Foundations of Math and Math I

     

    Math I and Foundation of Math I Outcomes and Learning Targets

     (Pacing is based on semester and yearlong* schedules with 90 minute classes)

    Module A: Equations & Introduction to Functions Outcome 1: I can create, solve and justify solutions for linear equations and inequalities in one variable.7 days 14 days*
    a. I can create and solve linear equations algebraically. A-CED.1, A-REI.3 b. I can justify the steps used in the algebraic process of solving a linear equation. A-REI.1 c. I can rearrange a formula to highlight a quantity of interest. A-CED.4, A-REI.1, 3 d. I can create linear inequalities in one variable. A-CED.1 e. I can solve linear inequalities in one variable. A-REI. 3, A-CED.1 f. Honors: I can create & solve a compound linear inequality in one variable.

    Outcome 2: I can apply the concept of a function to analyze and solve problems. 4 days 8 days* a. I can use and interpret function notation appropriately. F-IF.2 b. I can solve problems in context using a table and/or graph of a function. F-IF.1 c. I can represent the set of all solutions of a function. A-REI.10 d. I can determine if a relationship between two sets of values is a function. F-IF.1 e. Honors: I can describe the relationship between two variables and justify whether it is a function or not.   SMP 2 Outcome 3: I can identify key features of a function and interpret them in terms of the context. 4 days 8 days*

    a. I can describe an interval where a function is increasing or decreasing and where it is positive or    negative. F-IF.4 b. I can identify intercepts from a table or graph and interpret them in terms of the context. F-IF.4 c. I can sketch graphs showing key features given a verbal description in Context. F-IF.4 d. I can relate the domain & range of a function to its graph and, where applicable, to the relationship it describes. F-IF.5 e. I can calculate and interpret the average rate of change of a function over a specified interval. F-IF.6 f. Honors: I can analyze the average rate of change for equal intervals to describe how a function changes.F-IF.7 Module B: Linear Functions

    Outcome 4: I can create and analyze representations of linear functions. 5 days 10 days* a. I can create another representation of a linear pattern given any one of recursive rule, function rule (๐‘“(๐‘ฅ) =), table, graph, and/or contextual situation. A-CED.2, F-IF.7, F-BF.1 b. I can determine and explain the rate of change and/or the initial value of a linear pattern given any representation. A-SSE.1, F-IF.4,6, F-LE.5 c. I can add, subtract and multiply (by a constant) to rewrite linear expressions in equivalent forms. A-APR.1, F-BF.1b d. I can determine a reasonable domain and range for a linear function given a contextual situation and/or a graph. F-IF.5 e. I can compare and contrast two different linear functions given any representation. F-IF.9 f. Honors: I can use the x intercept and a scale factor to build a linear function.F-BF

    Outcome 5: I can create and solve linear systems of equations in context.5 days 10 days* a. I can create and graph linear functions in standard form given a contextual situation.A.CED.2 b. I can create a system of linear equations to model a situation in context. A.CED.3 c. I can solve a system of linear equations using tables and graphs. A.REI.11, A.REI.6, d. I can solve a system of linear equations by elimination. A.REI.5,6 e. I can solve a system of linear equations by substitution. A.REI.6 f. Honors: I can explain how the graph of a system changes with each step of the elimination process. F-IF.5

    Outcome 6: I can create and solve linear inequalities and systems of linear inequalities in context. 2 days 4 days* a. I can create a linear inequality in two variables to model a situation in context. A-CED.3 b. I can represent the solutions of a linear inequality. A-REI.12 c. I can create a system of linear inequalities to model a situation in context. A-CED.3 d. I can represent the solutions of a system of linear inequalities. A-REI.12 e. Honors: I can represent the solutions to a system of multiple linear inequalities.A-REI.12

    Module C: Statistics Outcome 7: I can compare two sets of data using graphs and summary statistics appropriate to the shapes of the distribution. 5 days 10 days* a. I can create a graph to represent data, using technology, including histograms and boxplots. S-ID.1 b. I can choose, calculate, and interpret a measure of center (mean or median) appropriate to the shape of a distribution to compare data sets. S-ID.2 c. I can choose, calculate, and interpret a measure of spread (interquartile range or standard deviation) appropriate to the shape of a distribution to compare data sets. S-ID.2 d. I can interpret, in context, differences in the shape, center, and spread of two or more sets of data. S-ID.2 e. I can describe the effects of extreme data points on shape, center, and/or spread. S-ID.3 f. Honors: I can apply the statistical process involving univariate data.SMP 4

    Outcome 8: I can create, interpret, and analyze linear models. 4 days 8 days* a. I can create a scatterplot and analyze it to describe how two variables are related. S-ID.6 b. I can fit a linear function to data and use it to solve problems in context. S-ID.6a,7 c. I can analyze residuals to assess the fit of a linear function. S-ID.6b d. I can interpret the slope and intercept of a linear model in the context of the data. S-ID.7 e. I can assess the strength and direction of a linear association by examining the correlation coefficient (calculated using technology). S-ID.8 f. I can distinguish between association and causation. S-ID.9 g. Honors: I can describe the characteristics of a least square regression line. S-ID
    Module D: Exponential Functions

    Outcome 9: I can rewrite expressions involving exponents. 3 days 6 days* a. I can multiply algebraic expressions with like bases. N-RN.2 b. I can divide algebraic expressions with like bases. N-RN.2 c. I can rewrite algebraic expressions by raising a power to a power. N-RN.2 d. I can rewrite algebraic expressions with negative exponents. N-RN.2 e. I can rewrite algebraic expressions with a combination of all of the above. N-RN.2 f. Honors: I can rewrite an algebraic expression given a specific structure.SMP7

    Outcome 10: I can create and analyze representations of exponential functions. 4 days 8 days* a. I can create another representation of an exponential pattern given any one of recursive rule, function rule, table, graph, and/or contextual situation. A-CED.1, 2, F-IF.7, F-BF.1 b. I can determine and explain the rate of change and/or initial value of an exponential pattern given any representation. A-SSE.1, F-IF.8b, F-LE.5 c. I can determine a reasonable domain and range for an exponential function given a contextual situation and/or a graph. F-IF.5 d. Honors: I can build a function to represent a situation by combining  linear and an exponential function.F-BF.1b 

    Outcome 11: I can create and solve exponential equations and inequalities. 3 days 6 days* a. I can fit an exponential function to data and use it to solve problems in context. S-ID.6c b. I can approximate solutions to exponential equations. A-CED.1 c. I can approximate solutions to exponential inequalities. A-CED.1 d. I can compare and contrast two different exponential functions represented in different ways. F-IF.9 e. Honors: I can analyze residuals to assess the fit of an exponential function.S-ID.6

    Module E: Sequences Outcome 12: I can build functions that model sequences. 4 days 8 days* a. I can recognize sequences and match them to recursively or explicitly defined functions. F-IF.3 b. I can write the explicit and recursive rule for an arithmetic sequence. F-IF.3, F-BF.1a,2 c. I can write the explicit and recursive rule for an exponential sequence. F-IF.3, F-BF.1a,2 d. I can identify and justify the most appropriate model (linear or exponential) for a given context. F-LE.1, F-BF.2 e. Honors: I can write the recursive rule for a shifted arithmetic/geometric sequence. SMP 8

    Module F: Geometry
    Outcome 13: I can use coordinates to solve geometric problems involving line segments.
    2 days 4 days* a. I can use coordinates to find the midpoint or endpoint of a line segment. G-GPE.6 b. I can use distance in the coordinate plane to find the perimeter of polygons. G-GPE.4 c. I can use distance in the coordinate plane to find the area of triangles and rectangles. G-GPE.4 d. Honors: I can describe the connection between the Pythagorean Theorem and the distance formula.SMP 3
    Outcome 14: I can use coordinates and slope criteria to solve problems. 3 days 6 days*

    a. I can write the equation of a line that is parallel to a given line (given two points, equation, or a graph). G-GPE.5 b. I can write the equation of a line that is perpendicular to a given line (given two points,  equation, or a graph). G-GPE.5 c. I can use coordinates to find distance and slope to identify types of triangles or quadrilaterals. G-GPE.4, G-GPE.5 d. Honors: I can explore properties of parallelograms using midpoint, distance, and slope.G-GPE

    Module G: Quadratic Functions Outcome 15: I can build and interpret quadratic models. 7 days 14 days * a. I can create and graph a quadratic function to model a given context (projectile motion, area, and/or profit). A -SSE.1 a, b, A -CED.2, F BF.1 b b. I can identify and interpret key features of a quadratic model. F -IF.5,7 c. I can determine a reasonable domain and range for a quadratic function given a contextual situation and/or a graph. F-IF.5 d. I can add and subtract quadratic expressions. A-APR.1,F-BF.1 e. I can multiply two linear expressions.A-APR.1,F-BF.1 f. Honors: I can determine the b value of a quadratic function given a, c and a point on the graph.A-CED.1

    Outcome 16: I can analyze quadratic models. 8 days 16 days* a. I can factor ๐‘Ž๐‘ฅ2 + ๐‘๐‘ฅ + ๐‘ when a = 1. A-SSE.3 b. I can factor ๐‘Ž๐‘ฅ2 + ๐‘๐‘ฅ + ๐‘ when a≠ 1 or 0. A-SSE.3 c. I can rewrite a quadratic expression to identify key features and sketch its graph. F-IF.7, 8a, 

    A-APR.3 d. I can compare the key features of two quadratic functions represented in different ways.F-IF.9 e. I can compare the end behaviors of linear, exponential and quadratic functions. F-LE.3 f. Honors: I can factor special quadratics (differences of squares & perfect square trinomials) and connect the expressions to their geometric representation. SMP 2

    Outcome 17: I can solve quadratic equations. 5 days 10 days* a. I can solve a quadratic equation using tables and/or graphs and interpret the solution(s) in context. A-CED.1 b. I can solve a quadratic equation by factoring.A-APR.3,A-REI.4 c. I can solve a quadratic equation by taking square roots.A-REI.4 d. I can justify the steps used in the algebraic process of solving a quadratic equation.A-REI.1 e. Honors: I can use a graph to identify the number of possible real solutions to a quadratic
    equations. SMP 7