8th Grade Math Instructional Focus Units
Course Description – Linear AlgebraIn Linear Algebra, ?Grade 8 ?instructional focuses will be on: (1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) using ideas about distance and angles, how they behave under translations, rotations, reflections, and dilations, and ideas about congruence and similarity to describe and analyze two-dimensional figures and to solve problems; and(4)?understand the statement of the Pythagorean Theorem and its converse and apply the Pythagorean Theorem to find distances between points on the coordinate plane, to find lengths, and to analyze polygons.Year-At-A-Glance Focus UnitChapter(s)Main IdeaEstimated Timeline (days)11, 2, 3, 4Algebraic Thinking 4525, 6, 7, 8, 9, 10Pythagorean Theorem and Transformational Geometry61311, 12, 13 Linear Systems & Properties of Exponents36414Volume 10515, 16, 17Data Analysis28Your feedback on the maps, timeline, and resource is greatly appreciated so changes and supplemental resources (if necessary) can be identified and added to future maps. Year - Long Scope SequenceCommon Core RP Progressions – Use for explanations of standards sequencing, pointing out cognitive difficulties and pedagogical solutions, and providing further detail of mathematical content. Focus 1: Linear Equations and Functions -This unit focuses on algebraic thinking. Students extend their understanding of equation solving to include equations with variables on both sides and equations involving rational numbers. Students are introduced to functions and relations. Students analyze equations, tables, and graphs of linear functions, specifically the interpretation of slope and y-intercept.Learning Goal and Scale:Assessment Bank:Pre-requisite standards/skills:Big Ideas: Essential Questions: Principal ResourceCarnegie Course 3 Chapter 1 – Linear EquationsPrincipal ResourceCarnegie Course 3 Chapter 2- Linear FunctionsPrincipal ResourceCarnegie Course 3 Chapter 3 – Analyzing Linear EquationsPrincipal ResourceCarnegie Course 3 Chapter 4 – Multiple Representations of Linear FunctionsStandards8.EE.C.7a8.EE.C.7bEstimated Time9 daysStandards8.F.A.18.F.A.28.F.A.38.F.B.48.F.B.5Estimated Time15 daysStandards8.EE.B.58.F.A.18.F.A.28.F.A.38.F.B.48.F.B.5Estimated Time10 daysStandards8.EE.B.58.EE.C.7b8.F.A.18.F.A.28.F.A.38.F.B.48.F.B.5Estimated Time11 daysRoutines:Instructional Notes:Feedback:Focus 2: Geometry- In this unit students apply and extend their understanding of numbers and their properties to include real numbers. Students solve a variety of problems using the Pythagorean Theorem. Students develop an understanding of congruence as a preservation of size and shape and an understanding of similarity as a preservation of shape. Students explore the necessary conditions for triangle similarity and congruence. Students explore angles formed by lines cut by a transversal. Learning Goal and Scale:Assessment Bank:Pre-requisite skills/standards:Big Ideas:Essential Questions: Principal ResourceCarnegie Course 3 Chapter 5- The Real Number SystemPrincipal ResourceCarnegie Course 3 Chapter 6- Pythagorean TheoremPrincipal ResourceCarnegie Course 3 Chapter 7- Translations, Reflections and RotationsStandards7.NS.A.38.NS.A.18.NS.A.28.EE.A.2Estimated Time7 days Standards8.NS.A.8.EE.A.28.G.B.68.G.B.78.G.B.8Estimated Time14 daysStandards8.G.A.1.a8.G.A.1.b8.G.A.28.G.A.3Estimated Time10 daysPrincipal ResourceCarnegie Course 3 Chapter 8- Congruence of TrianglesPrincipal ResourceCarnegie Course 3 Chapter 9- Similarity**Section 9.3 and 9.4 go beyond 8th grade standards, please use professional judgement.Principal ResourceCarnegie Course 3 Chapter 10- Line and Angle RelationshipsStandards8.G.A.1.a8.G.A.1.b8.G.A.28.G.A.38.G.B.8Estimated Time10 daysStandards8.G.A.38.G.A.4Estimated Time8 daysStandards7.G.B.58.G.A.1.c8.G.A.58.F.B.3Estimated Time12 daysRoutines:Instructional Notes:Feedback:Focus 3: Algebraic Thinking – Students analyze and solve systems of linear equations algebraically and graphically. Students derive properties of exponents including the use of exponents with scientific notation. Learning Goal and Scale:Assessment Bank:Pre-requisite skills/standards:Big Ideas:Essential Questions: Principal ResourceCarnegie Course 3 Chapter 11- Systems of EquationsPrincipal ResourceCarnegie Course 3 Chapter 12- More with Systems of EquationsPrincipal ResourceCarnegie Course 3 Chapter 13- Properties of ExponentsStandards8.EE.C.8.a8.EE.C.8.b8.EE.C.8.c8.EE.C.8.dEstimated Time10 daysStandards8.EE.C.7.b8.EE.C.8.b8.EE.C.8.c8.EE.C.8.dEstimated Time12 daysStandards8.EE.A.18.EE.A.28.EE.A.38.EE.A.4Estimated Time14 daysRoutines:Notes:Feedback:Focus 4: Geometry- Students develop formulas for the volumes of cones, cylinders, and spheres. Learning Goal and Scale:Assessment Bank:Pre-requisite skills/standards:Big Ideas:Essential Questions: Principal ResourceCarnegie Course 3 Chapter 14- VolumeStandards8.G.C.9Estimated Time10 daysRoutines:Instructional Notes:Feedback:Focus 5: Statistical Thinking and Probability- Students are introduced to bivariate data through the use of tables and scatter plots. Students determine a line of best fit for data set and use that line to make predictions. Learning Goal and Scale:Assessment Bank:Pre-requisite skills/standards:Big Ideas:Essential Questions: Principal ResourceCarnegie Course 3 Chapter 15- Data Display and Analysis Principal ResourceCarnegie Course 3 Chapter 16- Lines of Best FitPrincipal ResourceCarnegie Course 3 Chapter 17- Non-linear Data RepresentationsStandards8.SP.A.1Estimated Time8 daysStandards8.SP.A.18.SP.A.28.SP.A.3Estimated Time12 daysStandards8.SP.A.18.SP.A.4Estimated Time8 daysRoutines: Instructional Notes:Feedback: ................
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