First Quarter ** NOTE: Include SOL review throughout each quarter. Stress application problems throughout the year. A good resource for fractions is on pp. 914-915. Review of prerequisite skills can be done in flex period, resource periods or math labs. Review, Expressions & Order of Operations Represent verbal quantitative situations algebraically & evaluate these expressions for given replacement values of the variables. Choose an appropriate computational technique, such as mental mathematics, calculator, or paper and pencil. A.2 1.1-1.4 Intro Activity 1.1 Translate verbal expressions into algebraic expressions with three or fewer terms 1.3, 1.4 Relate a polynomial expression with three or fewer terms to a verbal expression. Apply appropriate computational techniques to evaluate an algebraic expression. 1.1, 1.2 Evaluate algebraic expressions for a given replacement set to include integers & rational numbers. Justify steps used in simplifying expressions. Justifications will include the use of concrete objects; pictorial representations; A.3 2.1-2.6 and the properties of real number, equality, and inequality. Simplify expressions using the commutative, associative, & distributive properties. 2.5 Simplify expressions using the order of operations. 2.1-2.4, 2.6 Create and interpret pictorial representations for simplifying expressions. Algeblocks Matrices Use matrices to organize & manipulate data, including matrix addition, subtraction, & scalar multiplication. Data will arise from business, industrial, & consumer situations. A.4 extension 2.4, p.94-95 Calculate the sum or difference of two given matrices that are no larger than 4 x 4. Calculate the product of a scalar & a matrix that is no larger than 4 x 4. Read & interpret the data in a matrix representing the solution to a practical problem. Represent data from practical problems in matrix form. Solve practical problems involving matrix addition, subtraction, & scalar multiplication, using matrices that are no larger than 4 x 4. Equations Justify steps used in solving equations. Justifications will include the use of concrete objects; pictorial representations; & the A.3 *See Alg2 for basic matrix resources. 3.1, 3.2 properties of real numbers and equality. One Step Equations (This is a review of 7th grade material if needed) 3.1, 3.2 Two Step Equations (This is a review of 8th grade material if needed) Multi Step Equations Solve equations using the order of operations 3.2 Check solution from replacement set. 3.1 Solve equations, using addition, multiplication, closure, identify, & inverse properties. Solve equations using the commutative, associative, & distributive properties. Solve equations, using reflexive, symmetric transitive and substitution properties of equality Create and interpret pictorial representations for solving equations Algeblocks **First Quarter continued on next page**
First Quarter con't ** NOTE: Include SOL review throughout each quarter. Emphasize accuracy of graphs and include point-slope form. 3.3-3.6, 3.8, Solve multistep linear equations & inequalities in one variable, solve literal equations (formulas) for a given variable, and apply 6.5 these skills to solve practical problems. Graphing calculators will be used to confirm algebraic solutions. Solve multistep linear equations in one variable with rational coefficients & constants. 3.3, 3.4 Solve multistep linear equations in one variable with the variable in both sides of the equation. Solve multistep linear equations in one variable with grouping symbols in one or both sides of the equation. A.1 Confirm algebraic solutions to linear equations using a graphing calculator. Applications of Equations Translate verbal sentences to algebraic equations in one variable. Include problem solving. 3.8 Apply skills for solving linear equations to practical situations. Include problem solving. 3.8 Solve a literal equation (formula) for a specified variable. Include problem solving. Inequalities Justify steps used in solving inequalities. Justifications will include the use of concrete objects; pictorial representations; & the A.3 6.1-6.4 properties of real numbers, equality, & inequality. One Step Inequalities (This is a review of 7th grade material, if needed.) 6.1, 6.2 Two Step Inequalities (This is a review of 8th grade material, if needed.) Multi Step Inequalities Solve inequalities using the commutative, associative, & distributive properties. Solve inequalities using the order of operations. Create and interpret pictorial representations for solving inequalities. Algeblocks Solve multistep inequalities in one variable with rational coefficients & constants. A.1 ESS: p.74 Solve multistep noncompound inequalities in one variable with the variable in both sides of the inequality. Solve and graph multistep linear inequalities in one variable with grouping symbols in one or both sides of the inequality. Confirm algebraic solutions to inequalities, using a graphing calculator. Applications of Inequalities Translate verbal sentences to algebraic inequalities in one variable. Introduction to Functions A.15 Given a rule, find the values of a function for elements in its domain. The value of f (x ) will be related to the ordinate on the graph. 4.7 For each x in the domain of f, find f (x ). 4.7 Create and use tabular, symbolic, graphical, verbal and physical representations to analyze a given set of data for the existence of a pattern, determine the domain and range of relations, and identify the relations that are functions. As needed, review creating a table of values, quadrants and axes, plotting data onto a coordinate plane given the table of values or ordered pairs. Analyze a table of ordered pairs for the existence of a pattern that defines the change relating input and output values 1.6, 1.7, 4.1, 4.2 *p80 of ESS Write a linear equation to represent a pattern in which there is a constant rate of change between variables. Identify the domain & range for a relation, given a set of ordered pairs, a table, or a graph. 1.6, 1.7 Determine from a set of ordered pairs, a table, or a graph whether a relation is a function. 4.1, 4.2 Use physical representations, such as algebra manipulatives, to represent quantitative data. Review and assessments A.5
Second Quarter ** NOTE: Include SOL review throughout each quarter. Emphasize format of final equation. Use the appropriate method to write the equation of a line when given specific information. Use a variety of forms for the final answer. Graphing Linear Equations & Functions Select, justify, & apply an appropriate technique to graph linear functions in two variables. Techniques will include slopeintercept, x- and y- intercepts, graphing by transformation, & the use of the graphing calculator. 4.3, 4.5, and p76-78 of ESS Linear Equations Express linear functions in slope-intercept form, and use the graphing calculator to display the relationship. 4.5 Use the line y = x as a reference, and apply transformations defined by changes in the slope or y -intercept. Graph using x - and y - intercepts, slope-intercept, and point-slope. 4.3 Explain why a given technique is appropriate for graphing a linear function. Linear Equations & Inequalities (Two Variables) Determine the slope of a line when given an equation of the line, the graph of the line, or two points on the line. Slope will be described as rate of change and will be positive, negative, zero, or undefined. The graphing calculator will be used to investigate the effect of changes in the slope of the graph of the line. A.7 Compare the slopes of graphs of linear functions, using the graphing calculator. Describe slope as a constant rate of change between two variables. Find the slope of a line, given the graph of a line. Calculate the slope of a line, given the coordinates of two points on the line. Recognize that m represents the slope in the equation of the form y = mx + b. Find the slope of the line, given the equation of a linear function. Recognize & describe a line with a slope that is positive, negative, zero, or undefined. Graphing Applications 4.4 & p. 76-78 of Enhanced S&S Graph linear equations in two variables that arise from a variety of practical situations. A.6 4.5 extension Direct Variation & Inverse Variation Analyze a relation to determine whether a direct variation or inverse variation exists and represent it algebraically and graphically A.18 & 4.6, 12.1 if possible. A.LC.6 Given a table of values, determine whether a direct variation exists. Write an equation for a direct variation, given a set of data. Graph a direct variation from a table of values or a practical situation. Linear Inequalities - Include dotted vs. solid lines and shading Select, justify, & apply an appropriate technique to graph linear inequalities in two variables. Techniques will include slopeintercept, A.6 6.7 x- and y- intercepts, graphing by transformation, & the use of the graphing calculator. Express linear inequalities in slope-intercept form and use the graphing calculator to display the relationship. Use the line y = x as a reference, and apply transformations defined by changes in the slope or y-intercept. Graph using x- and y- intercepts, slope-intercept, and point-slope. Graph linear inequalities in two variables that arise from a variety of practical situations. Review and assessments A.6
Third Quarter ** NOTE: Include SOL review throughout each quarter. Emphasize no solution and infinite solutions. Also emphasize writing equations from application problems. 7.6 will be covered at the end of the year. Writing the Equation of a Line Write an equation of a line when given the graph of the line, two points on the line, or the slope & a point on the line. A.8 5.1-5.5 Write an equation of a line when given the graph of a line. 5.1, 5.2 Write an equation of a line when given the slope and a point of the line whose coordinates are integers. Write an equation of a line when given two points on the line whose coordinates are integers. Analyze a table of ordered pairs for the existence of a pattern that defines the change relating input and output values. A.5 Write an equation of a horizontal line as y = c. A.8 Write an equation of a vertical line as x = c. Write an equation in point-slope form. 5.3, 5.4 Graph an equation written in point-slope form. Recognize that equations of the form y = mx + b and Ax + By = C are equations of lines. Recognize equations of parallel lines. 5.5 Recognize equations of perpendicular lines. Application: Writing the Equation of a Line Given a set of data points, write an equation for a line of best fit and use the equation to make predictions. A.16 5.6, 5.7 Write an equation for the line of best fit, given a set of six to ten data points in a table, on a graph, or from a practical situation. Make predictions about unknown outcomes, using the equation of a line of best fit. Systems of Linear Equations Solve systems of two linear equations in two variables both algebraically and graphically and apply these techniques to solve practical problems. Graphing calculators will be used both as a primary tool for solution and to confirm an algebraic solution. A.9 7.1-7.5 Given a system of two linear equations in two variables that has a unique solution, solve the system graphically to find the point of 7.1 intersection. Given a system of two linear equations in two variables that has a unique solution, solve the system by substitution or elimination to find the 7.2-7.4 ordered pair which satisfies both equations. Determine whether a system of two linear equations has one solution, no solution, or infinite solutions. 7.5 Write a system of two linear equations that describes a practical situation. Interpret and determine the reasonableness of the algebraic or graphical solution of a system of two linear equations that describes a practical situation. Exponents Apply the laws of exponents to perform operations on expressions with integral exponents, using scientific notation when appropriate. Identify the base, exponent, & coefficient in a monomial expression. Simplify monomial expressions & ratios of monomial expressions in which the exponents are integers, using the laws of exponents. Express numbers, using scientific notation, & perform operations, using the laws of exponents. **Third Quarter continued on next page** A.10 p35-41 of Enhanced S&S 8.1-8.4, pg 502 for zero and negative exponents p93-94 of Enhanced S&S
Third Quarter con't ** NOTE: Include SOL review throughout each quarter. Representing & Simplifying Expressions Add and subtract polynomials using concrete objects, pictorial & area representations & algebraic manipulations. A.11 9.1 Create & interpret pictorial representations for simplifying expressions. A.3 *Algeblocks Model sums and differences of polynomials with concrete objects & their related pictorial representations. A.11 *Algeblocks Relate concrete and pictorial representations for polynbomial operations to their corresponding algebraic manipulations. Find sums & differences of polynomials. Polynomials Multiply polynomials & divide polynomials with monomial divisors, using concrete objects, pictorial & area representations, & 9.2, 9.3, 12.3 algebraic manipulations. Operations with Monomials Simplify polynomial expressions using the distributive property. 9.2 Multiply polynomials by monomials. Divide polynomials by monomials. 12.3 Review and assessments
Fourth Quarter ** NOTE: Include SOL review throughout each quarter. Operations with Polynomials A.11 Model products & quotients of polynomials with concrete objects & their related pictorial representations. 9.2, 9.3 Multiply binomials by binomials symbolically. (FOIL) Multiply polynomials by binomials symbolically. Relate concrete & pictorial representations for polynomial operations to their corresponding algebraic manipulations. A.12 Factor completely first- & second-degree binomials and trinomials in one or two variables. The graphing calculator will be used as a tool for factoring & for confirming algebraic factorizations. 9.5-9.8 *emphasize 9.7 Use the distributive property to "factor out" all common monomial factors. (GCF) p576, ex.#2 Factor second-degree polynomials & binomials with integral coefficients & a positive leading coefficient less than four. Factor special products (i.e. difference of two squares and perfect squares) 9.7 Identify polynomials that cannot be factored over the set of real numbers. (Prime) Use the x -intercepts from the graphical representation of the polynomial to determine and confirm its factors. 5.7 Essential Quadratic Skills Express the square root of a whole number in simplest radical form and approximate square roots to the nearest tenth. A.13 11.2 Find the square root of a number, and make a reasonable interpretation of the displayed value for a given situation, using a calculator. Estimate the square root of a non-perfect square to the nearest tenth by identifying the two perfect squares it lies between; finding the square root of those two perfect squares; and using those values to estimate the square root of the non-perfect square. Express the square root of a whole number less than 1,000 in simplest radical form. Simplify radical expressions only by adding and subtracting if time permits. Solve quadratic equations in one variable both algebraically and graphically. Graphing calculators will be used both as a tool in solving problems and to verify algebraic solutions. A.14 10.1-10.4; 10.6, 10.7 The graphing calculator will be used as a tool for factoring and for confirming algebraic factorizations. A.12 Solve quadratic equations algebraically by factoring. A.14 10.4 Solve quadratic equations algebraically or by using the graphing calculator. When solutions are represented in radical form, the decimal approximation will also be given. Identify the x-intercepts of the quadratic function as the solution(s) to the quadratic equation that is formed by setting the given quadratic expression equal to zero. A.14 Ext. 10.2, 10.3, 9.4 Given a rule, locate the zeros of the function both algebraically and with a graphing calculator. Identify the zeros of the function algebraically and confirm them, using the graphing calculator. A.15 Ext. 10.2, 10.3 The value of f(x) will be related to the ordinate on the graph. Solve quadratic equations by using the quadratic formula. When solutions are represented in radical form, the decimal approximation will also be given. A.14 10.6 Determine the number of solutions to a quadratic equation by using the discriminant. A.LC.7 10.7 Graph quadratic equations by hand, identifying the vertex, the axis of symmetry, the x- and y- intercepts (when appropriate) and if it turns up or down. 10.1, 10.2 Verify algebraic solutions using the graphing calculator. A.14 **Fourth Quarter continued on next page**
Fourth Quarter con't ** NOTE: Include SOL review throughout each quarter. Compare and contrast multiple one-variable data sets, using statistical techniques that include measures of central tendency, range, and box-and-whisker graphs. A.17 13.6-13.8 Calculate the measures of central tendency(mean, mode, median) and range of a set of data with no more than 20 data points. 13.6 Compare measures of central tendency using numerical data from a table with no more than 20 data points. Compare and contrast two sets of data, each set having no more than 20 data points, using measures of central tendency and the range. 13.7 Compare and analyze two sets of data, each set having no more than 20 data points, using box-and-whisker plots. 13.8 Review and Assessments After SOLs Systems of Linear Inequalities. Graph systems of linear inequalities. 7.6 Radical expressions and equations 11.2, 11.3 Pythagorean Theorem 11.4 Distance and midpoint formula 11.5 Rational expressions and equations 12.4, 12.5, 12.7 Ratios and Proportions. A.LC.1 3.5, 3.6 Solve absolute value equations. A.LC.5 6.5 Supplemental Resources *Resource Book: Practices A, B, C : Study Guide *Transparency Book: Warm-Up : Daily Quizzes : Notetaking *Algebra with Pizzazz *Enhanced Scope and Sequence (VDOE) *VDOE Algebra 1: Sample Scope and Sequence (with many specific websites and resources listed) *Project Graduation (VDOE) *SOL Practice Tests *Algebra 1 Blueprint (VDOE)