Linear Algebra - 8th Grade Math Instructional Focus Units
In 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)?Understanding 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.UnitChapter(s)Main IdeaEstimated DaysMATHiaX Module1 1.1, 2, 3, 4Linear Equations and Functions40Linear Functions25, 6,Pythagorean Theorem18Right Triangles37, 8, 9Transformational Geometry23Geo Transformations410Line and Angle Relationships11Angle Relationships51.2-1.4, 11, 12Solving Linear Equations and Systems of Equations30Linear Equations & Systems of Linear Equations613Properties of Exponents14Exponents714Volume9Volume815, 16, 17Data Analysis25Bivariate DataEE/F = 57%NS/SP = 18%G = 25%HELPFUL LINKSAZ College and Career Ready Standards - Carnegie Course Content Map- Course 3 - Common Core 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 FunctionsBig Ideas:Define, evaluate, and compare functions (8.F.A)Use functions to model relationships between quantities. (8.F.B)Learning Goal and Scale: Pre-requisite cluster/skills:Analyze proportional relationships and use them to solve real‐world and mathematical problems (7.RP.A)Principal ResourceCarnegie Course 3 Chapter 1 – Section 1.1 onlyCarnegie Course 3 Chapter 2- Linear FunctionsPrincipal ResourceCarnegie Course 3 Chapter 3 – Analyzing Linear EquationsPrincipal ResourceCarnegie Course 3 Chapter 4 – Multiple Representations of Linear FunctionsSECTION 4.2 – SKIPSECTION 4.3 – Keep focus on changing to S-I formSECTION 4.5 – SKIP & use ENY lesson for 8.F.5SECTION 4.6 – NEW lesson found in Toolkit only!Standards8.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 Time13 daysStandards8.EE.B.58.EE.C.7.b8.F.A.18.F.A.28.F.A.38.F.B.48.F.B.5Estimated Time12 daysFocus 2: The Pythagorean TheoremBig Ideas: Know that there are numbers that are not rational, and approximate them by rational numbers (8.NS.A)Understand and apply the Pythagorean Theorem. (8.G.B)Learning Goal and ScalePre-requisite cluster/skills:Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. (7.NS.A)Solve real‐life and mathematical problems using numerical and algebraic expressions and equations (7.EE.B)Solve real‐life and mathematical problems involving angle measure, area, surface area, and volume. (7.G.A)/(6.G.A)Principal ResourceCarnegie Course 3 Chapter 5 - The Real Number System**5.1 Concept of open and close does not meet grade levelPrincipal ResourceCarnegie Course 3 Chapter 6 - Pythagorean TheoremSupplement for 8.EE.A.2 – Cube Roots (Engage NY) Standards8.NS.A.18.NS.A.28.EE.A.2Estimated Time6 daysStandards8.NS.A.2 **8.NS.A.2 is briefly addressed in the chapter. Consider including more work on estimating the value of irrational number & placing them on a number line.8.EE.A.2 **8.EE.A.2 requires work in cube roots. Cube roots are NOT ADDRESSED in Carnegie.8.G.B.78.G.B.8Estimated Time12 daysFocus 3: Transformational GeometryBig Ideas:Understand congruence and similarity using physical models, transparencies, or geometry software. (8.G.A)Learning Goal and Scale:Pre-requisite cluster/skills:Draw, construct, and describe geometrical figures and describe the relationships between them (7.G.A)Solve real-life and mathematical problems involving angle measure, area, surface area and volume (7.G.B)Principal ResourceCarnegie Course 3 Chapter 7- Translations, Reflections and RotationsPrincipal ResourceCarnegie Course 3 Chapter 8- Congruence of Triangles**Section 8.3 and 8.4 go beyond 8th grade standards, please use professional judgement.Principal ResourceCarnegie Course 3 Chapter 9- Similarity**Section 9.3 and 9.4 go beyond 8th grade standards, please use professional judgement.**8.EE.B.6 – addressed in added Lesson – Lesson 9.5 in Resource CenterStandards8.G.A.1.a8.G.A.1.b8.G.A.28.G.A.3Estimated Time11 daysStandards8.G.A.1.a8.G.A.1.b8.G.A.28.G.A.38.G.B.8Estimated Time6 days Standards8.G.A.38.G.A.48.EE.B.6Estimated Time6 daysFocus 4: Line and Angle RelationshipsBig Ideas:Understand congruence and similarity using physical models, transparencies, or geometry software. (8.G.A)Learning Goal and Scale:Pre-requisite cluster/skills:Solve real‐life and mathematical problems involving angle measure, area, surface area, and volume (7.G.B)Principal ResourceCarnegie Course 3 Chapter 10- Line and Angle RelationshipsStandards8.G.A.1.c8.G.A.58.F.B.3 Estimated Time11 daysFocus 5: Solving Linear Equations & System of EquationsBig Ideas:Analyze and solve linear equations and pairs of simultaneous linear equations (8.EE.C)Learning Goal and Scale:Pre-requisite cluster/skills:Reason about and solve one‐variable equations and inequalities (6.EE.B)Use properties of operations to generate equivalent expressions (7.EE.B)Solve real‐life and mathematical problems using numerical and algebraic expressions and equations (7.EE.B)Principal ResourceCarnegie Course 3 Chapter 1- 1.2-1.4 – Linear EquationsPrincipal ResourceCarnegie Course 3 Chapter 11- Systems of Equations**11.3 – standards require students to write equations in slope-intercept form to compare them.Principal ResourceCarnegie Course 3 Chapter 12- More with Systems of Equations**12.1 – standards require students to write equations in slope-intercept form to compare them.**Portions of lesson 12.3 align to above grade level standards.Standards8.EE.C.7.a8.EE.C.7.bEstimated Time9 daysStandards8.EE.C.88.EE.C.8.a8.EE.C.8.b8.EE.C.8.c8.EE.C.7.b8.F.B.4Estimated Time9 daysStandards8.EE.C.7.b8.EE.C.8.a8.EE.C.8.b8.EE.C.8.c8.F.B.4Estimated Time12 daysFocus 6: Properties of ExponentsBig Ideas:Work with radicals and integer exponents. (8.EE.A)Learning Goal and Scale:Pre-requisite cluster/skills:Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole‐number exponents to denote powers of 10. (5.NBT.A.2)Apply and extend previous understandings of arithmetic to algebraic expressions (6.EE.A)Reason about and solve one‐variable equations and inequalities (6.EE.B)Solve real‐life and mathematical problems using numerical and algebraic expressions and equations (6.EE.B)Solve real‐life and mathematical problems using numerical and algebraic expressions and equations (7.EE.B)Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.7.NS.APrincipal ResourceCarnegie Course 3 Chapter 13- Properties of Exponents** Portions of lesson 13.1 align to below grade level standards.Standards8.EE.A.18.EE.A.28.EE.A.38.EE.A.4Estimated Time14 daysFocus 7: VolumeBig Ideas:Solve real‐world and mathematical problems involving volume of cylinders, cones and spheres. (8.G.C)Learning Goal and Scale:Pre-requisite cluster/skills:Solve real‐life and mathematical problems involving angle measure, area, surface area, and volume. (7.G.B) Principal ResourceCarnegie Course 3 Chapter 14- Volume** Portions of lessons 14.1 & 14.4 align to above grade level standards.Standards8.G.C.9Estimated Time9 daysFocus 8: Data AnalysisBig Ideas:Investigate patterns of association in bivariate data. (8.SP.A)Learning Goal and Scale:Pre-requisite cluster/standards:Solve real‐life and mathematical problems using numerical and algebraic expressions and equations (7.EE.B)Apply and extend previous understandings of numbers to the system of rational numbers (6.NS.C)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 Time7 daysStandards8.SP.A.18.SP.A.28.SP.A.3Estimated Time10 daysStandards8.SP.A.18.SP.A.4Estimated Time8 days ................
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