Last updated 5/2/16
Linear Algebra (Part 2)
Linear algebra instructional focus 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;
Year-At-A-Glance – Algebra 1
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Linear Algebra (part 2)/Algebra 1 Math Instructional Focus Units / 2016/2017 /Last updated 5/2/16
Algebra I instructional focuses will be on:
- Use properties of rational and irrational numbers
- Reason 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 relationships
- Understand 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 notation
- Interpret 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 functions
- Construct and compare linear, quadratic, and exponential models and solve problems
- Interpret expressions for functions in terms of the situation they model
- Summarize, represent, and interpret data on a single count or measurement variable
- Summarize, represent, and interpret data on two categorical and quantitative variables
- Interpret linear models
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Linear Algebra (part 2)/Algebra 1 Math Instructional Focus Units / 2016/2017 /Last updated 5/2/16
Unit/ Module / Chapter(s) / Main Idea / Estimated Timeline (days)1 / Course 3 – chapters 1.1, 2.5, & 3 / Solving & analyzing linear equations / 9
2 / Algebra - 1, 2 & 3 / Quantitative Relationships w/Equations, Inequalities & Linear Functions / 27
3 / Algebra - 4, 5, 6, & 7 / Building Functions & Systems of Linear Equations & Inequalities / 41
4 / Algebra - 11, 12, & 13 / Quadratics / 38
5 / Algebra -8, 9, & 10 / Analyzing Data / 30
6 / Algebra - 14, 15, & 16 / Real number system, Other Functions, & Modeling / 25
Algebra (EE)& Functions – approximately82% / Statistics – approximately18%
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 Map
Focus 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 Resource
Carnegie Course 3 Chapter 1 – Linear Equations – Section 1.1
**Lesson1.1is 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 Resource
Carnegie Course 3 Chapter 2 -Section 2.5
**Lesson2.5is 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 Resource
Carnegie Course 3 Chapter 3 – Analyzing Linear Equations
Standards
8.EE.B.7a
8.EE.B.7b / Estimated Time
2 days
**Section 1.2 addressed in Algebra Section 6.1** / Standards
7.RP.A.2a
7.RP.A.2b
7.RP.A.2c
7.RP.A.2d / Estimated Time
1 day
**Section 2.1 – Algebra 4.
**Section 2.2-2.4 addressed in Algebra 1.1-1.3)
**Section 2.7 goes beyond 8th standards / Standards
8.F.A.3
8.F.B.4
8.F.B.5 / Estimated Time
6 days
** Do all, go through details
Focus 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 Resource
Carnegie Chapter 1 – Quantities and Relationships / Principal Resource
Carnegie Chapter 2- Graphs, Equations & Inequalities / Principal Resource
Carnegie Chapter 3 -Linear Functions
Standards
N-Q.A.2
F-LE.A.1b
F-LE.A.2
F-IF.A.1
F-IF.A.2
F-IF.B.4
F-IF.B.5
F-IF.C.7a
F-IF.C.9
A-CED.A.2
A-REI.D.10 / Estimated Time
9 days
(covers pieces of course 3 chapter 2) / Standards
A-REI.A.1
A-REI.B.3
A-REI.D.10
A-CED.A.1
A-CED.A.2
A-CED.A.3
A-SSE.A.1a
N-Q.A.1
N-Q.A.2
N-Q.A.3
F-IF.A.2
F-IF.B.6
F-LE.A.1b
F-LE.A.1c / Estimated Time
9 days
(covers pieces of course 3 chapter 2) / Standards
S-ID.B.6
S-ID.B.7
N-Q.A.2
A-REI.A.1
A-REI.B.3
A-SSE.A.1a
A-SSE.A.1b
A-CED.A.2
A-CED.A.3
A-CED.A.4
F-IF.A.2 / Estimated Time
9 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 graphically
Learning Goal & Scale:
Big Ideas:
Principal Resource
Carnegie Algebra I: Chapter 4- Sequences / Principal Resource
Carnegie Algebra I: Chapter 5- Exponential Functions
Standards
F-LE.A.1a
F-LE.A.1b
F-LE.A.1c
F-LE.A.2
F-LE.B.5
F-BF.A.1a
F-BF.A.2
A-SSE.A.1a
A-SSE.A.1b
F-IF.A.1
F-IF.A.2
F-IF.A.3
F-IF.B.4 / Estimated Time
11days
(covers pieces of course 3 chapter 2) / Standards
A-SSE.A.1a
A-SSE.A.1b
A-CED.A.1
A-CED.A.2
F-IF.A.3
F-IF.B.4
F-IF.B.6
F-IF.C.7e
F-BF.A.1a
F-BF.A.2
F-BF.B.3
F-LE.A.1a
F-LE.A.1b
F-LE.A.1c
F-LE.A.2
F-LE.A.3
F-LE.B.5
A-REI.B.3
A-REI.D.10
A-REI.D.11
N-RN.A.1
N-RN.A.2
N-Q. A.2 / Estimated Time
12 days
Principal Resource
Carnegie Algebra I: Chapter 6- Systems of Equations / Principal Resource
Carnegie Algebra I: Chapter 7- Systems of Inequalities
Standards
A-CED.A.2
A-REI.C.5
A-REI.C.6
A-REI.D.10
A-REI.D.11 / Estimated Time
9 days
(covers course 3 chapters11 & 12) / Standards
A-CED.A.3
A-REI.D.12 / Estimated Time
9 days
Focus 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 Resource
Carnegie Algebra I:Chapter 11- Introduction to Quadratic Functions / Principal Resource
CarnegieAlgebra I:Chapter 12- Polynomials and Quadratics / Principal Resource
Carnegie Algebra I:Chapter 13- Solving Quadratic Equations & Inequalities
Standards
A-CED.A.1
A-CED.A.2
F-BF.B.3
F-IF.B.4
F-IF.B.5
F-IF.B.6
F-IF.C.7a
F-LE.A.1a
A-SSE.A.1
A-SSE.B.3a / Estimated Time
14days / Standards
A-APR.A.1
A-CED.A.1
A-CED.A.2
A-REI.B.4
A-SSE.A.1a
A-SSE.A.2
A-SSE.B.3a
A-SSE.B.3b
F-BF.A.1b
N-RN.A.2 / Estimated Time
14days / Standards
A-CED.A.1
A-CED.A.2
A-REI.B.4a
A-REI.B.4b
A-REI.C.7
F-IF.C.7a / Estimated Time
10 days
Focus 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 Resource
Carnegie Algebra I: Chapter 8- Analyzing Data Sets for One Variable / Principal Resource
Carnegie 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 Resource
Carnegie Algebra I: Chapter 10- Analyzing Data Sets for Two Categorical Variables
Standards
S-ID.A.1
S-ID.A.2
S-ID.A.3 / Estimated Time
10 days / Standards
S-ID.B.6a
S-ID.B.6b
S-ID.B.6c
S-ID.C.7
S-ID.C.8
S-ID.C.9 / Estimated Time
10 days / Standards
S-ID.B.5 / Estimated Time
10 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 Resource
CarnegieAlgebra I:Chapter 14- Real Number System
**14.3 & 14.4 go beyond the limits of Algebra I / Principal Resource
Carnegie Algebra I:Chapter 15- Other Functions and Inverses / Principal Resource
Carnegie Algebra I:Chapter 16- Mathematical Modeling
Standards
N-RN.A.1
N-RN.A.2
N-RN.B.3
N-CN.1
N-CN.7 / Estimated Time
5days / Standards
F-IF.A.1
F-IF.A.2
F-IF.B.4
F-IF.B.5
F-IF.C.7
F-IF.C.7b
F-BF.A.1a
F-BF.B.4a
F-BF.B.4b
A-CED.A.1
A-CED.A.4 / Estimated Time
9days / Standards
F-IF.B.4
F-IF.B.5
F-IF.C.7
F-BF.A.1
F-BF.B.4
F-LE.A.1
F-LE.A.2 / Estimated Time
11 days
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