Mathematics (Grade 8)
Core Curriculum
MST3 Standard 3  Mathematics
Students will:
•understand the concepts of and become proficient with the skills of mathematics;
•communicate and reason mathematically;
•become problem solvers by using appropriate tools and strategies;
through the integrated study of number sense and operations, algebra, geometry, measurement,
and statistics and probability.
MST3.A CONTENT STRAND 2  Algebra
MST3.I.A Major Understanding 1  Students will represent and analyze algebraically a wide variety of problem solving situations.
MST3.I.A.08.01
 Translate verbal sentences into algebraic inequalities
MST3.I.A.08.02
 Write verbal expressions that match given mathematical expressions
MST3.I.A.08.03
 Describe a situation involving relationships that matches a given graph
MST3.I.A.08.04
 Create a graph given a description or an expression for a situation involving a linear or nonlinear relationship
MST3.I.A.08.05
 Use physical models to perform operations with polynomials

MST3.I.A Major Understanding 2  Students will perform algebraic procedures accurately.
MST3.I.A.08.06A
 Multiply monomials
MST3.I.A.08.06B
 Divide monomials
MST3.I.A.08.07
 Add and subtract polynomials (integer coefficients)
MST3.I.A.08.08
 Multiply a binomial by a monomial or a binomial (integer coefficients)
MST3.I.A.08.09
 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.
MST3.I.A.08.10
 Factor algebraic expressions using the GCF
MST3.I.A.08.11
 Factor a trinomial in the form ax squared + bx + c; a=1 and c having no more than three sets of factors
MST3.I.A.08.12
 Apply algebra to determine the measure of angles formed by or contained in parallel lines cut by a transversal and by intersecting lines
MST3.I.A.08.13
 Solve multistep inequalities and graph the solution set on a number line
MST3.I.A.08.14
 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)

MST3.I.A Major Understanding 3  Students will recognize, use, and represent algebraically patterns, relations, and functions.
MST3.I.A.08.15
 Understand that numerical information can be represented in multiple ways: arithmetically, algebraically, and graphically
MST3.I.A.08.16
 Find a set of ordered pairs to satisfy a given linear numerical pattern (expressed algebraically); then plot the ordered pairs and draw the line
MST3.I.A.08.17
 Define and use correct terminology when referring to function (domain and range)
MST3.I.A.08.18
 Determine if a relation is a function
MST3.I.A.08.19
 Interpret multiple representations using equation, table of values, and graph

MST3.CM PROCESS STRAND 3  Communication
MST3.I.CM Major Understanding 1  Students will organize and consolidate their mathematical thinking through communication.
MST3.I.CM.08.01
 Provide a correct, complete, coherent, and clear rationale for thought process used in problem solving
MST3.I.CM.08.02
 Provide an organized argument which explains rationale for strategy selection
MST3.I.CM.08.03
 Organize and accurately label work

MST3.I.CM Major Understanding 2  Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
MST3.I.CM.08.04
 Use both written and verbal form to share organized mathematical ideas through the manipulation of objects, numerical tables, drawings, pictures, charts, graphs, tables, diagrams, models, and symbols
MST3.I.CM.08.05
 Answer clarifying questions from others

MST3.I.CM Major Understanding 3  Students will analyze and evaluate the mathematical thinking and strategies of others.
MST3.I.CM.08.06
 Analyze mathematical solutions shared by other students
MST3.I.CM.08.07
 Compare strategies used and solutions found by others in relation to their own work
MST3.I.CM.08.08
 Formulate mathematical questions that elicit, extend, or challenge strategies, solutions, and/or conjectures of others

MST3.I.CM Major Understanding 4  Students will use the language of mathematics to express mathematical ideas precisely.
MST3.I.CM.08.09
 Increase their use of mathematical vocabulary and language when communicating with others
MST3.I.CM.08.10
 Use appropriate language, representations, and terminology when describing objects, relationships, mathematical solutions, and rationale
MST3.I.CM.08.11
 Draw conclusions about mathematical ideas through decoding,
comprehension, and interpretation of mathematical visuals, symbols, and technical writing

MST3.CN PROCESS STRAND 4  Connections
MST3.I.CN Major Understanding 1  Students will recognize and use connections among mathematical ideas.
MST3.I.CN.08.01
 Understand and make connections among multiple representations of the same mathematical idea
MST3.I.CN.08.02
 Recognize connections between subsets of mathematical ideas
MST3.I.CN.08.03
 Connect and apply a variety of strategies to solve problems

MST3.I.CN Major Understanding 2  Students will understand how mathematical ideas interconnect and build on one another to produce a coherent whole.
MST3.I.CN.08.04
 Model situations mathematically, using representations to draw conclusions and formulate new situations
MST3.I.CN.08.05
 Understand how concepts, procedures, and mathematical results in one area of mathematics can be used to solve problems in other areas of mathematics

MST3.I.CN Major Understanding 3  Students will recognize and apply mathematics in contexts outside of mathematics.
MST3.I.CN.08.06
 Recognize and provide examples of the presence of mathematics in their daily lives
MST3.I.CN.08.07
 Apply mathematics to solve problems situations that develop outside of mathematics
MST3.I.CN.08.08
 Investigate the presence of mathematics in careers and areas or interest
MST3.I.CN.08.09
 Recognize and apply mathematics to other disciplines and areas of interest, and societal issues

MST3.G CONTENT STRAND 3  Geometry
MST3.I.G Major Understanding 1  Students will use visualization and spatial reasoning to analyze characteristics and properties of geometric shapes.
MST3.I.G.08.00
 Construct the following using a straight edge and compass:
Segment congruent to a segment
Angle congruent to an angle
Perpendicular bisector
Angle bisector

MST3.I.G Major Understanding 2  Students will identify and justify geometric relationships, formally and informally.
MST3.I.G.08.01
 Identify pairs of vertical angles as congruent
MST3.I.G.08.02
 Identify pairs of supplementary and complementary angles
MST3.I.G.08.03
 Calculate the missing angle in a supplementary or complementary pair
MST3.I.G.08.04
 Determine angle pair relationships when given two parallel lines cut by a transversal
MST3.I.G.08.05
 Calculate the missing angle measurements when given two parallel lines cut by a transversal
MST3.I.G.08.06
 Calculate the missing angle measurements when given two intersecting lines and an angle

MST3.I.G Major Understanding 3  Students will apply transformations and symmetry to analyze problem solving situations.
MST3.I.G.08.07
 Describe and identify transformations in the plane, using proper function notation (rotations, reflections, translations, and dilations)
MST3.I.G.08.08
 Draw the image of a figure under rotations of 90 and 180 degrees
MST3.I.G.08.09
 Draw the image of a figure under a reflection over a given line
MST3.I.G.08.10
 Draw the image of a figure under a translation
MST3.I.G.08.11
 Draw the image of a figure under a dilation
MST3.I.G.08.12
 Identify the properties preserved and not preserved under a reflection, rotation, translation, and dilation

MST3.I.G Major Understanding 4  Students will apply coordinate geometry to analyze problem solving situations.
MST3.I.G.08.13
 Determine the slope of a line from a graph and explain the meaning of slope as a constant rate of change
MST3.I.G.08.14
 Determine the yintercept of a line from a graph and be able to explain the yintercept
MST3.I.G.08.15
 Graph a line using a table of values
MST3.I.G.08.16
 Determine the equation of a line given the slope and the yintercept
MST3.I.G.08.17
 Graph a line from an equation in slopeintercept form (y = mx + b )
MST3.I.G.08.18
 Solve systems of equations graphically (only linear, integral solutions, y = mx + b format, no vertical/horizontal lines)
MST3.I.G.08.19
 Graph the solution set of an inequality on a number line
MST3.I.G.08.20
 Distinguish between linear and nonlinear equations ax² + bx + c; a=1 (only graphically)
MST3.I.G.08.21
 Recognize the characteristics of quadratics in tables, graphs, equations, and situations

MST3.M CONTENT STRAND 4  Measurement
MST3.I.M Major Understanding 1  Students will determine what can be measured and how, using appropriate methods and formulas.
MST3.I.M.08.01
 Solve equations/proportions to convert to equivalent measurements within metric and customary measurement systems
Note: Also allow Fahrenheit to Celsius and vice versa

MST3.N CONTENT STRAND 1  Number Sense & Operations
MST3.I.N Major Understanding 2  Students will understand meanings of operations and procedures, and how they relate to one another.
MST3.I.N.08.01
 Develop and apply the laws of exponents for multiplication and division
MST3.I.N.08.02
 Evaluate expressions with integral exponents
MST3.I.N.08.03
 Read, write, and identify percents less than 1% and greater than 100%
MST3.I.N.08.04
 Apply percents to: Tax
Percent increase/decrease
Simple interest
Sale price
Commission
Interest rates
Gratuities

MST3.I.N Major Understanding 3  Students will compute accurately and make reasonable estimates.
MST3.I.N.08.05
 Estimate a percent of quantity, given an application
MST3.I.N.08.06
 Justify the reasonableness of answers using estimation

MST3.PS PROCESS STRAND 1  Problem Solving
MST3.I.PS Major Understanding 1  Students will build new mathematical knowledge through problem solving.
MST3.I.PS.08.01
 Use a variety of strategies to understand new mathematical content and to develop more efficient methods
MST3.I.PS.08.02
 Construct appropriate extensions to problem situations
MST3.I.PS.08.03
 Understand and demonstrate how written symbols represent mathematical ideas

MST3.I.PS Major Understanding 2  Students will solve problems that arise in mathematics and in other contexts.
MST3.I.PS.08.04
 Observe patterns and formulate generalizations
MST3.I.PS.08.05
 Make conjectures from generalizations
MST3.I.PS.08.06
 Represent problem situations verbally, numerically, algebraically, and graphically

MST3.I.PS Major Understanding 3  Students will apply and adapt a variety of appropriate strategies to solve problems.
MST3.I.PS.08.07
 Understand that there is no one right way to solve mathematical problem but that different methods have advantages and disadvantages
MST3.I.PS.08.08
 Understand how to break a complex problem into simpler
parts or use a similar problem type to solve a problem
MST3.I.PS.08.09
 Work backwards from a solution
MST3.I.PS.08.10
 Use proportionality to model problems
MST3.I.PS.08.11
 Work in collaboration with others to solve problems

MST3.I.PS Major Understanding 4  Students will monitor and reflect on the process of mathematical problem solving.
MST3.I.PS.08.12
 Interpret solutions within the given constraints of a problem
MST3.I.PS.08.13
 Set expectations and limits for possible solutions
MST3.I.PS.08.14
 Determine information required to solve the problem
MST3.I.PS.08.15
 Choose methods for obtaining required information
MST3.I.PS.08.16
 Justify solution methods through logical argument
MST3.I.PS.08.17
 Evaluate the efficiency of different representations of a problem

MST3.R PROCESS STRAND 5  Representation
MST3.I.R Major Understanding 1  Students will create and use representations to organize, record, and communicate mathematical ideas.
MST3.I.R.08.01
 Use physical objects, drawings, charts, tables, graphs, symbols, equations or objects created using technology as representations
MST3.I.R.08.02
 Explain, describe, and defend mathematical ideas using representations
MST3.I.R.08.03
 Recognize, compare, and use an array of representational forms
MST3.I.R.08.04
 Explain how different representations express the same relationship
MST3.I.R.08.05
 Use standard and nonstandard representations with accuracy and detail

MST3.I.R Major Understanding 2  Students will select, apply, translate among mathematical representations to solve problems.
MST3.I.R.08.06
 Use representations to explore problem situations
MST3.I.R.08.07
 Investigate relationships between different representations and their impact on a given problem
MST3.I.R.08.08
 Use representation as a tool for exploring and understanding mathematical ideas

MST3.I.R Major Understanding 3  Students will use representations to model and interpret physical, social, and mathematical phenomena
MST3.I.R.08.09
 Use mathematics to show and understand physical phenomena
(e.g., make and interpret scale drawings of figures or scale models of objects)
MST3.I.R.08.10
 Use mathematics to show and understand social phenomena (e.g., determine profit from sale of yearbooks)
MST3.I.R.08.11
 Use mathematics to show and understand mathematical phenomena (e.g., use tables graphs, and equations to show a pattern underlying a function)

MST3.RP PROCESS STRAND 2  Reasoning & Proof
MST3.I.RP Major Understanding 1  Students will recognize reasoning and proof as fundamental aspects of mathematics.
MST3.I.RP.08.01
 Recognize that mathematical ideas can be supported using a variety of strategies

MST3.I.RP Major Understanding 2  Students will make and investigate mathematical conjectures.
MST3.I.RP.08.02
 Use mathematical strategies to reach a conclusion
MST3.I.RP.08.03
 Evaluate conjectures by distinguishing relevant from irrelevant information to reach a conclusion or make appropriate estimates

MST3.I.PS Major Understanding 3  Students will develop and evaluate mathematical arguments and proofs.
MST3.I.RP.08.04
 Provide supportive arguments for conjectures
MST3.I.RP.08.05
 Develop, verify, and explain an argument, using appropriate mathematical ideas and language
MST3.I.RP.08.06
 Support an argument by using a systematic approach to test more than one case
MST3.I.RP.08.07
 Devise ways to verify results or use counterexamples to refute incorrect statements

MST3.I.RP Major Understanding 4  Students will select and use various types of reasoning and methods of proof.
MST3.I.RP.08.08
 Apply inductive reasoning in making and supporting mathematical conjectures



