Algebra 1 Math Instructional Focus Units



Linear Algebra (Part 2) Linear algebra instructional focus will be on: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; grasping the concept of a function and using functions to describe quantitative relationships; Year-At-A-Glance – Algebra 1Algebra I instructional focuses will be on: Use properties of rational and irrational numbersReason quantitatively and use units to solve problems Interpret the structure of expressions Write expressions in equivalent forms to solve problems Perform arithmetic operations on polynomials Understand the relationship between zeros and factors of polynomials Create equations that describe numbers or relationshipsUnderstand solving equations as a process of reasoning and explain the reasoning Solve equations and inequalities in one variable Solve systems of equations Represent and solve equations and inequalities graphically Understand the concept of a function and use function notationInterpret functions that arise in applications in terms of the context Analyze functions using different representations Build a function that models a relationship between two quantities Build new functions from existing functionsConstruct and compare linear, quadratic, and exponential models and solve problems Interpret expressions for functions in terms of the situation they modelSummarize, represent, and interpret data on a single count or measurement variableSummarize, represent, and interpret data on two categorical and quantitative variablesInterpret linear modelsUnit/ ModuleChapter(s)Main IdeaEstimated Timeline (days)1Course 3 – chapters 1.1, 2.5, & 3 Solving & analyzing linear equations 92Algebra - 1, 2 & 3Quantitative Relationships w/Equations, Inequalities & Linear Functions273Algebra - 4, 5, 6, & 7Building Functions & Systems of Linear Equations & Inequalities414Algebra - 11, 12, & 13Quadratics385Algebra -8, 9, & 10Analyzing Data306Algebra - 14, 15, & 16Real number system, Other Functions, & Modeling25Algebra (EE)& Functions – approximately 82%Statistics – approximately 18%Your 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. Common Core RP Progressions – Use for explanations of standards sequencing, pointing out cognitive difficulties and pedagogical solutions, and providing further detail of mathematical content. StandardsCarnegie Course 3 Course Content MapCarnegie Algebra Course Content MapFocus 1: Solving & Analyzing linear Equations: This unit focuses on the 8th grade pre-requisite skills of solving & analyzing linear equations, including slope & y-intercept as well as understanding the different forms of a linear equations –Slope-intercept form, standard form, & point-slope form.Big Ideas:Learning Goal and Scale:Principal ResourceCarnegie Course 3 Chapter 1 – Linear Equations – Section 1.1**Lesson 1.1 is a prerequisite below grade level standard for 8.EE.B.7. This lesson is a refresher on solving multi-step equations. Use your professional judgement to determine if your students need this lesson. (Section 1.3 and 1.4 could be used for practice if necessary)Principal ResourceCarnegie Course 3 Chapter 2 - Section 2.5**Lesson 2.5 is a prerequisite below grade level standard for 8.F.A & 8.F.B. This lesson is a good introduction to the work students will be doing in Chapter 3. Use your professional judgement to determine if your students need this lesson. Principal ResourceCarnegie Course 3 Chapter 3 – Analyzing Linear EquationsStandards8.EE.B.7a8.EE.B.7bEstimated Time2 days **Section 1.2 addressed in Algebra Section 6.1**Standards7.RP.A.2a7.RP.A.2b7.RP.A.2c7.RP.A.2dEstimated Time1 day**Section 2.1 – Algebra 4. **Section 2.2-2.4 addressed in Algebra 1.1-1.3)**Section 2.7 goes beyond 8th standardsStandards8.F.A.38.F.B.48.F.B.5Estimated Time6 days** Do all, go through detailsFocus 2: Quantitative Relationships w/Equations, Inequalities & Linear Functions – This focus begins with an introduction to the concept of functions. Students explore functions, including linear, exponential, quadratic, linear absolute value functions, and linear piecewise functions through problem situations, graphs, and equations. The focus continues with solving linear equations and inequalities with an emphasis towards connecting the numeric, graphic, and algebraic methods for solving linear functions. Student explore and comprehend different forms of linear equations.Learning Goal & Scale: Big Ideas: Principal ResourceCarnegie Chapter 1 – Quantities and Relationships Principal ResourceCarnegie Chapter 2- Graphs, Equations & InequalitiesPrincipal ResourceCarnegie Chapter 3 - Linear FunctionsStandardsN-Q.A.2F-LE.A.1bF-LE.A.2F-IF.A.1F-IF.A.2F-IF.B.4F-IF.B.5F-IF.C.7aF-IF.C.9A-CED.A.2A-REI.D.10Estimated Time9 days(covers pieces of course 3 chapter 2)StandardsA-REI.A.1A-REI.B.3A-REI.D.10A-CED.A.1A-CED.A.2A-CED.A.3A-SSE.A.1aN-Q.A.1N-Q.A.2N-Q.A.3F-IF.A.2F-IF.B.6F-LE.A.1bF-LE.A.1cEstimated Time9 days(covers pieces of course 3 chapter 2)StandardsS-ID.B.6S-ID.B.7N-Q.A.2A-REI.A.1A-REI.B.3A-SSE.A.1aA-SSE.A.1bA-CED.A.2A-CED.A.3A-CED.A.4F-IF.A.2Estimated Time9 days(covers pieces of course 3 chapter 2, & chapters 4, 15, 16)Focus 3: Building Functions & Systems of Linear Equations & Inequalities – In this focus, the relationship between arithmetic and linear functions and some geometric sequences and exponential functions is developed. Students also examine the graphical behavior of exponential functions. The focus continues with students solving systems of linear equations and inequalities algebraically and graphicallyLearning Goal & Scale:Big Ideas:Principal ResourceCarnegie Algebra I: Chapter 4- SequencesPrincipal ResourceCarnegie Algebra I: Chapter 5- Exponential FunctionsStandardsF-LE.A.1aF-LE.A.1bF-LE.A.1cF-LE.A.2F-LE.B.5F-BF.A.1aF-BF.A.2A-SSE.A.1aA-SSE.A.1bF-IF.A.1F-IF.A.2F-IF.A.3F-IF.B.4Estimated Time 11 days(covers pieces of course 3 chapter 2)StandardsA-SSE.A.1aA-SSE.A.1bA-CED.A.1A-CED.A.2F-IF.A.3F-IF.B.4F-IF.B.6F-IF.C.7eF-BF.A.1aF-BF.A.2F-BF.B.3F-LE.A.1aF-LE.A.1bF-LE.A.1cF-LE.A.2F-LE.A.3F-LE.B.5A-REI.B.3A-REI.D.10A-REI.D.11N-RN.A.1N-RN.A.2N-Q. A.2Estimated Time12 daysPrincipal ResourceCarnegie Algebra I: Chapter 6- Systems of EquationsPrincipal ResourceCarnegie Algebra I: Chapter 7- Systems of InequalitiesStandardsA-CED.A.2A-REI.C.5A-REI.C.6A-REI.D.10A-REI.D.11Estimated Time9 days(covers course 3 chapters 11 & 12)StandardsA-CED.A.3A-REI.D.12Estimated Time9 daysFocus 4: Quadratics – This focus examines the graphical behavior of quadratic functions & their key features, solving quadratics in multiple ways as well as solving systems of quadratics. Operations with polynomials, including factoring quadratic trinomials is introduced.Learning Goal & Scales:Big Ideas:Principal ResourceCarnegie Algebra I: Chapter 11- Introduction to Quadratic FunctionsPrincipal ResourceCarnegie Algebra I: Chapter 12- Polynomials and QuadraticsPrincipal ResourceCarnegie Algebra I: Chapter 13- Solving Quadratic Equations & InequalitiesStandardsA-CED.A.1A-CED.A.2F-BF.B.3F-IF.B.4F-IF.B.5F-IF.B.6F-IF.C.7aF-LE.A.1aA-SSE.A.1A-SSE.B.3aEstimated Time14 daysStandardsA-APR.A.1A-CED.A.1A-CED.A.2A-REI.B.4A-SSE.A.1aA-SSE.A.2A-SSE.B.3aA-SSE.B.3bF-BF.A.1bN-RN.A.2Estimated Time14 daysStandardsA-CED.A.1A-CED.A.2A-REI.B.4aA-REI.B.4bA-REI.C.7F-IF.C.7aEstimated Time10 daysFocus 5: Analyzing Data – This focus begins with a brief review of analysis of data sets with one variable and leads into an introduction of causation and correlation. Students are introduced to categorical data and analyze the data to problem solve and make decisions.Learning Goal & Scale:Big Ideas:Principal ResourceCarnegie Algebra I: Chapter 8- Analyzing Data Sets for One Variable Principal ResourceCarnegie Algebra I: Chapter 9- Correlation and Residuals**This chapter goes beyond the limits of Algebra I. Algebra I students are not required to use the least squares regression formula to find the line of best fit.Principal ResourceCarnegie Algebra I: Chapter 10- Analyzing Data Sets for Two Categorical VariablesStandardsS-ID.A.1S-ID.A.2S-ID.A.3Estimated Time10 days StandardsS-ID.B.6aS-ID.B.6bS-ID.B.6cS-ID.C.7S-ID.C.8S-ID.C.9Estimated Time10 daysStandardsS-ID.B.5Estimated Time10 days(covers course 3 chapter 17)Focus 6: Real number system, Other Functions, & Modeling – This focus reviews the real number system and leads students to explore whether quadratic functions have one, two, or no real roots. Other functions, such as piecewise functions, absolute value functions, and step functions are explored. Inverses of linear and non-linear functions are introduced. Students are provided opportunities to model real-world data using linear, exponential, quadratic, and piecewise functions. Determining the appropriate function or functions for a given data set is a main focus.Learning Goal & Scale:Big Ideas:Principal ResourceCarnegie Algebra I: Chapter 14- Real Number System**14.3 & 14.4 go beyond the limits of Algebra I Principal ResourceCarnegie Algebra I: Chapter 15- Other Functions and InversesPrincipal ResourceCarnegie Algebra I: Chapter 16- Mathematical ModelingStandardsN-RN.A.1N-RN.A.2N-RN.B.3N-CN.1N-CN.7Estimated Time5 daysStandardsF-IF.A.1F-IF.A.2F-IF.B.4F-IF.B.5F-IF.C.7F-IF.C.7bF-BF.A.1aF-BF.B.4aF-BF.B.4bA-CED.A.1A-CED.A.4Estimated Time 9 daysStandardsF-IF.B.4F-IF.B.5F-IF.C.7F-BF.A.1F-BF.B.4F-LE.A.1F-LE.A.2Estimated Time11 days ................
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