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IN.AI.ALGEBRA I
ALGEBRA I
AI.DS. DATA ANALYSIS AND STATISTICS
AI.DS.1. Distinguish between random and non-random sampling methods, identify possible sources of bias in sampling, describe how such bias can be controlled and reduced, evaluate the characteristics of a good survey and well-designed experiment, design simple expe
AI.F.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. Understand that if f is a function and x is an element of its domain, then f(x) denotes t
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
AI.F.2. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear, has a maximum or minimum value). Sketch a graph that exhibits the qualitative featur
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
AI.L. LINEAR EQUATIONS, INEQUALITIES, AND FUNCTIONS
AI.L.1. Understand that the steps taken when solving linear equations create new equations that have the same solution as the original. Solve fluently linear equations and inequalities in one variable with integers, fractions, and decimals as coefficients. Explai
AI.L.4. Represent linear functions as graphs from equations (with and without technology), equations from graphs, and equations from tables and other given information (e.g., from a given point on a line and the slope of the line).
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
AI.L.6. Translate among equivalent forms of equations for linear functions, including slope-intercept, point-slope, and standard. Recognize that different forms reveal more or less information about a given situation.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
AI.QE. QUADRATIC AND EXPONENTIAL EQUATIONS AND FUNCTIONS
AI.QE.1. Distinguish between situations that can be modeled with linear functions and with exponential functions. Understand that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal inter
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
AI.QE.2. Represent real-world and other mathematical problems that can be modeled with exponential functions using tables, graphs, and equations of the form y = ab^x (for integer values of x > 1, rational values of b > 0 and b ≠ 1); translate fluently among
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
AI.RNE. REAL NUMBERS AND EXPRESSIONS
AI.RNE.1. Understand the hierarchy and relationships of numbers and sets of numbers within the real number system.
AI.RNE.2. 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.
AI.RNE.7. Understand polynomials are closed under the operations of addition, subtraction, and multiplication with integers; add, subtract, and multiply polynomials and divide polynomials by monomials.
AI.SEI.1. Understand the relationship between a solution of a pair of linear equations in two variables and the graphs of the corresponding lines. Solve pairs of linear equations in two variables by graphing; approximate solutions when the coordinates of the soluti
AI.SEI.2. Understand 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. Solve pairs of linear equations in two variables using substitutio
AII.DSP. DATA ANALYSIS, STATISTICS, AND PROBABILITY
AII.DSP.1. Make inferences and justify conclusions from sample surveys, experiments, and observational studies. Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.
AII.DSP.3. Organize, graph (e.g., line plots and box plots), and compare univariate data of two or more different data sets using measures of center (mean and median) and spread (range, inter-quartile range, standard deviation, percentiles, and variance). Understand
Quiz, Flash Cards, Worksheet, Game & Study GuideDisplaying data
AII.DSP.4. Record multiple observations (or simulated samples) of random events and construct empirical models of the probability distributions. Construct a theoretical model and apply the law of large numbers to show the relationship between the two models.
AII.EL. EXPONENTIAL AND LOGARITHMIC EQUATIONS AND FUNCTIONS
AII.EL.4. Use the properties of exponents to transform expressions for exponential functions (e.g., the expression 1.15^t can be rewritten as (1.15^1/12)^12t ≈ 1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%).
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
AII.F. FUNCTIONS
AII.F.1. Determine whether a relation represented by a table, graph, or equation is a function.
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
AII.PR. POLYNOMIAL, RATIONAL, AND OTHER EQUATIONS AND FUNCTIONS
AII.PR.3. Solve real-world and other mathematical problems involving rational and radical equations, including direct, inverse, and joint variation. Give examples showing how extraneous solutions may arise.
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
FM.P.3. Understand and use the multiplication rule to calculate probabilities for independent and dependent events. 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
FM.P.4. Understand the multiplication counting principle, permutations, and combinations; use them to solve real-world problems. Use simulations with and without technology to solve counting and probability problems.
G.CI.4. Solve real-world and other mathematical problems that involve finding measures of circumference, areas of circles and sectors, and arc lengths and related angles (central, inscribed, and intersections of secants and tangents).
G.LP.2. Know precise definitions for angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, and plane. Use standard geometric notation.
Quiz, Flash Cards, Worksheet, Game & Study GuidePlane figures
G.PL.3. Prove and apply theorems about lines and angles, including the following: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent, alternate exterior angles are congruent, and corresponding angles
G.PL.4. Know that parallel lines have the same slope and perpendicular lines have opposite reciprocal slopes. Determine if a pair of lines are parallel, perpendicular, or neither by comparing the slopes in coordinate graphs and in equations. Find the equation of
Quiz, Flash Cards, Worksheet, Game & Study GuidePlane figures
G.QP. QUADRILATERALS AND OTHER POLYGONS
G.QP.4. Identify types of symmetry of polygons, including line, point, rotational, and self-congruencies.
G.T.4. Given two triangles, 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 angl
G.T.5. Use properties of congruent and similar triangles to solve real-world and mathematical problems involving sides, perimeters, and areas of triangles.
G.T.8. Develop the distance formula using the Pythagorean Theorem. Find the lengths and midpoints of line segments in one- or two-dimensional coordinate systems. Find measures of the sides of polygons in the coordinate plane; apply this technique to compute the
Quiz, Flash Cards, Worksheet, Game & Study GuidePlane figures
G.TR. TRANSFORMATIONS
G.TR.1. Use geometric descriptions of rigid motions to transform figures and to predict and describe the results of translations, reflections and rotations on a given figure. Describe a motion or series of motions that will show two shapes are congruent.
G.TR.2. Understand 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. Verify experimentally the properties of dilations given by a center and a scale factor. Understan
G.TS.1. Describe relationships between the faces, edges, and vertices of three-dimensional solids. Create a net for a given three-dimensional solid. Describe the three-dimensional solid that can be made from a given net (or pattern).
G.TS.3. Know properties of congruent and similar solids, including prisms, regular pyramids, cylinders, cones, and spheres; solve problems involving congruent and similar solids.
G.TS.5. Solve real-world and other mathematical problems involving volume and surface area of prisms, cylinders, cones, spheres, and pyramids, including problems that involve algebraic expressions.
G.TS.6. 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).
MA10.DASP. Data Analysis, Statistics, and Probability
MA10.DASP.1. Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantitative variables. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonli
MA10.DASP.3. For events with a large number of outcomes, understand the use of the multiplication counting principle. Develop the multiplication counting principle and apply it to situations with a large number of outcomes.
MA10.DASP.4. Distinguish between random and non-random sampling methods, identify possible sources of bias in sampling, describe how such bias can be controlled and reduced, evaluate the characteristics of a good survey and well-designed experiment, design simple expe
MA10.EI.1. Solve linear equations with rational number coefficients fluently, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Represent real-world problems using linear equations and inequa
MA10.EI.2. Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by transforming a given equation into simpler forms, until an equivalent equation of the form x
MA10.F.1. Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. Describe similarities and differences between linear and nonlinear functions from tables, graphs, verbal descr
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
MA10.F.2. Construct a function to model a linear relationship between two quantities given a verbal description, table of values, or graph. Recognize in y = mx + b that m is the slope (rate of change) and b is the y-intercept of the graph, and describe the meaning
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
MA10.F.3. Represent linear functions as graphs from equations (with and without technology), equations from graphs, and equations from tables and other given information (e.g., from a given point on a line and the slope of the line).
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
MA10.F.5. Translate among equivalent forms of equations for linear functions, including slope-intercept, point-slope, and standard. Recognize that different forms reveal more or less information about a given situation.
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
MA10.F.7. Understand that a function from one set (called the domain or independent variable) to another set (called the range or dependent variable) assigns to each element of the domain exactly one element of the range. Understand that if f is a function and x is
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
MA10.F.9. Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear, has a maximum or minimum value). Sketch a graph that exhibits the qualitative featur
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
MA10.GM. Geometry and Measurement
MA10.GM.1. Identify, define and describe attributes of three-dimensional geometric objects (right rectangular prisms, cylinders, cones, spheres, and pyramids). Explore the effects of slicing these objects using appropriate technology and describe the two-dimensional
MA10.NSEC. Number Sense, Expressions, and Computation
MA10.NSEC.1. Give examples of rational and irrational numbers and explain the difference between them. Understand that every number has a decimal expansion; for rational numbers, show that the decimal expansion terminates or repeats, and convert a decimal expansion th
MA10.NSEC.10. Understand polynomials are closed under the operations of addition, subtraction, and multiplication with integers; add, subtract, and multiply polynomials and divide polynomials by monomials.
MA10.NSEC.3. Given a numeric expression with common rational number bases and integer exponents, apply the properties of exponents to generate equivalent expressions.
MA10.NSEC.7. 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.
MA10.QEEF. Quadratic and Exponential Equations and Functions
MA10.QEEF.1. Distinguish between situations that can be modeled with linear functions and with exponential functions. Understand that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal inter
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
Quiz, Flash Cards, Worksheet, Game & Study GuideLinear equations
MA10.QEEF.6. Represent real-world and other mathematical problems that can be modeled with exponential functions using tables, graphs, and equations of the form y = ab^x (for integer values of x > 1, rational values of b > 0 and b ≠ 1 ); translate fluently among
Quiz, Flash Cards, Worksheet, Game & Study GuideFunctions
MA10.SEI. Systems of Equations and Inequalities
MA10.SEI.1. Understand the relationship between a solution of a pair of linear equations in two variables and the graphs of the corresponding lines. Solve pairs of linear equations in two variables by graphing; approximate solutions when the coordinates of the soluti
MA10.SEI.2. Understand 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. Solve pairs of linear equations in two variables using substitutio
Quiz, Flash Cards, Worksheet, Game & Study GuideSequences
IN.PS.PROBABILITY AND STATISTICS
PROBABILITY AND STATISTICS
PS.DA. DATA ANALYSIS
PS.DA.1. Create, compare, and evaluate different graphic displays of the same data, using histograms, frequency polygons, cumulative frequency distribution functions, pie charts, scatterplots, stem-and-leaf plots, and box-and-whisker plots. Draw these with and wit
PS.DA.2. Compute and use mean, median, mode, weighted mean, geometric mean, harmonic mean, range, quartiles, variance, and standard deviation. Use tables and technology to estimate areas under the normal curve. Fit a data set to a normal distribution and estimate
Quiz, Flash Cards, Worksheet, Game & Study GuideSequences
PS.ED.7. Understand and apply basic ideas related to the design, analysis, and interpretation of surveys and sampling, such as background information, random sampling, causality and bias.
PS.P.11. Understand the multiplication counting principle, permutations, and combinations; use them to solve real-world problems. Use simulations with and without technology to solve counting and probability problems.
PS.P.2. Understand and use the multiplication rule to calculate probabilities for independent and dependent events. 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
PS.P.3. Understand the multiplication counting principle, permutations, and combinations; use them to solve real-world problems. Use simulations with and without technology to solve counting and probability problems.
QR.M.4. Analyze real-world problem situations and use variables to construct and solve equations involving one or more unknown or variable quantities to answer questions about the situations, such as creating spreadsheet formulas to calculate prices based on perc
QR.N.1. Represent quantities in equivalent forms (fractions, decimals, and percentages) to investigate and describe quantitative relationships and solve real-world problems in a variety of contexts. Compare the size of numbers in different forms arising in authen
QR.N.2. Solve problems involving calculations with percentages and interpret the results, such as calculating percentage rates or differentiating between a discount of 30% and two consecutive discounts of 15%. Calculate relative change and explain how it differs
QR.N.3. Interpret numbers in different forms in terms of authentic contexts to solve real-world problems, such as interpreting a growth rate less than 1%. Compare and precisely communicate with numbers in different forms (including words, fractions, decimals, sta
QR.N.5. Perform accurate and efficient calculations using large and small numbers in different forms, to an appropriate precision, with and without technology. Include calculations in context, such as ratios representing water use per capita for a large populatio
QR.P.1. Determine the nature and number of elements in a finite sample space to model the outcomes of real-world events using counting techniques, and build the sample space by making lists, tables, or tree diagrams.
QR.P.3. Evaluate the validity of claims based on empirical, theoretical, and subjective probabilities. Draw conclusions or make decisions related to risk, pay-off, expected value, and false negatives/positives in various probabilistic contexts.
QR.P.4. Use data displays and models, such as two-way tables, tree diagrams, Venn diagrams, and area models, to determine probabilities (including conditional probabilities) and use these probabilities to make informed decisions.
QR.RP.2. Understand and communicate percentages as rates per 100, and identify uses and misuses of percentages related to a proper understanding of the base in real-world and mathematical problems.
QR.RP.3. Solve real-life problems requiring interpretation and comparison of various representations of ratios, (i.e. fractions, decimals, rate, and percentages), such as problems that involve non-standard ratios (e.g., media and risk reporting) or part-to-part ve
QR.RP.5. Distinguish between proportional and non-proportional situations, and, when appropriate, apply proportional reasoning, such as when solving for an unknown quantity in proportional situations; solving real-life problems requiring conversion of units using
QR.RP.6. Determine the constant of proportionality in proportional situations (both real-life and mathematical), leading to a symbolic model for the situation (i.e. an equation based upon a rate of change, y = kx).
QR.S.2. Identify limitations, strengths, or lack of information in studies, including data collection methods (e.g. sampling, experimental, observational) and possible sources of bias, and identify errors or misuses of statistics to justify particular conclusions
QR.S.5. Read, interpret, and make decisions about data summarized numerically using measures of center and spread, in tables, and in graphical displays (line graphs, bar graphs, scatterplots, and histograms), e.g., explain why the mean may not represent a typical
QR.S.6. Summarize, represent, and interpret data sets on a single count or measurement variable using plots and statistics appropriate to the shape of the data distribution to represent it.
TR.CO.6. 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.