Mafs 912 a rei 4.10 answer key

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Algebra 1 2020-2021 Course Code: 120031001

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Algebra 1

Course Code: 120031001

Pacing Guide

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MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Algebra 1 2020-2021 Course Code: 120031001

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MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Algebra 1 2020-2021 Course Code: 120031001

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1ST Nine Weeks 2nd Nine Weeks 3rd Nine Weeks 4th Nine Weeks

~ Introduction to Online Learning

I. Quantities and Modeling

A. Quantitative Reasoning B. Algebraic Models

STEM Lessons - Model Eliciting Activities

• Looking for the best Employment Option

• CollegeReview.com

• Efficient Storage

II. Understanding Functions

A. Functions and Models B. Patterns and Sequences

STEM Lessons - Model Eliciting Activities

• To The Limit

• My First Credit Card

• Plants vs. Pollutants

• The Friendly Confines or The Nat

III. Linear Functions, Equations,

and Inequalities – Part A A. Linear Functions B. Forms of Linear Equations

IV. Linear Functions, Equations, and Inequalities – Part B

A. Forms of Linear Equations (Cont.) B. Linear Equations and

Inequalities

STEM Lessons - Model Eliciting Activities

• Alternative Fuel Systems

• Preserving Our Marine Ecosystems

• Hybrid-Electric Vehicles vs. Gasoline- Powered Vehicles

V. Statistical Models A. Multi-Variable Categorical Data B. One-Variable Data Distributions C. Linear Modeling and

Regression

STEM Lessons - Model Eliciting Activities

• The Music Is On and Popping! Two-way Tables

VI. Linear Systems A. Solving Systems of Linear

Equations B. Modeling with Linear Systems

STEM Lessons - Model Eliciting Activities

• Manufacturing Designer Gear T-Shirts

VII. Exponential Relationships A. Rational Exponents and

Radicals B. Geometric Sequences and

Exponential Functions C. Exponential Equations and

Models

STEM Lessons - Model Eliciting Activities

• The Friendly Confines or The Nat - who has the best ballpark?

VIII. Polynomial Operations

A. Adding and Subtracting Polynomials

B. Multiplying Polynomials

IX. Quadratic Functions A. Graphing Quadratic Functions B. Connecting Intercepts, Zeros,

and Factors C. Graphing Polynomial Functions

X. Quadratic Equations and Modeling

A. Using Factors to Solve Quadratic Equations

B. Using Square Roots to Solve Quadratic Equations

C. Linear, Exponential, and Quadratic Models

STEM Lessons - Model Eliciting Activities

• Ranking Sports Players (Quadratic Equations Practice)

XI. EOC Review

XII. Functions and Inverses A. Piecewise-Defined Functions B. Understanding Inverse

Functions C. Graphing Square Root

Functions D. Graphing Cube Root Functions

Total Days Allotted for Instruction, Testing, and “Catch-up” Days:

T B Dates

Topic ~ 5 2 08/31-09/04

Topic I 12 6 09/08–09/23

Topic II 14 7 09/24-10/14

Topic III 6 3 10/15-10/22

Total 37 18

Total Days Allotted for Instruction, Testing, and “Catch-up” Days:

T B Dates

Topic IV 16 8 10/26-11/18

Topic V 16 8 11/19-12/15

Topic VI 17 8 12/16-01/22

Total

49

24

Total Days Allotted for Instruction, Testing, and “Catch-up” Days:

T B Dates

Topic VII 18 9 01/25-02/18 Topic VIII 9 4 02/23-03/03 Topic IX 16 8 03/04-03/25

Total 43 21

Total Days Allotted for Instruction, Testing, and “Catch-up” Days:

T B Dates

Topic X 14 7 04/05-04/22 Topic XI 6 3 04/23-04/30 Topic XII 27 13 05/03-06/09

Total 47 23

Social Emotional Learning Resources Are Available for All Topics

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MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Algebra 1 2020-2021 Course Code: 120031001

Division of Academics – Department of Mathematics Page 4 of 19 Year-at-a-Glance

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STANDARDS AT A GLANCE

1ST Nine Weeks 2nd Nine Weeks 3rd Nine Weeks 4th Nine Weeks

I. Quantities and Modeling MAFS.912.A-SSE.1.1a MAFS.912.A-CED.1.1 MAFS.912.A-CED.1.4 MAFS.912.A-REI.1.1 MAFS.912.A-REI.2.3 MAFS.912.N-Q.1.1* MAFS.912.N-Q.1.2* MAFS.912.N-Q.1.3*

II. Understanding Functions MAFS.912.F-BF.1.1a MAFS.912.F-IF.1.1 MAFS.912.F-IF.1.2 MAFS.912.F-IF.1.3 MAFS.912.F-IF.2.4 MAFS.912.F-IF.2.5

III. Linear Functions, Equations, and Inequalities – Part A MAFS.912.F-BF.2.3 MAFS.912.F-LE.1.1a,b MAFS.912.F-LE.1.2 MAFS.912.F-LE.2.5 MAFS.912.F-IF.2.6 MAFS.912.F-IF.3.7a MAFS.912.F-IF.3.9 MAFS.912.A-CED.1.2 MAFS.912.A-REI.4.10

*Assessed throughout

IV. Linear Functions, Equations, and Inequalities – Part B MAFS.912.A-CED.1.3 MAFS.912.A-REI.4.11 MAFS.912.A-REI.4.12 MAFS.912.S-ID.3.7

V. Statistical Models MAFS.912.S-ID.1.1 MAFS.912.S-ID.1.2 MAFS.912.S-ID.1.3 MAFS.912.S-ID.2.5 MAFS.912.S-ID.2.6 MAFS.912.S-ID.3.8 MAFS.912.S-ID.3.9

VI. Linear Systems MAFS.912.A-CED.1.3 MAFS.912.A-REI.3.5 MAFS.912.A-REI.3.6 MAFS.912.A-REI.4.12

VII. Exponential Relationships MAFS.912.N-RN.1.1 MAFS.912.N-RN.1.2 MAFS.912.N-RN.2.3 MAFS.912.F-BF.1.1a MAFS.912.F-BF.2.3 MAFS.912.F-LE.1.1a,b,c MAFS.912.F-LE.1.2 MAFS.912.F-LE.1.3 MAFS.912.F-LE.2.5 MAFS.912.F-IF.3.7e MAFS.912.F-IF.3.8b MAFS.912.A-CED.1.1 MAFS.912.A-SSE.2.3c MAFS.912.S-ID.2.6

VIII. Polynomial Operations MAFS.912.A-SSE.1.1b MAFS.912.A-SSE.1.2 MAFS.912.A-APR.1.1

IX. Quadratic Functions MAFS.912.F-BF.2.3 MAFS.912.F-IF.2.4 MAFS.912.F-IF.3.7a MAFS.912.F-IF.3.8a MAFS.912.A-APR.2.3 MAFS.912.A-REI.2.4

X. Quadratic Equations and Modeling MAFS.912.A-CED.1.2 MAFS.912.A-SSE.1.2 MAFS.912.A-SSE.2.3a MAFS.912.A-REI.2.4a MAFS.912.A-REI.2.4b MAFS.912.F-LE.1.1b

XI. EOC REVIEW

XII. Functions and Inverses MAFS.912.A-REI.2.3 MAFS.912.F-IF.3.7b MAFS.912.F-IF.3.7c MAFS.912.F-BF.2.4

Total Days Allotted for Instruction, Testing, and “Catch-up” Days:

T B Dates

Topic ~ 5 2 08/31-09/04

Topic I 12 6 09/08–09/23

Topic II 14 7 09/24-10/14

Topic III 6 3 10/15-10/22

Total 37 18

Total Days Allotted for Instruction, Testing, and “Catch-up” Days:

T B Dates

Topic IV 16 8 10/26-11/18

Topic V 16 8 11/19-12/15

Topic VI 17 8 12/16-01/22

Total

49

24

Total Days Allotted for Instruction, Testing, and “Catch-up” Days:

T B Dates

Topic VII 18 9 01/25-02/18 Topic VIII 9 4 02/23-03/03 Topic IX 16 8 03/04-03/25

Total 43 21

Total Days Allotted for Instruction, Testing, and “Catch-up” Days:

T B Dates

Topic X 14 7 04/05-04/22 Topic XI 6 3 04/23-04/30 Topic XII 27 13 05/03-06/09

Total 47 23

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Algebra 1 2020-2021 Course Code: 120031001

Division of Academics – Department of Mathematics Page 5 of 19 Year-at-a-Glance

THIS DOCUMENT IS SUBJECT TO CHANGE

Algebra 1 Core – H.M.H. Resources

Algebra 1 Intensive Math – H.M.H. Resources

Unit Resources Unit Resources

Unit Tests – A, B, and C Math in Careers Video

Performance Assessment Assessment Readiness (Mixed Review)

Module Resources Module Resources

Module Test B Module Test Modified

Common Core Assessment Readiness

RTI Tier 2 – Strategic Intervention

Advanced Learners – Challenge Worksheets Skills Module Pre-Test, Skills and RTI Post Test, Skills Worksheets

RTI Tier 3 – Intensive Intervention Worksheets

Lesson Resources Lesson Resources

Lessons – Work text/Interactive Student Edition Practice and Problem Solving: D (modified)

Practice and Problem Solving: A/B

RTI Tier 1 – Lesson Intervention Worksheets

Advanced Learners - Practice and Problem Solving: C Reteach

Reading Strategies AND Success for English Learners

PMT Preferences Auto-assign for intervention and enrichment: NO

PMT Preferences Auto-assign for intervention and enrichment: YES

Test and Quizzes Daily Intervention

Homework Standard-Based Intervention

Course Intervention

MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Algebra 1 2020-2021 Course Code: 120031001

Division of Academics – Department of Mathematics Page 6 of 19 Year-at-a-Glance

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Technology Integration: The SAMR Model

Video Link: Introduction to the SAMR Model

Link: Other Examples of Transformed Lessons/Tasks

Stages of the SAMR Model:

Examples of Tasks at each Stage:

https://youtu.be/9aJsmWzCRaw
https://www.dropbox.com/s/t915wmn1nwvd5y2/SAMR%20Transformed%20Lesson%20Examples-2.pdf?dl=0
MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Algebra 1 2020-2021 Course Code: 120031001

Division of Academics – Department of Mathematics Page 7 of 19 Year-at-a-Glance

THIS DOCUMENT IS SUBJECT TO CHANGE

YEAR AT A GLANCE ACADEMIC SUPPORT

REPORTING CATEGORY: ALGEBRA AND MODELING % of Test: 41% 2019 Average % Correct: 42%

Standards Previous Grade

Standards Algebra I Topic(s)

Algebra II Standard

MAFS.912.A-APR.1.1

Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

MAFS.6.EE.1.3 MAFS.6.EE.1.4 MAFS.7.EE.1.1 MAFS.8.EE.1.1

Topic IX X

MAFS.912.A-CED.1.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and

quadratic functions, and simple rational, absolute, and exponential functions.★

MAFS.7.EE.2.4

MAFS.8.EE.3.7 Topic I Topic VIII

X

MAFS.912.A-REI.2.3

Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. MAFS.7.EE.2.4 MAFS.8.EE.3.7

Topic I

X

MAFS.912.A-CED.1.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example,

rearrange Ohm’s law V = IR to highlight resistance R. ★

MAFS.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with

labels and scales. ★

MAFS.8.EE.3.8 MAFS.8.F.1.3 MAFS.8.F.2.4

Topic III Topic XII

X

MAFS.912.A-REI.3.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

MAFS.8.EE.3.8

Topic VI

MAFS.912.A-REI.3.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

MAFS.8.EE.3.8 X

MAFS.912.A-REI.4.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

MAFS.912.A-CED.1.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints

on combinations of different foods. ★

Topic VI X

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MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Algebra 1 2020-2021 Course Code: 120031001

Division of Academics – Department of Mathematics Page 8 of 19 Year-at-a-Glance

THIS DOCUMENT IS SUBJECT TO CHANGE

YEAR AT A GLANCE ACADEMIC SUPPORT

REPORTING CATEGORY: ALGEBRA AND MODELING % of Test: 41% 2019 Average % Correct: 42%

Standards Previous Grade

Standards Algebra I Topic(s)

Algebra II Standard

MAFS.912.A-REI.1.1 Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

MAFS.7.EE.2.4 MAFS.8.EE.3.7 Topic I X

MAFS.912.A-REI.2.4 Solve quadratic equations in one variable.

a) Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions. Derive the quadratic formula from this form.

b) Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives

complex solutions and write them as a ± bi for real numbers a and b.

MAFS.7.EE.1.1 MAFS.8.EE.1.2

Topic X Topic Xi

X

MAFS.912.A-REI.4.11 Explain why the x-coordinates of the points where the graphs of the equations 𝑦 = 𝑓(𝑥) and 𝑦 = 𝑔(𝑥) intersect are the solutions of the equation 𝑓(𝑥) = 𝑔(𝑥); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where 𝑓(𝑥) and/or 𝑔(𝑥) are linear, polynomial, rational, absolute value,

exponential, and logarithmic functions. ★

MAFS.8.EE.3.8 Topic III X

MAFS.912.A-REI.4.10 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

MAFS.8.EE.2.5 Topic IV

MAFS.912.A-SSE.2.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the

expression. ★

a. Factor a quadratic expression to reveal the zeros of the function it defines. b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines. c. Use the properties of exponents to transform expressions for exponential functions. For example the expression can be

rewritten as (1.15 1

12) 12𝑡

≈ 1.01212𝑡 to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

MAFS.6.EE.1.3 MAFS.7.EE.1.1 MAFS.8.EE.1.1

Topic VIII Topic XI Topic XII

X

MAFS. 912.A-SSE.1.1

Interpret expressions that represent a quantity in terms of its context. ★

a. Interpret parts of an expression, such as terms, factors, and coefficients. b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret as the

product of P and a factor not depending on P.

MAFS.6.EE.1.2 MAFS.7.EE.1.2

Topic I Topic IX

X

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MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Algebra 1 2020-2021 Course Code: 120031001

Division of Academics – Department of Mathematics Page 9 of 19 Year-at-a-Glance

THIS DOCUMENT IS SUBJECT TO CHANGE

YEAR AT A GLANCE ACADEMIC SUPPORT

REPORTING CATEGORY: ALGEBRA AND MODELING % of Test: 41% 2019 Average % Correct: 42%

Standards Previous Grade

Standards Algebra I Topic(s)

Algebra II Standard

MAFS.912.A-SSE.1.2

Use the structure of an expression to identify ways to rewrite it. For example, see 𝑥4 − 𝑦 4, as (𝑥2)2– (𝑦2)2 thus recognizing it as a difference of squares that can be factored as (𝑥² – 𝑦²)(𝑥² + 𝑦²).

MAFS.6.EE.1.3 MAFS.7.EE.1.1

Topic IX Topic XI Topic XII

X

YEAR AT A GLANCE ACADEMIC SUPPORT

REPORTING CATEGORY: FUNCTIONS AND MODELING % of Test: 40% 2019 Average % Correct: 35%

Standards Previous Grade

Standards Algebra I Topic(s)

Algebra II Standard

MAFS.912.F-BF.2.3 Identify the effect on the graph of replacing 𝑓(𝑥) 𝑏𝑦 𝑓(𝑥) + 𝑘, 𝑘 𝑓(𝑥), 𝑓(𝑘𝑥), 𝑎𝑛𝑑 𝑓(𝑥 + 𝑘) for specific values of 𝑘 (both positive and negative); find the value of 𝑘 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Topic III Topic VIII Topic X

X

MAFS.912.F-IF.1.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

MAFS.6.EE.1.2c

Topic II MAFS.912.F-IF.1.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If 𝑓 is a function and 𝑥 is an element of its domain, then 𝑓(𝑥) denotes the output of 𝑓 corresponding to the input 𝑥. The graph of 𝑓 is the graph of the equation 𝑦 = 𝑓(𝑥).

MAFS.8.F.1.1 MAFS.8.F.1.2 MAFS.8.F.1.3

MAFS.912.F-IF.2.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function ℎ(𝑛) gives the number of person-hours it takes to assemble engines in a factory, then the positive integers would

be an appropriate domain for the function. ★

Topic II Topic VIII

X

MAFS.912.F-IF.2.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end

behavior; and periodicity. ★

MAFS.8.F.2.5 Topic II Topic X

X

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MIAMI-DADE COUNTY PUBLIC SCHOOLS District Pacing Guide

Algebra 1 2020-2021 Course Code: 120031001

Division of Academics – Department of Mathematics Page 10 of 19 Year-at-a-Glance

THIS DOCUMENT IS SUBJECT TO CHANGE

YEAR AT A GLANCE ACADEMIC SUPPORT

REPORTING CATEGORY: FUNCTIONS AND MODELING % of Test: 40% 2019 Average % Correct: 35%

Standards Previous Grade

Standards Algebra I Topic(s)

Algebra II Standard

MAFS.912.F-IF.3.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

Topic III X

MAFS.912.F-IF.2.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval.

Estimate the rate of change from a graph. ★ MAFS.8.F.2.4 Topic III X

MAFS.912.S-ID.3.7

Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. ★ MAFS.8.SP.1.3 Topic IV

MAFS.912.F-IF.3.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of

change in functions such as 𝑦 = (1.02)𝑡 , 𝑦 = (0.97)𝑡 , 𝑦 = (1.01)12𝑡 , 𝑦 = (0.97) 𝑡

10, and classify them as representing exponential growth or decay.

Topic VIII Topic X

X

MAFS.912.A-APR.2.3 Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

MAFS.7.EE.1.1 Topic X X

MAFS. 912.F-IF.3.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology

for more complicated cases. ★

a. Graph linear and quadratic functions and show intercepts, maxima, and minima. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior. d. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end

behavior. (Algebra II) e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing

period, midline, and amplitude, and using phase shift.

MAFS.8.EE.2.5 MAFS.8.F.1.3

Topic III Topic VIII Topic X

X

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Algebra 1 2020-2021 Course Code: 120031001

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REPORTING CATEGORY: FUNCTIONS AND MODELING % of Test: 40% 2019 Average % Correct: 35%

Standards Previous Grade

Standards Algebra I Topic(s)

Algebra II Standard

MAFS.912.F-LE.1.1

Distinguish between situations that can be modeled with linear functions and with exponential functions. ★

a. Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another. c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

MAFS.8.F.1.3 MAFS.8.F.2.4

Topic III Topic VIII Topic XII

MAFS.912.F-LE.2.5

Interpret the parameters in a linear or exponential function in terms of a context. ★ Topic III Topic VIII

X

MAFS.912.F-LE.1.2 Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a

relationship, or two input-output pairs (include reading these from a table).★ MAFS.8.F.2.4

Topic III Topic VIII

MAFS.912.F-BF.1.1

Write a function that describes a relationship between two quantities. ★

a. Determine an explicit expression, a recursive process, or steps for calculation from a context. b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature

of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model. c. Compose functions. For example, if 𝑇(𝑦) is the temperature in the atmosphere as a function of height, and ℎ(𝑡) is the

height of a weather balloon as a function of time, then 𝑇(ℎ(𝑡)) is the temperature at the location of the weather balloon as a function of time.

MAFS.8.F.2.4 Topic II Topic VIII

X

MAFS. 912.F-IF.1.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by 𝑓(0) = 𝑓(1) = 1, 𝑓(𝑛 + 1) = 𝑓(𝑛) + 𝑓(𝑛 − 1) for 𝑛 ≥ 1.

Topic II

MAFS.912.F-LE.1.3 Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly,

quadratically, or (more generally) as a polynomial function. ★ Topic VIII

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Standards Previous Grade

Standards Algebra I Topic(s)

Algebra II Standard

MAFS.912.N-RN.1.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

Topic VII

X

MAFS.912.N-RN.2.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

MAFS.8.NS.1.1

MAFS.912.N-RN.1.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define to be the cube root of

5 because we want (5 1

3) 3

= 5 (

1

3 )

3

to hold, so 5 (

1

3 )

3

must equal 5.

MAFS.8.EE.1.1 MAFS.8.EE.1.2

X

MAFS.912.S-ID.1.1

Represent data with plots on the real number line (dot plots, histograms, and box plots). ★ MAFS.6.SP.2.4 Topic V

MAFS.912.S-ID.1.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range,

standard deviation) of two or more different data sets. ★

MAFS.6.SP.1.2 MAFS.6.SP.2.5

Topic V MAFS.912.S-ID.1.3

Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme

data points (outliers). ★ MAFS.6.SP.2.5

MAFS.912.S-ID.2.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data

(including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data. ★ MAFS.8.SP.1.4 Topic V

MAFS.912.S-ID.2.6

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. ★

a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, and exponential models.

b. Informally assess the fit of a function by plotting and analyzing residuals. c. Fit a linear function for a scatter plot that suggests a linear association.

MAFS.8.SP.1.1 MAFS.8.SP.1.2 MAFS.8.SP.1.3

Topic V

MAFS.912.S-ID.3.8

Compute (using technology) and interpret the correlation coefficient of a linear fit. ★

MAFS.912.S-ID.3.9

Distinguish between correlation and causation. ★

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CAN DO Descriptors: Grade Level Cluster 9-12

Level 1 Entering Level 2 Emerging Level 3 Developing Level 4 Expanding Level 5 Bridging

L IS

T E

N IN

G

• Point to or show basic parts, components, features, characteristics, and properties of objects, organisms, or persons named orally

• Match everyday oral information to pictures, diagrams, or photographs

• Group visuals by common traits named orally (e.g., “These are polygons.”)

• Identify resources, places, products, figures from oral statements, and visuals

• Match or classify oral descriptions to real-life experiences or visually- represented, content- related examples

• Sort oral language statements according to time frames

• Sequence visuals according to oral directions

• Evaluate information in social and academic conversations

• Distinguish main ideas from supporting points in oral, content- related discourse

• Use learning strategies described orally

• Categorize content-based examples described orally

• Distinguish between multiple meanings of oral words or phrases in social and academic contexts

• Analyze content-related tasks or assignments based on oral discourse

• Categorize examples of genres read aloud

• Compare traits based on visuals and oral descriptions using specific and some technical language

• Interpret cause and effect scenarios from oral discourse

• Make inferences from oral discourse containing satire, sarcasm, or humor

• Identify and react to subtle differences in speech and register (e.g., hyperbole, satire, comedy)

• Evaluate intent of speech and act accordingly

S P

E A

K IN

G

• Answer yes/no or choice questions within context of lessons or personal experiences

• Provide identifying information about self

• Name everyday objects and pre- taught vocabulary

• Repeat words, short phrases, memorized chunks of language

• Describe persons, places, events, or objects

• Ask WH- questions to clarify meaning

• Give features of content- based material (e.g., time periods)

• Characterize issues, situations, regions shown in illustrations

• Suggest ways to resolve issues or pose solutions

• Compare/contrast features, traits, characteristics using general and some specific language

• Sequence processes, cycles, procedures, or events

• Conduct interviews or gather information through oral interaction

• Estimate, make predictions or pose hypotheses from models

• Take a stance and use evidence to defend it

• Explain content-related issues and concepts

• Compare and contrast points of view

• Analyze and share pros and cons of choices

• Use and respond to gossip, slang, and idiomatic expressions

• Use speaking strategies (e.g., circumlocution)

• Give multimedia oral presentations on grade-level material

• Engage in debates on content- related issues using technical language

• Explain metacognitive strategies for solving problems (e.g., “Tell me how you know it.”)

• Negotiate meaning in pairs or group discussions

R E

A D

IN G

• Match visual representations to words/phrases

• Read everyday signs, symbols, schedules, and school-related words/phrases

• Respond to WH- questions related to illustrated text

• Use references (e.g., picture dictionaries, bilingual glossaries, technology)

• Match data or information with its source or genre

• Classify or organize information presented in visuals or graphs

• Follow multi-step instructions supported by visuals or data

• Match sentence-level descriptions to visual representations

• Compare content-related features in visuals and graphics

• Locate main ideas in a series of related sentences

• Apply multiple meanings of words/phrases to social and academic contexts

• Identify topic sentences or main ideas and details in paragraphs

• Answer questions about explicit information in texts

• Differentiate between fact and opinion in text

• Order paragraphs or sequence information within paragraphs

• Compare/contrast authors’ points of view, characters, information, or events

• Interpret visually- or graphically- supported information

• Infer meaning from text

• Match cause to effect

• Evaluate usefulness of data or information supported visually or graphically

• Interpret grade-level literature

• Synthesize grade-level expository text

• Draw conclusions from different sources of informational text

• Infer significance of data or information in grade-level material

• Identify evidence of bias and credibility of source

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W R

IT IN

G

• Label content-related diagrams, pictures from word/phrase banks

• Provide personal information on forms read orally

• Produce short answer responses to oral questions with visual support

• Supply missing words in short sentences

• Make content-related lists of words, phrases, or expressions

• Take notes using graphic organizers or models

• Formulate yes/no, choice and WH- questions from models

• Correspond for social purposes (e.g., memos, e-mails, notes)

• Complete reports from templates

• Compose short narrative and expository pieces

• Outline ideas and details using graphic organizers

• Compare and reflect on performance against criteria (e.g., rubrics)

• Summarize content-related notes from lectures or text

• Revise work based on narrative or oral feedback

• Compose narrative and expository text for a variety of purposes

• Justify or defend ideas and opinions

• Produce content-related reports

• Produce research reports from multiple sources

• Create original pieces that represent the use of a variety of genres and discourses

• Critique, peer-edit and make recommendations on others’ writing from rubrics

• Explain, with details, phenomena, processes, procedures

Mathematical Practices

MAFS.K12.MP.1.1 Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, “Does this make sense?” They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Context Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.K12.MP.2.1 Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Context Complexity: Level 3: Strategic Thinking & Complex Reasoning

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Mathematical Practices

MAFS.K12.MP.3.1 Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Context Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.K12.MP.4.1 Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Context Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.K12.MP.5.1 Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Context Complexity: Level 2: Basic Application of Skills & Concepts

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Mathematical Practices

MAFS.K12.MP.6.1 Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Context Complexity: Level 3: Strategic Thinking & Complex Reasoning

MAFS.K12.MP.7.1 Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well-remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x² + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 – 3(x – y)² as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. Context Complexity: Level 2: Basic Application of Skills & Concepts

MAFS.K12.MP.8.1 Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3. Noticing the regularity in the way terms cancel when expanding (x – 1)(x + 1), (x – 1)(x² + x + 1), and (x – 1)(x³ + x² + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. Context Complexity: Level 3: Strategic Thinking & Complex Reasoning

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Literacy Standards

LAFS.910.RST.1.3 Follow precisely a complex multistep procedure when carrying out experiments, taking measurements, or performing technical tasks, attending to special cases or exceptions defined in the text. Context Complexity: Level 2: Basic Application of Skills & Concepts

LAFS.910.RST.2.4 Determine the meaning of symbols, key terms, and other domain-specific words and phrases as they are used in a specific scientific or technical context relevant to grades 9–10 texts and topics. Context Complexity: Level 2: Basic Application of Skills & Concepts

LAFS.910.RST.3.7 Translate quantitative or technical information expressed in words in a text into visual form (e.g., a table or chart) and translate information expressed visually or mathematically (e.g., in an equation) into words. Context Complexity: Level 2: Basic Application of Skills & Concepts

LAFS.1112.WHST.1.1 Write arguments focused on discipline-specific content. a. Introduce precise, knowledgeable claim(s), establish the significance of the claim(s), distinguish the claim(s) from alternate or opposing claims, and

create an organization that logically sequences the claim(s), counterclaims, reasons, and evidence. b. Develop claim(s) and counterclaims fairly and thoroughly, supplying the most relevant data and evidence for each while pointing out the strengths

and limitations of both claim(s) and counterclaims in a discipline-appropriate form that anticipates the audience’s knowledge level, concerns, values, and possible biases.

c. Use words, phrases, and clauses as well as varied syntax to link the major sections of the text, create cohesion, and clarify the relationships between claim(s) and reasons, between reasons and evidence, and between claim(s) and counterclaims.

d. Establish and maintain a formal style and objective tone while attending to the norms and conventions of the discipline in which they are writing. e. Provide a concluding statement or section that follows from or supports the argument presented.

Context Complexity: Level 4: Extended Thinking &Complex Reasoning

LAFS.1112.WHST.1.2 Write informative/explanatory texts, including the narration of historical events, scientific procedures/ experiments, or technical processes. a. Introduce a topic and organize complex ideas, concepts, and information so that each new element builds on that which precedes it to create a

unified whole; include formatting (e.g., headings), graphics (e.g., figures, tables), and multimedia when useful to aiding comprehension. b. Develop the topic thoroughly by selecting the most significant and relevant facts, extended definitions, concrete details, quotations, or other

information and examples appropriate to the audience’s knowledge of the topic. c. Use varied transitions and sentence structures to link the major sections of the text, create cohesion, and clarify the relationships among complex

ideas and concepts. d. Use precise language, domain-specific vocabulary and techniques such as metaphor, simile, and analogy to manage the complexity of the topic;

convey a knowledgeable stance in a style that responds to the discipline and context as well as to the expertise of likely readers. e. Provide a concluding statement or section that follows from and supports the information or explanation provided (e.g., articulating implications or

the significance of the topic). Context Complexity: Level 4: Extended Thinking &Complex Reasoning