Year at a Glance August September October November December January February March April May 1. Functions, 4.Systems Expressions, 2. Polynomials and 6. Exponential STAAR SLA 3. Linear Functions of Break 5. Quadratics Extension Equations, and Powers Functions Prep Equations Inequalities Time Unit Title 10 Unit 1: Functions, Expressions, Equations, and Inequalities 9 Unit 2: Polynomials and Powers CA 1 (Unit 2 continues after CA1) 9 Unit 3: Linear Functions 5 Unit 4: Systems of Equations CA 2 12 Unit 5: Quadratics CA3 8 Unit 6: Exponential Functions STAAR Test 3 Extension Correlations and Regressions; Series & Sequences Pearson Algebra 1 Text and Online McGraw Hill textbooks for middle school math courses The National Library of Virtual Manipulatives http://nlvm.usu.edu/ Engage NY ixl.com http://www.ixl.com/math/grade-6 Algebra Worksheet Generator http://www.math.com/students/worksheet/algebra_sp.htm RegentsPrep.org General Emathinstruction.com Openmiddle.com Wyrmath.com Wodb.ca http://www.projectsharetexas.org/resource-index Estimation180.com Interactive Math Glossary Notes TIME FRAME: Unit time frames are approximate and subject to change dependent on data and scholars needs, as well as campus testing schedules. TEKS: All readiness TEKS are represented in bold text. Most supporting TEKS are represented where appropriate and deemed necessary. MYP UP Stage 1: Global contexts, key concepts, related concepts, and assessment criteria have been selected carefully to ensure Uplift meets IB requirements. If you choose to change any of these to personalize your units, please ensure you are assessing each global context, key concept, and related concept at least 1x per year and each assessment criteria at least 2x per year. PERFORMANCE TASKS: A minimum of 2 investigations and 2 real world projects are required. The first must be completed before Collaboration Day 2, and the second before the end of the year. You may choose to use the tasks detailed in the scope (indicated as investigations) or you may create your own, but the task must be assessed using MYP Criterion B, C, and D, depending on the assessment.
10 class periods Unit 1: Functions, Expressions, Equations, and Inequalities Define a function, identify functions using multiple representations, and use function notation to evaluate functions Identify the domain and range of both discrete and continuous data Solve multi-step one variable linear equations and inequalities o o Including the distributive property Manipulate equations to isolate a given variable Definition of a function Function notation One variable equations Translating to basic expressions Combine like terms Evaluate expressions Add and subtract expressions Match inequalities with number lines Manipulate expressions and equations Solve and graph linear inequalities A.2A A.5A A.5B A.12A A.12B A.12E A 201 A 301 A 302 A 303 A 401 A 402 A 403 A 405 AF 502 AF 503 A 503 A 504 AF 602 A 601 A 602 A 603 Fairness and Development Logic Equivalence Justification Representation Fairness is not everyone getting the same thing, it is everyone getting what they need. Optional: Diagnostic Test for basic/pre-requisite skills Unit Test (Criterion A) Function Representations (Criterion C): Scholars select two real-world situations, one which can be modeled by a function and one which cannot, and support their choice with multiple representations of each situation (graph, table, equation, mapping, verbal description) Concrete and virtual manipulatives for solving equations Desmos graphing software Pearson textbook and online resources Topic 1, 2
Time 9 Class Total 4 Class Before CA 1 5 Class After CA 1 Unit 2: Polynomials and Powers A.10A A 509 A.10B A 510 Globalization and A.10C A 511 Sustainability A.10D A 512 A.11A Relationships A.11B Apply laws of exponents to simplify or evaluate expressions o Rewrite expressions with radicals using rational exponents and expressions with rational exponents using radicals Add, subtract, multiply, and divide polynomials Apply the distributive property to rewrite polynomial equations Add polynomials Subtract polynomials Multiply polynomials Squares and Square roots Cubes and Cube roots Scientific Notation Positive integer exponents TEKS 10A, 10B, 10C and 10D will be assessed on CA 1. All TEKS may be assessed on CA 2. Pattern Simplification A small change may have the power to make a large impact in the future. Exponent Lab (Criterion B): Scholars investigate power rules through a multi-step lab where they look at exponential form, expanded form, and solutions in order to generate the rules themselves. Scholars verify their results using additional examples. Polynomial Farm (Criterion A): This performance task is planned to give students an opportunity to add, subtract, multiply, and divide polynomials in order to solve real-world problems. This task is designed to encourage students to make connections and to communicate their mathematical thinking clearly and accurately. Modified from: http://www.radford.edu/ru mathsmpdc/performance/src/em ily%20o'rourke%20- %20Polynomial%20Farm.pd f Pearson textbook and online resources Topic 5, 7 Algebra tiles for polynomial operations
9 Class Unit 3: Linear Functions Write linear equations and inequalities given a table, graph, or description o Write equations in slope-intercept, point slope, and standard form o Write equations of parallel and perpendicular lines, including those parallel/perpendicular to an axis Understand slope as a rate of change and calculate slope given a table, graph, equation, points, or situation. Graph linear functions and identify key characteristics Graph linear inequalities Transform linear equations and describe transformations given an equation or graph Calculate slope Evaluate linear and quadratic functions Match linear equations and graphs Translations Change in speed corresponding to change in slope Locate points in Q1 Reflections of a point A.2B A.2C A.2D A.2E A.2F A.2G A.2H A.3A A.3B A.3C A.3D A.3E A 406 F 401 AF 503 A 514 F 503 F 504 F 505 F 506 F 507 F 511 AF 604 F 601 F 602 G 304 G 407 G 510 G 607 Personal and Cultural Expression Form Pattern Representation What one has experienced in their past impacts how they represent themselves to the world. Unit Test (Criterion A) Flags of the World Project (Criterion C and D): G: Learn about the history of countries around the world R: A globally minded scholar A: Your peers S: In school and college you meet people from around the world and want to be more knowledgeable about their home countries. You choose to learn about their country by examining their national flag and learning about what led to its adoption and any symbols of the country. P: Create a poster with a visual representation of a country s flag using multiple linear equations. Present your flag and equations with calculations, equations, and a table of values. Research the origin of the flag and history of the country and include a written description on your poster. Transformation Investigation (Criterion B): Scholars graph equations of lines (by hand or using technology) to investigate how changing parameters impacts the graph. Scholars write transformation rules and verify them using multiple other graphs. Pearson textbook and online resources Topic 3 Desmos graphing software Visualpatterns.org to show visual representations of linear and nonlinear functions
5 Class Unit 4: Systems of Equations Write a system of linear equations or inequalities Solve systems of equations by graphing, substitution, and elimination Solve systems of inequalities by graphing Solve systems of two linear equations A.2I A.3F A.3G A.3H A.5C A 604 Scientific and Technical Innovation Relationships Equivalence System Representation We can represent relationships using logical systems in order to make decisions. Car Comparison Project (Criterion C and D): Scholars research the price and gas mileage of two comparable vehicles and determine which will be a better purchase for them. Scholars create a system of equations and solve it by graphing and algebraically. Scholars then summarize their findings in writing. (Use cars.com and google maps for research.) Pearson textbook and online resources Topic 4 Desmos graphing software
Time 12 Class Unit 5: Quadratics Determine the domain and range of quadratic functions Graph quadratic functions and identify key characteristics Transform quadratic functions on the coordinate plane Factor trinomials and perfect square binomials Solve quadratic equations using various methods Write quadratic functions using given information Convert between standard and vertex form of quadratics Multiply two binomials Identify solutions to quadratic functions Solve factored quadratic equations Difference of squares Solve quadratic equations Squares and square roots A.6A A.6B A.6C A.7A A.7B A.7C A.8A A.8B A.10E A.10F A 404 A 501 A 505 A 506 A 507 A 508 A 509 A 605 Orientation in space and time Form Generalization Quantity Simplification Statement of Inquiry Through modeling we can analyze multiple ways to represent the same relationship. Parabola Transformation Investigation (Criterion B and C): Scholars work as consultants for Polly Parabola as she starts her company Professional Parabola Productions. Scholars are tasked with determining all the ways a graph of a parabola can be changed by changing its equations. They generate rules for the transformations and present them in a memo using graphs, equations, and verbal descriptions. X-Intercept Investigation (Criterion B): Scholars graph functions written as the product of two binomials and use their calculator to estimate the x-intercepts. They use various examples to look for a pattern between the binomials and the x-intercepts and generate a rule for finding the x-intercepts from the binomial factors. Transformations Lab (Criterion B): Scholars investigate transformations of quadratics through a multi-step lab where they look at variations of vertex form equations with changing parameters to generate the rules of transformations. Pearson textbook and online resources Topic 8 Desmos graphing software Fireworks Task (Criterion D): Scholars take on the role of a firework company owner and design a firework show using information about different quadratic equations and graphs. They design a new firework given parameters. They create a report including mathematical data and written reflections to analyze each type of firework in the context of the real world situation.
8 Class Unit 6: Exponential Functions Write exponential functions Interpret the meaning of exponential functions given an equation Graph exponential functions and identify key components including intercepts, asymptotes, domain and range. Determine the domain and range of exponential functions A.9A A.9B A.9C A.9D A.9E Globalization and Sustainability Form Measurement Change System Patterns can be used to determine and describe the impact of human action over time. Unit Test (Criterion A) Which is the best investment? (Criterion D): Scholars choose between investing a set amount of money in a savings account, in a car, or in a home. For each, they research the interest rate/rate of appreciation/ depreciation and calculate the value of that money at various increments of time. Scholars represent their findings with equations, calculations, and graphs and write a summary of which option they would select and how investing relates to their lives. Pearson textbook and online resources Topic 9 Desmos graphing software
5 Class STAAR Prep Reporting Categories: 1. Number and Algebraic Methods 2. Describing and graphing linear functions, equations, and inequalities 3. Writing and solving linear functions, equations, and inequalities 4. Quadratic functions and equations 5. Exponential functions and equations Focus on Readiness Standards with low mastery over the course of the year. A.10E A.11B A.3B A.3C A.3D A.2A A.2C A.2I A.5A A.5C A.6A A.7A A.7C A.8A CTL lesson plans and materials Pearson Algebra 1 Book Texas Coach STAAR Ready McGraw Hill Assessment Masters A.9C A.9D
3 Class Extension Correlations and Regressions; Series & Sequences Use technology to determine the line of best fit for realworld data, using linear, quadratic, or exponential functions Determine the correlation between variables in a realworld situation Arithmetic and Geometric sequences Pattern Seeking Geometric Sequences Recursive formulas A.4A A.4B A.4C A.8B A.9E A.12C A.12D F 201 F 301 F 502 F 603 F 703 Scientific and Technical Innovation Relationships Pattern Change Model Recognizing variation patterns in real world relationships can be used to make informed decisions. Sequences Lab (Criterion B): Scholars investigate both algebraic and geometric sequences in order to derive the rules for writing sequences or finding specific terms in a sequence. Correlation Study (Criterion D): Scholars explore a set of given or researched data in order to determine what type of function would best fit that data. Scholars draw conclusions and make predictions based on their data set and present their findings using calculations and in writing. Pearson textbook and online resources Topic 6
A.1A apply mathematics to problems arising in everyday life, society, and the workplace A.1B use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem solving process and the reasonableness of the solution A.1C select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems A.2(A) determine the domain and range of a linear function in mathematical problems; determine reasonable domain and range values for real-world situations, both continuous and discrete; and represent domain and range using inequalities A.2(B) write linear equations in two variables in various forms, including y = mx + b, Ax + By = C, and y y 1 = m(x x 1), given one point and the slope and given two points A.2(C) write linear equations in two variables given a table of values, a graph, and a verbal description A.2(D) write and solve equations involving direct variation A.2(E) write the equation of a line that contains a given point and is parallel to a given line A.2(F) write the equation of a line that contains a given point and is perpendicular to a given line A.2(G) write an equation of a line that is parallel or perpendicular to the x- or y-axis and determine whether the slope of the line is zero or undefined A.2(H) write linear inequalities in two variables given a table of values, a graph, and a verbal description A.2(I) write systems of two linear equations given a table of values, a graph, and a verbal description A.3(A) determine the slope of a line given a table of values, a graph, two points on the line, and an equation written in various forms, including y = mx + b, Ax + By = C, and y y 1 = m(x x 1) A.3(B) calculate the rate of change of a linear function represented tabularly, graphically, or algebraically in context of mathematical and real-world problems A.3(C) graph linear functions on the coordinate plane and identify key features, including x- intercept, y-intercept, zeros, and slope, in mathematical and real-world problems A.3(D) graph the solution set of linear inequalities in two variables on the coordinate plane TEKS A.1D communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate A.1E create and use representations to organize, record, and communicate mathematical ideas A.1F analyze mathematical relationships to connect and communicate mathematical ideas A.1G display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication A.7(A) graph quadratic functions on the coordinates plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry A.7(B) describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions A.7(C) determine the effects on the graph of the parent function f(x) = x 2 when f(x) is replaced by af(x), f(x) + d, f(x c), f(bx) for specific values of a, b, c, and d A.8(A) solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula A.8(B) write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems A.9(A) determine the domain and range of exponential functions of the form f(x) = ab x and represent the domain and range using inequalities A.9(B) interpret the meaning of the values of a and b in exponential functions of the form f(x) = ab x in real-world problems A.9(C) write exponential functions in the form f(x) = ab x (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay A.9(D) graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems A.9(E) write, using technology, exponential function that provide a reasonable fit to data and make predications for real-world problems A.10(A) add and subtract polynomials of degree one and degree two A.10(B) multiply polynomials of degree one and degree two A.10(C) determine the quotient of a polynomial of degree one and polynomial of degree two when divided by a polynomial of degree one and polynomial of degree two when the degree of the divisor does not exceed the degree of the dividend
A.3(E) determine the effects on the graph of the parent function f(x) = x when f(x) is replaced by af(x), f(x) + d, f(x c), f(bx) for specific values of a, b, c, and d A.3(F) graph systems of two linear equations in two variables on the coordinate plane and determine the solutions if they exist A.3(G) estimate graphically the solutions to systems of two linear equations with two variables in real-world problems A.3(H) graph the solution set of systems of two linear inequalities in two variables on the coordinate plane A.4(A) calculate, using technology, the correlation coefficient between two quantitative variables and interpret the quantity as a measure of the strength of the linear association A.4(B) compare and contract associate and causation in real-world problems A.4(C) write, with and without technology, linear functions that provide a reasonable fit to data to estimate solutions and make predications for real-world problems A.5(A) solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides A.5(B) solve linear inequalities in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides A.5(C) solve systems of two linear equations with two variables for mathematical and realworld problems A.6(A) determine the domain and range of quadratic functions and represent the domain and range using inequalities A.6(B) write equations of quadratic functions given the vertex and another point on the graph, write the equation in vertex form (f(x) = a(x h) 2 + k), and rewrite the equation from vertex form to standard form (f(x) = ax 2 + bx + c) A.6(C) write quadratic functions when given real solutions and graphs of their related equations A.10(D) rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property A.10(E) factor, if possible, trinomials with real factors in the form ax 2 + bx + c, including perfect square trinomials of degree two A.10(F) decide if a binomial can be written as the difference of two square and, if possible, use the structure of a difference of two squares to rewrite the binomial A.11(A) simplify numerical radical expressions involving square roots A.11(B) simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents A.12(A) decide whether relations represented verbally, tabularly, graphically, and symbolically define a function A.12(B) evaluate functions, expressed in function notation, given one of more elements in their domains A.12(C) identify terms of arithmetic and geometric sequences when the sequences are given in function form using recursive processes A.12(D) write a formula for the n th term of arithmetic and geometric sequences, given the value of several of their terms A.12(E) solve mathematical and scientific formulas, and other literal equations, for a specified variable