Grade 8

Problem Solving Strand

Students will build new mathematical knowledge through problem solving.

8.PS.1
Use a variety of strategies to understand new mathematical content and to develop more efficient methods

8.PS.2 Construct appropriate extensions to problem situations

8.PS.3 Understand and demonstrate how written symbols represent mathematical ideas

Students will solve problems that arise in mathematics and in other contexts.

8.PS.4
Observe patterns and formulate generalizations

8.PS.5 Make conjectures from generalizations

8.PS.6 Represent problem situations verbally, numerically, algebraically, and graphically

Students will apply and adapt a variety of appropriate strategies to solve problems.

8.PS.7
Understand that there is no one right way to solve mathematical problems but that different methods have advantages and disadvantages

8.PS.8 Understand how to break a complex problem into simpler parts or use a similar problem type to solve a problem

8.PS.9 Work backwards from a solution

8.PS.10 Use proportionality to model problems

8.PS.11 Work in collaboration with others to solve problems

Students will monitor and reflect on the process of mathematical problem solving.

8.PS.12 Interpret solutions within the given constraints of a problem

8.PS.13 Set expectations and limits for possible solutions

8.PS.14 Determine information required to solve the problem

8.PS.15 Choose methods for obtaining required information

8.PS.16 Justify solution methods through logical argument

8.PS.17 Evaluate the efficiency of different representations of a problem

Reasoning and Proof Strand

Students will recognize reasoning and proof as fundamental aspects of mathematics.

8.RP.1 Recognize that mathematical ideas can be supported by a variety of strategies

Students will make and investigate mathematical conjectures.

8.RP.2 Use mathematical strategies to reach a conclusion

8.RP.3 Evaluate conjectures by distinguishing relevant from irrelevant information to reach a conclusion or make appropriate estimates

Students will develop and evaluate mathematical arguments and proofs.

8.RP.4 Provide supportive arguments for conjectures

8.RP.5 Develop, explain, and verify an argument using mathematical ideas and language

Students will select and use various types of reasoning and methods of proof.

8.RP.6 Support an argument by using a systematic approach to test more than one case

8.RP.7
Devise ways to verify results or use counterexamples to refute incorrect statements

8.RP.8 Apply inductive reasoning in making and supporting mathematical conjectures

Communication Strand

Students will organize and consolidate their mathematical thinking through communication.

8.CM.1
Provide a correct, complete, coherent, and clear rationale for thought process used in problem solving

8.CM.2
Provide an organized argument which explains rationale for strategy selection

8.CM.3 Organize and accurately label work

Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.

8.CM.4 Share organized mathematical ideas through the manipulation of objects, numerical tables, drawings, pictures, charts, graphs, tables, diagrams, models and symbols in written and verbal form

8.CM.5
Answer clarifying questions from others

Students will analyze and evaluate the mathematical thinking and strategies of others.

8.CM.6 Analyze mathematical solutions shared by others

8.CM.7
Compare strategies used and solutions found by others in relation to their own work

8.CM.8 Formulate mathematical questions that elicit, extend, or challenge strategies, solutions, and/or conjectures of others

Students will use the language of mathematics to express mathematical ideas precisely.

8.CM.9 Increase their use of mathematical vocabulary and language when communicating with others

8.CM.10 Use appropriate language, representations, and terminology when describing objects, relationships, mathematical solutions, and rationale

8.CM.11 Draw conclusions about mathematical ideas through decoding, comprehension, and interpretation of mathematical visuals, symbols, and technical writing

Connections Strand

Students will recognize and use connections among mathematical ideas.

8.CN.1
Understand and make connections among multiple representations of the same mathematical idea

8.CN.2 Recognize connections between subsets of mathematical ideas

8.CN.3 Connect and apply a variety of strategies to solve problems

Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole.

8.CN.4 Model situations mathematically, using representations to draw conclusions and formulate new situations

8.CN.5
Understand how concepts, procedures, and mathematical results in one area of mathematics can be used to solve problems in other areas of mathematics

Students will recognize and apply mathematics in contexts outside of mathematics.

8.CN.6 Recognize and provide examples of the presence of mathematics in their daily lives

8.CN.7 Apply mathematical ideas to problem situations that develop outside of mathematics

8.CN.8 Investigate the presence of mathematics in careers and areas of interest

8.CN.9 Recognize and apply mathematics to other disciplines, areas of interest, and societal issues

Representation Strand

Students will create and use representations to organize, record, and communicate mathematical ideas.

8.R.1 Use physical objects, drawings, charts, tables, graphs, symbols, equations, or objects created using technology as representations

8.R.2 Explain, describe, and defend mathematical ideas using representations

8.R.3 Recognize, compare, and use an array of representational forms

8.R.4 Explain how different representations express the same relationship

8.R.5 Use standard and non-standard representations with accuracy and detail

Students will select, apply, and translate among mathematical representations to solve problems.

8.R.6 Use representations to explore problem situations

8.R.7 Investigate relationships between different representations and their impact on a given problem

8.R.8 Use representation as a tool for exploring and understanding mathematical ideas

Students will use representations to model and interpret physical, social, and mathematical phenomena.

8.R.9 Use mathematics to show and understand physical phenomena (e.g., make and interpret scale drawings of figures or scale models of objects)

8.R.10 Use mathematics to show and understand social phenomena (e.g., determine profit from sale of yearbooks)

8.R.11
Use mathematics to show and understand mathematical phenomena (e.g., use tables, graphs, and equations to show a pattern underlying a function)

Number Sense and Operations Strand

Students will understand meanings of operations and procedures, and how they relate to one another.

Operations

8.N.1 Develop and apply the laws of exponents for multiplication and division

8.N.2 Evaluate expressions with integral exponents

8.N.3 Read, write, and identify percents less than 1% and greater than 100%

8.N.4
Apply percents to:

Tax

Percent increase/decrease

Simple interest

Sale price

Commission

Interest rates

Gratuities

Students will compute accurately and make reasonable estimates.

Estimation

8.N.5 Estimate a percent of quantity, given an application

8.N.6 Justify the reasonableness of answers using estimation

Algebra Strand

Students will represent and analyze algebraically a wide variety of problem solving situations.

Variables and Expressions

8.A.1 Translate verbal sentences into algebraic inequalities

8.A.2 Write verbal expressions that match given mathematical expressions

8.A.3 Describe a situation involving relationships that matches a given graph

8.A.4 Create a graph given a description or an expression for a situation involving a linear or nonlinear relationship

8.A.5 Use physical models to perform operations with polynomials

Students will perform algebraic procedures accurately.

Variables and Expressions

8.A.6 Multiply and divide monomials

8.A.7 Add and subtract polynomials (integer coefficients)

8.A.8 Multiply a binomial by a monomial or a binomial (integer coefficients)

8.A.9 Divide a polynomial by a monomial (integer coefficients) Note: The degree of the denominator is less than or equal to the degree of the numerator for all variables.

8.A.10 Factor algebraic expressions using the GCF

8.A.11
Factor a trinomial in the form ax²+ bx + c; a=1 and c having no more than three sets of factors

Equations and Inequalities

8.A.12 Apply algebra to determine the measure of angles formed by or contained in parallel lines cut by a transversal and by intersecting lines

8.A.13 Solve multi-step inequalities and graph the solution set on a number line

8.A.14 Solve linear inequalities by combining like terms, using the distributive property, or moving variables to one side of the inequality (include multiplication or division of inequalities by a negative number)

Students will recognize, use, and represent algebraically patterns, relations, and functions.

Patterns, Relations, And Functions

8.A.15 Understand that numerical information can be represented in multiple ways: arithmetically, algebraically, and graphically

8.A.16 Find a set of ordered pairs to satisfy a given linear numerical pattern (expressed algebraically); then plot the ordered pairs and draw the line

8.A.17 Define and use correct terminology when referring to function (domain and range)

8.A.18 Determine if a relation is a function

8.A.19 Interpret multiple representations using equation, table of values, and graph

Geometry Strand

Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.

Constructions

8.G.0

Construct the following using a straight edge and compass:

Segment congruent to a segment
Angle congruent to an angle Perpendicular bisector
Angle bisector

Students will identify and justify geometric relationships, formally and informally.

Geometric Relationships

8.G.1 Identify pairs of vertical angles as congruent

8.G.2 Identify pairs of supplementary and complementary angles

8.G.3 Calculate the missing angle in a supplementary or complementary pair

8.G.4 Determine angle pair relationships when given two parallel lines cut by a transversal

8.G.5 Calculate the missing angle measurements when given two parallel lines cut by a transversal

8.G.6 Calculate the missing angle measurements when given two intersecting lines and an angle

Students will apply transformations and symmetry to analyze problem solving situations.

Transformational Geometry

8.G.7 Describe and identify transformations in the plane, using proper function notation (rotations, reflections, translations, and dilations)

8.G.8 Draw the image of a figure under rotations of 90 and 180 degrees

8.G.9 Draw the image of a figure under a reflection over a given line

8.G.10 Draw the image of a figure under a translation

8.G.11 Draw the image of a figure under a dilation

8.G.12 Identify the properties preserved and not preserved under a reflection, rotation, translation, and dilation

Students will apply coordinate geometry to analyze problem solving situations.

Coordinate Geometry

8.G.13 Determine the slope of a line from a graph and explain the meaning of slope as a constant rate of change

8.G.14 Determine the y-intercept of a line from a graph and be able to explain the y-intercept

8.G.15 Graph a line using a table of values

8.G.16 Determine the equation of a line given the slope and the y-intercept

8.G.17 Graph a line from an equation in slope-intercept form (y=mx+b)

8.A.18 Solve systems of equations graphically (only linear, integral solutions, y=mx+b format, no vertical/horizontal lines)

8.A.19 Graph the solution set of an inequality on a number line

8.A.20 Distinguish between linear and nonlinear equations ax² + bx + c; a=1 (only graphically)

8.A.21 Recognize the characteristics of quadratics in tables, graphs, equations, and situations

Measurement Strand

Students will determine what can be measured and how, using appropriate methods and formulas.

Units of Measurement

8.M.1 Solve equations/proportions to convert to equivalent measurements within metric and customary measurement systems Note: Also allow Fahrenheit to Celsius and vice versa.

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06/20/2006

8.PS.1	Use a variety of strategies to understand new mathematical content and to develop more efficient methods
8.PS.2	Construct appropriate extensions to problem situations
8.PS.3	Understand and demonstrate how written symbols represent mathematical ideas

8.PS.4	Observe patterns and formulate generalizations
8.PS.5	Make conjectures from generalizations
8.PS.6	Represent problem situations verbally, numerically, algebraically, and graphically

8.PS.7	Understand that there is no one right way to solve mathematical problems but that different methods have advantages and disadvantages
8.PS.8	Understand how to break a complex problem into simpler parts or use a similar problem type to solve a problem
8.PS.9	Work backwards from a solution
8.PS.10	Use proportionality to model problems
8.PS.11	Work in collaboration with others to solve problems

8.PS.12	Interpret solutions within the given constraints of a problem
8.PS.13	Set expectations and limits for possible solutions
8.PS.14	Determine information required to solve the problem
8.PS.15	Choose methods for obtaining required information
8.PS.16	Justify solution methods through logical argument
8.PS.17	Evaluate the efficiency of different representations of a problem

8.RP.2	Use mathematical strategies to reach a conclusion
8.RP.3	Evaluate conjectures by distinguishing relevant from irrelevant information to reach a conclusion or make appropriate estimates

8.RP.4	Provide supportive arguments for conjectures
8.RP.5	Develop, explain, and verify an argument using mathematical ideas and language

8.RP.6	Support an argument by using a systematic approach to test more than one case
8.RP.7	Devise ways to verify results or use counterexamples to refute incorrect statements
8.RP.8	Apply inductive reasoning in making and supporting mathematical conjectures

8.CM.1	Provide a correct, complete, coherent, and clear rationale for thought process used in problem solving
8.CM.2	Provide an organized argument which explains rationale for strategy selection
8.CM.3	Organize and accurately label work

8.CM.4	Share organized mathematical ideas through the manipulation of objects, numerical tables, drawings, pictures, charts, graphs, tables, diagrams, models and symbols in written and verbal form
8.CM.5	Answer clarifying questions from others

8.CM.6	Analyze mathematical solutions shared by others
8.CM.7	Compare strategies used and solutions found by others in relation to their own work
8.CM.8	Formulate mathematical questions that elicit, extend, or challenge strategies, solutions, and/or conjectures of others

8.CM.9	Increase their use of mathematical vocabulary and language when communicating with others
8.CM.10	Use appropriate language, representations, and terminology when describing objects, relationships, mathematical solutions, and rationale
8.CM.11	Draw conclusions about mathematical ideas through decoding, comprehension, and interpretation of mathematical visuals, symbols, and technical writing

8.CN.1	Understand and make connections among multiple representations of the same mathematical idea
8.CN.2	Recognize connections between subsets of mathematical ideas
8.CN.3	Connect and apply a variety of strategies to solve problems

8.CN.4	Model situations mathematically, using representations to draw conclusions and formulate new situations
8.CN.5	Understand how concepts, procedures, and mathematical results in one area of mathematics can be used to solve problems in other areas of mathematics

8.CN.6	Recognize and provide examples of the presence of mathematics in their daily lives
8.CN.7	Apply mathematical ideas to problem situations that develop outside of mathematics
8.CN.8	Investigate the presence of mathematics in careers and areas of interest
8.CN.9	Recognize and apply mathematics to other disciplines, areas of interest, and societal issues

8.R.1	Use physical objects, drawings, charts, tables, graphs, symbols, equations, or objects created using technology as representations
8.R.2	Explain, describe, and defend mathematical ideas using representations
8.R.3	Recognize, compare, and use an array of representational forms
8.R.4	Explain how different representations express the same relationship
8.R.5	Use standard and non-standard representations with accuracy and detail

8.R.6	Use representations to explore problem situations
8.R.7	Investigate relationships between different representations and their impact on a given problem
8.R.8	Use representation as a tool for exploring and understanding mathematical ideas

8.R.9	Use mathematics to show and understand physical phenomena (e.g., make and interpret scale drawings of figures or scale models of objects)
8.R.10	Use mathematics to show and understand social phenomena (e.g., determine profit from sale of yearbooks)
8.R.11	Use mathematics to show and understand mathematical phenomena (e.g., use tables, graphs, and equations to show a pattern underlying a function)

8.N.1	Develop and apply the laws of exponents for multiplication and division
8.N.2	Evaluate expressions with integral exponents
8.N.3	Read, write, and identify percents less than 1% and greater than 100%
8.N.4	Apply percents to: Tax Percent increase/decrease Simple interest Sale price Commission Interest rates Gratuities

8.N.5	Estimate a percent of quantity, given an application
8.N.6	Justify the reasonableness of answers using estimation

8.A.1	Translate verbal sentences into algebraic inequalities
8.A.2	Write verbal expressions that match given mathematical expressions
8.A.3	Describe a situation involving relationships that matches a given graph
8.A.4	Create a graph given a description or an expression for a situation involving a linear or nonlinear relationship
8.A.5	Use physical models to perform operations with polynomials

8.A.6	Multiply and divide monomials
8.A.7	Add and subtract polynomials (integer coefficients)
8.A.8	Multiply a binomial by a monomial or a binomial (integer coefficients)
8.A.9	Divide a polynomial by a monomial (integer coefficients) Note: The degree of the denominator is less than or equal to the degree of the numerator for all variables.
8.A.10	Factor algebraic expressions using the GCF
8.A.11	Factor a trinomial in the form ax²+ bx + c; a=1 and c having no more than three sets of factors

8.A.12	Apply algebra to determine the measure of angles formed by or contained in parallel lines cut by a transversal and by intersecting lines
8.A.13	Solve multi-step inequalities and graph the solution set on a number line
8.A.14	Solve linear inequalities by combining like terms, using the distributive property, or moving variables to one side of the inequality (include multiplication or division of inequalities by a negative number)

8.A.15	Understand that numerical information can be represented in multiple ways: arithmetically, algebraically, and graphically
8.A.16	Find a set of ordered pairs to satisfy a given linear numerical pattern (expressed algebraically); then plot the ordered pairs and draw the line
8.A.17	Define and use correct terminology when referring to function (domain and range)
8.A.18	Determine if a relation is a function
8.A.19	Interpret multiple representations using equation, table of values, and graph

8.G.1	Identify pairs of vertical angles as congruent
8.G.2	Identify pairs of supplementary and complementary angles
8.G.3	Calculate the missing angle in a supplementary or complementary pair
8.G.4	Determine angle pair relationships when given two parallel lines cut by a transversal
8.G.5	Calculate the missing angle measurements when given two parallel lines cut by a transversal
8.G.6	Calculate the missing angle measurements when given two intersecting lines and an angle

8.G.7	Describe and identify transformations in the plane, using proper function notation (rotations, reflections, translations, and dilations)
8.G.8	Draw the image of a figure under rotations of 90 and 180 degrees
8.G.9	Draw the image of a figure under a reflection over a given line
8.G.10	Draw the image of a figure under a translation
8.G.11	Draw the image of a figure under a dilation
8.G.12	Identify the properties preserved and not preserved under a reflection, rotation, translation, and dilation

8.G.13	Determine the slope of a line from a graph and explain the meaning of slope as a constant rate of change
8.G.14	Determine the y-intercept of a line from a graph and be able to explain the y-intercept
8.G.15	Graph a line using a table of values
8.G.16	Determine the equation of a line given the slope and the y-intercept
8.G.17	Graph a line from an equation in slope-intercept form (y=mx+b)
8.A.18	Solve systems of equations graphically (only linear, integral solutions, y=mx+b format, no vertical/horizontal lines)
8.A.19	Graph the solution set of an inequality on a number line
8.A.20	Distinguish between linear and nonlinear equations ax² + bx + c; a=1 (only graphically)
8.A.21	Recognize the characteristics of quadratics in tables, graphs, equations, and situations