# SpringBoard Algebra 1 Correlations Crosswalk to New Louisiana Standards

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1 SpringBoard Algebra 1 Correlations Crosswalk SpringBoard Algebra 1 Correlations Crosswalk to New Louisiana Stards N: Number Quantity N: Number Quantity N: Number Quantity N: Number Quantity Domain Cluster Louisiana Student Stards New Louisiana Student Stards RN: The Real Number System A: Algebra SSE: Seeing Structure in A: Algebra SSE: Seeing Structure in B. Use properties of rational irrational numbers. Q: Quantities A. Reason quantitatively use units to solve problems. Q: Quantities A. Reason quantitatively use units to solve problems. Q: Quantities A. Reason quantitatively use units to solve problems. A. Interpret the structure of expressions. A. Interpret the structure of expressions. 3. Explain why the sum or product of two rational numbers are rational; that the sum of a rational number an irrational number is irrational; that the product of a nonzero rational number an irrational number is irrational. 1. Use units as a way to underst problems to guide the solution of multi-step problems; choose interpret units consistently in formulas; choose interpret the scale the origin in graphs data displays. 2. Define appropriate quantities for the purpose of descriptive modeling. 3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. 1. Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, coefficients. 1. Interpret expressions that represent a quantity in terms of its context. b. 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 a factor not depending on P. 3. Explain why the sum or product of two rational numbers are rational; that the sum of a rational number an irrational number is irrational; that the product of a nonzero rational number an irrational number is irrational. 1. Use units as a way to underst problems to guide the solution of multi-step problems; choose interpret units consistently in formulas; choose interpret the scale the origin in graphs data displays. 2. Define appropriate quantities for the purpose of descriptive modeling. 3. Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. 1. Interpret expressions that represent a quantity in terms of its context. a. Interpret parts of an expression, such as terms, factors, coefficients. 1. Interpret expressions that represent a quantity in terms of its context. b. 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 a factor not depending on P. SpringBoard Correlations A: Algebra SSE: Seeing Structure in A. Interpret the structure of expressions. 2. Use the structure of an expression to identify ways to 2. Use the structure of an expression to identify ways to rewrite it. For example, see x^4 y^4 as (x^2)^2 (y^2)^2, rewrite it. For example, see x^4 y^4 as (x^2)^2 thus recognizing it as a difference of squares that can be (y^2)^2, thus recognizing it as a difference of squares factored as (x^2 y^2)(x^2 + y^2). that can be factored as (x^2 y^2)(x^2 + y^2) or see (2x^2 + 8x) as (2x)(x) + (2x)(4), thus recognizing it as a polynomial whose terms are products of monomials the polynomial can be factored as 2x(x+4). p Activity 26: Factoring p Activity 27: Factoring Trinomials SpringBoard Page 1

4 SpringBoard Algebra 1 Correlations Crosswalk A: Algebra REI: C. Solve systems of Reasoning equations. Inequalities Domain Cluster Louisiana Student Stards New Louisiana Student Stards 6. Solve systems of linear equations exactly approximately (e.g., graphs), focusing on pairs of linear equations in two variables. 6. Solve systems of linear equations exactly approximately (e.g., graphs), focusing on pairs of linear equations in two variables. SpringBoard Correlations A: Algebra REI: Reasoning Inequalities A: Algebra REI: Reasoning Inequalities A: Algebra REI: Reasoning Inequalities D. Represent solve equations inequalities graphically. D. Represent solve equations inequalities graphically. D. Represent solve equations inequalities graphically. 10. Underst 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). 11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) 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 values, or find successive approximations. Include cases where f(x) /or g(x) are linear, polynomial, rational, absolute value, exponential, logarithmic functions. 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), graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. 10. Underst 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). 11. Explain why the x-coordinates of the points where the graphs of the equations y = f(x) 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 values, or find successive p approximations. Include cases where f(x) /or g(x) are Activity 17: Systems of Linear linear, polynomial, rational, piecewise linear (to include absolute value), exponential functions. p Activity 35: Systems of 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), graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes. F: IF: A. Underst the concept of a function use function notation. 1. Underst that a function from one set (called the 1. Underst that a function from one set (called the domain) to another set (called the range) assigns to each domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. element of the domain exactly one element of the range. If f is a function x is an element of its domain, then f(x) If f is a function x is an element of its domain, then denotes the output of f corresponding to the input x. The f(x) denotes the output of f corresponding to the input x. graph of f is the graph of the equation y = f(x). The graph of f is the graph of the equation y = f(x). F: IF: F: IF: A. Underst the concept of a function use function notation. A. Underst the concept of a function use function notation. 2. Use function notation, evaluate functions for inputs in their domains, interpret statements that use function notation in terms of a context. 3. Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n 1 2. Use function notation, evaluate functions for inputs in their domains, interpret statements that use function notation in terms of a context. 3. Recognize that sequences are functions whose domain is a subset of the integers. Relate arithmetic sequences to linear functions geometric sequences to exponential functions. p Activity 11: Arithmetic Sequences p Activity 21: Geometric Sequences SpringBoard Page 4

5 SpringBoard Algebra 1 Correlations Crosswalk Course Conceptual Domain Cluster Louisiana Student Stards New Louisiana Student Stards F: IF: B. Interpret functions that arise in applications in terms of the context. F: IF: F: IF: F: IF: F: IF: F: IF: B. Interpret functions that arise in applications in terms of the context. B. Interpret functions that arise in applications in terms of the context. C. Analyze functions using different representations. C. Analyze functions using different representations. C. Analyze functions using different representations. 4. For a function that models a relationship between two 4. For linear, piecewise linear (to include absolute quantities, interpret key features of graphs tables in terms of the quantities, 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 minimums; symmetries; end behavior; periodicity. 5. Relate the domain of a function to its graph, 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 would be an appropriate domain for the function. 6. Calculate 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. 7. Graph functions expressed symbolically show key features of the graph, by h in simple cases using technology for more complicated cases. a. Graph linear quadratic functions show intercepts, maxima, minima. 7. Graph functions expressed symbolically show key features of the graph, by h in simple cases using technology for more complicated cases. b. Graph square root, cube root, piecewise-defined functions, including step functions absolute value functions. value), quadratic, exponential functions that model a relationship between two quantities, interpret key features of graphs tables in terms of the quantities, 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 minimums; symmetries; end behavior. 5. Relate the domain of a function to its graph, 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 would be an appropriate domain for the function. 6. Calculate interpret the average rate of change of a linear, quadratic, piecewise linear (to include absolute value) exponential function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. 7. Graph functions expressed symbolically show key features of the graph, by h in simple cases using technology for more complicated cases. a. Graph linear quadratic functions show intercepts, maxima, minima. 7. Graph functions expressed symbolically show key features of the graph, by h in simple cases using technology for more complicated cases. b. Graph piecewise linear (to include absolute value) exponential functions. 8. Write a function defined by an expression in different 8. Write a function defined by an expression in different but equivalent forms to reveal explain different but equivalent forms to reveal explain different properties of the function. properties of the function. a. Use the process of factoring completing the square a. Use the process of factoring completing the in a quadratic function to show zeros, extreme values, square in a quadratic function to show zeros, extreme symmetry of the graph, interpret these in terms of a values, symmetry of the graph, interpret these context. in terms of a context. SpringBoard Correlations p Activity 6: Graphs of p Activity 7: Graphs of p Activity 29: Introduction to Quadratic p Activity 9: Rates of Change p Activity 14: Piecewise-Defined Linear p Activity 6: Graphs of p Activity 14: Piecewise-Defined Linear SpringBoard Page 5

8 SpringBoard Algebra 1 Correlations Crosswalk S: Statistics Domain Cluster Louisiana Student Stards New Louisiana Student Stards ID: Categorical B. Summarize, represent, interpret data on two categorical quantitative variables. 6. Represent data on two quantitative variables on a scatter plot, describe how the variables are related. a. 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 suggested by the context. Emphasize linear, quadratic, exponential models. SpringBoard Correlations 6. Represent data on two quantitative variables on a scatter plot, describe how the variables are related. a. 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 suggested by the context. p Emphasize linear quadratic models. Activity 13: From S: Statistics S: Statistics S: Statistics S: Statistics S: Statistics ID: Categorical ID: Categorical ID: Categorical ID: Categorical ID: Categorical B. Summarize, represent, interpret data on two categorical quantitative variables. B. Summarize, represent, interpret data on two categorical quantitative variables. C. Interpret linear models. C. Interpret linear models. C. Interpret linear models. 6. Represent data on two quantitative variables on a scatter plot, describe how the variables are related. b. Informally assess the fit of a function by plotting analyzing residuals. 6. Represent data on two quantitative variables on a scatter plot, describe how the variables are related. c. Fit a linear function for a scatter plot that suggests a linear association. 7. Interpret the slope (rate of change) the intercept (constant term) of a linear model in the context of the data. 8. Compute (using technology) interpret the correlation coefficient of a linear fit. 6. Represent data on two quantitative variables on a scatter plot, describe how the variables are related. b. Informally assess the fit of a function by plotting analyzing residuals. 6. Represent data on two quantitative variables on a scatter plot, describe how the variables are related. c. Fit a linear function for a scatter plot that suggests a linear association. 7. Interpret the slope (rate of change) the intercept (constant term) of a linear model in the context of the data. 8. Compute (using technology) interpret the correlation coefficient of a linear fit. 9. Distinguish between correlation causation. 9. Distinguish between correlation causation. p Activity 38: Correlation SpringBoard Page 8

9 SpringBoard Geometry Correlations Crosswalk SpringBoard Geometry Correlations Crosswalk to New Louisiana Stards Domain Cluster Louisiana Student Stards New Louisiana Student Stards SpringBoard Correlations CO: Congruence A. Experiment transformations in the plane. 1. Know precise definitions of angle, circle, perpendicular line, parallel line, line segment, based on the undefined notions of point, line, distance along a line, distance around a circular arc. 1. Know precise definitions of angle, circle, perpendicular line, parallel line, line segment, based on the undefined notions of point, line, distance along a line, distance around a circular arc. CO: Congruence A. Experiment transformations in the plane. CO: Congruence A. Experiment transformations in the plane. CO: Congruence A. Experiment transformations in the plane. CO: Congruence A. Experiment transformations in the plane. CO: Congruence B. Underst congruence in terms of rigid motions. CO: Congruence B. Underst congruence in terms of rigid motions. CO: Congruence B. Underst congruence in terms of rigid motions. CO: Congruence C. Prove geometric theorems. CO: Congruence C. Prove geometric theorems. 2. Represent transformations in the plane using, e.g., transparencies geometry software; describe transformations as functions that take points in the plane as inputs give other points as outputs. Compare transformations that preserve distance angle to those that do not (e.g., translation versus horizontal stretch). 3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations reflections that carry it onto itself. 4. Develop definitions of rotations, reflections, translations in terms of angles, circles, perpendicular lines, parallel lines, line segments. 5. Given a geometric figure a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. 6. Use geometric descriptions of rigid motions to transform figures 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. 7. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if only if corresponding pairs of sides corresponding pairs of angles are congruent. 8. Explain how the criteria for triangle congruence (ASA, SAS, SSS) follow from the definition of congruence in terms of rigid motions. 9. Prove theorems about lines angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment s endpoints. 10. Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 ; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side half the length; the medians of a triangle meet at a point. 2. Represent transformations in the plane using, e.g., transparencies, tracing paper or geometry software; describe transformations as functions that take points in the plane as inputs give other points as outputs. Compare transformations that preserve distance angle to those that do not (e.g., translation versus horizontal stretch). 3. Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations reflections that carry it onto itself. 4. Develop definitions of rotations, reflections, translations in terms of angles, circles, perpendicular lines, parallel lines, line segments. 5. Given a geometric figure a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. 6. Use geometric descriptions of rigid motions to transform figures 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. 7. Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if only if corresponding pairs of sides corresponding pairs of angles are congruent. 8. Explain how the criteria for triangle congruence (ASA, SAS, SSS) follow from the definition of congruence in terms of rigid motions. 9. Prove apply theorems about lines angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment s endpoints. 10. Prove apply theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180 ; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side half the length; the medians of a triangle meet at a point. p Activity 9: Translations, Reflections, Rotations p Activity 6: Proofs about Line Segments Angles p Activity 7: Parallel Perpendicular Lines p Activity 13: Properties of Triangles p Activity 14: Concurrent Segments in Triangles SpringBoard Geometry Page 9

10 SpringBoard Geometry Correlations Crosswalk Domain Cluster Louisiana Student Stards New Louisiana Student Stards SpringBoard Correlations CO: Congruence C. Prove geometric theorems. 11. Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, conversely, rectangles are parallelograms congruent diagonals. 11. Prove apply theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, conversely, rectangles are parallelograms congruent diagonals. p Activity 15: Quadrilaterals Their Properties p Activity 16: More About Quadrilaterals CO: Congruence D. Make geometric constructions. CO: Congruence D. Make geometric constructions. SRT: Similarity, A. Underst Right Triangles, similarity in terms of Trigonometry similarity transformations. 12. Make formal geometric constructions a variety of tools methods (compass straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; constructing a line parallel to a given line through a point not on the line 13. Construct an equilateral triangle, a square, a regular hexagon inscribed in a circle. 1. Verify experimentally the properties of dilations given by a center a scale factor: a. A dilation takes a line not passing through the center of the dilation to a parallel line, leaves a line passing through the center unchanged. 12. Make formal geometric constructions a variety of tools methods e.g. compass straightedge, string, reflective devices, paper folding or dynamic geometric software. Examples: Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; constructing a line parallel to a given line through a point not on the line. 13. Construct an equilateral triangle, a square, a regular hexagon inscribed in a circle. 1. Verify experimentally the properties of dilations given by a center a scale factor: a. A dilation takes a line not passing through the center of the dilation to a parallel line, leaves a line passing through the center unchanged. p Activity 29: Constructions SRT: Similarity, A. Underst Right Triangles, similarity in terms of Trigonometry similarity transformations. 1. Verify experimentally the properties of dilations given by a center a scale factor: b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. 1. Verify experimentally the properties of dilations given by a center a scale factor: b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor. SRT: Similarity, A. Underst Right Triangles, similarity in terms of Trigonometry similarity transformations. SRT: Similarity, A. Underst Right Triangles, similarity in terms of Trigonometry similarity transformations. SRT: Similarity, B. Prove theorems Right Triangles, involving similarity. Trigonometry SRT: Similarity, B. Prove theorems Right Triangles, involving similarity. Trigonometry 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 the proportionality of all corresponding pairs of sides. 3. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. 4. Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, conversely; the Pythagorean Theorem proved using triangle similarity. 5. Use congruence similarity criteria for triangles to solve problems to prove relationships in geometric figures. 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 the proportionality of all corresponding pairs of sides. 3. Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. 4. Prove apply theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, conversely; the Pythagorean Theorem proved using triangle similarity; SAS similarity criteria; SSS similarity criteria; ASA similarity. 5. Use congruence similarity criteria for triangles to solve problems to prove relationships in geometric figures. p Activity 18: Similar Triangles p Activity 20: The Pythagorean Theorem Its Converse SRT: Similarity, Right Triangles, Trigonometry C. Define trigonometric ratios solve problems involving right triangles. 6. Underst that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. 6. Underst that by similarity, side ratios in right triangles, including special right triangles ( ), are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. p Activity 21: Special Right Triangles p Activity 22: Basic Trigonometric Relationships SpringBoard Geometry Page 10

12 SpringBoard Geometry Correlations Crosswalk I SP: Statisitcs I SP: Statisitcs I SP: Statisitcs I SP: Statisitcs I SP: Statisitcs I SP: Statisitcs Domain Cluster Louisiana Student Stards New Louisiana Student Stards SpringBoard Correlations GMD: Geometric Measurement Dimension GMD: Geometric Measurement Dimension MG: Modeling Geometry MG: Modeling Geometry MG: Modeling Geometry CP: Conditional CP: Conditional CP: Conditional CP: Conditional CP: Conditional CP: Conditional A. Explain volume formulas use them to solve problems. B. Visualize relationships between two-dimensional three-dimensional A. Apply geometric concepts in modeling situations. A. Apply geometric concepts in modeling situations. A. Apply geometric concepts in modeling situations. A. Underst independence conditional probability use them to interpret data. A. Underst independence conditional probability use them to interpret data. A. Underst independence conditional probability use them to interpret data. A. Underst independence conditional probability use them to interpret data. A. Underst independence conditional probability use them to interpret data. B. Use the rules of probability to compute probabilities of compound events in a uniform probability model. 3. Use volume formulas for cylinders, pyramids, cones, spheres to solve problems. 4. Identify the shapes of two-dimensional cross-sections of threedimensional objects, identify three-dimensional objects generated by rotations of two-dimensional objects. 1. Use geometric shapes, their measures, their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). 2. Apply concepts of density based on area volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). 3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working typographic grid systems based on ratios). 1. Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ( or,, not ). 2. Underst that two events A B are independent if the probability of A B occurring together is the product of their probabilities, use this characterization to determine if they are independent. 3. Underst the conditional probability of A given B as P(A B)/P(B), interpret independence of A B as saying that the conditional probability of A given B is the same as the probability of A, the conditional probability of B given A is the same as the probability of B. 4. Construct interpret two-way frequency tables of data when two categories are associated each object being classified. Use the two-way table as a sample space to decide if events are independent to approximate conditional probabilities. For example, collect data from a rom sample of students in your school on their favorite subject among math, science, English. Estimate the probability that a romly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects compare the results. 5. Recognize explain the concepts of conditional probability independence in everyday language everyday situations. For example, compare the chance of having lung cancer if you are a smoker the chance of being a smoker if you have lung cancer. 6. Find the conditional probability of A given B as the fraction of B s outcomes that also belong to A, interpret the answer in terms of the model. 3. Use volume formulas for cylinders, pyramids, cones, spheres to solve problems. 4. Identify the shapes of two-dimensional cross-sections of threedimensional objects, identify three-dimensional objects generated by rotations of two-dimensional objects. 1. Use geometric shapes, their measures, their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). 2. Apply concepts of density based on area volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). 3. Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working typographic grid systems based on ratios). 1. Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ( or,, not ). p Underst that two events A B are independent if the probability of A B occurring together is the product of their probabilities, use this characterization to determine if they are independent. p Underst the conditional probability of A given B as P(A B)/P(B), interpret independence of A B as saying that the conditional probability of A given B is the same as the probability of A, the conditional probability of B given A is the same as the probability of B. 4. Construct interpret two-way frequency tables of data when two categories are associated each object being classified. Use the two-way table as a sample space to decide if events are independent to approximate conditional probabilities. For example, collect data from a rom sample of students in your school on their favorite subject among math, science, English. Estimate the probability that a romly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects compare the results. 5. Recognize explain the concepts of conditional probability independence in everyday language everyday situations. For example, compare the chance of having lung cancer if you are a smoker the chance of being a smoker if you have lung cancer. p Find the conditional probability of A given B as the fraction of B s outcomes that also belong to A, interpret the answer in terms of the model. Activity 38: Sample Space Activity 42: Independent Events p Activity 41: Dependent Events p Activity 38: Sample Space Activity 41: Dependent Events p Activity 41: Dependent Events SpringBoard Geometry Page 12

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