Correlations to the Secondary Mathematics Benchmarks

KEY:

Probability and Statistics

PS.A.1 Simple probability.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Represent probabilities using ratios and percents. G.1 PK.F.1 L4.1 14
b. Compare probabilities of two or more events and recognize when certain events are equally likely. G.1 PK.F.1 L4 22
c. Use sample spaces to determine the (theoretical) probabilities of events. G.1 PK.F.1 L4.4 23
d. Know and use the relationship between probability and odds. G.1 PK.F.1 14

PS.A.2 Relative frequency and probability.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Describe the relationship between probability and relative frequency. G.2 H.1 R1.d L4.2
b. Identify, create, and describe the key characteristics of frequency distributions of both discrete and continuous data. G.2 H.1 R1.d
c. Analyze and interpret actual data to estimate probabilities and predict outcomes. G.2 H.1 R1.e L4.5
d. Compare theoretical probabilities with the results of simple experiments (e.g., tossing dice, flipping coins, spinning spinners). G.2 H.1 R1.f L4.5 22
e. Compute and graph cumulative frequencies. G.2 H.1 L4.2

PS.A.3 Question formulation and data collection.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Formulate questions about a phenomenon of interest that can be answered with data. F.1 I.1 L3.2 5
b. Design a plan to collect appropriate data. G.1 I.1 L3.2 5
c. Collect and record data. F.1 I.1 L1.1 5

PS.A.4 Linear trends.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Determine whether a scatter plot suggests a linear trend. G.5 I.5 L3.4 11, 29
b. Visually determine a line of good fit to estimate the relationship in bivariate data that suggests a linear trend. G.5 I.5 L3.4 11

PS.B.1 Compound probability.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Calculate probabilities of compound events. F.1 F.1 R1.c L4.5 13, 23
b. Use probability to interpret odds and risks and recognize common misconceptions. F.1 F.1 L4.5 14
c. Show how a two-way frequency table can be used effectively to calculate and study relationships among probabilities for two events. F.1 F.1 R1.c L4.2, L4.5 13
d. Recognize probability problems that can be represented by geometric diagrams, the number line, or in the coordinate plane; represent such situations geometrically and apply geometric properties of length or area to calculate the probabilities. F.1 A.1

PS.B.2 Analysis and interpretation categorical and quantitative data.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Represent both univariate and bivariate categorical data accurately and effectively. F.2 PK.E.1 S1.a 11
b. Represent both univariate and bivariate quantitative (measurement) data accurately and effectively. G.2 I.2 S1.a
c. Summarize and compare data sets by using a variety of statistics. G.3 I.3 S1.a L1.3 11
d. Read, interpret, interpolate, and judiciously extrapolate from graphs and tables. G.4 I.4 L1.2 29
e. Judge accuracy, reasonableness, and potential for misrepresentation. F.2 I.2 S2.c L2, L2.1, L2.2, L2.3
f. Interpret data and communicate conclusions. G.4 I.4 S2.b L1.2

PS.C.1 Probability distributions.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Identify and distinguish between discrete and continuous probability distributions. A.1 F.2 R2.a L4
b. Know and use the chief characteristics of the normal distribution. A.2 F.2 R2.b L1.6 15
c. Calculate and use the mean and standard deviation to describe the characteristics of a distribution. A.1 F.2 L1.3 15
d. Understand how to calculate and interpret the expected value of a random variable having a discrete probability distribution. A.3 F.2

PS.C.2 Correlation and regression.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Determine a line of good fit for a scatter plot. F.3 F.6 H.3 S1.c, S2.a L1.5, L3.4 11, 29
b. Determine and interpret correlation coefficients. F.3 F.6 part H.3 part/opt S1.c, S2.a L1.5, L3.4

PS.D.1 Sample surveys, experiments, and observational studies.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Describe the nature and purpose of sample surveys, experiments, and observational studies, relating each to the types of research questions they are best suited to address. F.1 H.1 S2.c L3, L3.1 5
b. Recognize and explain the rationale for using randomness in research designs. F.2 H.2 S2.c L3, L3.1 5
c. Use simulations to analyze and interpret key concepts of statistical inference. F.2 H.2
d. Plan and conduct sample surveys to estimate population characteristics and experiments to compare treatments. F.2 H.2 L3.2 5
e. Explain why observational studies generally do not lead to good estimates of population characteristics or cause and effect statements on treatments. F.1 H.1 L3.3

PS.D.2 Risks and decisions.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Apply probability to practical situations to make informed decisions. A.3 F.3 L4.5

PS.E.1 Transformations of data.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Explore transformations of data of the purpose of "linearizing" a scatter plot that shows curvature. F.4 opt H.3 opt
b. Estimate the rate of exponential growth or decay by fitting a regression model to appropriate data transformed by logarithms. F.4 opt H.3 opt
c. Estimate the power term in a power model by fitting a regression model to appropriate data transformed by logarithms. F.4 opt H.3 opt
d. Analyze how linear transformations of data affect measures of center and spread, the slope of a regression line, and the correlation coefficient. F.4 opt H.3 opt L1.3, L.1.4

PS.E.2 Advanced probability.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Interpret and use the Central Limit Theorem: The distribution of the average of independent samples approaches a normal distribution. L1.6
b. Know and use equations for the binomial and normal distributions.
c. Use and interpret the normal approximation to the binomial distribution.
d. Calculate and apply expected value.

PS.E.3 Cross-classified data.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Recognize problems that call for the use of conditional probability and calculate conditional probability in such cases.
b. Use contingency tables to analyze categorical data.
c. Use Χ2 tests to evaluate significance of conditional probabilities.

PS.E.4 Statistical reasoning.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Explain the protocol for hypothesis testing and apply it in problem situations.
b. Explain statistical estimation and error.
c. Design, conduct, and interpret a simple comparative experiment. L3.2

PS.E.5 Statistical inference.

Expectation MS 1 MS 2 MS A Int 1 Int 2 Int 3 Alg I Geo Alg II EOC A2
Core		 EOC A2
Mod		 ADP Tasks
a. Estimate population parameters (point estimators and confidence intervals).
b. Know common tests of significance and use them to test hypotheses.
c. Know and explain the difference between mathematical and statistical inference.