Westerville City Schools COURSE OF STUDY Math Lab for Algebra MA101. Course Details

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1 : Recommended Grade Level: 9, 10 Westerville City Schools COURSE OF STUDY for Algebra MA101 Course Details Course Length: Semester Credits:.25/semester mathematics elective credit Course Weighting: 1.0 Course Fee: None Course Description is designed to help students be successful in their Algebra 1 course. Math lab is a.25 elective credit per semester. In order to receive credit, students must earn a grade of satisfactory. is designed to give additional opportunities to learn and apply algebraic concepts. The class will be activity based and students will need to fully participate. Some homework help and review for Algebra assessments will also be incorporated into the course. Course Rationale Students may enter Algebra 1 having not been successful in previous math courses or not having the prerequisite knowledge and skills necessary to be successful in Algebra. The goal of is to support each student to be successful in the Algebra classroom by providing the opportunity to acquire the background understandings necessary as well as to front load the Algebra content. Math Lab will provide opportunities for students to fill gaps and improve on their foundational mathematical knowledge and skills. Some students may be ready to exit this course during or at the end of the year based on the grades in their Algebra 1 class. does not have a scope and sequence in the traditional sense. As each student will have an individual path through the school year, the units below are meant as general guidelines; the work in the classroom must necessarily be responsive to the gaps and needs of the particular students in each individual section. Scope and Sequence 1

2 Topics of Study Estimated Time (in weeks) 1 Number Sense: Integers, Fractions/Decimals, Order of 4 weeks Operations, Absolute Value, Evaluating Expressions 2 Combining like Terms 1 week 3 Solving Equations 2 weeks 4 Linear Equations: Multiple Representations 3 weeks 5 Unit Rate and Proportions 1 week 6 Area and Perimeter of Circles and Composite Figures 1 week 7 Simplifying Exponents 2 weeks 8 Generic Rectangle practice/ Solving Equations 2 weeks 9 Solve Multivariable Equations for a Single Variable 1 week 10 Solving Systems of Equations 2 weeks 11 Sequences 2 weeks 12 Graphing calculator practice 1 week 13 Scatterplots and Association checkpoints from course 2 1 week and 3 14 Exponential Equations: Multiple Representations 2 weeks 15 Factoring 3 weeks 16 Solving Quadratic Equations 3 weeks 17 Applications of Quadratics and graphing 2 weeks 18 Review for Exam 1 week Text: CPM textbooks - Course 1, 2, 3 and Algebra 1 Primary Material Recommendation Other Resources: ALEKS for diagnostic and gap filling; assessment tool braingenie - online individualized practice; assessment tool kahoot - assessment tool quizizz - assessment tool desmos - online graphing utility 2

3 Topic #1: Functions Content Standards Essential Questions Topics of Study F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of fcorresponding to the input x. The graph of f is the graph of the equation y = f(x). F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. F.IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. F.IF.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. F.IF.7a Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a) Graph linear and quadratic functions and show intercepts, maxima, and minima. b) Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. A.REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). 1. What are the multiple ways to represent a function? 2. How do you describe a graph? Enduring Understandings Key Concepts/ Vocabulary A graph, table, and equation can all represent the same idea. Students will use their knowledge of order of operations, evaluating expressions and graphing points to investigate many different types of functions order of operations, evaluating expressions, absolute value, function, domain, range, maximum, minimum, x and y-intercepts, input, output, line of symmetry, graph and table. 3

4 Content Elaborations Learning Targets Assessments Instructional Strategies and Materials Considerations for Intervention and Acceleration Fluency in these checkpoints from Course 1, 2, and 3 needed for success in this chapter: Course 1 Checkpoint #6: Locating points on a number line and on a coordinate graph Course 2 Checkpoint #5. Order of Operations Course 3: Checkpoint #2: Evaluating Expressions and using order of operations I can: use order of operations to simplify expressions, including those with absolute value evaluate expressions create a table when given an equation create a graph from a table describe a graph Students will be assessed in their regular Algebra 1 class. Students will be given checkpoint materials from College Preparatory Mathematics Course 1,2, and 3 Students will use ALEKS dynamic computer software for tracking skill mastery. CPM Parent guides Study team strategies Teacher created additional practice This is an intervention class. The teacher will modify materials, as needed, on an individual basis. Topic #2: Linear Relationships Content Standards A-CED.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales 4

5 A-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). A-SSE.1a Interpret expressions that represent a quantity in terms of its context. a) Interpret parts of an expression, such as terms, factors, and coefficients. b) Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P. F-BF.1 Write a function that describes a relationship between two quantities. a) Determine an explicit expression, a recursive process, or steps for calculation from a context. F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. F-IF.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. F-IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a) Graph linear and quadratic functions and show intercepts, maxima, and minima. b) Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. F-IF.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. F-LE.1 Distinguish between situations that can be modeled with linear functions and with exponential functions. a)prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. b) Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. F-LE.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a 5

6 Essential Questions Enduring Understandings Key Concepts/ Vocabulary Content Elaborations relationship, or two input-output pairs (include reading these from a table). F-LE.5 Interpret the parameters in a linear or exponential function in terms of a context. N-Q.1istinguish between situations that can be modeled with linear functions and with exponential functions. a) Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. b)recognize situations in which one quantity changes at a constant rate per unit interval relative to another. c) Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another. N-Q.2 1. Can I create a representation of a problem, consider the units involved, and understand the meaning of the quantities using tables, graphs and equations? Multiple representations to describe linear relationships are all interconnected. graph, linear equation, starting value, figure 0, function, y = mx +b, variable, y-intercept, zero slope, rate of change, parameter, slope triangle, unit rate, growth, slope, steepness, x-intercept, coefficient, table Fluency in the following checkpoints from Course 1, 2, and 3 needed to be successful in this course: Course 1 Checkpoint # 8A: Rewriting and Evaluating Variable Expressions Course 2 Checkpoint #6: Writing and Evaluating Algebraic Expressions Course 3 Checkpoint # 3: Unit Rates Checkpoint # 5: Solving Equations Checkpoint #6: Multiple Representations of Linear Equations Learning Targets I can: Represent expressions See growth in linear relationships Identify slope 6

7 Assessments Instructional Strategies and Materials Considerations for Intervention and Acceleration Compare the change in y over the change in x Create the equation of a line Find the rate of change Find the equation of a line given the slope and a point Find the equation of a line through two points Finding y = mx + b from tables and graphs Students will be assessed in their regular Algebra class ALEKs dynamic computer software for tracking skill mastery CPM Parent Guides Checkpoints from previous courses Study Team Strategies Teacher created additional practice Please see attached documents addressing the challenges and response to exception students of all levels. Topic #3: Algebra: Simplifying and Solving Equations Content Standards A-SSE.1 Interpret expressions that represent a quantity in terms of its context. a) Interpret parts of an expression, such as terms, factors, and coefficients A-SSE.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. a) Factor a quadratic expression to reveal the zeros of the function it defines. c) Use the properties of exponents to transform expressions for exponential functions.for example the expression 1.15t can be rewritten as (1.151/12)12t t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%. A-REI.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. A-APR.1 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function 7

8 Essential Questions Enduring Understandings Key Concepts/ Vocabulary Content Elaborations defined by the polynomial. A-CED.4, Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm's law V = IR to highlight resistance R. 1. Can I simplify exponential expressions? 2. Can I write expressions as a product equal to a sum? 3. Can I solve equations and multi-variable equations? Students will gain an understanding of how to simplify and solve multiple types of expressions and equations. area, polynomial, equation, solve, binomial, exponent, terms, expression, integers, product, sum, standard form, distributive property, dimensions, solution, evaluate, base Checkpoint topics from Course 1,2, and 3 needed to be successful in this course: Course 1: Checkpoint # 8A: Rewriting and Evaluating Variable Expressions Checkpoint # 9B: Solving One-Step Equations Course 2: Checkpoint #5: Order of Operations Checkpoint # 7A: Simplifying Expressions Checkpoint #8: Solving Multi-Step Equations Course 3: Checkpoint #2: Evaluating Expressions and Using Order of Operations Checkpoint # 4: Area and Perimeter of Circles and Composite Figures Checkpoint #5: Solving Equations Checkpoint # 6: Multiple Representations of Linear Equations Learning Targets Assessments Instructional I can: simplify exponential expressions solve equations rewrite equations multiply binomials using generic rectangles solve absolute value equations work with multi-variable equations. Students will be assessed in their regular Algebra 1 class. ALEKS dynamic computer software for tracking skill mastery 8

9 Strategies and Resources Considerations for Intervention and Acceleration CPM Parent Guides Checkpoints from previous courses Study team strategies Teacher created additional practice Please see attached documents addressing the challenges and response to exception students of all levels. Topic #4: Systems of Equations: Solving Systems of Equations using various methods and writing systems of equations to model real-world scenarios Content Standards A-CED.1 Create equations and inequalities in one variable and use them to solve problems.include equations arising from linear and quadratic functions, and simple rational and exponential functions. A-CED.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. A-CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.for example, represent inequalities describing nutritional and cost constraints on combinations of different foods. A-REI.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. A-REI.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. A-REI.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). F-LE.1b Distinguish between situations that can be modeled with linear functions and with exponential functions. a) Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. b) Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data 9

10 Essential Questions Enduring Understandings Key Concepts/ Vocabulary Content Elaborations displays. N-Q.2 Define appropriate quantities for the purpose of descriptive modeling. 1. Can students choose the most efficient method when presented with a system of equations? 2. Can students use each of the methods correctly and effectively? 3. Can students write a systems of equations from a scenario? Students will be able to recognize when a system of equations is needed to solve future problems and effectively choose and apply the appropriate method. variable, slope, y-intercept, point of intersection, parallel, substitution method, elimination method, equal values method, no solution, infinite solutions Students will need fluency in the following checkpoints: Course 3: Checkpoint 6 - Multiple Representations of Linear Equations Checkpoint 7 - Solving Equations with Fractions Course 2: Checkpoint 8 - Solving Multi-step Equations Learning Targets Assessments I can: solve systems of equations by graphing solve systems of equations using the Equal Values method solve systems of equations using the Substitution method solve systems of equations using the Elimination method write a system of equations to model a real-world scenario solve word problems by writing a pair of equations, called a system of equations solve the system of equations with the same multiple representations you used for solving linear equations: table, graph, and by manipulating the equations. develop ways to solve different forms of systems, and will learn how to recognize when one method may be more efficient than another. know multiple ways to find the point of intersection of two lines and will be able to solve systems that arise from different situations. Students will be assessed in the regular Algebra 1 class ALEKS dynamic computer software for tracking skill mastery 10

11 Instructional Strategies and Resources Considerations for Intervention and Acceleration Desmos dynamic graphing software to aide in graphing and checking solutions CPM parent guides Checkpoints from previous courses Study Team Strategies Teacher created additional practice Please see attached documents addressing the challenges and response to exception students of all levels. Acknowledgements It is through the hard work and dedication of high school Mathematics team that the Westerville City Schools High School Algebra Course of Study is presented to the Board of Education. Sincere appreciation is extended to the following individuals for their assistance and expertise. Central HS North HS South HS District Jennifer Horn Jessica Martin Kasandra Sliney Michael Huler Brittany Barnhart Richard Gary 11