References to probability and statistics in the Washington State Math Standards in Algebra 1 and Algebra 2


(All content on this page has been taken from the text of the Math Standards)

Explanation of terms used in the Standards:
Core Content areas describe the major mathematical focuses of each grade level or course. A limited number of priorities for each grade level in grades K–8 and for each high school course are identified, so teachers know which topics call for the most time and emphasis.
Additional Key Content contains important expectations that do not warrant the same amount of instructional time as the Core Content areas. These are expectations that might extend a previously learned skill, plant a seed for future development, or address a focused topic, such as scientific notation. Although they need less classroom time, these expectations are important, are expected to be taught, and may be assessed as part of Washington State’s assessment system.
Core Processes include expectations that address reasoning, problem solving, and communication. While these processes are incorporated throughout other content expectations, they are presented in this section to clearly describe the breadth and scope of what is expected in each grade or course.
Explanatory Comments and Examples accompany most of the expectations.... The comments expand upon the meaning of the expectations. Explanatory text might clarify the parameters regarding the type or size of numbers, provide more information about student expectations regarding mathematical understanding, or give expanded detail to mathematical definitions, laws, principles, and forms included in the expectation.

All page numbers pertain to the 6-12 grade Standards.

Pages 128-130 in the Standards: A1.6. Core Content: Data and distributions (Data/Statistics/Probability) Students select mathematical models for data sets and use those models to represent, describe, and compare data sets. They analyze data to determine the relationship between two variables and make and defend appropriate predictions, conjectures, and generalizations. Students understand limitations of conclusions based on results of a study or experiment and recognize common misconceptions and misrepresentations in interpreting conclusions.

Students are expected to:
A1.6.A Use and evaluate the accuracy of summary statistics to describe and compare data sets. A univariate set of data identifies data on a single variable, such as shoe size. This expectation extends what students have learned in earlier grades to include evaluation and justification. They both compute and evaluate the appropriateness of measure of center and spread (range and interquartile range) and use these measures to accurately compare data sets. Students will draw appropriate conclusions through the use of statistical measures of center, frequency, and spread, combined with graphical displays.
A1.6.B Make valid inferences and draw conclusions based on data. Determine whether arguments based on data confuse association with causation. Evaluate the reasonableness of and make judgments about statistical claims, reports, studies, and conclusions.
A1.6.C Describe how linear transformations affect the center and spread of univariate data.
A1.6.D Find the equation of a linear function that best fits bivariate data that are linearly related, interpret the slope and y-intercept of the line, and use the equation to make predictions. A bivariate set of data presents data on two variables, such as shoe size and height. In high school, the emphasis is on using a line of best fit to interpret data and on students making judgments about whether a bivariate data set can be modeled with a linear function. Students can use various methods, including technology, to obtain a line of best fit. Making predictions involves both interpolating and extrapolating from the original data set. Students need to be able to evaluate the quality of their predictions, recognizing that extrapolation is based on the assumption that the trend indicated continues beyond the unknown data. Describe the correlation of data in scatterplots in terms of strong or weak and positive or negative.

Pages 165-166 in the Standards: A2.6. Core Content: Probability, data, and distributions (Data/Statistics/Probability) Students formalize their study of probability, computing both combinations and permutations to calculate the likelihood of an outcome in uncertain circumstances and applying the binominal theorem to solve problems. They extend their use of statistics to graph bivariate data and analyze its shape to make predictions. They calculate and interpret measures of variability, confidence intervals, and margins of error for population proportions. Dual goals underlie the content in the section: students prepare for the further study of statistics and become thoughtful consumers of data.

Students are expected to:
A2.6.A Apply the fundamental counting principle and the ideas of order and replacement to calculate probabilities in situations arising from two-stage experiments (compound events).
A2.6.B Given a finite sample space consisting of equally likely outcomes and containing events A and B, determine whether A and B are independent or dependent, and find the conditional probability of A given B.
A2.6.C Compute permutations and combinations, and use the results to calculate probabilities.
A2.6.D Apply the binomial theorem to solve problems involving probability. The binominal theorem is also applied when computing with polynomials.
A2.6.E Determine if a bivariate data set can be better modeled with an exponential or a quadratic function and use the model to make predictions. In high school, determining a formula for a curve of best fit requires a graphing calculator or similar technological tool.
A2.6.F Calculate and interpret measures of variability and standard deviation and use these measures and the characteristics of the normal distribution to describe and compare data sets. Students should be able to identify unimodality, symmetry, standard deviation, spread, and the shape of a data curve to determine whether the curve could reasonably be approximated by a normal distribution. Given formulas, student should be able to calculate the standard deviation for a small data set, but calculators ought to be used if there are very many points in the data set. It is important that students be able to describe the characteristics of the normal distribution and identify common examples of data that are and are not reasonably modeled by it. Common examples of distributions that are approximately normal include physical performance measurements (e.g., weightlifting, timed runs), heights, and weights. Apply the Empirical Rule (68-95-99.7 Rule) to approximate the percentage of the population meeting certain criteria in a normal distribution.
A2.6.G Calculate and interpret margin of error and confidence intervals for population proportions. Students will use technology based on the complexity of the situation. Students use confidence intervals to critique various methods of statistical experimental design, data collection, and data presentation used to investigate important problems, including those reported in public studies.