Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
List of important publications in mathematics wikipedia , lookup
Elementary algebra wikipedia , lookup
Line (geometry) wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Partial differential equation wikipedia , lookup
System of linear equations wikipedia , lookup
History of algebra wikipedia , lookup
South Carolina MIDDLE SCHOOL ALGEBRA I 2011-2012 Pacing Guide (Traditional) Note: The Process Standards (1.1-1.7) have been included throughout the pacing guide in accordance with the Assessment Guidelines provided by the South Carolina State Department of Education. Unit Days Introduction (Days 1-3) 3 Days Foundations of Algebra and the Real Number System (Days 4-17) Solving Equations (Days 18-41) CASE21 Inc. 14 Days 24 Days Standard/ Indicator Common Core Major Topics/Concepts Start of school/Introduction to the course EA-1.1 EA-1.2 EA-1.3 EA-1.4 EA-1.6 EA-2.1 EA-2.2 EA-2.5 EA-2.6 EA-2.7 EA-2.9 EA-2.10 A.SSE.1a A.SSE.1b A.SSE.2 N.RN.2 N.RN.3 N.VM.6 N.VM.7 N.VM.8 N.VM.9 N.VM.10 EA-1.2 EA-1.3 EA-1.4 EA-1.5 EA-1.6 EA-2.4 EA-3.7 EA-3.8 EA-4.7 A.CED.1 A.CED.4 A.REI.1 A.REI.3 N.Q.1 N.Q.2 N.Q.3 1 Variables and expressions Simplify Translate Evaluate Order of Operations Real numbers Classify Compare Add, subtract, multiply, and divide Graph on number line Use Venn diagrams to organize Square roots Find square root values Classify and order Absolute value representation Properties of real numbers Apply properties to simplify and evaluate expressions Include expressions with exponents Distributive Property Matrix organization Operations with matrices Add and subtract Use scalar multiplication Real-world application One-step equations & multi-step equations Translate verbal sentences into equations and vice versa Use properties to solve Include equations with variables on both sides Solve absolute value equations Include fractions and decimals Practice 1 solution, no solution, and infinitely many solutions Check solutions Proportions Apply proportional reasoning Set up and solve unit conversion www.case21inc.com Unit Days Days 42-43 Solving Inequalities (Days 44-58) 15 Days Linear Functions (Days 59-74) 16 Days The Coordinate Plane and Slope (Days 75-84) 10 Days CASE21 Inc. Standard/ Indicator Common Core Major Topics/Concepts problems Understand concept of dimensional analysis Direct variation Use direction variation with distance problems Methods for solving for a specific variable Use inverse operations Use formulas Real-world application Review/1st Cumulative Benchmark (covering all content through day 41) Methods for solving inequalities in onevariable Write inequalities that model a given problem situation Assign a variable and restrictions to EA-1.3 the variable EA-1.4 A.CED.1 Solve absolute value inequalities EA-1.5 A.REI.1 Include fractions and decimals EA-4.8 A.REI.3 Use properties to solve EA-5.12 Include inequalities with variables on both sides Check solutions using appropriate methods Graph solutions on a number line A.CED.2 A.REI.10 F.BF.1 F.IF.1 Introduction to functions EA-1.1 F.IF.2 Patterns and equations EA.1.4 F.IF.3 Analyze relationship between x EA-1.5 F.IF.4 and y values EA-1.6 F.IF.5 Determine if a relation is a function EA-3.1 F.IF.6 Identify domain and range EA-3.2 F.IF.9 Write functions EA-3.3 F.LE.1b Analyze and apply function rules EA-3.6 F.LE.2 Direct variation vs. inverse variation N.Q.1 N.Q.2 N.Q.3 S.ID.7 Coordinate plane EA-1.1 F.IF.6 Locate and graph points EA-1.4 N.Q.1 Represent relations in various ways EA-1.5 N.Q.2 Find inverse of a relation EA-1.6 N.Q.3 Slope EA-1.7 S.ID.7 Interpret slope as a rate of change Find slope using two points 2 www.case21inc.com Unit Days Standard/ Indicator Common Core EA-5.6 EA-5.7 EA-5.8 Days 85-86 Writing and Graphing Linear Functions (Days 87-102) 16 Days Scatterplots (Days 103-112) 10 Days Systems (Days 113-130) 18 Days CASE21 Inc. Major Topics/Concepts Introduce intercepts Introduce y = mx + b Review/2nd Cumulative Benchmark (covering all content through day 84) Slopes and intercepts Use slopes and intercepts to graph EA-1.1 functions EA-1.4 Use slope to determine ∥ and ⊥ EA-1.5 lines EA-1.6 A.REI.10 Analyze functions EA-1.7 A.REI.12 Equations of lines EA-3.4 F.BF.3 Write using two points EA-4.1 F.IF.7a Write in slope-intercept form EA-4.2 F.LE.1 Write in point-slope form EA-4.3 F.LE.2 Write in standard form EA-4.6 N.Q.1 Parallel and perpendicular lines EA-5.1 N.Q.2 Write equations of ∥ and ⊥ lines EA-5.2 N.Q.3 Continuous functions EA-5.3 Analyze graphs to find domain and EA-5.4 range EA-5.5 Two-variable inequalities EA-5.8 Write EA-5.9 Graph and analyze EA-5.10 Calculator tips Real-world application Scatterplots Relationships Identify positive, negative, no A.CED.2 EA-1.1 correlation F.BF.1a EA-1.2 Linear regression and line-of-best fit F.LE.2 EA-1.3 Identify axis to represent F.LE.5 EA-1.4 independent and dependent S.ID.6a EA-1.5 variables S.ID.6b EA-1.6 Determine reasonableness of a line S.ID.6c EA-1.7 of best fit S.ID.7 EA-4.4 Write equation of trend line S.ID.8 EA-4.5 Draw conclusions and make S.ID.9 predictions Calculator tips A.CED.2 EA-1.1 Systems of equations and inequalities A.CED.3 EA-1.3 Write a system to model situations A.REI.5 EA-1.4 Methods for solving systems of equations A.REI.6 EA-1.7 Solve by graphing A.REI.10 3 www.case21inc.com Unit Days Days 131-133 Polynomials (Days 134-149) Quadratics (Days 150-155) Days 156-160 CASE21 Inc. 16 Days 6 Days Standard/ Indicator EA-4.9 EA-4.10 EA-5.8 EA-5.11 Common Core Major Topics/Concepts Solve using substitution Solve using elimination Interpret solutions Calculator tips Real-world application rd Review/3 Cumulative Benchmark (covering all content through day 130) Exponents (positive, negative, and zero) Use properties to evaluate and simplify Polynomials Add and subtract Multiply and divide Use concrete models Scientific Notation EA-1.1 Multiply EA-1.2 A.APR.1 Divide EA-1.3 A.SSE.1a Prime factorization of polynomials EA-1.7 A.SSE.2 Greatest common factor (GCF) of EA-2.2 A.SSE.3a polynomials EA-2.3 F.IF.8b Factoring polynomials EA-2.7 N.RN.2 Factor x 2 + bx + c EA-2.8 Factor ax 2 + bx + c EA-6.4 Recognize prime polynomials Use concrete models Perfect squares Difference of squares Radical expressions Simplify using Property of Square Roots and Quotient Property of Square Roots A.REI.12 A.REI.4 A.REI.4a A.REI.4b A.SSE.3a A.SSE.3b A.SSE.3c F.BF.1b F.BF.3 F.IF.4 F.IF.5 F.IF.7a F.IF.7b F.IF.8a F.IF.9 F.LE.1b F.LE.3 EA-1.1 EA-1.2 EA-1.3 EA-1.4 EA-1.5 EA-1.6 EA-1.7 EA-2.8 EA-3.5 EA-6.1 EA-6.2 EA-6.3 EA-6.4 EA-6.5 EA-6.6 Quadratics Use discriminant to determine solutions Methods for solving Graph Factor using quadratic methods Associate x-intercepts with factored form Graphs of parent functions Analysis of quadratic graphs Determine equation from graph Approximate solutions of graphs Determine domain of graphs Identify how a and c affect graph Calculator tips Real-world application Review/Optional Comprehensive Benchmark 4 www.case21inc.com Unit Days Standard/ Indicator Common Core Days 161-165 Days 166-180 Major Topics/Concepts PASS Tests *Enrichment/Remediation *Additional Common Core standards as determined at district level CASE21 Inc. 5 www.case21inc.com