between one-step, two-step and Equations 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. Solving Equations 1. Differentiate between an equation with variables with Variables on on both sides and a multi-step equation or two-step Both Sides 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. Write Ratios and 1. Differentiate between a ratio and a proportion. Proportions 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. Solve Percent 1. Apply number sense to remember that a percent Problems is a number out of 100. 2. Solve percent problems by writing a proportion or using the percent equation. 3. Write and solve real-world word problems involving percents. Rewrite Equations 1. Successfully manipulate equations to solve for a and Formulas variable instead of a number. 2. Solve problems using the manipulation of an equation. Section 4.1 4.2 4.3 4.4 4.5 4.6 4.7 Chapter 4: Graphing Linear Equations and Functions Section Title Learning Target(s) I can… Plot Points in a 1. Plot points when given coordinates. Coordinate Plane 2. Give coordinates when points have been plotted. Graph Linear 1. Recognize a vertical and horizontal line by their Equations equation. 2. Write an equation in standard form. 3. Graph an equation by using a table. Graph Using 1. Understand the concept of X- and Y-Intercepts. Intercepts 2. Use the intercepts to find an equation. 3. Use a graph to find the intercepts. Find Slope and 1. Differentiate between positive, negative, 0 and no Rate of Change slopes. 2. Use the formula to find slope of lines. 3. Relate Rate of Change to Slope. Graph Using Slope 1. Recognize Slope-Intercept Form (in equation Intercept Form form). 2. Identify different parts of the equation (Slope & Intercept). 3. Graph using slope intercept form. Model Direct 1. Graph direct variation equations. Variation 2. Write direct variation equations. Graph Linear 1. Apply earlier knowledge of Standard and SlopeFunctions Intercept Forms to graph functions. 2. Find values when given a function. Section 5.1 5.2 5.3 5.4 5.5 5.6 5.7 Chapter 5: Writing Linear Equations Section Title Learning Target(s) I can… Write Linear 1. Write an equation of a line when given two Equations in Slope- points. Intercept form 2. Use slope and y-intercept to write an equation. Use Linear 1. Write equations when given the slope and yEquations in Slope- intercept. Intercept Form 2. Recall information from section 5.1 and apply it to real world situations. Write Linear 1. Recognize difference between slope-intercept, Equations in Point- standard and point-slope forms. Slope Form 2. Write equations using point-slope forms. Write Linear 1. Transfer between slope-intercept, standard and Equations in point-slope forms. Standard Form Write Equations of 1. Differentiate between parallel and perpendicular Parallel and lines. Perpendicular Lines 2. Recognize parallel and perpendicular lines based on their slopes. 3. Determine whether lines are parallel or perpendicular. Fit a Line to Data 1. Discuss correlation and differentiate between positive, negative and no correlation. 2. Sketch a line of best fit. Predict with Linear 1. Find a linear equation that represents the data Models well. 2. Make an estimate for given values. Section 6.1 6.2 6.3 6.4 6.5 6.6 6.7 Chapter 6: Solving and Graphing Linear Inequalities Section Title Learning Target(s) I can… Solve Inequalities 1. Write and graph basic inequalities. using Addition and 2. Solve and graph an inequality using addition or Subtraction subtraction. 3. Differentiate between inequality signs. Solve Inequalities 1. Solve and graph inequalities using multiplication using and division. Multiplication and 2. Differentiate between dividing by and negative Division number and simply dividing a negative number. Solve Multi-Step 1. Solve and graph inequalities that require more Inequalities than one step. 2. Recognize both “no solution” and “infinite solution” inequalities. 1. Differentiate between compound inequalities Solving Compound from simple inequalities. Inequalities 2. Differentiate between or and and compound inequalities. 3. Write and graph both types of compound inequalities. Solve Absolute 1. Understand and apply the absolute value concept. Value Equations 2. Solve one-, two- and multi-step equations with absolute values. 3. Graph absolute value equations. Solve Absolute 1. Understand the difference between or and and Value Inequalities inequalities. 2. Solve and graph absolute value inequalities. Graph Linear 1. Manipulate inequalities to graph them more Inequalities in Two easily (slope-intercept form). Variables 2. Graph two variable inequalities with proper shading and line type. Section 7.1 7.2 7.3 7.4 Chapter 7A: Solving Systems of Equations Section Title Learning Target(s) I can… Solving Linear 1. Identify a linear system of equations. Systems by 2. Graph two linear equations on the same Graphing coordinate plane. 3. Estimate and identify exactly the solution of a linear system. Solve Linear 1. Solve an equation for an identified variable. Systems by 2. Substitute and solve an equation for a variable. Substitution 3. Solve word problems by using substitution. Solve Linear 1. Re-order equations to place variables in the same Systems by order. Elimination 2. Determine whether to use addition or subtraction (Adding and to eliminate a variable. Subtracting) 3. Solve word problems using elimination. Solve Linear 1. Determine when multiplication is necessary. Systems by 2. Decide whether one or both equations must be Multiplying First multiplied. 3. Solve using elimination as in section 7.3 Section 7.5 7.6 Chapter 7B: Solving Systems of Inequalities Section Title Learning Target(s) I can… Solve Special 1. Solve systems of equations through graphing, Types of Linear elimination or substitution, whichever is easiest. Systems 2. Recognize a system of equations with one solution, infinite solutions or no solution Solving Systems of 1. Solve and graph multiple (2 or 3) linear Linear Inequalities 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. Section 8.1 8.2 8.3 8.4 8.5 8.6 Chapter 8: Exponents and Exponential Functions Section Title Learning Target(s) I can… Apply Exponent 1. Understand and apply the Product of Powers Properties Property, the Power of a Power Property and the Involving Products Power of a Product Property. 2. Differentiate between all three properties. 3. Write and solve word problems. Apply Exponent 1. Understand and apply the Quotient of Powers Properties Property and the Power of a Quotient Property. Involving Quotients 2. Combine knowledge of section 8.1 properties with section 8.2 properties. Define and Use 1. Understand and apply the Zero Exponent and Zero and Negative Negative Exponent Properties. Exponents 2. Combine knowledge of section 8.1 and 8.2 properties with section 8.3 properties. Using Scientific 1. Recognize and differentiate between standard Notation 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. Write and Graph 1. Recognize an exponential function as compared Exponential to a linear function. Growth Functions 2. Graph an exponential function. 3. Use formulas to solve exponential growth word problems. Write and Graph 1. Recognize and write a rule for an exponential Exponential Decay function. Functions 2. Graph exponential functions. 3. Differentiate between exponential growth and exponential decay. Section 11.2 11.3 11.4 Chapter 11: Square Roots Continued Section Title Learning Target(s) I can… Simplifying Radical 1. Multiply radicals. Expressions 2. Divide radicals 3. Add and subtract radicals 4. Rationalize the denominator of a fraction. Solve Radical 1. Recognize a radical equation. Equations 2. Simplify radical equations. 3. Solve radical equations by squaring both sides. Apply the 1. Plug numbers into the Pythagorean Theorem and Pythagorean determine whether they are in fact a Pythagorean Theorem and Its Triple or not. Converse 2. Solve for missing sides of right triangles. 3. Use the Pythagorean Theorem to solve word problems. Section 9.1 9.2 9.3 9.4 Chapter 9A: Simplifying Polynomials Section Title Learning Target(s) I can… Add and Subtract 1. Determine the degree of a monomial. Polynomials 2. Determine the degree of a polynomial. 3. Differentiate between monomials, binomials, trinomials and polynomials. 4. Simplify polynomials by adding and subtracting. Multiply 1. Multiply a polynomial by a monomial. Polynomials 2. Multiply a binomial by a binomial. 3. Multiply a polynomial by a polynomial. 4. Simplify after multiplication using skills from section 9.1. Find Special 1. Recognize special products. Products of 2. Simplify special products with and without using Polynomials the FOIL method. Solve Polynomial 1. Find the solutions (roots) of a polynomial Equations in equation. Factored Form 2. Solve equations by factoring out a Greatest Common Factor (GCF). 3. Solve word problems using factoring. Section 9.5 9.6 9.7 9.8 Chapter 9B: Factoring Polynomials Section Title Learning Target(s) I can… 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. Factor Trinomials 1. Recognize differences between problems in with Leading section 9.5 and in this section. Coefficients 2. Solve problems using guess and check method. Factoring Special 1. Recognize perfect square trinomials. Products 2. Factor a difference of two squares both before and after factoring out a greatest common factor. Factor Polynomials 1. Factor out a GCF or common binomial. Completely 2. Factor by grouping. 3. Find all solutions to a polynomial with a degree of 2 or higher. Section 10.1 10.2 10.3 10.4 10.5 Chapter 10A: Solving and Graphing Quadratics Section Title Learning Target(s) I can… Graphing Quadratic 1. Find the vertex and axis of symmetry of a Equations parabola. 2. Use the vertex and axis of symmetry to graph parabolas. 3. Graph using a table of values. Graph Quadratic 1. Find the vertex and axis of symmetry of a Equations 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. Solving Quadratic 1. Find whole number solutions for quadratic Equations by equations by graphing. Graphing 2. Recognize when a graph will have two solutions, one solution and no solution. Use Square Roots 1. Solve quadratic equations algebraically through to Solve Quadratic manipulation of numbers and variables. Equations 2. Use the square root in order to remove squared terms. Solve Quadratic 1. Understand and apply the steps of forming a Equations by perfect square trinomial using guided notes and Completing the example problems. Square Chapter 10B: Solving Quadratics using the Quadratic Formula Section Section Title Learning Target(s) I can… 10.6 Solve Quadratic 1. Recognize different portions of a quadratic Equations by the equation (a, b and c). Quadratic Formula 2. Memorize and recall the quadratic formula. 3. Successfully substitute numbers for letters in the formula and solve to find solutions. 10.7 Interpret the 1. Memorize and recall the formula necessary to use Discriminant the discriminant. 2. Find the number of solutions without actually finding the actual solutions. 3. Recognize no solution problems by using the discriminant. Section 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 Chapter 13: Probability and Statistics Section Title Learning Target(s) I can… Find Probabilities 1. Define terms often used in probability (event, and Odds outcome, sample space, etc.). 2. Use simple division to find the probability of events. Find Probabilities 1. Recognize and define permutations. Using Permutations 2. Memorize, recall and substitute into permutation formula. Find Probabilities 1. Recognize and define combinations. Using 2. Memorize, recall and substitute into combination Combinations formula. Find Probabilities 1. Recognize differences between simple and of Compound compound events. Events 2. Define independent and dependent events. 3. Define mutually exclusive events and understand events that are counted twice. Analyze Surveys 1. Define different types of samples and classify and Samples examples of different types as one of the methods. 2. Identify biased samples and suggest potentially more appropriate samples. Use Measures of 1. Define measures of center (measures of central Central Tendency 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. Interpret Stem and 1. Understand construction of both types of graphs Leaf Plots and and interpret their meaning. Histograms 2. Determine which type of plot may be most appropriate for different types of data. 3. Construct a stem and leaf plot and histogram. Interpret Box and 1. Understand construction of and interpret meaning Whisker Plots of a box and whisker plot. 2. Define key terms, including quartiles, median, minimum and maximum. 3. Construct a box and whisker plot.