Your Mathematics Standards Companion, Grades 3-5

Winner of the Presidential Award for Excellence in Science and Mathematics Teaching, Linda M. Gojak directed the Center for Mathematics and Science Education, Teaching, and Technology (CMSETT) at John Carroll University for 16 years. She has spent 28 years teaching elementary and middle school mathematics, and has served as the president of the National Council of Teachers of Mathematics (NCTM), the National Council of Supervisors of Mathematics (NCSM), and the Ohio Council of Teachers of Mathematics. 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.

• Indexes Cross-Referencing Your State StandardsQuick Reference GuideAcknowledgmentsLetter to Grades 3–5 TeachersLetter to Elementary 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. Operations and Algebraic ThinkingDomain OverviewSuggested Materials for This DomainKey VocabularyGrade 3Cluster A: Represent and solve problems involving multiplication and division.Cluster B: Understand properties of multiplication and the relationship between multiplication and division.Cluster C: Multiply and divide within 100.Cluster D: Solve problems involving the four operations, and identify and explain patterns in arithmetic.Sample Planning Page: Operations and Algebraic Thinking, Grade 3, Cluster APlanning PagesGrade 4Cluster A: Use the four operations with whole numbers to solve problems.Cluster B: Gain familiarity with factors and multiples.Cluster C: Generate and analyze patterns.Sample Planning Page: Operations and Algebraic Thinking, Grade 4, Cluster BPlanning PagesGrade 5Cluster A: Write and interpret numerical expressions.Cluster B: Analyze patterns and relationships.Sample Planning Page: Operations and Algebraic Thinking, Grade 5, Cluster APlanning PagesReflection Questions: Operations and Algebraic ThinkingPart 2. Number and Operations in Base TenDomain OverviewSuggested Materials for This DomainKey VocabularyGrade 3Cluster A: Use place value understanding and properties of operations to perform multi-digit arithmetic.Sample Planning Page: Number and Operations in Base Ten, Grade 3, Cluster APlanning PageGrade 4Cluster A: Generalize place value understanding for multi-digit whole numbers.Cluster B: Use place value understanding and properties of operations to perform multi-digit arithmetic.Sample Planning Page: Number and Operations in Base Ten, Grade 4, Cluster BPlanning PagesGrade 5Cluster A: Understand the place value system.Cluster B: Perform operations with multi-digit whole numbers and with decimals to hundredths.Sample Planning Page: Number and Operations in Base Ten, Grade 5, Cluster BPlanning PagesReflection Questions: Number and Operations in Base TenPart 3. Number and Operations—FractionsDomain OverviewSuggested Materials for This DomainKey VocabularyGrade 3Cluster A: Develop understanding of fractions as numbers.Sample Planning Page: Number and Operations—Fractions, Grade 3, Cluster APlanning PageGrade 4Cluster A: Extend understanding of fraction equivalence and ordering.Cluster B: Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.Cluster C: Understand decimal notation for fractions, and compare decimal fractions.Sample Planning Page: Number and Operations—Fractions, Grade 4, Cluster CPlanning PagesGrade 5Cluster A: Use equivalent fractions as a strategy to add and subtract fractions.Cluster B: Apply and extend previous understandings of multiplication and division to multiply and divide fractions.Sample Planning Page: Number and Operations—Fractions, Grade 5, Cluster APlanning PagesReflection Questions: Number and Operations—FractionsPart 4. Measurement and DataDomain OverviewSuggested Materials for This DomainKey VocabularyGrade 3Cluster A: Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.Cluster B: Represent and interpret data.Cluster C: Geometric measurement: Understand concepts of area and relate area to multiplication and to addition.Cluster D: Geometric measurement: Recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.Sample Planning Page: Measurement and Data, Grade 3, Cluster APlanning PagesGrade 4Cluster A: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.Cluster B: Represent and interpret data.Cluster C: Geometric measurement: Understand concepts of angle and measure angles.Sample Planning Page: Measurement and Data, Grade 4, Cluster APlanning PagesGrade 5Cluster A: Convert like measurement units within a given measurement system.Cluster B: Represent and interpret data.Cluster C: Geometric measurement: Understand concepts of volume and relate volume to multiplication and to addition.Sample Planning Page: Measurement and Data, Grade 5, Cluster CPlanning PagesReflection Questions: Measurement and DataPart 5. GeometryDomain OverviewSuggested Materials for This DomainKey VocabularyGrade 3Cluster A: Reason with shapes and their attributes.Sample Planning Page: Geometry, Grade 3, Cluster APlanning PageGrade 4Cluster A: Draw and identify lines and angles, and classify shapes by properties of their lines and angles.Sample Planning Page: Geometry, Grade 4, Cluster APlanning PageGrade 5Cluster A: Graph points on the coordinate plane to solve real-world and mathematical problems.Cluster B: Classify two-dimensional figures into categories based on their properties.Sample Planning Page: Geometry, Grade 5, Cluster APlanning PagesReflection Questions: GeometryResourcesTable 1. Addition and Subtraction Situations, Grades 3–5Table 2. Multiplication and Division Situations, Grades 3–5Table 3. Standards for Mathematical PracticeTable 4. Effective Teaching PracticesReproduciblesReproducible 1. Hundreds ChartReproducible 2. Place Value Chart to HundredsReproducible 3. Grid PaperReproducible 4. Base-Ten BlocksReproducible 5. Fraction Area Models (Circular)Reproducible 6. Fraction Area Models (Rectangular)Reproducible 7. Fraction Strips/BarsReproducible 8. Place Value ChartReproducible 9. Geoboard PaperReproducible 10. Dot Paper (Centimeter)Reproducible 11. Pattern BlocksReproducible 12. Tangram PatternAdditional ResourcesAbout the Authors