6th Grade Math Instructional Focus Units



In Principles?of Algebra, Grade 6 instructional focuses will be on: (1) Connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.QuarterUnitChapter(s)Main IdeaEstimated DaysMATHiaX ModuleQ112, 3, 4Number Sense29Fraction & Dec Operations25, 6Ratios, Rates & Percents30Ratios, Rates, & PercentsQ237, 8Algebraic Thinking36Number & Alg ExpressionsQ349Equations and Inequalities17One-Step Eq & Ineq510, 11Integers17Neg Numbers & QuadrantsQ4612Units of Measure6Geo Measurement713Geometry – Area9814Geometry – 3D Figures 9915, 16Statistical Thinking17Measures of Cent TendencyRP = 21%NS = 27%EE = 31%G/SP = 21%AZ College and Career Ready Standards Carnegie Course 1 Content MapCommon Core Progressions – Use for explanations of standards sequencing, pointing out cognitive difficulties and pedagogical solutions, and providing further detail of mathematical content. Focus 1: Number SenseBig Ideas: Apply and extend previous understandings of multiplication and division to divide fractions by fractions (6.NS.A)Compute fluently with multi-digit numbers including decimals and find common factors and multiples (6.NS.B)Learning Goals & Scales: 6.NPre-requisite clusters/skills: Apply and extend previous understandings of multiplication and division to multiply and divide fractions (5.NF.B)Preform operations with multi-digit whole numbers and with decimals to hundredths (5.NBT.B)Gain familiarity with factors and multiples (4.OA.B)Principal ResourceCarnegie Course 1 Chapter 2: 2.1-2.4 Prime Factorization and the Fundamental Theory of ArithmeticPrincipal ResourceCarnegie Course 1 Chapter 3: 3.9 & 3.10 Fractions **Lessons 3.1-3.8 are prerequisite below grade level standards for 6.NS.A.1. Principal ResourceCarnegie Course 1 Chapter 4: 4.4-4.7 Decimals**Lessons 4.1-4.3 are prerequisite below grade level standards 6.NS.B.2 and 6.NS.B.3Standards6.NS.B.46.EE.A.1Estimated Time10 daysStandards6.NS.A.1Estimated Time7 days Standards6.NS.B.26.NS.B.3Estimated Time12 daysRoutines:Instructional Notes: Chapter 1 was not included due to alignment to below grade level standards, use lessons as needed based on your students. Focus 2: Ratios, Rates & PercentBig Ideas: Use ratio concepts and ratio reasoning to solve problems (6.RP.A)Learning Goal & Scale:Pre-requisite clusters/skills: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit (4.MD.A)Apply and extend previous understandings of multiplication and division to multiply and divide fractions (5.NF.B)Analyze patterns and relationships (5.OA.B) Principal ResourceCarnegie Course 1 Chapter 5 - RatiosPrincipal ResourceCarnegie Course 1 Chapter 6 - PercentsStandards6.RP.A.16.RP.A.3.a6.RP.A.3.b6.RP.A.3.dEstimated Time17 days Standards6.RP.A.3.cAZ.6.NS.C.9 - Convert between expressions for positive rational numbers, including fractions, decimals, & percents. 6.1 & 6.2 has students convert between fractions, decimals & percents.Estimated Time13 daysRoutines: Focus 3: Algebraic ExpressionsBig Ideas: Apply and extend previous understandings of arithmetic to algebraic expressions (6.EE.A) Learning Goal & Scale:Pre-requisite clusters/skills: Write and interpret numerical expressions (5.OA.A)Analyze patterns and relationships (5.OA.B) Understand the place value system (5.NBT.A.2) – Powers of ten and decimal system Principal ResourceCarnegie Course 1 Chapter 7 - Introduction to Expressions Principal ResourceCarnegie Course 1 Chapter 8 - Algebraic ExpressionsStandards6.EE.A.16.EE.A.2a6.EE.A.2b6.EE.A.2c6.EE.B.66.NS.B.3Estimated Time17 days**Lesson 7.2 simplifying radicals on page 477 through #12 on page 479, and cube roots on page 480 go beyond 6th grade standards 7.6 Problem 2 beyond 6th grade standards**Suggest using the terminology – term, coefficient, sum, product, factor, quotient – when expressions are introducedStandards6.EE.A.2.a6.EE.A.2.b6.EE.A.2.c6.EE.A.36.EE.A.46.EE.A.16.EE.B.66.NS.B.36.NS.B.6.cEstimated Time19 days**8.4 – graphing expressions goes beyond 6th grade standardsRoutines: Focus 4 Equations and InequalitiesBig Ideas: Reason about and solve one variable equations and inequalities (6.EE.B)Learning Goal & Scale:Pre-requisite clusters/skills: Write and interpret numerical expressions (5.OA.A)Analyze patterns and relationships (5.OA.B) Apply and extend previous understandings of arithmetic to algebraic expressions (6.EE.A)Principal ResourceCarnegie Course 1 Chapter 9 - Inequalities and Equations** portions of 9.1 align to lower grade level standardsStandards6.NS.B.36.NS.C.6.c6.EE.B.56.EE.B.66.EE.B.76.EE.B.86.EE.C.96.RP.A.3.b6.RP.A.3.cEstimated Time 17 daysRoutines:Focus 5 IntegersBig Ideas:Apply and extend previous understands of the system of rational numbers (6.NS.C)Represent and analyze quantitative relationships between independent and dependent variables (6.EE.C)Learning Goal & Scale:Pre-requisite clusters/skills: Gain familiarity with factors and multiples (4.OA.B)Perform operations with multi-digit whole numbers and with decimals to hundredths (5.NBT.B)Graph points on the coordinate plane to solve real world and mathematical problems (5.G.A)Principal ResourceCarnegie Course 1 Chapter 10 - IntegersPrincipal ResourceCarnegie Course 1 Chapter 11 - The Cartesian Coordinate PlaneStandards6.NS.C.56.NS.C.6.a6.NS.C.6.c6.NS.C.7.a6.NS.C.7.b6.NS.C.7.c6.NS.C.7.dEstimated Time9 daysStandards6.NS.B.36.NS.C.56.NS.C.6.b6.NS.C.6.c6.NS.C.7.c6.NS.C.86.EE.C.96.G.A.36.RP.A.3.bEstimated Time8 days**Lesson 11.4 goes beyond 6th grade standardsRoutines:Focus 6: Geometry – Units of MeasureBig Ideas: Solve real‐world and mathematical problems involving area, surface area, and volume (6.G.A)Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities (6.RP.A.3.d)Learning Goal and Scale: Pre-requisite clusters/skills: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit (4.MD.A)Apply and extend previous understandings of multiplication and division to multiply and divide fractions (5.NF.B)Principal ResourceCarnegie Course 1 Chapter 12 - Units of MeasureStandards6.RP.A.16.RP.A.3.d6.SP.B.5.c6.NS.B.36.NS.C.7.cEstimated Time 6 days **Portions of lesson 12.1, 12.2 and 12.4 align to lower grade level standards Routines:Focus 7: Geometry – AreaBig Ideas: Solve real‐world and mathematical problems involving area, surface area, and volume (6.G.A)Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities (6.RP.A.3.d)Learning Goal and Scale: Pre-requisite clusters/skills: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit (4.MD.A)Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition (5.MD.C)Apply and extend previous understandings of multiplication and division to multiply and divide fractions (5.NF.B)Graph points on the coordinate plane to solve real‐world and mathematical problems (5.G.A)Principal ResourceCarnegie Course 1 Chapter 13 – Area** Portions of lesson 13.1 & 13.2 align to lower grade level standards. ** Portions of lesson 13.6 aligns to above grade level standards.Standards6.G.A.16.G.A.46.NS.B.3Estimated Time9 daysRoutines:Focus 8: Geometry – 3-D FiguresBig Ideas: Solve real‐world and mathematical problems involving area, surface area, and volume (6.G.A)Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities (6.RP.A.3.d)Learning Goal and Scale: Pre-requisite clusters/skills: Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit (4.MD.A)Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition (5.MD.C)Apply and extend previous understandings of multiplication and division to multiply and divide fractions (5.NF.B)Graph points on the coordinate plane to solve real‐world and mathematical problems (5.G.A)Principal ResourceCarnegie Course 1 Chapter 14 - Introduction to the Third Dimension Standards6.G.A.26.G.A.46.RP.A.3Estimated Time9 days** Portions of lesson 14.2 align to lower grade level standards** Portion of 14.3 & 14.5 align to above grade level standards.Routines:Focus 9: Statistical ThinkingBig Ideas:Develop understanding of statistical variability (6.SP.A)Summarize and describe distributions (6.SP.B)Learning Goal and Scale:Pre-requisite clusters/skills: Represent and interpret data (5.MD.B)Principal ResourceCarnegie Course 1 Chapter 15 - Collecting and Displaying Data Principal ResourceCarnegie Course 1 Chapter 16 - Analyzing and Interpreting DataStandards6.SP.A.16.SP.A.26.SP.B.46.SP.B.5.aEstimated Time6 days** Portions of 15.2, 15.3, & 15.5 align to above grade level standards.Standards6.SP.A.26.SP.A.36.SP.B.46.SP.B.5.b6.SP.B.5.c6.SP.B.5.dEstimated Time11 daysRoutines: ................
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