Curriculum & Grade 4: Mathematics Guide Algebra I Updated Spring 2014
Martinsville City Public Schools Plan of Action The Martinsville City Public Schools Curriculum Guide was developed using thestandards of Learning for Virginia Public Schools and the State Curriculum work. Also, an emphasis was placed on the integration of 21 st Century Skills into all areas of K-12 education. Martinsville City Public Schools believes that to compete in a global community, all children must develop lifelong independent skills that demonstrate initiative, self-direction, and the ability to problem-solve, innovate and create, and communicate by writing and speaking effectively. To provide an avenue for students to develop these important qualifications and provide a more rigorous learning environment, Martinsville City Public Schools encourages problem-based learning in all classrooms. The collaboration between students in this type of learning environment develops skills in leadership, accountability, social, and cross-cultural understanding as they communicate and think critically to problem-solve real world applications of the curriculum. Martinsville City Public Schools Core curriculum prepares students to achieve these 21 st Century skills through competent cross- curricular activities that apply knowledge of concepts learned in other areas of study and in the community. Standard benchmark assessments along with project-based assessments and end of year SOL tests are administered to ensure mastery of the concepts. PALS assessments are used to ensure proficiency in Reading for grades Pre-K through Eight. To further ensure that all students learn to the best of their abilities, a Response to Intervention (RtI) system, using, STAR Reading, Algebra Readiness Diagnostic Test (), is in place to guide classroom instruction, screen and progress monitor students so that intervention and enrichment activities are scheduled based on the students individual needs throughout the year. Curriculum Guide OVERVIEW The Martinsville City Public Schools Curriculum Guide is designed to provide a reference document for each subject and grade level that indicates The Curriculum s Big Ideas, Strategies, Model lessons, & Instruments and suggested time frames to be used as a Guide for classroom instruction. In addition, Learning Targets at a Glance contains an overview of the curriculum taught for each grading period for each subject and grade level. 21 st Century Internet Safety procedures are listed, and for Grades Three through Twelve, an SOL Testing BlueprintTarget is included to give insight to the strands that will receive the most focus on the SOL. Two symbols will be used to denote the 21st Century Focus: This symbol is used through to denote a 21 st Century skill. This symbol is used throughout to denote a 21 st Century Global Connection.
Learning Overview The Algebra I student will be provided many opportunities to engage in experiences involving problem solving, data collection and analysis, and algebraic thinking. The Virginia Standards of Learning provide the foundation for fifth grade mathematics. The standards are organized into 6 strands: Number/Number Sense: The focus of instruction allows students to investigate and develop strategies for reading, writing, and judging the size of whole numbers, fractions, and decimals by comparing them, using a variety of models benchmarks as referents. Using their knowledge to investigate and solve problems. Computation and Estimation: The focus of instruction allows students to develop fluency in multiplication and division with whole numbers, fractions and decimals, using models, explanation, and proficiency with basic facts and algorithms. Measurement: The focus of instruction allows students to be actively involved in active exploration of the real world in order to apply concepts from the two systems of measurement (metric/u.s. Customary) and enhance their understanding of measurement by using appropriate tools. Geometry: The focus of instruction allows students to discover the relationships between geometric figures by constructing, drawing, measuring, comparing, and classifying these figures. Students will investigate, identify, and draw representations and describe relationships between and among points, lines, line segments, rays and angles. Probability and Statistics: The focus of instructions allows students to further develop and investigate data collection strategies. Patterns,Functions and Algebra: The focus of instruction is to help students develop a solid use of patterning as a problem solving tool. Curriculum Big Ideas Strategies & Model Lessons The organizing topics, big ideas, or strands under which student learning is organized and the Understandings, Knowledge and Skills students must develop in order to master these concepts (typically from the standards found in the VDOE curriculum framework). Understandings what we want students to understand about this idea, topic, or concept Knowledge What students must know in order to develop this understanding Skills What students must be able to do in order to demonstrate that understanding, strategies, and models for delivery of the curriculum. Includes suggested teaching strategies, links to model lesson plans links to frequently referenced online sites, and suggested teacher resources and where to find them (online and hard copy, such as texts, primary source documents, etc.) Examples of formative and summative assessments for measuring student mastery of the curriculum. Includes essential questions, writing prompts, sample test items, benchmark test links, model performance-based assessments, and other assessment resources. Standards of Learning that meet the criteria for 21 st Century skills will be identified by this symbol Standards of Learning that meet the 21st Century Learning of Global Connections will be designated with this symbol
Learning Targets at a Glance Algebra I First 9 A.1 A.2 A.3 A.4 a, b, d, f A.5 b A.6 a. b Second 9 A.4 c, e, f A.5 a, c, d A.7 A.8 A.9 A.10 A.11 Algebra I Test Blueprint Summary Table 50 question test Expressions and Operations Equations and Inequalities Functions and Statistics 12 18 20
21 st Century Internet Safety Procedures 1. Teachers should review all internet sites and links prior to using them in the classroom. During this review, teachers need to ensure the appropriateness of the content on the site. Checking for broken links and paying attention to inappropriate pop-ups or solicitations of information. 2. Teachers should circulate throughout the classroom while students are on the internet to make sure the students are on the appropriate site and are not minimizing other inappropriate sites. 3. Teachers should periodically check and update any web addresses that they have on their MCPS webpage. 4. Teachers should assure that the use of these websites correlate with the objectives of the lesson and provide students with the appropriate challenges.
Grade Level:Algebera I Strategies & Model Lessons 1 st Nine SOL A.1 The student will represent verbal quantitative situations algebraically and evaluate these expressions for given replacement values of the variables The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to: Translate verbal quantitative situations into algebraic expressions and vice versa Model real-world situations with algebraic expressions in a variety of representations (concrete, pictorial, symbolic, verbal) Evaluate algebraic expressions for a given replacement set to include rational numbers Evaluate expressions that contain absolute value, square roots, and cube roots. Variables Algebraic Expression Power Base Exponent Open Sentence Solution Expression Replacement Set Solution Set Inequality Identity Inverse Reciprocal Like Terms Equivalent Coefficient Word Wall Voc Powerpoint/Smartboard SOL A.1 resource Ch. 1-1 through 1-6 Ch. 2-1 through 2-4 2-7 Lesson 1-6 Expressions Lesson 1-4 Positive & Negative # s A.1 Translate and Evaluate A.1 Evaluating & Simplifying Expressions Lessons: 1,2, 5 Students must be able to translate verbal to algebraic and vice versa. Students must be able to connect real-world applications. SOL A.1 Natural Number Whole Number
Strategies & Model Lessons 3 rd Nine SOL A.2 The student will perform operations on polynomials, including a.) Applying the laws of exponents to perform operations on expressions b.) Adding, subtracting, multiplying, and dividing polynomials c.) Factoring completely first-and seconddegree binomials and trinomials in one or two variables. Graphing calculators will be used as a tool for factoring and for confirming algebraic factorization The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to: Simplify monomial expressions and ratios of monomial expressions in which the exponents are integers, using the laws of exponents Model sums, differences, products, and quotients of polynomials with concrete objects and their related pictorial representations Relate concrete and pictorial manipulations that model polynomial operations to their corresponding symbolic representations Find products of polynomials. The factors will have no more than five total terms. (See Curriculum work) Find the quotient of polynomials, using a monomial or binomial divisor, or a completely factored divisor. Monomial Constant Zero Exponent Negative Exponent Scientific Notation Polynomial Binomial Trinomial Degree of a Monomial Degree of a Polynomial FOIL Method Difference of Squares Algeblocks Graphing Calculators Powerpoint/Smart board SOL A.2 a,b,c Unit 6.1 6.4 Ch. 8-1 thru 8-8 12-1 Ch. 9-1 thru 9-6 11-1 Lesson 1-8 Polynomials Lesson 1-6 Factoring A.2 Multiplying Polynomials Using Algebra Tiles A.2 Adding/Subtracting Polynomials Using Algebra Tiles A.2 Exponents A,2 Scientifically Speaking A.2 Dividing Polynomials Using Algebra Tiles A.2 Factoring Lessons: 2, 3, 4, 6,8 SOL A.2
Strategies & Model Lessons 4 th Nine SOL A.3 The student will express the square roots and cube roots of whole numbers and the square root of a monomial algebraic expression in simplest radical form. The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to: Express square roots of a whole number in simplest form. Express the cube root of a whole number in simplest form Express the principal square root of a monomial algebraic expression in simplest form where variables are assumed to have positive values. Perfect square Perfect cube Square Root Cube Simplify Factor Tree Principal Square Root Powerpoint/Smart board SOL A.3 Ch. 11-1 thru 11-3 Lesson 1-3 Radicals A.3 Simplifying Square Roots A.3 Simplify Radicals Lessons: Students must be able to graph and determine solutions when looking at the graph. Students must use the Quadratic formula. SOL A.3
Strategies & Model Lessons 1 st Nine SOL A.4 The student will solve multistep linear and quadratic equations in two variables. a.) Solving literal equations (formulas) for a given variable b.) Justifying steps used in simplifying expressions and solving equations, using field properties and axioms of equality that are valid for the set of real numbers and its subset d.) solving multistep linear equations in two variables algebraically and graphically f.) Solving real-world problems involving equations and systems of equations The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to: Solve Linear equations (formula) for a specified variable Simplify expressions and solve equations, using the field properties of the real numbers and properties of equality to justify simplification and solution Solve multistep linear equations in one variable Confirm algebraic solutions to linear and quadratic equations, using a graphing calculator Literal Equations Integers Rational Numbers Real Numbers Infinity Graph Coordinate Absolute Values Opposites Square Roots Perfect Square Radical Irrational Real Numbers Linear Equations Algeblocks Graphing calculator Powerpoint/Smart board SOL A.4 c SOL A.4 a,b,d,f A.5 Episode Unit 1.1 1.5 Ch. 3-1 through 3-6 3-8 Ch. 6-1 through 6-3 Lesson 1-6 Solving Equations Lesson 1-3 Solving Inequalities A.4 Solve for the Unknown A.4 A Mystery to Solve A.4 Cover-Up Problems A.4 Algebra Tiles and Equation Solving Lessons: 5, 7, 9 Students must be able to use multiple ways of solving equations. They need to know how to use the calculator for solving equations. SOL A.4, A.5
Strategies & Model Lessons 1 st Nine SOL A.5 The student will solve multistep linear inequalities in two variables, including: b. Justifying steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers and its subsets The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to: Solve multistep linear inequalities in one variable Justify steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers Solve real-world problems involving inequalities Inequalities Variables Axioms of Inequalities Properties of Order Algeblocks Powerpoint/Smart board SOL A.5 Episode Unit 1.1 1.5 Ch. 6-1 through 6-3 Lesson 1-3 Solving Inequalities A.5 Inequalities A.5 Greetings Lessons: 9 Students must be able to determine slope in different ways. Student also need to know how to look at systems of equations graphically and algebraically. SOL A.5
SOL A.6 The student will graph linear equations and linear inequalities in two variables, Including a.) Determining 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 b.) Writing the equation of a line when given the graph of the line, two points on the line, or the slope and a point on the line. The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to: Parallel lines Perpendicular lines Slopes variables Graphing Calculators Strategies & Model Lessons Powerpoint/Smartboard SOL A.6 a, b Episode Unit 2.1 2.3 Ch. 4-1 through 4-6 A.6 Transformation Investigation A.6 Transformationally Speaking A.6 Slope-2-Slope A.6 Slippery Slope A.6 The Submarine Lessons: 8 Students must be able to determine slope in different ways, Students also need to know how to look at systems of equations graphically and algebraically. SOL A.6 1st Nine Write an equation of a line when given two points on the line whose coordinates are integers Write an equation of a line when given the slope and a point on the line whose coordinates are integers Write an equation of a vertical line as x=a Write the equation of a horizontal line as y=c Lesson 1-6 Relations & Functions
Strategies & Model Lessons 2 nd Nine SOL A.4 The student will solve multistep linear and quadratic equations in two variables. c.) e.) f.) Solving quadratic equations algebraically and graphically Solving systems of two linear equations in two variables algebraically and graphically Solving real-world problems involving equations and systems of equations The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to: 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 ordered pair which satisfies both equations Given a system of two linear equations in two variables that has a unique solution, solve the system graphically by identifying the point of intersection Solve quadratic equations Identify roots or zeros of a quadratic function over the real number system as the solution(s) to the quadratic equation that is formed by setting the given quadratic expression equal to zero System of Equations Consistent Inconsistent Independent Dependent Substitution Elimination Systems of Inequalities Graphic calculator Powerpoint/Smart board SOL A.4c SOL A.4 e Unit 6.1-6.4 7.1, 7.2 Unit 4.1 4.3 Ch. 9-1 thru 9-6, 11-1 Ch. 7-1 through 7-4 Lesson 1-8 Polynomials Lessons 1-6 Factoring Lesson 1-5 Systems of Equations A.4 How much is that Tune? Factoring for Zeros A.4 The Exercise Fields Lessons: 2,3,4,6,8 Students must be able to use multiple ways of solving equations. They need to know how to use the calculator for solving equations. SOL A.4
Strategies & Model Lessons 2 nd Nine SOL A.5 The student will solve multistep linear inequalities in two variables, including: a. Solving multistep linear inequalities algebraically and graphically c. Solving real-world problems involving inequalities d. Solve systems of linear inequalities algebraically and graphically The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to: Solve multistep linear inequalities in one variable Justify steps used in solving inequalities, using axioms of inequality and properties of order that are valid for the set of real numbers Solve real-world problems involving inequalities Inequalities Variables Axioms of Inequalities Properties of Order Algeblocks Powerpoint/Smart board SOL A.5 SOL A.5d Episode Unit 1.1 1.5 Episode Unit 4.1 4.3 Ch. 6-1 through 6-3 Ch. 7-1 through 7-4 A.5 Inequalities A.5 Greetings A.5 Graphing Systems of Inequalities Lessons: 9 Students must be able to determine slope in different ways. Student also need to know how to look at systems of equations graphically and algebraically. SOL A.5 Lesson 1-3 Solving Inequalities Lesson 1-5 Systems of Equations
Strategies & Model Lessons SOL A.7 The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including a.) Determining whether a relation is a function b.) Domain and range c.) Zeros of a function d.) X- and y-intercepts e.) Finding the values of a function for elements in its domain f.) Making connections between and among multiple representations of functions including concrete, verbal, numeric, graphic and algebraic The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to: Function Vertical Line Test Function Notation Quantitative Data Graphing Calculators Word Wall Voc Powerpoint/Smartboard SOL A.7 a,b,c,d,e,f Episode Unit 2.1 2.3 Ch. 3.1 through 3.5 Ch. 4-1 through 4-6 Ch. 5-1 through 5-4 A.7 Function 1 A.7 Functions 2 Lessons: 6 Students need to know the coordinate plane before moving on. Must use a graphing calculator. Student must be able to determine whether a relation is a function by using multiple ways. SOL A.7 2 nd Nine Determine the relation, represented by a set of ordered pairs, a table, or a graph is a function Identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically For each x in the domain of f, find f(x) Represent relations and functions using concrete, verbal, numeric, graphic, and algebraic forms. Given one representation, students will be able to represent the relation in another form Detect patterns in data and represent arithmetic and geometric patterns algebraically Lesson 1-6 Relations & Functions Lesson 1-6 Linear Equations
Strategies & Model Lessons 2 nd Nine SOL A.8 The student, given a situation in a real-world context, will analyze a relation to determine whether a direct or inverse variation exists, and represent a direct variation algebraically and graphically and an inverse variation algebraically The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to: Given a situation, including a real-world situation, determine whether a direct variation exists Given an situation, including a real-world situation, determine whether an inverse variation exists. Write an equation for a direct variation, given a set of data Write an equation for an inverse variation, given a set of data Graph an equation representing a direct variation, given a set of data Direct variation Inverse variation Rate of Change Slope Constant Variation Family of Graphs Parent Graph Slope-Intercept Form Point-Slope Form Parallel Lines Perpendicular Lines Graphing Calculators Powerpoint/Smartboard SOL A.8 Ch. 5-1 through 5-4 Lesson 1-6 Relations & Functions A.8 Direct Variation A.8 Inverse Variation Lessons: 8 SOL A.8
Strategies & Model Lessons 2nd Nine SOL A.9 The student will, given a set of data, will interpret variation in real-world contexts and calculate and interpret mean absolute deviation, standard deviation, and z-scores. The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to: Analyze descriptive statistics to determine the implications for the realworld situations from which the data derive Given data, including data in a realworld context, calculate and interpret the mean absolute deviation of a data set. Given data, including data in real-world context, calculate variance and standard deviation of a data set and interpret the standard deviation. Given data, including data in a realworld context, calculate and interpret z-scores for a data set. Explain ways in which standard deviation addresses dispersion by examining the formula for standard deviation Compare and contrast mean absolute deviation in a real-world context. Variances Standard deviation Statistics Data Points Data distribution Outliers Mean absolute deviation z-scores Data set Powerpoint/Smart board SOL A.9 Units 5.2, 5.3, 5.5 Ch. 1-9, 2-5, 5-7, 13-2 thru 13-5 Lesson 1-5 Data Analysis A.9 Exploring Statistics A.9 Z-scores A.9 Analyzing & Interpreting Statistics A.9 Calculating Measures of Dispersion Lessons: 10 Students must be able to use the new formula sheet using standard and absolute deviations. Students also should be able to look at different graphs and determine solutions from looking at the graph. SOL A.9
Strategies & Model Lessons SOL A.10 The student will compare and contrast multiple univariate data sets, using box-and-whisker plots The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to: Compare, contrast, and analyze data, including data from real-world situations displayed in box-and-whisker plots.. Box-and Whisker Plots Powerpoint/Smart board SOL A.10 Units 5.2, 5.3, 5.5 A.10 Box-and Whisker Plots Lessons: 10 Students must be able to use the new formula sheet using standard and absolute deviations. Students also should be able to look at different graphs and determine solutions from looking at the graph. SOL A.10 2 nd Nine Ch. 1-9, 2-5, 5-7, 13-2 thru 13-5 Lesson 1-5 Data Analysis
Strategies & Model Lessons 2 nd Nine SOL A.11 The student will collect and analyze data, determine the equation of the curve of best fit in order to make predictions, and solve real-world problems, using mathematical models. Mathematical models will include linear and quadratic functions. The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to: Write an equation for a curve of best fit, given a set of no more than twenty data points in a table, a graph, or realworld situation. Make predictions about unknown outcome, using the equation of the curve of best fit. Design experiments and collect data to address specific, real-world questions. Evaluate the reasonableness of a mathematical model of a real-world situation Scatter Plot Positive Relationship Negative Relationship Line of Fit Best Fit Line Linear Interpolation Matrix Dimensions Row Column Element Scalar Multiplication Frequency Table Histogram Powerpoint/Smart board SOL A.11 Units 5.2, 5.3, 5.5 Ch. 1-9, 2-5, 5-7, 13-2 thru 13-5 Lesson 1-5 Data Analysis A.11 Quadratic Curve of Best Fit A.11 Line of Best Fit A.11 Linear Curve of Best Fit Lessons: 10 Students must be able to use the new formula sheet using standard and absolute deviations. Students also should be able to look at different graphs and determine solutions from looking at the graph. SOL A.11 Frequency Range Quartile Lower Quartile Upper Quartile Interquartile Range