Port Angeles School District

High School Grades 9-12 Introduction: Math Practice Problems

Click for Practice Problems in Specific Strands

NUMBERS

GEOMETRY

MEASURE-MENT

ALGEBRA

DATA ANALYSIS, STATISTICS & PROBABILITY

LOGIC

STRATEGIES

OSPI Released Items

Problem Solving PowerPoint

Scoring Criteria

WASHINGTON GRADES 9-12 MATHEMATICS STANDARDS
(from the Review Draft of 2008)

Current Washington K-12 Mathematics Standards

Algebraic Structure and Number Systems
A1. Numbers, expressions, and operations: Students use variables and expressions to solve a wide variety of mathematical and applied problems. They generate expressions and rewrite them as equivalent expressions when appropriate. Students extend their understanding of arithmetic operations and their properties, enabling them to manipulate a wide variety of algebraic expressions. They demonstrate this understanding by using models and algebraic procedures to solve problems in both mathematical and applied contexts.

Algebraic Structure and Number Systems
A2. Equations and inequalities: Students write and solve equations and inequalities that arise in a wide range of mathematical and applied problems. They learn algebraic techniques for solving linear equations and inequalities, and extend these techniques to other types of equations. Students also learn graphical and numerical methods for approximating solutions to equations. Students interpret the meaning of problem solutions and explain their limitations. These algebraic skills are applied in other Core Content areas across the 9–12 standards.

Functions and Analysis
F1. Formalizing functions: Students formalize and deepen their understanding of real-valued functions, their defining characteristics and uses, and the mathematical language to describe functions. They study a variety of functions, their representations, and basic transformations of these functions. Students learn the practical and mathematical limitations that must be considered when working with functions or when using functions to model situations.

Functions and Analysis
F2. Linear functions: Students understand that linear functions can be used to model situations involving a constant rate of change. They use linear functions and functions containing an absolute value of a linear expression to analyze relationships, represent and model problems, and answer questions.

Functions and Analysis
F3. Exponential functions: Students develop an understanding of exponential functions, their graphs and representations, and where exponential functions appear in application problems. Students sketch graphs of simple exponential functions and use technology to approximate function values and to graph more complex exponential functions. Students compare the characteristics of exponential functions to those of linear functions.

Functions and Analysis
F4. Quadratic and other functions: Students develop an understanding of quadratic functions, their graphs and representations, and how to use quadratic functions to analyze relationships, represent and model problems, and answer questions. Students extend their study of functions to include those containing polynomials of higher degree, and rational and radical expressions.

Geometry and Geometric Measurement
G1. Logical arguments and proofs: Students formulate conjectures about geometric relationships and use deductive reasoning to establish the truth of conjectures or to reject them on the basis of counterexamples. They distinguish between inductive and deductive reasoning and apply each to geometric situations when appropriate. Students explain their reasoning as they form, test, and prove or refute conjectures using precise mathematical language and symbols.

Geometry and Geometric Measurement
G2. Attributes and properties of two- and three-dimensional figures: Students know and can prove theorems about two- and three-dimensional geometric figures. They demonstrate an understanding of the Euclidean system of geometry and what it means to prove something mathematically. They apply this understanding to solve problems in both mathematical and applied contexts.

Geometry and Geometric Measurement
G3. Geometry in the coordinate plane: Students develop an understanding of the connection between geometry and algebra by studying geometric properties and attributes that can be represented on a coordinate plane. They use the coordinate plane to represent mathematical and applied situations. Students apply algebraic methods to interpret and represent geometric relationships, verify properties, and prove conjectures.

Geometry and Geometric Measurement
G4. Geometric transformations: Students formalize their study of geometric transformations, focusing on the effect of such transformations on the attributes of geometric figures. They study techniques for establishing congruence and similarity by means of transformations.

Geometry and Geometric Measurement
G5. Geometry and measurement in the physical world: Students extend and formalize their work with geometric formulas for perimeter, area, surface area, and volume of two- and three-dimensional figures, focusing on mathematical derivations of these formulas and their applications in complex problems. They use properties of geometry and measurement to solve problems in mathematical and applied situations. Students understand the role of units in measurement and apply what they know to solve problems involving derived measures like speed or density. They understand that all measurement is approximate and specify precision in measurement problems.

Data/Statistics/Probability
D1. Data and distributions: Students select mathematical models for data sets and use those models to represent, describe, and compare data sets. They analyze the relationship between two variables, and make and defend appropriate predictions, conjectures and generalizations based on data. They understand limitations of conclusions based on results of a study or experiment and recognize common misconceptions and misrepresentations.

Data/Statistics/Probability
D2. Statistical experiments and studies: Students explore sources of variability, a defining feature of statistical reasoning. They examine how variability affects statistical experiments and studies and apply techniques to minimize variability. They formulate questions that can be answered by conducting a study, carry out the study, interpret results, and report conclusions. Students critique the design and methodology of statistical experiments and studies, and learn to identify possible sources of bias.

Data/Statistics/Probability
D3. Probability, relative frequency, and uncertainty: Students formalize their study of probability, recognizing that probability is the measure of the likelihood of an outcome in uncertain circumstances. They distinguish between experimental and theoretical probability and apply these concepts to a wide range of practical situations involving uncertainty.

Mathematical Processes
P1. Reasoning, problem solving, and communication: Students analyze and synthesize mathematical information from a variety of sources, and use that information to form and defend generalizations. Students justify their reasoning using accepted standards and techniques of mathematical evidence and proof that they formalize at this level. Students extend the problem solving practices developed in earlier grades and apply them to more complex mathematical and applied problems, sometimes modeling problem situations with functions or other mathematical models. Students become more sophisticated and precise in their use of mathematical terms and symbols. They interpret and use the symbols and language of mathematics to assimilate, organize, represent, record, and communicate mathematical ideas, reasoning, justifications, solutions, inferences, and conclusions.