Your Mathematics Standards Companion, Grades 6-8

Ruth Harbin Miles coaches rural, suburban, and inner-city school mathematics teachers.  Her professional experiences include coordinating the K-12 Mathematics Teaching and Learning Program for the Olathe, Kansas, Public Schools for more than 25 years; teaching mathematics methods courses at Virginia’s Mary Baldwin College; and serving on the Board of Directors for the National Council of Teachers of Mathematics, the National Council of Supervisors of Mathematic, and both the Virginia Council of Teachers of Mathematics and the Kansas Association of Teachers of Mathematics.  Ruth is a co-author of five Corwin books including A Guide to Mathematics Coaching, A Guide to Mathematics Leadership, Visible Thinking in the K-8 Mathematics Classroom, The Common Core Mathematics Standards, and Realizing Rigor in the Mathematics Classroom.  As co-owner of Happy Mountain Learning, Ruth specializes in developing teachers’ content knowledge and strategies for engaging students to achieve high standards in mathematics.After teaching mathematics in grades K-8 for 20 years, Lois served as the middle school mathematics specialist for the Virginia Department of Education. Here she worked on curriculum and teacher professional learning. She served the Virginia Council of Teachers of Mathematics and was a board member for the local Jefferson Council of Teachers of Mathematics. After receiving her doctorate in curriculum and instruction at The University of Virginia, she began serving as adjunct faculty to Mary Baldwin College and is in her 15th year working with pre-service teachers. Currently Lois is an International Fellow with the Charles A. Dana Center working with classroom teachers in the Department of Defense Schools helping them implement their College and Career Readiness Standards. Among her recognitions are a Fulbright Teacher Exchange and Virginia Middle School Mathematics Teacher of the Year.

• Indexes Cross-Referencing Your State StandardsQuick Reference GuideAcknowledgmentsLetter to Grades 6–8 TeachersLetter to Middle School PrincipalsIntroductionA Brief History of Current State StandardsCollege and Career Ready Standards for MathematicsInstructional ShiftsTerminology Used in This BookEffective Teaching PracticesHow to Use This BookReflection QuestionsPart 1. Ratios and Proportional RelationshipsDomain OverviewSuggested Materials for This DomainKey VocabularyGrade 6Cluster A: Understand ratio concepts and use ratio reasoning to solve problems.Sample Planning Page: Ratios and Proportional Relationships, Grade 6, Cluster APlanning PageGrade 7Cluster A: Analyze proportional relationships and use them to solve real-world and mathematical problems.Sample Planning Page: Ratios and Proportional Relationships, Grade 7, Cluster APlanning PageReflection Questions: Ratios and Proportional RelationshipsPart 2. The Number SystemDomain OverviewSuggested Materials for This DomainKey VocabularyGrade 6Cluster A: Apply and extend previous understandings of multiplication and division to divide fractions by fractions.Cluster B: Compute fluently with multi-digit numbers and find common factors and multiples.Cluster C: Apply and extend previous understandings of numbers to the system of rational numbers.Sample Planning Page: The Number System, Grade 6, Cluster CPlanning PagesGrade 7Cluster A: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.Sample Planning Page: The Number System, Grade 7, Cluster APlanning PageGrade 8Cluster A: Know that there are numbers that are not rational, and approximate them by rational numbers.Sample Planning Page: The Number System, Grade 8, Cluster APlanning PageReflection Questions: The Number SystemPart 3. Expressions and EquationsDomain OverviewSuggested Materials for This DomainKey VocabularyGrade 6Cluster A: Apply and extend previous understandings of arithmetic to algebraic expressions.Cluster B: Reason about and solve one-variable equations and inequalities.Cluster C: Represent and analyze quantitative relationships between dependent and independent variables.Sample Planning Page: Expressions and Equations, Grade 6, Cluster CPlanning PagesGrade 7Cluster A: Use properties of operations to generate equivalent expressions.Cluster B: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.Sample Planning Page: Expressions and Equations, Grade 7, Cluster APlanning PagesGrade 8Cluster A: Work with radicals and integer exponents.Cluster B: Understand the connections between proportional relationships, lines, and linear equations.Cluster C: Analyze and solve linear equations and pairs of simultaneous linear equations.Sample Planning Page: Expressions and Equations, Grade 8, Cluster APlanning PagesReflection Questions: Expressions and EquationsPart 4. FunctionsDomain OverviewSuggested Materials for This DomainKey VocabularyGrade 8Cluster A: Define, evaluate, and compare functions.Cluster B: Use functions to model relationships between quantities.Sample Planning Page: Functions, Grade 8, Cluster APlanning PagesReflection Questions: FunctionsPart 5. GeometryDomain OverviewSuggested Materials for This DomainKey VocabularyGrade 6Cluster A: Solve real-world and mathematical problems involving area, surface area, and volume.Sample Planning Page: Geometry, Grade 6, Cluster APlanning PageGrade 7Cluster A: Draw, construct, and describe geometrical figures and describe the relationships between them.Cluster B: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.Sample Planning Page: Geometry, Grade 7, Cluster BPlanning PagesGrade 8Cluster A: Understand congruence and similarity using physical models, transparencies, or geometry software.Cluster B: Understand and apply the Pythagorean Theorem.Cluster C: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.Sample Planning Page: Geometry, Grade 8, Cluster APlanning PagesReflection Questions: GeometryPart 6. Statistics and ProbabilityDomain OverviewSuggested Materials for This DomainKey VocabularyGrade 6Cluster A: Develop understanding of statistical variability.Cluster B: Summarize and describe distributions.Sample Planning Page: Statistics and Probability, Grade 6, Cluster BPlanning PagesGrade 7Cluster A: Use random sampling to draw inferences about a population.Cluster B: Draw informal comparative inferences about two populations.Cluster C: Investigate chance processes and develop, use, and evaluate probability models.Sample Planning Page: Statistics and Probability, Grade 7, Cluster CPlanning PagesGrade 8Cluster A: Investigate patterns of association in bivariate data.Sample Planning Page: Statistics and Probability, Grade 8, Cluster APlanning PageReflection Questions: Statistics and ProbabilityResourcesTable 1. Standards for Mathematical PracticeTable 2. Effective Teaching PracticesReproduciblesReproducible 1. Percent WheelReproducible 2. Frayer ModelReproducible 3. Net of a CubeReproducible 4. Example for MAD (Mean Absolute Deviation)Additional ResourcesAbout the Authors