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Unit 1 Benchmark Blueprint Algebra CLAIMS 1-Concept and Procedures 2-Problem Solving 3-Communicating 4-Modeling and Data Analysis 8/10/15 MATHEMATICAL PRACTICES 1. 2. 3. 4. 5. 6. 7. 8. Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct viable arguments and critique the reasoning of others Model with mathematics Use appropriate tools strategically Attend to precision Look for and make use of structure Look for and express regularity in repeated reasoning CONCEPTUAL CATEGORYDOMAIN CLUSTER (SBAC Target) STANDARDS Framework Pages11-20, 22-26, 28-38 Benchmark Blueprint Number and QuantityQuantities. Target C: Reason Quantitatively and use units to solve problems. 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 displays. N-Q.2 Define appropriate quantities for the purpose of descriptive modeling. N-Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. A-SSE.1 Interpret expressions that represent a quantity in terms of its context. 1a Interpret parts of an expression, such as terms, factors, and coefficients. 1b Interpret complicated expressions by viewing one or more of their parts as a n single entity. For example, interpret P(1 + r) as the product of P and a factor not depending on P. Not Assessed Algebra-Seeing Structure in Expressions. Target D: Interpret the Structure of Expressions. A-SSE.2 Use the structure of an expression to identify ways to rewrite it. Algebra-Creating Equations. Target G: Create equations that describe numbers or relationships A-CED.1 Create equations and inequalities in one variable and use them to solve problems. 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.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. Not Assessed 3 SR 3 SR PT PART A, PART D Notes Use this section to write information from the framework Algebra-Reasoning with Equations and Inequalities. Target H: Understand solving equations as a process of reasoning and explain the reasoning. 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. 2 SR PT PART C Algebra-Reasoning with Equations and Inequalities. Target I: Solve equations and inequalities in one variable. A-REI.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. A-REI.3.1 (CA) Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context. 3 SR PT PART B Algebra-Reasoning with Equations and Inequalities. Target K: (Target J on SBAC blueprint) Represent and solve equations and inequalities graphically 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). Not Assessed Functions-Interpreting Functions. Target L (Target K on SBAC blueprint) Understand the concept of a function and use function notation. Functions-Interpreting Functions. Target M: (Target L on SBAC blueprint) Interpret functions that arise in applications in terms of the context. 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 f corresponding to the input x. The graph of f is the graph of the equation y = f(x). 4 SR 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. 2 SR 1 CR Functions-Interpreting Functions. Target N: Analyze functions using different representations. 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. Graph linear and quadratic functions and show intercepts, maxima, and minima Not Assessed Functions-Building Functions. Target O: Build a function that models a relationship between two quantities. F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms. Not Assessed Functions-Linear, Quadratic, and Exponential Models. Target Q: Construct and compare linear, quadratic, and exponential models and solv3 problems. F-LE.1a Distinguish between situations that can be modeled with linear functions and with exponential functions. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals. F.LE.1b Distinguish between situations that can be modeled with linear functions and with exponential functions. 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 relationship, or two inputoutput pairs (include reading these from a table). Not Assessed Indicates a modeling standard linking mathematics to everyday life, work, and decision-making (see CA Math Framework) 7.NS.2d 7.EE.2 7.EE.3 7.EE.4 7.EE.4a 7.EE.4b 7th/8th Algebra N-Q1, 2 & 3 A-SSE1a, 1b & 2 A-CED1, 2 & 4 A-REI3 & 3-1 A-REI 10 F-IF1,4 & 6 F-IF7a F-BF2 F-LE1a, 1b & 2 Progressions • • • • • • Geometry Congruence Experiment with transformations in the plane, Understand congruence in terms of rigid motions, Prove geometric theorems, Make geometric constructions Similarity, Right Triangles, and Trigonometry Understand similarity in terms of similarity transformations, Prove theorems involving similarity, Define trigonometric ratios and solve problems involving right triangles, Apply trigonometry to general triangles Circles Understand and apply theorems about circles, Find arc lengths and areas of sectors of circles Expressing Geometric Properties with Equations Translate between the geometric description and the equation for a conic section, Use coordinates to prove simple geometric theorems algebraically Geometric Measurement and Dimension Explain volume formulas and use them to solve problems, Visualize relationships between twodimensional and three-dimensional objects Modeling with Geometry Apply geometric concepts in modeling situations Benchmark Item Types and Points 17 Selected Responses (1 point) 1 Constructed Response (2 points) 1 Performance Task with 4 parts (6 points)