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## WA.8.1.Core Content: Linear functions and equations (Algebra) Students solve a variety of linear equations and inequalities. They build on their familiarity with proportional relationships and simple linear equations to work with a broader set of linear relationships, and they learn what functions are. They model applied problems with mathematical functions represented by graphs and other algebraic techniques. This Core Content area includes topics typically addressed in a high school algebra or a first-year integrated math course, but here this content is expected of all middle school students in preparation for a rich high school mathematics program that goes well beyond these basic algebraic ideas.

Core Content: Linear functions and equations (Algebra) Students solve a variety of linear equations and inequalities. They build on their familiarity with proportional relationships and simple linear equations to work with a broader set of linear relationships, and they learn what functions are. They model applied problems with mathematical functions represented by graphs and other algebraic techniques. This Core Content area includes topics typically addressed in a high school algebra or a first-year integrated math course, but here this content is expected of all middle school students in preparation for a rich high school mathematics program that goes well beyond these basic algebraic ideas.
8.1.A. Solve one-variable linear equations.
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and Inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Algebra

8.1.B. Solve one- and two-step linear inequalities and graph the solutions on the number line.
Flip Charts Inequalities
Flip Charts Inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Algebraic Inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Equations and Inequalities
Quiz, Flash Cards, Worksheet, Game & Study Guide Integer operations
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational numbers and operations

8.1.C. Represent a linear function with a verbal description, table, graph, or symbolic expression, and make connections among these representations.
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

8.1.D. Determine the slope and y-intercept of a linear function described by a symbolic expression, table, or graph.
Flip Charts Slope
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions
Quiz, Flash Cards, Worksheet, Game & Study Guide Linear equations

8.1.E. Interpret the slope and y-intercept of the graph of a linear function representing a contextual situation.
Quiz, Flash Cards, Worksheet, Game & Study Guide Introduction to Functions

## WA.8.2.Core Content: Properties of geometric figures (Numbers, Geometry/Measurement) Students work with lines and angles, especially as they solve problems involving triangles. They use known relationships involving sides and angles of triangles to find unknown measures, connecting geometry and measurement in practical ways that will be useful well after high school. Since squares of numbers arise when using the Pythagorean Theorem, students work with squares and square roots, especially in problems with two- and three-dimensional figures. Using basic geometric theorems such as the Pythagorean Theorem, students get a preview of how geometric theorems are developed and applied in more formal settings, which they will further study in high school.

Core Content: Properties of geometric figures (Numbers, Geometry/Measurement) Students work with lines and angles, especially as they solve problems involving triangles. They use known relationships involving sides and angles of triangles to find unknown measures, connecting geometry and measurement in practical ways that will be useful well after high school. Since squares of numbers arise when using the Pythagorean Theorem, students work with squares and square roots, especially in problems with two- and three-dimensional figures. Using basic geometric theorems such as the Pythagorean Theorem, students get a preview of how geometric theorems are developed and applied in more formal settings, which they will further study in high school.
8.2.A. Identify pairs of angles as complementary, supplementary, adjacent, or vertical, and use these relationships to determine missing angle measures.
Flip Charts Plane Geometry
Quiz, Flash Cards, Worksheet, Game & Study Guide Finding Volume

8.2.B. Determine missing angle measures using the relationships among the angles formed by parallel lines and transversals.
Flip Charts Plane Geometry

8.2.E. Quickly recall the square roots of the perfect squares from 1 through 225 and estimate the square roots of other positive numbers.
Flip Charts The Real Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Rational and Irrational Numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide Real numbers
Quiz, Flash Cards, Worksheet, Game & Study Guide The Pythagorean Theorem

8.2.F. Demonstrate the Pythagorean Theorem and its converse and apply them to solve problems.
Quiz, Flash Cards, Worksheet, Game & Study Guide The Pythagorean Theorem

## WA.8.3.Core Content: Summary and analysis of data sets (Algebra, Data/Statistics/Probability) Students build on their extensive experience organizing and interpreting data and apply statistical principles to analyze statistical studies or short statistical statements, such as those they might encounter in newspapers, on television, or on the Internet. They use mean, median, and mode to summarize and describe information, even when these measures may not be whole numbers. Students use their knowledge of linear functions to analyze trends in displays of data. They create displays for two sets of data in order to compare the two sets and draw conclusions. They expand their work with probability to deal with more complex situations than they have previously seen. These concepts of statistics and probability are important not only in students' lives, but also throughout the high school mathematics program.

Core Content: Summary and analysis of data sets (Algebra, Data/Statistics/Probability) Students build on their extensive experience organizing and interpreting data and apply statistical principles to analyze statistical studies or short statistical statements, such as those they might encounter in newspapers, on television, or on the Internet. They use mean, median, and mode to summarize and describe information, even when these measures may not be whole numbers. Students use their knowledge of linear functions to analyze trends in displays of data. They create displays for two sets of data in order to compare the two sets and draw conclusions. They expand their work with probability to deal with more complex situations than they have previously seen. These concepts of statistics and probability are important not only in students' lives, but also throughout the high school mathematics program.
8.3.A. Summarize and compare data sets in terms of variability and measures of center.
Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data
Quiz, Flash Cards, Worksheet, Game & Study Guide Organizing Data
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

8.3.B. Select, construct, and analyze data displays, including box-and-whisker plots, to compare two sets of data.
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data

8.3.D. Describe different methods of selecting statistical samples and analyze the strengths and weaknesses of each method.
Quiz, Flash Cards, Worksheet, Game & Study Guide Collecting and describing data
Quiz, Flash Cards, Worksheet, Game & Study Guide Experimental Probability

8.3.E. Determine whether conclusions of statistical studies reported in the media are reasonable.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

8.3.F. Determine probabilities for mutually exclusive, dependent, and independent events for small sample spaces.
Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting
Quiz, Flash Cards, Worksheet, Game & Study Guide Using Probability

8.3.G. Solve single- and multi-step problems using counting techniques and Venn diagrams and verify the solutions.
Quiz, Flash Cards, Worksheet, Game & Study Guide Theoretical probability and counting
Quiz, Flash Cards, Worksheet, Game & Study Guide Using graphs to analyze data
Quiz, Flash Cards, Worksheet, Game & Study Guide Using Probability

## WA.8.4.Additional Key Content (Numbers, Operations) Students deal with a few key topics about numbers as they prepare to shift to higher level mathematics in high school. First, they use scientific notation to represent very large and very small numbers, especially as these numbers are used in technological fields and in everyday tools like calculators or personal computers. Scientific notation has become especially important as ''extreme units'' continue to be identified to represent increasingly tiny or immense measures arising in technological fields. A second important numerical skill involves using exponents in expressions containing both numbers and variables. Developing this skill extends students' work with order of operations to include more complicated expressions they might encounter in high school mathematics. Finally, to help students understand the full breadth of the real-number system, students are introduced to simple irrational numbers, thus preparing them to study higher level mathematics in which

Additional Key Content (Numbers, Operations) Students deal with a few key topics about numbers as they prepare to shift to higher level mathematics in high school. First, they use scientific notation to represent very large and very small numbers, especially as these numbers are used in technological fields and in everyday tools like calculators or personal computers. Scientific notation has become especially important as ''extreme units'' continue to be identified to represent increasingly tiny or immense measures arising in technological fields. A second important numerical skill involves using exponents in expressions containing both numbers and variables. Developing this skill extends students' work with order of operations to include more complicated expressions they might encounter in high school mathematics. Finally, to help students understand the full breadth of the real-number system, students are introduced to simple irrational numbers, thus preparing them to study higher level mathematics in which
8.4.A. Represent numbers in scientific notation, and translate numbers written in scientific notation into standard form.
Quiz, Flash Cards, Worksheet, Game & Study Guide Exponents, Factors and Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

8.4.D. Identify rational and irrational numbers.
Flip Charts The Real Numbers

## WA.8.4.Additional Key Content (Numbers, Operations) Students deal with a few key topics about numbers as they prepare to shift to higher level mathematics in high school. First, they use scientific notation to represent very large and very small numbers, especially as these numbers are used in technological fields and in everyday tools like calculators or personal computers. Scientific notation has become especially important as ''extreme units'' continue to be identified to represent increasingly tiny or immense measures arising in technological fields. A second important numerical skill involves using exponents in expressions containing both numbers and variables. Developing this skill extends students' work with order of operations to include more complicated expressions they might encounter in high school mathematics. Finally, to help students understand the full breadth of the real-number system, students are introduced to simple irrational numbers, thus preparing them to study higher level mathematics in which properties and procedures are generalized for the entire set of real numbers.

Additional Key Content (Numbers, Operations) Students deal with a few key topics about numbers as they prepare to shift to higher level mathematics in high school. First, they use scientific notation to represent very large and very small numbers, especially as these numbers are used in technological fields and in everyday tools like calculators or personal computers. Scientific notation has become especially important as ''extreme units'' continue to be identified to represent increasingly tiny or immense measures arising in technological fields. A second important numerical skill involves using exponents in expressions containing both numbers and variables. Developing this skill extends students' work with order of operations to include more complicated expressions they might encounter in high school mathematics. Finally, to help students understand the full breadth of the real-number system, students are introduced to simple irrational numbers, thus preparing them to study higher level mathematics in which properties and procedures are generalized for the entire set of real numbers.
8.4.A. Represent numbers in scientific notation, and translate numbers written in scientific notation into standard form.
Quiz, Flash Cards, Worksheet, Game & Study Guide Exponents, Factors and Fractions
Quiz, Flash Cards, Worksheet, Game & Study Guide Polynomials and Exponents

8.4.D. Identify rational and irrational numbers.
Flip Charts The Real Numbers

## WA.8.5.Core Processes: Reasoning, problem solving, and communication - Students refine their reasoning and problem-solving skills as they move more fully into the symbolic world of algebra and higher level mathematics. They move easily among representations - numbers, words, pictures, or symbols - to understand and communicate mathematical ideas, to make generalizations, to draw logical conclusions, and to verify the reasonableness of solutions to problems. In grade eight, students solve problems that involve proportional relationships and linear relationships, including applications found in many contexts outside of school. These problems dealing with proportionality continue to be important in many applied contexts, and they lead directly to the study of algebra. Students also begin to deal with informal proofs for theorems that will be proven more formally in high school.

Core Processes: Reasoning, problem solving, and communication - Students refine their reasoning and problem-solving skills as they move more fully into the symbolic world of algebra and higher level mathematics. They move easily among representations - numbers, words, pictures, or symbols - to understand and communicate mathematical ideas, to make generalizations, to draw logical conclusions, and to verify the reasonableness of solutions to problems. In grade eight, students solve problems that involve proportional relationships and linear relationships, including applications found in many contexts outside of school. These problems dealing with proportionality continue to be important in many applied contexts, and they lead directly to the study of algebra. Students also begin to deal with informal proofs for theorems that will be proven more formally in high school.
8.5.A. Analyze a problem situation to determine the question(s) to be answered.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

8.5.B. Identify relevant, missing, and extraneous information related to the solution to a problem.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

8.5.C. Analyze and compare mathematical strategies for solving problems, and select and use one or more strategies to solve a problem.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

8.5.D. Represent a problem situation, describe the process used to solve the problem, and verify the reasonableness of the solution.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

8.5.F. Apply a previously used problem-solving strategy in a new context.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

8.5.G. Extract and organize mathematical information from symbols, diagrams, and graphs to make inferences, draw conclusions, and justify reasoning.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

8.5.H. Make and test conjectures based on data (or information) collected from explorations and experiments.
Quiz, Flash Cards, Worksheet, Game & Study Guide Mathematical processes

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