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MD.MA.AI.Algebra I
Algebra I
Unit 1: Relationships between Quantities and Reasoning with Equations
HSA-CED.A. Create equations that describe numbers or relationships.
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.2.3. Ability to determine unknown parameters needed to create an equation that accurately models a given situation.
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.
A.CED.4.1. Ability to recognize/create equivalent forms of literal equations.
HSA-SSE.A. Interpret the structure of expressions.
A.SSE.1a. Interpret expressions that represent a quantity in terms of its context – Interpret parts of an expression, such as terms, factors, and coefficients.
A.SSE.1a.1. Ability to make connections between symbolic representations and proper mathematics vocabulary.
A.SSE.1b. Interpret expressions that represent a quantity in terms of its context – 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.
A.SSE.1b.1. Ability to interpret and apply rules for order of operations.
HSA-APR.A. Perform arithmetic operations on polynomials.
A.APR.1. Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
A.APR.1.1. Ability to show that when polynomials are added, subtracted or multiplied that the result is another polynomial.
HSA-CED.A. Create equations that describe numbers or relationships.
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.2.3. Ability to determine unknown parameters needed to create an equation that accurately models a given situation.
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.
A.CED.4.2. Ability to recognize and create different forms of literal equations.
HSA-REI.B. Solve equations and inequalities in one variable.
A.REI.4a. Solve quadratic equations in one variable – Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x–p)^2 = q that has the same solutions. Derive the quadratic formula from this form.
A.REI.4a.1. Ability to solve literal equations for a variable of interest.
HSA-SSE.B. Write expressions in equivalent forms to solve problems.
A.SSE.3a. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression – Factor a quadratic expression to reveal the zeros of the function it defines.
A.SSE.3a.1. Ability to connect the factors, zeros and x-intercepts of a graph.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
A.SSE.3a.2. Ability to connect the factors, zeros and x-intercepts of a graph.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
A.SSE.3c. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression – Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^t
A.SSE.3c.1. Ability to connect experience with properties of exponents from Unit 2 of this course to more complex expressions.
HSN-RN.B. Use properties of rational and irrational Numbers.
N.RN.3. Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
N.RN.3.1. Ability to perform operations on both rational and irrational numbers.
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.5.1. Ability to use various methods for solving systems of equations algebraically.
HSA-REI.D. Represent and solve equations and inequalities graphically.
A.REI.11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of va
A.REI.11.2. Ability to show the equality of two functions using multiple representations.
A.REI.12. Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the correspondin
A.REI.12.1. Ability to explain why a particular shaded region represents the solution of a given linear inequality or system of linear inequalities.
HSF-IF.A. Understand the concept of a function and use function notation.
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 c
F.IF.1.1. Ability to determine if a relation is a function.
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
HSF-IF.B. Interpret functions that arise in applications in terms of a context.
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.6.1. Knowledge that the rate of change of a function can be positive, negative or zero.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
F.IF.6.3. Ability to identify the rate of change from multiple representations.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
HSF-IF.C. 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.
F.IF.7a.1. See the skills and knowledge that are stated in the Standard.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
HSF-LE.A. Construct and compare linear, quadratic, and exponential models and solve 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.1a.1. See the skills and knowledge that are stated in the Standard.
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
HSF-LE.B. Interpret expressions for functions in terms of the situation they model.
F.LE.5. Interpret the parameters in a linear or exponential function in terms of a context.
F.LE.5.1. Ability to interpret the slope and y-intercept of a linear model in terms of context.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
Unit 5: Quadratic Functions and Modeling
HSF-IF.B. Interpret functions that arise in applications 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: intercep
F.IF.4.2. Ability to connect experiences with linear and exponential functions from Unit 2 of this course to quadratic, square root, cube root, absolute value, step and piecewise defined models.
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
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 w
F.IF.5.3. Ability to connect experiences with linear and exponential functions from Unit 2 of this course to quadratic, square root, cube root, absolute value, step and piecewise defined models.
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
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.6.2. Knowledge that the rate of change of a function can be positive, negative, zero or can have no change.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
F.IF.6.3. Ability to identify the rate of change from multiple representations.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
Unit 3: Descriptive Statistics
HSS-ID.A. Summarize, represent, and interpret data on a single count or measurement variable.
S.ID.1. Represent data with plots on the real number line (dot plots, histograms, and box plots).
S.ID.1.1. Ability to determine the best data representation to use for a given situation.
S.ID.2. Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
S.ID.2.1. Ability to interpret measures of center and spread (variability) as they relate to several data sets.
S.ID.3. Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
S.ID.3.1. Ability to recognize gaps, clusters, and trends in the data set.
HSS-ID.B. Summarize, represent, and interpret data on two categorical and quantitative variables.
S.ID.5. Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
S.ID.5.2. Ability to read and use a two-way frequency table.
S.ID.6a. Represent data on two quantitative variables on a scatter-plot, and describe how the variables are related – Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function su
S.ID.6a.1. Ability to recognize types of relationships that lend themselves to linear and exponential models.
S.ID.6b. Represent data on two quantitative variables on a scatter-plot, and describe how the variables are related – Informally assess the fit of a function by plotting and analyzing residuals.
S.ID.6b.1. Ability to create a graphic display of residuals.
S.ID.6c. Represent data on two quantitative variables on a scatter-plot, and describe how the variables are related – Fit a linear function for a scatter plot that suggests a linear association.
S.ID.6c.1. Ability to recognize a linear relationship displayed in a scatter plot.
HSA-REI.D. Represent and solve equations and inequalities graphically.
A.REI.11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of va
A.REI.11.2. Ability to show the equality of two functions using multiple representations.
HSA-SSE.B. Write expressions in equivalent forms to solve problems.
A.SSE.3c. Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression – Use the properties of exponents to transform expressions for exponential functions. For example, the expression 1.15^t
A.SSE.3c.2. Ability to connect experience with properties of exponents from Unit 4 of Algebra I to more complex expressions
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
HSF-IF.C. Analyze functions using different representations.
F.IF.7c. Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases – Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end
F.IF.7c.2. Ability to identify key features of a function: max, min, intercepts, zeros, and end behaviors.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
HSG-GPE.A. Translate between the geometric description and the equation for a conic section.
G.GPE.2. Derive the equation of a parabola given a focus and directrix.
G.GPE.2.2. Ability to connect the algebraic and geometric definitions of a parabola.
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
Unit 4: Inferences and Conclusions from Data
HSS-IC.A. Understand and evaluate random processes underlying statistical experiments.
S.IC.1. Understand statistics as a process for making inferences about population parameters based on a random sample from that population.
S.IC.1.1. Knowledge of various sampling methods (e.g., simple random, convenience, stratified…).
S.IC.2. Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question th
S.IC.2.1. Ability to calculate and analyze theoretical and experimental probabilities accurately.
HSS-IC.B. Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
S.IC.3. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
S.IC.3.1. Ability to conduct sample surveys, experiments and observational studies.
HSS-ID.B. Summarize, represent, and interpret data on two categorical and quantitative variables.
S.ID.6a. Represent data on two quantitative variables on a scatter-plot, and describe how the variables are related – Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function su
S.ID.6a.1. Ability to recognize types of relationships that lend themselves to linear and exponential models.
HSS-CP.A. Understand independence and conditional probability and use them to interpret data.
S.CP.2. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
S.CP.2.3. Ability to determine if two events are dependent or independent.
HSS-MD.A. Use probability to evaluate outcomes of decisions.
S.MD.7. (+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).
S.MD.7.2. Knowledge of and ability to use a variety of data collection techniques.
HSF-BF.A. Build a function that models a relationship between two quantities.
F.BF.1a. Write a function that describes a relationship between two quantities – Determine an explicit expression, a recursive process, or steps for calculation from a context.
F.BF.1a.1. Ability to connect experience with linear and exponential functions from Algebra I Unit 2 to quadratic functions.
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
HSF-IF.B. Interpret functions that arise in applications 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: intercep
F.IF.4.4. Knowledge of the key features of linear, exponential, polynomial, root, absolute value, piece-wise, simple rational, logarithmic and trigonometric functions.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
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.6.4. Ability to apply this skill to linear, quadratic, polynomial, root and simple rational functions.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
HSF-IF.C. Analyze functions using different representations.
F.IF.8. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
F.IF.8.1. Ability to connect experience with writing linear, quadratic and exponential functions in various forms from Algebra I to writing all functions in various forms.
F.IF.8b. Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function – Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate
F.IF.8b.1. Ability to connect experience with properties of exponents from Algebra I Unit 2: Linear and Exponential Relationships to more complex expressions.
HSF-LE.B. Interpret expressions for functions in terms of the situation they model.
F.LE.5. Interpret the parameters in a linear or exponential function in terms of a context.
F.LE.5.1. Ability to interpret the slope and y-intercept of a linear model in terms of context.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
F.LE.5.2. Ability to identify the initial amount present in an exponential model (f(0) = b^0+k = 1+k).
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
F.LE.5.3. Ability to interpret the rate of increase/decrease in an exponential model.
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
MD.MA.G.Geometry
Geometry
Unit 1: Congruence, Proof, and Constructions
HSG-CO.A. Experiment with transformations in the plane.
G.CO.1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
G.CO.1.1. Ability to use mathematical vocabulary accurately.
G.CO.2. Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and an
G.CO.2.1. Ability to see parallels between function transformations (F.BF.3) and geometric transformations.
G.CO.3.2. Ability to use the characteristics of a figure to determine and then describe what happens to the figure as it is rotated (such as axis of symmetry, congruent angles or sides…).
G.CO.4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
G.CO.4.1. Ability to construct a definition for each term based upon a synthesis of experiences.
HSG-CO.B. Understand congruence in terms of rigid motions.
G.CO.6. Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
G.CO.6.1. Ability to recognize the effects of rigid motion on orientation and location of a figure.
G.CO.7. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
G.CO.7.1. Knowledge of vocabulary corresponding parts and the connection to the given triangles.
Unit 4: Connecting Algebra and Geometry Through Coordinates
HSG-GPE.B. Use coordinates to prove simple geometric theorems algebraically.
G.GPE.4. Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle.
G.GPE.4.1. Ability to use distance, slope and midpoint formulas…
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
G.GPE.6. Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
G.GPE.6.1. Ability to use the slope formula.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
Unit 2: Similarity, Proof, and Trigonometry
HSG-MG.A. Apply geometric concepts in modeling situations.
G.MG.1. Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).
G.MG.1.1. See the skills and knowledge that are stated in the Standard.
G.MG.3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
G.MG.3.1. See the skills and knowledge that are stated in the Standard.
HSG-SRT.A. Understand similarity in terms of similarity transformations.
G.SRT.1a. Verify experimentally the properties of dilations given by a center and a scale factor – A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
G.SRT.1a.1. Ability to connect experiences with dilations and orientation to experiences with lines.
G.SRT.1b. Verify experimentally the properties of dilations given by a center and a scale factor – The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
G.SRT.1b.1. Ability to develop a hypothesis based on observations.
G.SRT.2. Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles
G.SRT.2.1. Ability to make connections between the definition of similarity and the attributes of two given figures.
HSG-GMD.A. Explain volume formulas and use them to solve problems.
G.GMD.1. Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments.
G.GMD.1.1. See the skills and knowledge that are stated in the Standard.