AASL/Common Core State Standards Crosswalk
Common Core State Standards Mathematics:
7.NS.3 » Mathematics » The Number System » Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. » 3. Solve real-world and mathematical problems involving the four operations with rational numbers. (7)
Mathematics » High School - Functions » Linear, Quadratic, and Exponential Models » Construct and compare linear, quadratic, and exponential models and solve problems (9,10,11,12)
8.NS.1 » Mathematics » The Number System » Know that there are numbers that are not rational, and approximate them by rational numbers. » 1. Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. (8)
7.SP.8.b » Mathematics » Statistics and Probability » Investigate chance processes and develop, use, and evaluate probability models. » 8. Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation. » b. Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event. (7)
7.RP.1 » Mathematics » Ratios and Proportional Relationships » Analyze proportional relationships and use them to solve real-world and mathematical problems. » 1. Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. (7)
S-IC.6 » Mathematics » High School - Statistics and Probability » Making Inferences and Justifying Conclusions » Make inferences and justify conclusions from sample surveys, experiments, and observational studies » 6. Evaluate reports based on data. (9,10,11,12)
8.SP.2 » Mathematics » Statistics and Probability » Investigate patterns of association in bivariate data. » 2. Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. (8)
8.F.3 » Mathematics » Functions » Define, evaluate, and compare functions. » 3. 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. (8)
8.F.2 » Mathematics » Functions » Define, evaluate, and compare functions. » 2. Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (8)
7.RP.3 » Mathematics » Ratios and Proportional Relationships » Analyze proportional relationships and use them to solve real-world and mathematical problems. » 3. Use proportional relationships to solve multistep ratio and percent problems. (7)
S-MD.6 » Mathematics » High School - Statistics and Probability » Using Probability to Make Decisions » Use probability to evaluate outcomes of decisions » 6. (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). (9,10,11,12)
S-MD.5.b » Mathematics » High School - Statistics and Probability » Using Probability to Make Decisions » Use probability to evaluate outcomes of decisions » 5. (+) Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.|b. Evaluate and compare strategies on the basis of expected values. (9,10,11,12)
S-CP.9 » Mathematics » High School - Statistics and Probability » Conditional Probability and the Rules of Probability » Use the rules of probability to compute probabilities of compound events in a uniform probability model » 9. (+) Use permutations and combinations to compute probabilities of compound events and solve problems. (9,10,11,12)
S-CP.8 » Mathematics » High School - Statistics and Probability » Conditional Probability and the Rules of Probability » Use the rules of probability to compute probabilities of compound events in a uniform probability model » 8. (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. (9,10,11,12)
S-CP.7 » Mathematics » High School - Statistics and Probability » Conditional Probability and the Rules of Probability » Use the rules of probability to compute probabilities of compound events in a uniform probability model » 7. Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model. (9,10,11,12)
S-CP.8 » Mathematics » High School - Statistics and Probability » Conditional Probability and the Rules of Probability » Use the rules of probability to compute probabilities of compound events in a uniform probability model » 6. Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model. (9,10,11,12)
S-CP.3 » Mathematics » High School - Statistics and Probability » Conditional Probability and the Rules of Probability » Understand independence and conditional probability and use them to interpret data » 3. Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. (9,10,11,12)
S-CP.2 » Mathematics » High School - Statistics and Probability » Conditional Probability and the Rules of Probability » Understand independence and conditional probability and use them to interpret data » 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. (9,10,11,12)
Mathematics » High School - Statistics and Probability » Conditional Probability and the Rules of Probability » Understand independence and conditional probability and use them to interpret data (9,10,11,12)
S-IC.5 » Mathematics » High School - Statistics and Probability » Making Inferences and Justifying Conclusions » Make inferences and justify conclusions from sample surveys, experiments, and observational studies » 5. Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. (9,10,11,12)
S-IC.4 » Mathematics » High School - Statistics and Probability » Making Inferences and Justifying Conclusions » Make inferences and justify conclusions from sample surveys, experiments, and observational studies » 4. Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. (9,10,11,12)
S-IC.2 » Mathematics » High School - Statistics and Probability » Making Inferences and Justifying Conclusions » Understand and evaluate random processes underlying statistical experiments » 2. Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. (9,10,11,12)
G-MG.2 » Mathematics » High School - Geometry » Modeling with Geometry » Apply geometric concepts in modeling situations » 2. Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot). (9,10,11,12)
G-MG.1 » Mathematics » High School - Geometry » Modeling with Geometry » Apply geometric concepts in modeling situations » 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). (9,10,11,12)
Mathematics » High School - Number and Quantity » Quantities » Reason quantitatively and use units to solve problems. (9,10,11,12)
7.NS.1.c » Mathematics » The Number System » Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. » 1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. » c. Understand subtraction of rational numbers as adding the additive inverse, p - q = p + (-q). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. (7)
7.NS.1.b » Mathematics » The Number System » Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. » 1. Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram. » b. Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. (7)
8.EE.4 » Mathematics » Expressions and Equations » Work with radicals and integer exponents. » 4. Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. (8)
7.EE.4.b » Mathematics » Expressions and Equations » Solve real-life and mathematical problems using numerical and algebraic expressions and equations. » 4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. » b. Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. (7)
7.EE.4.a » Mathematics » Expressions and Equations » Solve real-life and mathematical problems using numerical and algebraic expressions and equations. » 4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. » a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. (7)
7.EE.2 » Mathematics » Expressions and Equations » Use properties of operations to generate equivalent expressions. » 2. Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. (7)
8.EE.8.c » Mathematics » Expressions and Equations » Analyze and solve linear equations and pairs of simultaneous linear equations. » 8. Analyze and solve pairs of simultaneous linear equations. » c. Solve real-world and mathematical problems leading to two linear equations in two variables. (8)
8.EE.8.b » Mathematics » Expressions and Equations » Analyze and solve linear equations and pairs of simultaneous linear equations. » 8. Analyze and solve pairs of simultaneous linear equations. » b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. (8)
8.EE.8.a » Mathematics » Expressions and Equations » Analyze and solve linear equations and pairs of simultaneous linear equations. » 8. Analyze and solve pairs of simultaneous linear equations. » a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. (8)
7.SP.6 » Mathematics » Statistics and Probability » Investigate chance processes and develop, use, and evaluate probability models. » 6. Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. (7)