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8.PS
Problem Solving
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Students will build new mathematical knowledge through problem solving.
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8.PS.1
Use a variety of strategies to understand new mathematical content and to develop more efficient methods
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8.PS.2
Construct appropriate extensions to problem situations
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8.PS.3
Understand and demonstrate how written symbols represent mathematical ideas
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Students will solve problems that arise in mathematics and in other contexts.
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8.PS.4
Observe patterns and formulate generalizations
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8.PS.5
Make conjectures from generalizations
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8.PS.6
Represent problem situations verbally, numerically, algebraically, and graphically
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Students will apply and adapt a variety of appropriate strategies to solve problems.
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8.PS.7
Understand that there is no one right way to solve mathematical problems but that different methods have advantages and disadvantages
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8.PS.8
Understand how to break a complex problem into simpler parts or use a similar problem type to solve a problem
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8.PS.9
Work backwards from a solution
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8.PS.10
Use proportionality to model problems
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8.PS.11
Work in collaboration with others to solve problems
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Students will monitor and reflect on the process of mathematical problem solving.
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8.PS.12
Interpret solutions within the given constraints of a problem
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8.PS.13
Set expectations and limits for possible solutions
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8.PS.14
Determine information required to solve the problem
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8.PS.15
Choose methods for obtaining required information
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8.PS.16
Justify solution methods through logical argument
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8.PS.17
Evaluate the efficiency of different representations of a problem
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8.RP
Reasoning and Proof
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Students will recognize reasoning and proof as fundamental aspects of mathematics.
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8.RP.1
Recognize that mathematical ideas can be supported by a variety of strategies
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Students will make and investigate mathematical conjectures.
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8.RP.2
Use mathematical strategies to reach a conclusion
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8.RP.3
Evaluate conjectures by distinguishing relevant from irrelevant information to reach a conclusion or make appropriate estimates
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Students will develop and evaluate mathematical arguments and proofs.
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8.RP.4
Provide supportive arguments for conjectures
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8.RP.5
Develop, verify, and explain an argument, using appropriate mathematical ideas and language
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Students will select and use various types of reasoning and methods of proof.
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8.RP.6
Support an argument by using a systematic approach to test more than one case
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8.RP.7
Devise ways to verify results or use counterexamples to refute incorrect statements
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8.RP.8
Apply inductive reasoning in making and supporting mathematical conjectures
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8.CM
Communication
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Students will organize and consolidate their mathematical thinking through communication.
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8.CM.1
Provide a correct, complete, coherent, and clear rationale for thought process used in problem solving
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8.CM.2
Provide an organized argument which explains rationale for strategy selection
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8.CM.3
Organize and accurately label work
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Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
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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
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8.CM.5
Answer clarifying questions from others
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Students will analyze and evaluate the mathematical thinking and strategies of others.
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8.CM.6
Analyze mathematical solutions shared by others
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8.CM.7
Compare strategies used and solutions found by others in relation to their own work
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8.CM.8
Formulate mathematical questions that elicit, extend, or challenge strategies, solutions, and/or conjectures of others
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Students will use the language of mathematics to express mathematical ideas precisely.
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8.CM.9
Increase their use of mathematical vocabulary and language when communicating with others
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8.CM.10
Use appropriate language, representations, and terminology when describing objects, relationships, mathematical solutions, and rationale
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Number theory: Prime or composite (Eighth grade - A.3)
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Number theory: Greatest common factor (Eighth grade - A.5)
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Number theory: Least common multiple (Eighth grade - A.6)
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Number theory: Classify numbers (Eighth grade - A.8)
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Rational numbers: Identify rational and irrational numbers (Eighth grade - D.1)
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Rational numbers: Least common denominator (Eighth grade - D.3)
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Operations with rational numbers: Reciprocals and multiplicative inverses (Eighth grade - E.1)
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Ratios and proportions: Rate of change (Eighth grade - H.11)
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Proportional relationships: Find the constant of variation: graphs (Eighth grade - I.2)
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Percents: Percent of change (Eighth grade - J.10)
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Measurement: Precision (Eighth grade - L.5)
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Charts and graphs: Choose the best type of graph (Eighth grade - N.16)
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Coordinate graphs: Quadrants and axes (Eighth grade - P.2)
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Geometry: Identify complementary, supplementary, vertical, adjacent, and congruent angles (Eighth grade - Q.1)
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Geometry: Transversal of parallel lines (Eighth grade - Q.3)
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Geometry: Classify triangles (Eighth grade - Q.4)
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Geometry: Classify quadrilaterals (Eighth grade - Q.5)
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Geometry: Identify and classify polygons (Eighth grade - Q.7)
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Geometry: Similar and congruent figures (Eighth grade - Q.9)
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Geometry: Perimeter (Eighth grade - Q.14)
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Geometry: Parts of a circle (Eighth grade - Q.17)
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Geometry: Names and parts of 3-dimensional figures (Eighth grade - Q.23)
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Transformations: Identify reflections, rotations, and translations (Eighth grade - R.1)
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Transformations: Symmetry (Eighth grade - R.11)
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Number sequences: Identify arithmetic and geometric sequences (Eighth grade - S.1)
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Variable expressions: Identify terms and coefficients (Eighth grade - T.3)
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Nonlinear functions: Identify linear and nonlinear functions (Eighth grade - W.1)
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Monomials and polynomials: Identify monomials (Eighth grade - Y.1)
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Properties: Distributive property (Eighth grade - Z.2)
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Statistics: Calculate mean, median, mode, and range (Eighth grade - BB.1)
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Statistics: Quartiles (Eighth grade - BB.5)
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Statistics: Identify representative, random, and biased samples (Eighth grade - BB.6)
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8.CM.11
Draw conclusions about mathematical ideas through decoding, comprehension, and interpretation of mathematical visuals, symbols, and technical writing
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8.CN
Connections
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Students will recognize and use connections among mathematical ideas.
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8.CN.1
Understand and make connections among multiple representations of the same mathematical idea
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8.CN.2
Recognize connections between subsets of mathematical ideas
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8.CN.3
Connect and apply a variety of strategies to solve problems
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Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
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8.CN.4
Model situations mathematically, using representations to draw conclusions and formulate new situations
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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
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Students will recognize and apply mathematics in contexts outside of mathematics.
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8.CN.6
Recognize and provide examples of the presence of mathematics in their daily lives
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8.CN.7
Apply mathematical ideas to problem situations that develop outside of mathematics
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8.CN.8
Investigate the presence of mathematics in careers and areas of interest
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8.CN.9
Recognize and apply mathematics to other disciplines, areas of interest, and societal issues
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8.R
Representation
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Students will create and use representations to organize, record, and communicate mathematical ideas.
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8.R.1
Use physical objects, drawings, charts, tables, graphs, symbols, equations, or objects created using technology as representations
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8.R.2
Explain, describe, and defend mathematical ideas using representations
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8.R.3
Recognize, compare, and use an array of representational forms
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8.R.4
Explain how different representations express the same relationship
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8.R.5
Use standard and non-standard representations with accuracy and detail
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Students will select, apply, and translate among mathematical representations to solve problems.
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8.R.6
Use representations to explore problem situations
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8.R.7
Investigate relationships between different representations and their impact on a given problem
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8.R.8
Use representation as a tool for exploring and understanding mathematical ideas
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Students will use representations to model and interpret physical, social, and mathematical phenomena.
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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)
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8.R.10
Use mathematics to show and understand social phenomena (e.g., determine profit from sale of yearbooks)
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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)
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8.N
Number Sense and Operations
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Students will understand meanings of operations and procedures, and how they relate to one another.
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Operations
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8.N.1
Develop and apply the laws of exponents for multiplication and division
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8.N.2
Evaluate expressions with integral exponents
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8.N.3
Read, write, and identify percents less than 1% and greater than 100%
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8.N.4
Apply percents to:
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8.N.4.a
Tax
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8.N.4.b
Percent increase/decrease
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8.N.4.c
Simple interest
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8.N.4.d
Sale price
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8.N.4.e
Commission
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8.N.4.f
Interest rates
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8.N.4.g
Gratuities
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Students will compute accurately and make reasonable estimates.
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Estimation
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8.N.5
Estimate a percent of quantity, given an application
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8.N.6
Justify the reasonableness of answers using estimation
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8.A
Algebra
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Students will represent and analyze algebraically a wide variety of problem solving situations.
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Variables and Expressions
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8.A.1
Translate verbal sentences into algebraic inequalities
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8.A.2
Write verbal expressions that match given mathematical expressions
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8.A.3
Describe a situation involving relationships that matches a given graph
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8.A.4
Create a graph given a description or an expression for a situation involving a linear or nonlinear relationship
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8.A.5
Use physical models to perform operations with polynomials
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Students will perform algebraic procedures accurately.
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Variables and Expressions
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8.A.6
Multiply and divide monomials
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8.A.7
Add and subtract polynomials (integer coefficients)
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8.A.8
Multiply a binomial by a monomial or a binomial (integer coefficients)
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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.
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8.A.10
Factor algebraic expressions using the GCF
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8.A.11
Factor a trinomial in the form ax2 + bx + c; a=1 and c having no more than three sets of factors
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Equations and Inequalities
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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
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8.A.13
Solve multi-step inequalities and graph the solution set on a number line
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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)
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Students will recognize, use, and represent algebraically patterns, relations, and functions.
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Patterns, Relations, And Functions
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8.A.15
Understand that numerical information can be represented in multiple ways: arithmetically, algebraically, and graphically
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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
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8.A.17
Define and use correct terminology when referring to function (domain and range)
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8.A.18
Determine if a relation is a function
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8.A.19
Interpret multiple representations using equation, table of values, and graph
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8.G
Geometry
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Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.
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Constructions
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8.G.0
Construct the following, using a straight edge and compass:
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8.G.0.a
Segment congruent to a segment
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8.G.0.b
Angle congruent to an angle
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8.G.0.c
Perpendicular bisector
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8.G.0.d
Angle bisector
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Students will identify and justify geometric relationships, formally and informally.
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Geometric Relationships
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8.G.1
Identify pairs of vertical angles as congruent
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8.G.2
Identify pairs of supplementary and complementary angles
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8.G.3
Calculate the missing angle in a supplementary or complementary pair
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8.G.4
Determine angle pair relationships when given two parallel lines cut by a transversal
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8.G.5
Calculate the missing angle measurements when given two parallel lines cut by a transversal
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8.G.6
Calculate the missing angle measurements when given two intersecting lines and an angle
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Students will apply transformations and symmetry to analyze problem solving situations.
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Transformational Geometry
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8.G.7
Describe and identify transformations in the plane, using proper function notation (rotations, reflections, translations, and dilations)
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8.G.8
Draw the image of a figure under rotations of 90 and 180 degrees
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8.G.9
Draw the image of a figure under a reflection over a given line
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8.G.10
Draw the image of a figure under a translation
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8.G.11
Draw the image of a figure under a dilation
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8.G.12
Identify the properties preserved and not preserved under a reflection, rotation, translation, and dilation
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Students will apply coordinate geometry to analyze problem solving situations.
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Coordinate Geometry
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8.G.13
Determine the slope of a line from a graph and explain the meaning of slope as a constant rate of change
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8.G.14
Determine the y-intercept of a line from a graph and be able to explain the y-intercept
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8.G.15
Graph a line using a table of values
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8.G.16
Determine the equation of a line given the slope and the y-intercept
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8.G.17
Graph a line from an equation in slope-intercept form (y = mx + b)
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8.G.18
Solve systems of equations graphically (only linear, integral solutions, y = mx + b format, no vertical/horizontal lines)
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8.G.19
Graph the solution set of an inequality on a number line
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8.G.20
Distinguish between linear and nonlinear equations ax? + bx + c; a=1 (only graphically)
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8.G.21
Recognize the characteristics of quadratics in tables, graphs, equations, and situations
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8.M
Measurement
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Students will determine what can be measured and how, using appropriate methods and formulas.
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Units of Measurement
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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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IXL Learning. All rights reserved.