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Wisconsin Math Standards - Grades 5-8
MathScore aligns to the Wisconsin Math Standards for Grades 5-8. The standards appear below along with the MathScore topics that match. If you click on a topic name, you will see sample problems at varying degrees of difficulty that MathScore generated. When students use our program, the difficulty of the problems will automatically adapt based on individual performance, resulting in not only true differentiated instruction, but a challenging game-like experience.
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View the Wisconsin Math Standards at other levels.
Mathematical Processes
A.8.1 Use reasoning abilities to:• evaluate information (Algebraic Sentences 2 )
• perceive patterns (Patterns: Numbers )
• identify relationships (Number Comparison , Algebraic Sentences 2 )
• formulate questions for further exploration
• evaluate strategies
• justify statements (Word Problems With Remainders )
• test reasonableness of results (Estimated Addition , Estimated Subtraction , Money Addition , Money Subtraction )
• defend work
A.8.2 Communicate logical arguments clearly to show why a result makes sense
A.8.3 Analyze non-routine problems by modeling, illustrating, guessing, simplifying, generalizing, shifting to another point of view, etc. (Perimeter and Area of Composite Figures )
A.8.4 Develop effective oral and written presentations that include
• appropriate use of technology
• the conventions of mathematical discourse (e.g., symbols, definitions, labeled drawings)
• mathematical language (Algebraic Terms )
• clear organization of ideas and procedures
• understanding of purpose and audience
A.8.5 Explain mathematical concepts, procedures, and ideas to others who may not be familiar with them
A.8.6 Read and understand mathematical texts and other instructional materials and recognize mathematical ideas as they appear in other contexts (Percentage Pictures , Stem And Leaf Plots , Tally and Pictographs , Bar Graphs , Line Graphs )
Number Operations and Relationships
B.8.1 Read, represent, and interpret various rational numbers (whole numbers, integers, decimals, fractions, and percents) with verbal descriptions, geometric models, and mathematical notation (e.g., expanded, scientific, exponential) (Place Value , Decimal Place Value , Positive Number Line , Number Line , Compare Integers , Percentage Pictures , Scientific Notation )B.8.2 Perform and explain operations on rational numbers (add, subtract, multiply, divide, raise to a power, extract a root, take opposites and reciprocals, determine absolute value) (Using Parentheses , Order Of Operations , Small Decimal Division , Money Multiplication , Money Division , Fraction Addition , Fraction Subtraction , Fraction Multiplication , Fraction Division , Decimal Addition , Decimal Subtraction , Decimal Multiplication , Decimal Division , Integer Addition , Integer Subtraction , Positive Integer Subtraction , Integer Multiplication , Integer Division , Integer Equivalence , Absolute Value 1 , Absolute Value 2 , Exponent Basics , Estimating Square Roots , Perfect Squares )
B.8.3 Generate and explain equivalencies among fractions, decimals, and percents (Fraction Simplification , Fractions to Decimals , Decimals To Fractions , Repeating Decimals , Percentages )
B.8.4 Express order relationships among rational numbers using appropriate symbols (>, <, >, <, ≠) (Number Comparison , Order Large Numbers , Order Decimals , Compare Mixed Values , Compare Mixed Values 2 , Fraction Comparison , Compare Decimals , Compare Integers )
B.8.5 Apply proportional thinking in a variety of problem situations that include, but are not limited to
• ratios and proportions (e.g., rates, scale drawings, similarity) (Unit Cost , Proportions 1 , Proportions 2 , Distance, Rate, and Time , Ratios )
• percents, including those greater than 100 and less than one (e.g., discounts, rate of increase or decrease, sales tax) (Percentage Change , Purchases At Stores , Restaurant Bills , Commissions , Percent of Quantity )
B.8.6 Model and solve problems involving number-theory concepts such as
• prime and composite numbers (Prime Numbers , Prime Factoring , Prime Factoring 2 )
• divisibility and remainders (Division with Remainders , Long Division with Remainders , Word Problems With Remainders , Divisibility Rules )
• greatest common factors (Greatest Common Factor , Factoring )
• least common multiples (Least Common Multiple )
B.8.7 In problem-solving situations, select and use appropriate computational procedures with rational numbers such as (Arithmetic Word Problems , Basic Word Problems 2 , Fraction Word Problems , Fraction Word Problems 2 )
• calculating mentally
• estimating (Rounding Large Numbers , Decimal Rounding , Estimated Addition , Estimated Subtraction , Money Addition , Money Subtraction , Estimated Multiplication , Estimated Division , Estimated Multiply Divide Word Problems )
• creating, using, and explaining algorithms
• using technology (e.g., scientific calculators, spreadsheets)
Geometry
C.8.1 Describe special and complex two- and three-dimensional figures (e.g., rhombus, polyhedron, cylinder) and their component parts (e.g., base, altitude, and slant height) by:• naming, defining, and giving examples (Triangle Types , Quadrilateral Types , Polygon Names )
• comparing, sorting, and classifying them
• identifying and contrasting their properties (e.g., symmetrical, isosceles, regular) (Triangle Types , Quadrilateral Types )
• drawing and constructing physical models to specifications
• explaining how these figures are related to objects in the environment
C.8.2 Identify and use relationships among the component parts of special and complex two- and three-dimensional figures (e.g., parallel sides, congruent faces). (Triangle Area 2 , Rectangular Solids 2 , Irregular Shape Areas , Parallel and Perpendicular Lines , Proportions 2 )
C.8.3 Identify three-dimensional shapes from two-dimensional perspectives and draw two-dimensional sketches of three-dimensional objects preserving their significant features
C.8.4 Perform transformations on two-dimensional figures and describe and analyze the effects of the transformations on the figures (Translations and Reflections )
C.8.5 Locate objects using the rectangular coordinate system (Ordered Pairs )
Measurement
D.8.1 Identify and describe attributes in situations where they are not directly or easily measurable (e.g., distance, area of an irregular figure, likelihood of occurrence)D.8.2 Demonstrate understanding of basic measurement facts, principles, and techniques including the following
• approximate comparisons between metric and US Customary units (e.g., a liter and a quart are about the same; a kilometer is about six-tenths of a mile)
• knowledge that direct measurement produces approximate, not exact, measures
• the use of smaller units to produce more precise measures
D.8.3 Determine measurement directly using standard units (metric and US Customary) with these suggested degrees of accuracy
• lengths to the nearest mm or 1/16 of an inch
• weight (mass) to the nearest 0.1 g or 0.5 ounce
• liquid capacity to the nearest ml
• angles to the nearest degree
• temperature to the nearest C or F
• elapsed time to the nearest second (Time Intervals )
D.8.4 Determine measurements indirectly using
• estimation
• conversion of units within a system (e.g., quarts to cups, millimeters to centimeters) (Distance Conversion , Time Conversion , Volume Conversion , Weight Conversion , Temperature Conversion )
• ratio and proportion (e.g., similarity, scale drawings) (Area and Volume Conversions , Unit Cost , Proportions 2 , Distance, Rate, and Time )
• geometric formulas to derive lengths, areas, volumes of common figures (e.g., perimeter, circumference, surface area) (Circle Measurements , Triangle Area , Parallelogram Area , Perimeter , Rectangular Solids , Circle Area , Circle Circumference , Triangular Prisms , Cylinders , Trapezoids )
• the Pythagorean relationship (Pythagorean Theorem )
• geometric relationships and properties for angle size (e.g., parallel lines and transversals; sum of angles of a triangle; vertical angles) (Triangle Angles , Quadrilateral Angles , Triangle Angles 2 , Identifying Angles , Solving For Angles , Polygon Angles , Angle Measurements , Angle Measurements 2 )
Statistics and Probability
E.8.1 Work with data in the context of real-world situations by:• formulating questions that lead to data collection and analysis
• designing and conducting a statistical investigation
• using technology to generate displays, summary statistics, and presentations
E.8.2 Organize and display data from statistical investigations using:
• appropriate tables, graphs, and/or charts (e.g., circle, bar or line for multiple sets of data) (Tally and Pictographs , Bar Graphs , Line Graphs )
• appropriate plots (e.g., line, stem-and-leaf, box, scatter) (Stem And Leaf Plots )
E.8.3 Extract, interpret, and analyze information from organized and displayed data by using: (Stem And Leaf Plots , Bar Graphs , Line Graphs )
• frequency and distribution, including mode and range (Mean, Median, Mode )
• central tendencies of data (mean and median) (Mean, Median, Mode )
• indicators of dispersion (e.g., outliers)
E.8.4 Use the results of data analysis to:
• make predictions (Batting Averages )
• develop convincing arguments
• draw conclusions
E.8.5 Compare several sets of data to generate, test, and, as the data dictate, confirm or deny hypotheses
E.8.6 Evaluate presentations and statistical analyses from a variety of sources for:
• credibility of the source
• techniques of collection, organization, and presentation of data
• missing or incorrect data
• inferences
• possible sources of bias
E.8.7 Determine the likelihood of occurrence of simple events by:
• using a variety of strategies to identify possible outcomes (e.g., lists, tables, tree diagrams)
• conducting an experiment
• designing and conducting simulations
• applying theoretical notions of probability (e.g., that four equally likely events have a 25% chance of happening) (Probability , Probability 2 , Object Picking Probability )
Algebraic Relationships
F.8.1 Work with algebraic expressions in a variety of ways, including• using appropriate symbolism, including exponents and variables (Phrases to Algebraic Expressions , Algebraic Word Problems , Algebraic Sentences 2 , Algebraic Sentences , Exponent Basics )
• evaluating expressions through numerical substitution (Variable Substitution , Variable Substitution 2 )
• generating equivalent expressions (Simplifying Algebraic Expressions 2 , Binomial Fraction Simplification , Polynomial Fraction Simplification )
• adding and subtracting expressions (Simplifying Algebraic Expressions )
F.8.2 Work with linear and nonlinear patterns and relationships in a variety of ways, including
• representing them with tables, with graphs, and with algebraic expressions, equations, and inequalities
• describing and interpreting their graphical representations (e.g., slope, rate of change, intercepts) (Determining Slope , Graphs to Linear Equations , Graphs to Linear Equations 2 , Graphs to Linear Inequalities , Nonlinear Functions )
• using them as models of real-world phenomena
• describing a real-world phenomenon that a given graph might represent
F.8.3 Recognize, describe, and analyze functional relationships by generalizing a rule that characterizes the pattern of change among variables. These functional relationships include exponential growth and decay (e.g., cell division, depreciation)
F.8.4 Use linear equations and inequalities in a variety of ways, including
• writing them to represent problem situations and to express generalizations
• solving them by different methods (e.g., informally, graphically, with formal properties, with technology) (Linear Equations , Number Line Inequalities )
• writing and evaluating formulas (including solving for a specified variable) (Linear Equations , Single Variable Equations , Single Variable Equations 2 , Single Variable Equations 3 , Single Variable Inequalities , Simple Interest , Compound Interest , Continuous Compound Interest , Distance, Rate, and Time , Two Variable Equations )
• using them to record and describe solution strategies
F.8.5 Recognize and use generalized properties and relations, including
• additive and multiplicative property of equations and inequalities
• commutativity and associativity of addition and multiplication (Associative Property 1 , Associative Property 2 , Commutative Property 1 , Commutative Property 2 )
• distributive property (Distributive Property , Distributive Property 2 , Basic Distributive Property )
• inverses and identities for addition and multiplication (Inverse Equations 1 , Inverse Equations 2 )
• transitive property
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