Pre-Algebra - 7th Grade Math Instructional Focus Units
In Pre-Algebra, Grade 7 instructional focuses will be on: (1) Developing understanding of and applying proportional relationships; (2) Developing understanding of operations with rational numbers and working with expressions; (3) Solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) Drawing inferences about populations based on samples, and investigate chance processes and develop, use, and evaluate probability models.UnitChapter(s)Main IdeaEstimated DaysMATHiaX Module11, 2Proportional Reasoning27Prop Relationships23Percents12Prop Reasoning & Percents34, 5Rational Number Operations36Rational Numb & Operations46, 7, 8Algebraic Expressions and Equations40Two-Step Eq and Ineq59, 10Triangles7Geometry611Scale Drawings5712Circles5813Slicing, Volume and Surface Area8914, 15Statistical Thinking 14Data Comparisons and Probability1016, 17Probability16RP = 23%NS = 21%EE = 24%G/SP = 32%HELPFUL LINKSAZ College and Career Ready Standards HYPERLINK "" Carnegie Course Content Map Course 2Common Core Progressions – Use for explanations of standards sequencing, pointing out cognitive difficulties and pedagogical solutions, and providing further detail of mathematical content.Focus 1: Proportional ReasoningBig Ideas: Analyze proportional relationships and use them to solve real‐world and mathematical problems. (7.RP.A)Learning Goals and Scales:Pre-requisite standards/skills:Use ratio concepts and ratio reasoning to solve problems. (6.RP.A)Principal ResourceCarnegie Course 2 Chapter 1 - Ratios and Rates** Portions of 1.1-1.3 are below grade levelPrincipal ResourceCarnegie Course 2 Chapter 2- Direct Variation and Constant of ProportionalityStandards7.RP.A.17.RP.A.2.b7.RP.A.2.c7.RP.A.3Estimated Time11 days Standards7.RP.A.2.a7.RP.A.2.b7.RP.A.2.c7.RP.A.2.dEstimated Time16 daysRoutines: Focus 2: PercentsBig Ideas: Analyze proportional relationships and use them to solve real‐world and mathematical problems.Learning Goals and Scales:Pre-requisite standards/skills:Use ratio concepts and ratio reasoning to solve problems. (6.RP.A)Principal ResourceCarnegie Course 2 Chapter 3 – Rates & PercentsStandards7.RP.A.17.RP.A.2.a7.RP.A.2.b7.RP.A.2.c7.RP.A.3Estimated Time12 daysRoutines: Focus 3: Rational Number OperationsBig Ideas:Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers. (7.NS.A)Learning Goals and Scales:Pre-requisite standards/skills:Compute fluently with multi-digit numbers including decimals and find common factors and multiples. (6.NS.B)Apply and extend previous understands of the system of rational numbers (6.NS.C)Compute fluently with multi-digit numbers including decimals and find common factors and multiples. (5.NF.B)Principal ResourceCarnegie Course 2 Chapter 4 –Addition & Subtraction w/Rational NumbersPrincipal ResourceCarnegie Course 2 Chapter 5 – Multiplication & Division w/Rational NumbersSupplement for complex fractions - Standards7.NS.A.1.a7.NS.A.1.b7.NS.A.1.c7.NS.A.1.dEstimated Time18 days**need additional resources to address real – world application**Standards7.NS.A.1.d7.NS.A.2.a7.NS.A.2.b7.NS.A.2.c7.NS.A.2.d7.NS.A.3 – Carnegie does not use complex fractionsEstimated Time18 days**need additional resources to address real – world application**Focus 4: Algebraic Expressions and EquationsBig Ideas:Use properties of operations to generate equivalent expressions. (7.EE.A)Solve real‐life and mathematical problems using numerical and algebraic expressions and equations. (7.EE.B)Learning Goals and Scale:Pre-requisite standards/skills: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)Principal ResourceCarnegie Course 2 Chapter 6 – Numerical & Algebraic Expressions & Equations*6.1 Activity 1 & 2 are below grade level*6.4 use for possible extension – standards aligned to identifying equivalent expressionsPrincipal ResourceCarnegie Course 2 Chapter 7 – Solving Linear Equations & InequalitiesAdditional Lessons- Inequalities- EngageNY Module 3 Topic B Lessons 12-15Principal ResourceCarnegie Course 2 Chapter 8 – Solving Problems with Equations & InequalitiesStandards7.NS.A.37.EE.A.1Estimated Time13 days Standards7.EE.A.17.EE.A.27.EE.B.37.EE.B.4.a7.EE.B.4.bEstimated Time12 daysStandards7.EE.B.37.EE.B.4.a7.EE.B.4.bEstimated Time15 daysFocus 5: TrianglesBig Ideas: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)Learning Goal and Scale:Pre-requisite standards/skills:Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real‐world and mathematical problems. (6.G.A.3)Principal ResourceCarnegie Course 2 Chapter 9 – Using Geometry** Portions of Lessons 9.1, 9.2 & 9.3 align to both below & above grade level standardsPrincipal ResourceCarnegie Course 2 Chapter 10 – Triangles**Portions of lesson 10.1 align to above grade level standards**10.2 Aligns to above grade level standards**Portions of lesson 10.3 aligned to above grade level standardsStandards7.G.A.27.G.B.5Estimated Time1 dayStandards7.G.A.27.G.B.57.NS.A.3Estimated Time6 daysFocus 6: Scale Drawings & Scale FactorsBig Ideas:Draw, construct, and describe geometrical figures and describe the relationships between them. (7.G.A)Learning Goal and Scale:Pre-requisite standards/skills:Use ratio concepts and ratio reasoning to solve problems. (6.RP.A)Analyze proportional relationships and use them to solve real‐world and mathematical problems. (7.RP.A)Principal ResourceCarnegie Course 2 Chapter 11 – Scale Drawing & Scale FactorStandards7.G.A.1Estimated Time5 daysRoutines:Focus 7: CirclesBig Ideas:Solve real‐life and mathematical problems involving angle measure, area, surface area, and volume. (7.G.B)Learning Goal and Scale:Pre-requisite standards/skills:Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real‐world and mathematical problems. (6.G.A.1) Principal ResourceCarnegie Course 2 Chapter 12 – Circles** Portions of Lesson 12.1 to above grade level standards**12.3 – Use alternate lesson to derive formula for area of circles – see pages 42-42 of 7th grade flipbookStandards7.G.B.47.NS.A.3Estimated Time5 days Routines:Focus 8: Slicing, Volume and Surface AreaBig Ideas: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)Learning Goal and Scale:Pre-requisite standards/skills:Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems. (6.G.A.2) Represent three-dime surface area of three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems. (6.G.A.4)Principal ResourceCarnegie Course 2 Chapter 13 – Slicing 3 Dimensional FiguresStandards7.G.A.37.G.B.6Estimated Time8 daysRoutines:Focus 9: Statistical ThinkingBig Ideas:Use random sampling to draw inferences about a population. (7.SP.A)Draw informal comparative inferences about two populations. (7.SP.B)Learning Goal and Scale:Pre-requisite standards/skills:Develop understanding of statistical variability. (6.SP.A) Principal ResourceCarnegie Course 2 Chapter 14 –Data CollectionPrincipal ResourceCarnegie Course 2 Chapter 15- Comparing PopulationsStandards7.SP.A.17.SP.A.2Estimated Time8 daysStandards7.SP.A.27.SP.B.37.SP.B.4Estimated Time6 daysRoutines:Focus 10: ProbabilityBig Ideas:Investigate chance processes and develop, use, and evaluate probability models. (7.SP.C)Learning Goal and Scale:Pre-requisite standards/skills:Analyze proportional relationships and use them to solve real‐world and mathematical problems. (7.RP.A)Principal ResourceCarnegie Course 2 Chapter 16 – Introduction to ProbabilityPrincipal ResourceCarnegie Course 2 Chapter 17 – Probability of Compound EventsStandards7.SP.C.57.SP.C.67.SP.C.77.SP.C.7.b7.SP.C.8.cEstimated Time8 daysStandards7.SP.C.7.a7.SP.C.7.b7.SP.C.8.a7.SP.C.8.b7.SP.C.8.cEstimated Time8 daysRoutines: ................
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