High School AP Statistics

Student Learnings: What students should know and be able to do

Mathematical Reasoning

Apply skills of mathematical representation, communication and reasoning throughout the remaining three content strands.

• Assess the reasonableness of a solution by comparing the solution to appropriate graphical or numerical estimates or by recognizing the feasibility of solutions in a given context and rejecting extraneous solutions.
• Appropriately use examples and counterexamples to make and test conjectures, justify solutions, and explain results.
• Translate a problem described verbally or by tables, diagrams or graphs, into suitable mathematical language, solve the problem mathematically and interpret the result in the original context.
• Support mathematical results by explaining why the steps in a solution are valid and why a particular solution method is appropriate.
• Determine whether or not relevant information is missing from a problem and if so, decide how to best express the results that can be obtained without that information.

Number Sense, Computation and Operations

Number Sense
Use real numbers, represented in a variety of ways, to quantify information and to solve real-world and mathematical problems.

• Use real numbers, represented in a variety of ways, to quantify information and to solve real-world and mathematical problems.

Computation and Operation
Appropriately use calculators and other technologies to solve algebraic, geometric, probabilistic and statistical problems.

• Apply the correct order of operations and grouping symbols when using calculators and other technologies.
• Know, use and translate calculator notational conventions to mathematical notation.
• Understand the limitations of calculators such as missing or additional features on graphs due to viewing parameters or misleading representations of zero or very large numbers.
• Understand that use of a calculator requires appropriate mathematical reasoning and does not replace the need for mental computation.

Patterns, Functions, and Algebra

Patterns and Functions
Represent and analyze real-world and mathematical problems using numeric, graphic and symbolic methods for a variety of functions.

• Know the numeric, graphic and symbolic properties of linear, step, absolute value and quadratic functions. Graphic properties may include rates of change, intercepts, maxima and minima.
• Model exponential growth and decay, numerically, graphically and symbolically, using exponential functions with integer inputs.
• Apply basic concepts of linear, quadratic and exponential expressions or equations in real-world problems such as loans, investments and the path of a projectile.

Algebra (Algebraic Thinking)
Solve simple equations and inequalities numerically, graphically and symbolically. Use recursion to model and solve real-world and mathematical problems.

• Find equations of a line given two points on the line, a point and the slope of the line or the slope and the y-intercept of the line.
• Use a variety of models such as equations, inequalities, algebraic formulas, written statements, tables and graphs or spreadsheets to represent functions and patterns in real-world and mathematical problems.
• Apply the laws of exponents to perform operations on expressions with integer exponents.
• Solve linear equations and inequalities in one variable with numeric, graphic and symbolic methods.
• Find real solutions to quadratic equations in one variable with numeric, graphic and symbolic methods.
• Understand how slopes can be used to determine whether lines are parallel or perpendicular. Given a line and a point not on the line, find the equations for the lines passing through that point and parallel or perpendicular to the given line.

Data Analysis, Statistics and Probability

Data and Statistics
Represent data and use various measures associated with data to draw conclusions and identify trends. Understand the effects of display distortion and measurement error on the interpretation of data.

• Construct and analyze the circle graphs, bar graphs, histograms, box-and-whisker plots, scatter plots and tables, and demonstrate the strengths and weaknesses of each format by choosing appropriately among them for a given situation.
• Use measures of central tendency and variability, such as, mean, median, maximum, minimum, range, standard deviation, quartile and percentile, to describe, compare and draw conclusions about sets of data.
• Determine an approximate best-fit line from a given scatter plot and use the line to draw conclusions.
• Know the influence of outliers on various measures and representations of data about real-world and mathematical problems.
• Know the influence of outliers on various measures and representations of data about real-world and mathematical problems.
• Understand the relationship between correlation and causation.
• Interpret data credibility in the context of measurement error and display distortion.

Probability
Use appropriate counting procedures, calculate probabilities in various ways and apply theoretical probability concepts to solve real-world and mathematical problems.

• Select and apply appropriate counting procedures to solve real-world and mathematical problems, including probability problems.
• Use area, trees, unions and intersections to calculate probabilities and relate the results to mutual exclusiveness, independence and conditional probabilities, in real-world and mathematical problems.
• Use probability models, including area and binomial models, in real-world and mathematical problems.
• For simple probability models, determine the expected values of random variables.
• Know the effect of sample size on experimental and simulation probabilities.
• Use a variety of experimental, simulation and theoretical methods to calculate probabilities.

Spatial Sense, Geometry and Measurement

Geometry
Apply basic theorems of plane geometry, right triangle trigonometry, coordinate geometry and a variety of visualization tools to solve real-world and mathematical problems.

• Know and use properties of two- and three-dimensional figures to solve real-world and mathematical problems such as finding area, perimeter, volume and surface area; applying direct or indirect methods of measurement; the Pythagorean theorem and its converse; and properties of 45º-45º-90º triangles.

Measurement
Use the interconnectedness of geometry, algebra and measurement to explore real-world mathematical problems.

• Use the interconnectedness of geometry, algebra and measurement to explore real-world mathematical problems.

Statistics

Use tables of the normal distribution and properties of that distribution to make judgments about populations based on random samples from these populations.

• Use the concept of normal distribution and its properties to answer questions about sets of data.
• Describe and use sampling distributions and the central limit theorem. Calculate confidence intervals when appropriate.
• Understand the importance of appropriate sampling methods. For instance, the time of day of a survey could lead to inaccuracies in the outcome.

Algebra

Demonstrate facility with a wide range of algebraic operations and use the relationship between coordinate geometry and algebraic equations to solve real- world and mathematical problems.

• Apply the laws of exponents to perform operations on expressions with fractional exponents.
• Know the numeric, graphic and symbolic properties of power, logarithmic and exponential functions.
• Solve a wide variety of mathematical and real-world problems involving power, exponential and logarithmic functions and equations, discard extraneous solutions and present results graphically.

Instructional resources used for this curriculum:

Copyright 2003, Bedford Freeman Worth Publishing
The Practice of Statistics, 2nd Edition, by Yates, Moore, and Starnes