Algebra I, 1st 4.5 weeks

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1 The following practice standards will be used throughout the 4.5 weeks:. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. TN Academic Standards Student Friendly I Can Statements Prerequisite Knowledge ACT Readiness Instructio nal Time TN Ready Questions/Resou rces ACT Questions/Re sources A.REI.A. Explain each step in solving an 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. I can solve a simple equation and justify each step using properties.

2 2 N.Q.A. 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.A.2 Identify, interpret, and justify appropriate quantities for the purpose of descriptive modeling. N.Q.A.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. I can give the solution of an equation using the correct units. I can define appropriate quantities, and use the scale to read the data correctly. I can determine the accuracy of values based on their limitations in the context of situations. Simplify ratios A.SSE.A. Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, and coefficients. Translate real-world problems into expressions using variables to represent values

3 3 B. Interpret complicated expressions by viewing one or more of their parts as a single entity. A.CED.A. Create equations and inequalities in one variable and use them to solve problems. I can create linear equations and inequalities in one variable and use them in a contextual situation to solve problems. Add and subtract polynomials Factor a monomial from a polynomial Translate real-world problems into expressions using variables to represent values Solve single-step and multistep equations and inequalities in one variable Solve equations that contain absolute value Write linear equations in standard form and form when given two points, a point and the slope, or the graph of the equation Identify, formulate, and obtain solutions to problems involving direct and inverse

4 4 A.CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. A.CED.A.3 Represent constraints by equations or inequalities, and by I can solve multi-variable formulas or literal equations, for a specific variable. I can write and use inequalities to variation Graph linear inequalities in one variable on the real number line to solve problems Solve quadratic equations using multiple methods, including graphing, factoring, and the square root principle Relate factors, solutions (roots), zeros of related functions, and x-intercepts in equations that arise from quadratic functions Evaluate and simplify rational expressions Solve formulas for a specified variable Give the domain

5 5 systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. solve a real world problem. I can graph the solution of an inequality on a number line. and range of relations and functions Evaluate functions at given values Identify graphs of relations and functions and analyze them to determine whether a relation is a function (e.g., vertical line test) Graph a linear equation using a table of values, x- and y-intercepts, form, and technology A.CED.A. Create equations and inequalities in one variable and use them to solve problems. I can create compound inequalities in one variable and use them in a contextual situation to solve problems. I can graph the solutions of a compound Translate real-world problems into expressions using variables to represent values Solve single-step and multistep equations and inequalities in one variable Solve equations that

6 inequality on a number line. contain absolute value Write linear equations in standard form and form when given two points, a point and the slope, or the graph of the equation Identify, formulate, and obtain solutions to problems involving direct and inverse variation Graph linear inequalities in one variable on the real number line to solve problems Solve quadratic equations using multiple methods, including graphing, factoring, and the square root principle Relate factors, solutions (roots), zeros of related functions, 6

7 7 and x-intercepts in equations that arise from quadratic functions Evaluate and simplify rational expressions F.IF.B.3 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. F.IF.B..4 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. I can(given a linear function) identify key features in graphs and tables including: intercepts, intervals where the function is increasing, decreasing, positive or negative; relative maximums and minimums; symmetries. I can interpret and explain features of the graph of the function in terms of the context of the problem. Recognize the concept of slope as a rate of change and determine the slope when given the equation of a line in standard form or form, the graph of a line, two points, or a verbal description Translate between different representations of relations and functions: graphs, equations, sets of ordered pairs, verbal descriptions, and tables Interpret

8 8 I can sketch a graph if given the key features of a function. I can use the problem situation to explain the end behavior of the function. data from line, bar, and circle graphs, histograms, scatterplots, box-and-whisker plots, stem-and-leaf plots, and frequency tables to draw inferences and make predictions F.IF.A. 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). I can (given the function f(x)) identify x as an element of the domain, the input, and f(x) is an element in the range, the output. I can know that the graph of the function, f, is the graph of the equation y = f(x) Give the domain and range of relations and functions Evaluate functions at given values I can write an expression in function notation

9 9 F.IF.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. I can find function values for expressions written in function notation I can write a function to express a contextual problem I can write an algebraic expression or equation to generalize the pattern in a table I can represent a relation in different formats (graph, table, lists & mapping) Give the domain and range of relations and functions Evaluate functions at given values Evaluate and simplify rational expressions Evaluate and simplify radical expressions I can determine whether or not a relation is a function and use the f(x) notation I can evaluate functions for inputs in their domain

10 0 F.LE.A.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (Geometric Sequence in Q 4) F.BF.A. 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. I can interpret statements that use function notation in terms of the context in which they are used I can convert a list of numbers (a sequence) into a function by making the whole numbers the inputs and the elements of the sequence the outputs before it (e.g, If I want to know the th number on the list, I plug the number into the explicit formulas). I can explain that a recursive formula tells me how a sequence starts and tells me how to use the previous value(s) to generate the next Identify arithmetic sequences and patterns in a set of data Identify patterns of growth (e.g., patterns of exponential growth) in a set of data

11 element of the sequence. I can explain that an explicit formula allows me to find any element of a sequence without knowing the element before it. I can distinguish between explicit and recursive formulas for sequences and use that knowledge to write equations based on functions. Write linear equations in standard form and form when given two points, a point and the slope, or the graph of the equation Identify arithmetic sequences and patterns in a set of data F.LE.A. Distinguish between situations that can be modeled with linear functions and with exponential functions. a. Recognize that linear functions grow that equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals. I can describe whether a given situation in question has a linear pattern of change or an exponential pattern of change. Recognize the concept of slope as a rate of change and determine the slope when given the equation of a line in standard form or form, the graph of

12 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 factor per unit interval relative to another. I can show that linear functions change at the same rate over time and that exponential functions change by equal factors over time. a line, two points, or a verbal description Identify arithmetic sequences and patterns in a set of data Identify patterns of growth (e.g., patterns of exponential growth) in a set of data 2 Write and graph linear equations and inequalities from real-world situations (e.g., a constant-rate distance/time

13 3 problem) Graph linear inequalities with two variables on the standard (x,y) coordinate plane Translate between different representations of relations and functions: graphs, equations, sets of ordered pairs, verbal descriptions, and tables Relate factors, solutions (roots), zeros of related functions, and x-intercepts in equations that arise from quadratic functions F.IF.B.5 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. I can explain the connection between average rate of change and the slope formula I can calculate the average rate of change over a Recognize the concept of slope as a rate of change and determine the slope when given the equation of a line in standard form or

14 specified interval of a function presented symbolically or in a table I can estimate the average rate of change over a specified interval of a function from the function's graph I can interpret the meaning of the average rate of change as it relates to a real world problem form, the graph of a line, two points, or a verbal description 4 F.IF.C.6 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and I can compare the rates of change of two or more functions when represented with the function notation, with a graph, or with a table I can determine the parent function for the line f(x) = x. Write and graph linear equations

15 using technology for more complicated cases. a. Graph linear and quadratic functions and show intercepts, maxima, and minima. I can identify and compare the different forms of linear functions. (point-slope, standard, ). I can compare the key features of two linear functions represented in different ways. I can describe a line as a translation of the parent function y = x. I can describe situations where one quantity changes at a constant rate per unit interval as compared to another I can identify the intercepts of a function and inequalities from real-world situations (e.g., a constant-rate distance/time problem) Graph linear inequalities with two variables on the standard (x,y) coordinate plane Translate between different representations of relations and functions: graphs, equations, sets of ordered pairs, verbal descriptions, and tables Relate factors, solutions (roots), zeros of related functions, and x-intercepts in equations that arise from quadratic functions 5

16 6 A.REI.D.5 Understand that the graph of an equation in two variable is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line) I can explain that all solutions to an equation in two variables are contained on the graph of that equation. Write linear equations in standard form and form when given two points, a point and the slope, or the graph of the equation Give the domain and range of relations and functions Evaluate functions at given values Identify graphs of relations and functions and analyze them to determine whether a relation is a function (e.g., vertical line test) Graph a linear equation using a table of values, x- and y-intercepts, form, and technology Translate between different representations of

17 7 relations and functions: graphs, equations, sets of ordered pairs, verbal descriptions, and tables Solve quadratic equations using multiple methods, including graphing, factoring, and the square root principle A.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations with two variables on coordinate axes with labels and scales. I can create equations in two or more variables to represent relationships between quantities. I can graph equations in two variables on a coordinate plane and label the axes and scales. I can decide which functions are Translate real-world problems into expressions using variables to represent values Solve single-step and multistep equations and inequalities in one variable Solve equations that contain absolute value Write linear equations in standard form and

18 relatively easy to sketch accurately by hand and which should be graphed using technology. form when given two points, a point and the slope, or the graph of the equation Identify, formulate, and obtain solutions to problems involving direct and inverse variation Graph linear inequalities in one variable on the real number line to solve problems Solve quadratic equations using multiple methods, including graphing, factoring, and the square root principle Relate factors, solutions (roots), zeros of related functions, and x-intercepts in equations that arise from quadratic 8

19 9 functions Evaluate and simplify rational expressions F.IF.C.8 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). I can compare properties of two functions and show their relationship using graphs, tables and verbal descriptions. Recognize the concept of slope as a rate of change and determine the slope when given the equation of a line in standard form or form, the graph of a line, two points, or a verbal description Translate between different representations of relations and functions: graphs, equations, sets of ordered pairs, verbal descriptions, and tables Interpret data from line, bar, and circle graphs, histograms, scatterplots,

20 20 box-and-whisker plots, stem-and-leaf plots, and frequency tables to draw inferences and make predictions

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