unit 1 solving equations and inequalities · unit 1 – solving equations and inequalities eureka...

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UNIT 1 – SOLVING EQUATIONS AND INEQUALITIES

Eureka Math Module 1, Topics C

(Approximately 13 Days ● 8/8/19-8/26/19)

Unit 1 Overview

In Topic C, instead of just solving equations, they formalize descriptions of what they learned before (variable, solution sets, etc.) and are able to explain, justify, and evaluate their reasoning as they strategize methods for solving linear and nonlinear equations. Students take their experience solving systems of linear equations further as they prove the validity of the addition method, learn a formal definition for the graph of an equation and use it to explain the reasoning of solving systems graphically, and represent the solution to systems of linear inequalities graphically. Specifically

Students will solve linear equations Students will solve linear inequalities Students will solve linear system Students will rearrange formula to solve missing variable

Focus Standards

Addressed in Eureka Math Resource – Use of supplemental resources is not needed Partially Addressed in Eureka Math Resource – Use of supplemental resources may/may not be needed Not Adequately Addressed in Eureka Math Resource – Use of supplemental resources is necessary LOUISIANA CONNECTORS When teaching students with significant disabilities who are eligible to take the LEAP Connect assessment, use the specific Louisiana Connectors that are aligned to the unit’s focus standards.

A-CED.A.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 and exponential functions

Remediation Standard(s): 7.EE.B.4

https://www.louisianabelieves.com/docs/default-source/students-with-disabilities/k-12-louisiana-connectors-for-students-with-significant-disabilities.pdf?sfvrsn=6

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A-CED.A.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

A-REI.A.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.

Remediation Standard(s): 7.EE.B.4

A-REI.B.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

A-CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

Remediation Standard(s): 8.EE.C.8, 8.F.A.3, and 8.F.B.4

Focus Standards for Mathematical Practice

MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP3 Construct viable arguments and critique the reasoning of others. MP4 Model with Mathematics MP.6 Attend to precision.

Unit Terms & Tools Spanish cognates are included (if applicable) for Tier 3 and Tier 2 vocabulary terms. Spanish cognates will be shown as follows: Vocab Term/Spanish Cognate.

New Unit Terms (Tier 3 Vocabulary)

Algebraic Expression, Degree of a Monomial, Equivalent Algebraic Expressions,

Numerical Expression, Solution Set, Variable Symbol

Familiar Terms (Tier 3 Vocabulary)

Algebra

Cross-Curricular Terms (Tier 2 Vocabulary)

Suggested Tools Coordinate Plane, and Equations and Inequalities

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Sample Calendar

Coding: 1.1-A represents Eureka Math Module 1. Lesson 1 – Topic A ● Addressed standard(s) listed below lesson Please note, this calendar suggests lessons that can be combined and taught in one class period. It also includes remediation and extension lessons that are recommended for classroom use. While this sample calendar helps guide instructional timing, it does not dictate exactly what lesson a teacher should be addressing on a given day. In addition, included FLEX days should be used for remediation, practice, enrichment, assessment, or other instructional activities.

Week Beginning: Monday Tuesday Wednesday Thursday Friday

August 5th No school for students

No school for students

No school for students

FLEX (First day of school for students) Module 1 Lesson 10 8.EE.C7a

Module 1 Lesson 11 8.EE.C7a

August 12th LEAP 360 Diagnostic (Window provided for administration)

Module 1 Lesson 12 and 13 A-REI.A.1 and A-REI.B.3

Module 1 Lesson 14 and 15 A-REI.B.3

Module 1 Lesson 16

Module 1 Lesson 17 and 18 A-REI.B.4b

August 19th Module 1 Lesson 19 A1: A-CED.A.4, A1: A-REI.B.3*

Flex Module 1 Lesson 20 C A1: A-CED.A.2, A1: A-REI.D.10

Module 1 Lesson 21 and 22 C A1: A-REI.C.6, A1: A-REI.D.12

Module 1 Lesson 23 and 24 C A1: A-REI.C.5

August 26th Flex Unit 2 Begins

Additional Information

Remediation Support (LDOE Remediation Guide)

Teachers may choose appropriate questions, activities, and or lessons from the table below to support students who have prior unfinished learning. Teachers should be strategic when choosing problems from suggested lessons in order to differentiate instruction to have the most impact on student achievement. For additional remediation support, teachers are encouraged to utilize the Coherence Map and the Louisiana Department of Education’s Algebra I Remediation Support Document

https://achievethecore.org/coherence-map/HS/A

http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/new-standards---algebra-i-remediation-guide.pdf?sfvrsn=6f838a1f_6


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Remedial Skills Support in Eureka Use to help students struggling with mastery of Lesson 10 8.EE.C7a

Grade 8 Module 4 Lesson 1-9

Use to help students struggling with mastery of Lesson 11 8.EE.C7a


Additional Lessons (Optional for remediation and enrichment)

Enrichment Lesson (s) 1.15-C and 1.16-C, These Lessons focus on solving compound equations and/or inequalities which is not the explicit expectation of the standards for any grade/course.

Assessment Information (Mid-Module and End-of-Module)

The end-module assessment is designed to be given after completing Topic D. .

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UNIT 2 – Creating Equations to Solve Problems

Eureka Math Module 1, Topics D


Unit 2 Overview

In Topic D, students are formally introduced to the modeling cycle through problems that can be solved by creating equations and inequalities in one variable, systems of equations, and graphing. Specifically

Students will Solving Problems in Two Ways—Rate and Algebra

Focus Standards


A-CED-A.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.

Remediation Standard(s): 8.EE.C.8

A-REI.C.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

A-REI-D.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).

Remediation Standard(s): 8.EE.C.8


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A-REI.D.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.

A-SSE-B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

Remediation Standard(s): 6.EE.A.3, 7.EE.A.1, and 8.EE.A.1


MP.1 Make sense of problems and persevere in solving them.

MP.2 Reason abstractly and quantitatively.

MP3 Construct viable arguments and critique the reasoning of others.

MP4 Model with Mathematics

MP.6 Attend to precision.

Suggested Tools None

Sample Calendar



August 26 Module 1 Lesson 25 A1: A-CED.A.1, A1: A-REI.B.3

Flex New Topic Unit 3


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Remediation Support

(LDOE Remediation Guide)


Additional Lessons

(Optional for remediation and enrichment)

Enrichment Optional Lesson --- Time permitting (Flex day)

1.26-D, 1.27-D,

This Lesson focuses on developing students understanding of recursive processes and using them to solve a modeling task.


.




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UNIT 3 – Linear and Exponential Sequences

Eureka Math Module 3, Topics A


Unit 3 Overview

In Topic A, students explore arithmetic and geometric sequences as an introduction to the formal notation of functions.

They interpret arithmetic sequences as linear functions with integer domains and geometric sequences as exponential

functions with integer domains. Students compare and contrast the rates of change of linear and exponential functions,

looking for structure in each, and distinguishing between additive and multiplicative change.

Specifically

Students will explore arithmetic and geometric sequence as introduction to function notations

Focus Standards


F-IF.A.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 (𝑥) denotes the output of 𝑓 corresponding to the input 𝑥. The graph of 𝑓 is the graph of the equation 𝑦=(𝑥).

Remediation Standard(s): 8.F.A.1, 8.F.A.2, and 8.F.A.3

F-IF.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Remediation Standard(s) 6.EE.A.2

F-IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.


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F-IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. .

F-LE.A.1 Distinguish between situations that can be modeled with linear functions and with exponential functions.

Remediation Standard(s) 8.F.A.3, and 8.F.B.4

F-LE.A.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).

Remediation Standard(s) 8.F.B.4


MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.4 Model with mathematics. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.



Domain Linear Function Function,

Range


Algebraic Expression Coefficient of a Monomial Constant Equation Equivalent Expressions Equivalent Polynomial

Expressions

Factored Expression Monomial Number Sentence Numerical Expression Numerical Symbol Polynomial Expression Simple Expression

Solution Solution Set Terms of a Polynomial Truth Values of a

Number Sentence Variable Symbol


Suggested Tools Coordinate Plane, Equations and Inequalities, and Graphing Calculator

Sample Calendar Coding: 1.1-A represents Eureka Math Module 1. Lesson 1 – Topic A ● Addressed standard(s) listed below lesson

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Please note, this calendar suggests lessons that can be combined and taught in one class period. It also includes remediation and extension lessons that are recommended for classroom use. While this sample calendar helps guide instructional timing, it does not dictate exactly what lesson a teacher should be addressing on a given day. In addition, included FLEX days should be used for remediation, practice, enrichment, assessment, or other instructional activities.


August 26 Module 3 Lesson 1 A1: F-IF.A.2*, A1: F-IF.A.3*

Module 3 Lesson 2 and 3 A1: A-SSE.A.1b, A1: F-IF.A.2

September 2nd Labor Day (Holiday)

Module 3 Lesson 5 A1: A-SSE.A.1b A1: F-IF.A.2*, A1: F-IF.A.3

Module 3 Lesson 6 and 7 A1: F-IF.A.2*, A1: F-IF.B.4, A1: F-IF.B.6

FLEX Unit 4 Begins




Remedial Skills Support in Eureka Use to help students struggling with mastery of Lessons 3-5 8.F.A.1 8.F.A.2



Enrichment Lesson: 3.2A This Lesson focuses on writing arithmetic and geometric sequences both recursively and with

an explicit formula.





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UNIT 4 – Functions and Their Graphs

Eureka Math Module 3, Topics B


Unit 4 Overview

In Topic B, students connect their understanding of functions to their knowledge of graphing from Grade 8. They learn the formal definition of a function and how to recognize, evaluate, and interpret functions in abstract and contextual situations. Students examine the graphs of a variety of functions and learn to interpret those graphs using precise terminology to describe such key features as domain and range, intercepts, intervals where the function is increasing or decreasing, and intervals where the function is positive or negative. Specifically, students will

examine the graphs of a variety of functions and learn to interpret those graphs using precise terminology to describe such key features as domain and range, intercepts, intervals.

examine graph of functions to determine if they are increasing or decreasing, as well as the function are positive or negative.

Focus Standards


F-IF.A.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 𝑥𝑥 is an element of its domain, then (𝑥) denotes the output of 𝑓 corresponding to the input 𝑥. The graph of 𝑓 is the graph of the equation 𝑦= (𝑥).

Remediation Standard(s): 8.F.A.1, 8.F.A.2, and 8.F.A.3

F-IF.A.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Remediation Standard(s): 6.EE.A.2


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F-IF.B.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.

Remediation Standard(s): 8.F.B.5

F-IF.C.7a 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.

Remediation Standard(s): 8.EE.B.5, and 8.F.A.3




Domain Linear Function Function,

Range


Algebraic Expression Coefficient of a

Monomial Constant Equation Equivalent Expressions Equivalent Polynomial

Expressions

Factored Expression Monomial Number Sentence Numerical Expression Numerical Symbol Polynomial Expression Simple Expression

Solution Solution Set Terms of a Polynomial Truth Values of a

Number Sentence Variable Symbol



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Sample Calendar



September 2nd Labor Day (Holiday)

Module 3 Lesson 8 A1: F-IF.A.2

September 9th Module 3 Lesson 9 and 10 A1: F-IF.A.1*, A1: F-IF.A.2, A1: F-IF.A.3*

Module 3 Lesson 11 and 12 A1: F-IF.A.2*, A1: F-IF.C.7a A1: F-IF.A.1, A1: F-IF.A.2, A1: F-IF.B.4

Module 3 Lesson 13 A1: N-Q.A.1, A1: F-IF.B.4

Module 3 Lesson 14 A1: F-IF.A.2, A1: F-BF.A.1a, A1: F-LE.A.1b, A1: F-LE.A.1c, A1: F-LE.A.2, A1: F-LE.A.3

FLEX

September 16th District PD (Student Holiday)

LEAP 360 Form 1

Unit 5 Begins




Remedial Skills Support in Eureka Use to help students struggling with mastery of Lessons 8-12 8.F.A.1 8.F.A.2





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None


Mid-module to be taken after topic B

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Unit 5 – The Structure of Expressions


(Approximately 5 Days ● 9/17/19 - 9/23/19)

Unit 5 Overview

In Topic B, students use the structure of expressions to define what it means for two algebraic expressions to be equivalent. In doing so, they discern that the commutative, associative, and distributive properties help link each of the expressions in the collection together, even if the expressions look very different themselves. They learn the definition of a polynomial expression and build fluency in identifying and generating polynomial expressions as well as adding, subtracting, and multiplying polynomial expressions. Specifically, students will

add and subtract polynomials multiply polynomials use special products of polynomials (sums and difference patterns) Interpret parts of an expression, such as terms, factors, and coefficients Interpret complicated expressions by viewing one or more of their parts as a single entity. Interpret parts of an expression, such as terms, factors, and coefficients solve polynomial equations in factored form

Focus Standards

Addressed in Eureka Math Resource – Use of supplemental resources is not needed

Partially Addressed in Eureka Math Resource – Use of supplemental resources may/may not be needed

Not Adequately Addressed in Eureka Math Resource – Use of supplemental resources is necessary

LOUISIANA CONNECTORS

When teaching students with significant disabilities who are eligible to take the LEAP Connect assessment, use the specific Louisiana Connectors that are aligned to the unit’s focus standards.

A-SSE-A.1 A-SSE.A.1 Interpret expressions that represent a quantity in terms of its context.

Remediation:

6.EE.A.2, and 7EE.A.2


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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 P(1 + r)n as the product of and a

factor not depending on P.

A-APR-A.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.

Remediation: 6.EE.A.3



New Unit Terms

(Tier 3 Vocabulary)

Degree of a Monomial, Degree of a Polynomial in Standard Form, Leading Term Leading Coefficient of a Polynomial in

Standard Form,

Monomial, Polynomial Expression, Standard Form of a Polynomial Expression

in One Variable, Zero Product Property

Familiar Terms

(Tier 3 Vocabulary)

Algebraic Expression, Coefficient of a Monomial, Solution

Solution Set

Cross-Curricular Terms

(Tier 2 Vocabulary)


Sample Calendar

Coding: 1.1-A represents Eureka Math Module 1. Lesson 1 – Topic A ● Addressed standard(s) listed below lesson

Please note, this calendar suggests lessons that can be combined and taught in one class period. It also includes remediation and extension lessons that are recommended for classroom use. While

17

this sample calendar helps guide instructional timing, it does not dictate exactly what lesson a teacher should be addressing on a given day. In addition, included FLEX days should be used for remediation, practice, enrichment, assessment, or other instructional activities.


September 16th District PD (Student Holiday)

LEAP 360

Form 1

Module 1

Lesson 6 and 7

A1: A-APR.A.1*

Module 1

Lesson 8

A1: A-APR.A.1*

Module 1

Lesson 9

A1: A-SSE.A.2,

A1: A-APR.A.1

September 23rd FLEX Unit 6


Remediation Support


For additional remediation support, teachers are encouraged to utilize the Coherence Map and the Louisiana Department of Education’s Algebra I Remediation Support Document

Additional Lessons


Remediation Lesson 1.7

This Lesson includes multiplying polynomials which will lead to mastery of A1: AAPR.A.1. • It should be noted that this Lesson extends students’ work with integer exponents from numerical expressions in Grade 8 to algebraic expressions.

• Reserve these Lessons to be used with students who need a review of Grade 6 concepts related to equivalent expressions prior to engaging with Algebra I concepts.


The mid-module assessment is designed to be given after completing Topic B.

.



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Unit 6 – The Structure of Expressions

Eureka Math Module 4, Topics A

(Approximately 10 Days ● 9/24/19c - 10/7/19)

Unit 6 Overview

Topic A introduces polynomial expressions. In Module 1, students learn the definition of a polynomial and how to add, subtract, and multiply polynomials. Here, their work with multiplication is extended and connected to factoring polynomial expressions and solving basic polynomial equations. They analyze, interpret, and use the structure of polynomial expressions to multiply and factor polynomial expressions. They understand factoring as the reverse process of multiplication. In this topic, students develop the factoring skills needed to solve quadratic equations and simple polynomial equations by using the zero product property. Students transform quadratic expressions from standard form, 𝑎x2+𝑏+𝑐, to factored form, (𝑥−𝑚) (𝑥−𝑛), and then solve equations involving those expressions. They identify the solutions of the equation as the zeroes of the related function. Students apply symmetry to create and interpret graphs of quadratic functions. They use average rate of change on an interval to determine where the function is increasing or decreasing. Using area models, students explore strategies for factoring more complicated quadratic expressions, including the product-sum method and rectangular arrays. They create one- and two-variable equations from tables, graphs, and contexts and use them to solve contextual problems represented by the quadratic function. Students then relate the domain and range for the function to its graph and the context. Specially students will

factor polynomial expressions and solving basic polynomial equations. transform quadratic expressions from standard form, 𝑎x2+𝑏+𝑐, to factored form, (𝑥−𝑚) (𝑥−𝑛), and then solve equations

involving those expressions. identify the solutions of equation as the zeroes of the related function. create one- and two-variable equations from tables, graphs, and contexts and use them to solve contextual problems

represented by the quadratic function

Focus Standards




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A-SSE.A.2 Use the structure of an expression to identify ways to rewrite it.

For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2) (x2 + y2).

A-SSE.B.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.4 b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

Remediation Standards: 6.EE.A.3

A-APR.A.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.

Remediation Standards: 6.EE.A.4, 7.EE.A.1, and 8.EE.A.1

A-APR.B.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.

Remediation Standards: 7.EE.A.1


MP.1 Make sense of problems and persevere in solving them

MP.2 Reason abstractly and quantitatively

MP.4 Model with mathematics.

MP.5 Use appropriate tools strategically.

MP.6 Attend to precision. MP.7 Look for and make use of structure.



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New Unit Terms

(Tier 3 Vocabulary)

Cube root function, Degree of a monomial term, Discriminant, Quadratic formula,

Roots of a polynomial function, Standard form for a quadratic function, Vertex form, Vertex of the graph of a quadratic function

Familiar Terms

(Tier 3 Vocabulary)

Binomial, Closed, Closure, Coefficient,

Term, Trinomial Zeroes of a function


(Tier 2 Vocabulary)

Suggested Tools Coordinate plane, Equations, Graphing calculator, and Graph paper

Sample Calendar


Please note, this calendar suggests lessons that can be combined and taught in one class period. It also includes remediation and extension lessons that are recommended for classroom use. While this sample calendar helps guide instructional timing, it does not dictate exactly what lesson a teacher should be addressing on a given day.

In addition, included FLEX days should be used for remediation, practice, enrichment, assessment, or other instructional activities.


September 23rd Module 4

Lesson 1 and 2

A1: A-SSE.A.2, A1: A-SSE.B.3a*, A1: A-APR.A.1*

Module 4

Lesson 3 and 4

A1: A-SSE.A.1, A1: A-SSE.A.1b, A1: A-SSE.A.2, A1: A-SSE.B.3a*, A1: A-APR.A.1*

Module 4

Lesson 5

A1: A-CED.A.1, A1: A-CED.A.3*, A1: A-REI.B.4b*

FLEX

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September 30th Module 4

Lesson 6

A1: A-SSE.A.1, A1: A-CED.A.1, A1: A-CED.A.3*, A1: A-REI.B.4b

Module 4

Lesson 7

A1: A-SSE.A.1, A1: A-CED.A.1, , A1: A-REI.B.4b

Module 4

Lesson 8

A1: F-IF.B.4, A1: F-IF.B.6*, A1: F-IF.C.7a

Module 4

Lesson 9

A1: A-SSE.B.3a, A1: A-APR.B.3, A1: F-IF.A.2, A1: F-IF.B.4, A1: F-IF.B.5, A1: F-IF.C.7a A1: F-IF.C.8a

FLEX

October 7th LEAP 360

Interim 2

Unit 7 Begins End of 1st marking Period


Remediation Support



Additional Lessons


None


The mid-module assessment is designed to be given after completing Topic A.

.



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Unit 7 – Using Different Forms for Quadratic Functions


(Approximately 7 Days ● 10/8/19 -10/18/19)

Unit 7 Overview

In Topic B Students will use different forms for solve and graph Quadratic Functions which include the following:

Specially student will

Completing the Square Using the Quadratic Formula Graphing Quadratic Equations/Functions

Focus Standards






A-APR.B.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.

Remediation Standard: 7.EE.A.1

A-REI.B.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


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quadratic formula gives complex solutions and write them as 𝑎±𝑏 for real numbers 𝑎 and 𝑏.

F-IF.B.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.

Remediation Standard: 8.F.B.5

A-CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales

F-IF.B.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.


F-IF.C.7a 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.

Remediation Standard: 8.F.A.3

F-IF.C.8a 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 zeroes, extreme values, and symmetry of the graph, and interpret these in terms of a context.

Remediation Standard: 7.EE.A.1







MP.7 Look for and make use of structure.

New Unit Terms Completing the Square, vertex form of a Quadratic Function, Quadratic Formula,

Standard form for a quadratic function Vertex form,

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(Tier 3 Vocabulary) Roots of a polynomial function,

Familiar Terms

(Tier 3 Vocabulary)

Cube root function,

Degree of a monomial term,

Discriminant,


(Tier 2 Vocabulary)

Graphing, Quadratic Function, Quadratic Equation, Solution

Suggested Tools White Board, Coordinate Grid, Graphing Calculator and Graph Paper

Sample Calendar





October 7th LEAP 360

Interim 2

Module 4

Lesson 11 and 12

A1: A-SSE.A.2, A1: A-SSE.B.3a*, A1: A-SSE.B.3b*

Module 4

Lesson 13

A1: N-RN.B.3, A1: A-REI.B.4a*, A1: A-REI.B.4b* End of 1st marking Period

FALL Break

October 14th Module 4

Lesson 14

A1: A-REI.B.4a,

Module 4

Lesson 15

A1: A-REI.B.4b,

Module 4

Lesson 16

A1: A-SSE.B.3b,

Module 4

Lesson 17

A1: A-SSE.B.3a

FLEX

25

A1: A-REI.B.4b* A1: F-IF.C.8a A1: F-IF.C.8a, A1: F-BF.B.3*

A1: A-SSE.B.3b, A1: F-IF.A.2, A1: F-IF.B.4, A1: F-IF.B.5, A1: F-IF.B.6,

*Additional Information

Remediation Support



Remedial Skills Support in Eureka Use to help students struggling with mastery of Lessons 11-17 8.F.B.4 8.F.B.5


Additional Lessons



The mid-module assessment is designed to be given after completing Topic C.


26

Unit 8– Transformations of Functions

(Piecewise Functions)



Unit 8 Overview

In Topic C, students extend their understanding of piecewise functions and their graphs including the absolute value and step functions. They learn a graphical approach to circumventing complex algebraic solutions to equations in one variable, seeing them as (𝑥) =𝑔 (𝑥) and recognizing that the intersection of the graphs of 𝑓 (𝑥) and 𝑔 (𝑥) are solutions to the original equation. Students use the absolute value function and other piecewise functions to investigate transformations of functions and draw formal conclusions about the effects of a transformation on the function’s graph. Specially student will

Evaluate, graph, and write piecewise functions. Graph and write step functions. Write and graph absolute value functions.

Focus Standards






A-REI.D.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.

Remediation Standards:

8.EE.C.8


27

Include cases where 𝑓 (𝑥) and/or 𝑔 (𝑥) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

F-IF.B.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.

Remediation Standards: 8.F.B.5

F-IF.C.7b Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

Remediation Standards: 8.EE.B.5 8.F.A.3







New Unit Terms

(Tier 3 Vocabulary)

Piecewise function, Stretching of a graph, Shrinking of graph,

Translation of a graph, Step functions, Transformation of a graph.

Familiar Terms

(Tier 3 Vocabulary)

Graphing of a function, Graph of a quadratic function,

Vertex of a graph, Standard form for a quadratic function


(Tier 2 Vocabulary)


28

Sample Calendar

Coding: 1.1-A represents Eureka Math Module 1.Lesson 1 – Topic A ● Addressed standard(s) listed below lesson




October 21st Module 1

Lesson 1 &

Module 3

Lesson 15

A1: A-REI.D.10, A1: F-IF.A.1, A1: F-IF.C.7b*

Module 3

Lesson 16

A1: A-REI.D.11, A1: F-IF.C.7a*, A1: F-IF.C.7b

Module 3

Lesson 17

A1: F-IF.C.7b*, A1: F-BF.B.3

Module 3

Lesson 18

A1: F-IF.C.7b*, A1: F-BF.B.3

FLEX


Remediation Support



Remedial Skills Support in Eureka Use to help students struggling with mastery of Lessons 15-18 8.F.A.3

Grade 8 Module 5 Lesson 2,3,4, and 5




29

Additional Lessons


None


The end-module assessment is designed to be given after completing Topics A through D.

30

Unit 9– Using Functions and Graphs to Solve Problems

And

Function Transformations and Modeling



Unit 9 Overview

In Topic C, students explore the families of functions that are related to the parent functions, specifically for quadratic ((𝑥) =𝑥2), square root (𝑓 (𝑥) =√𝑥), and cube root (𝑓 (𝑥) =√𝑥3), to perform horizontal and vertical translations as well as shrinking and stretching. They recognize the application of transformations in vertex form for a quadratic function and use it to expand their ability to efficiently sketch graphs of square and cube root functions. Students compare quadratic, square root, or cube root functions in context and represent each in different ways (verbally with a description, numerically in tables, algebraically, or graphically). In the final two lessons, students examine real-world problems of quadratic relationships presented as a data set, a graph, a written relationship, or an equation. They choose the most useful form for writing the function and apply the techniques learned throughout the module to analyze and solve a given problem, including calculating and interpreting the rate of change for the function over an interval.

Specially students will

use the transformation rules extend to linear, piecewise, quadratic, and exponential functions. graph the parent functions using a table of values and will again experiment with transformations to show that the

familiar function.

Focus Standards







31

F-IF.C.7b Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.


F-BF.B.3 Identify the effect on the graph of replacing 𝑓(𝑥) by 𝑓(𝑥)+𝑘, 𝑘, 𝑓(𝑥), 𝑓(𝑘), 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.

A-CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

F-IF.B.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.★


F-IF.C.9 Compare properties of two functions (linear, quadratic, piecewise linear [to include absolute value] or exponential) 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, determine which has the larger maximum.









New Unit Terms Parent functions

32

(Tier 3 Vocabulary)

Familiar Terms

(Tier 3 Vocabulary)

Graphing Square root , Graphing cubic root, maximum value, minimum value, and vertex


(Tier 2 Vocabulary)


Sample Calendar





October 28th Module 1

Lesson 2

A1: N-Q.A.1*, A1: N-Q.A.2, A1: F-IF.B.4, A1: F- IF.B.6

Module 4

Lesson 19

A1: F-IF.C.7a, A1: F-IF.C.7b, A1: F-BF.B.3

Module 4

Lesson 20

A1: F-IF.C.7a, A1: F-IF.C.7b, A1: F-BF.B.3

Module 4

Lesson 21

A1: A-SSE.B.3b, A1: F-IF.C.8a*, A1: F-BF.B.3*

Module 4

Lesson 22

A1: F-IF.B.4, A1: F-IF.B.6, A1: F-IF.C.9


Remediation Support Teachers may choose appropriate questions, activities, and or lessons from the table below to support students who have prior unfinished learning. Teachers should be strategic when choosing problems from suggested lessons in order to differentiate instruction to have the most impact on

33


student achievement. For additional remediation support, teachers are encouraged to utilize the Coherence Map and the Louisiana Department of Education’s Algebra I Remediation Support Document

Remedial Skills Support in Eureka

Use to help students struggling with mastery of Lessons 19-22 8.F.A.3

Grade 8 Module 5 Lesson 2,3,4, and 5

Additional Lessons


None


The end-module assessment is designed to be given after completing Topic C.

.




34

Unit 10– Shapes and Centers of Distributions

And

Describing Variability and Comparing Distributions

Eureka Math Module 2, Topics A and B


Unit 10 Overview

In this module, students reconnect with and deepen their understanding of statistics and probability concepts first introduced in Grades 6, 7, and 8. There is variability in data, and this variability often makes learning from data challenging. Students develop a set of tools for understanding and interpreting variability in data and begin to make more informed decisions from data. Students work with data distributions of various shapes, centers, and spreads. Measures of center and measures of spread are developed as ways of describing distributions. The choice of appropriate measures of center and spread is tied to distribution shape. Symmetric data distributions are summarized by the mean and mean absolute deviation, or standard deviation. The median and the interquartile range summarize data distributions that are skewed. Students calculate and interpret measures of center and spread and compare data distributions using numerical measures and visual representations. Specially students will

develop a set of tools for understanding and interpreting variability in data and begin to make more informed decisions from data

understand that the median and the interquartile range summarize data distributions that are skewed calculate and interpret measures of center and spread and compare data distributions using numerical measures and

visual representations.

Focus Standards




35



S-ID-B.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.

Remediation Standards 8.SP.A.4

S-ID-B.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, quadratic, 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.

Remediation Standards 8.SP.A.1, 8.SP.A.2, and 8.SP.A.3

S-ID-C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.★

Remediation Standards 8.SP.A.3

S-ID-C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.★

S-ID-C.9 Distinguish between correlation and causation.★

S-ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).

S-ID.A.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.

Remediation Standards 6.SP.A.2, and 6.SP.B.5

S-ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).★

Remediation Standards 6.SP.B.5


MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others.


36




New Unit Terms

(Tier 3 Vocabulary)

Correlation Correlation coefficient Causation

Interquartile range Standard Deviation

Familiar Terms

(Tier 3 Vocabulary)

Box Plot, Data Distribution, Mean , Mean Absolute Deviation,

Median, Quartile, Variability


(Tier 2 Vocabulary)

Suggested Tools Graphing Calculator ,Spreadsheet Software , Dot Plot , Box Plot , Histogram , and Residual Plot

Sample Calendar





November 4th LEAP 360

Interim 3

Module 2

Lesson 1 and 2

A1: S-ID.A.3

Module 2

Lesson 3

A1: S-ID.A.3

Module 2

Lesson 4

A1: S-ID.A.3

Module 2

Lesson 5

A1: S-ID.A.3

37

November 11 Student Holiday

Module 2 Lesson 6 A1: S-ID.A.3



Flex


Remediation Support




Use to help students struggling with mastery of Lessons 1-8 8.SP.A.1 8.SP.A.2 8.SP.A.3


Additional Lessons


Remediation Lesson

Module 2 Lesson 1

Reserve this Lesson to be used with students who need a review of Grade 6 concepts related to data distributions prior to engaging with Algebra I concepts.


The mid-module assessment is designed to be given after completing Topic B.

.




38

Unit 11– Categorical Data on Two Variables

And

Numerical Data on Two Variables

Eureka Math Module 2, Topics C and D

(Approximately Days 5 ● 11/18/19 - 11/22/19)

Unit 11 Overview

In this module, students build on their experience with bivariate quantitative data from Grade 8; they expand their understanding of linear relationships by connecting the data distribution to a model and informally assessing the selected model using residuals and residual plots. Students explore positive and negative linear relationships and use the correlation coefficient to describe the strength and direction of linear relationships. Students also analyze bivariate categorical data using two-way frequency tables and relative frequency tables. The possible association between two categorical variables is explored by using data summarized in a table to analyze differences in conditional relative frequencies. Students will specially

Summarize categorical data for two categories in two-way frequency tables. Establish and distinguish between correlation and causation. Compute (using technology) and interpret the correlation coefficient of a linear fit.

Focus Standards







39

S-ID.B.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

Remediation Standard(s): 8.SP.A.4

S-ID.C.9 Distinguish between correlation and causation.

S-ID.B.6

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

Remediation Standard(s): 8.SP.A.1, 8.SP.A.2, and 8.SP.A.3

S-ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

Remediation Standard(s): 8.SP.A.3

S-ID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.


MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics.



New Unit Terms

(Tier 3 Vocabulary)

Correlation Correlation coefficient Causation

Interquartile range Standard Deviation

Familiar Terms

(Tier 3 Vocabulary)

Box Plot, Data Distribution,

Median, Quartile, Variability

40

Mean ,

Mean Absolute Deviation, Cross-Curricular Terms

(Tier 2 Vocabulary)

Suggested Tools Graphing Calculator ,Spreadsheet Software , Dot Plot , Box Plot , Histogram , and Residual Plot

Sample Calendar





November 18 Module 2 Lesson 12 and 13 A1: S-ID.B.6a

Module 2 Lesson 14 and 15 A1: S-ID.B.6a, A1: S-ID.B.6c, A1: S-ID.C.7

Module 2 Lesson 17 and 18 A1: S-ID.B.6b

Module 2 Lesson 19 A1: S-ID.C.8, A1: S-ID.C.9

Flex


Remediation Support







41

Use to help students struggling with mastery of Lessons 12 (A1: S-ID.B.6a) 8.SP.A.1

Grade 8 Module 6 Lesson 6 and 7

Additional Lessons


Remediation Lesson

Module 2

Lesson 12

Reserve this Lesson to be used with students who need a review of Grade 8 concepts related to scatter plots prior to engaging with Algebra I concepts.


The end of module assessment is designed to be given after completing Topic D.

42

Unit 12– Elements of Modeling and

Completing the Modeling Cycle

Eureka Math Module 5, Topics A and B

(Approximately 5 Days ● 12/2/19 -12/6/19)

Unit 12 Overview

In Module 5: In this module, students expand their experience with functions to include more specialized functions—linear, exponential, quadratic, square, and cube root—and those that are piecewise-defined, including absolute value and step. Students select from among these functions to model phenomena using the modeling cycle. Specially students will

expand their experience with functions to include more specialized functions—linear, exponential, quadratic, square,

and cube root—and those that are piecewise-defined, including absolute value and step.

Focus Standards






F-IF.B.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.



43

F-IF.B.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(𝑛𝑛) gives the number of person-hours it takes to assemble 𝑛𝑛 engines in a factory, then the positive integers would be an appropriate domain for the function.

F-IF.B.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.


F-BF.A.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.


F-LE.A.1

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

Remediation Standard(s): 8.F.A.3, and 8.F.B.4

F-LE.A.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).



MP.1 Make sense of problems and persevere in solving them.

MP.2 Reason abstractly and quantitatively.



MP.6 Attend to precision


New Unit Terms

(Tier 3 Vocabulary)

Analytic Model, Descriptive Model

44

Familiar Terms

(Tier 3 Vocabulary)

Arithmetic Sequence Average Rate of Change Cube Root Function End Behavior Exponential Function Parameter

Parent Function Piecewise Defined Function Quadratic Function Range

Recursive Process Square Root Function Second Differences


(Tier 2 Vocabulary)

Suggested Tools Scientific Calculator Graphing Calculator Geometer’s Sketch Pad and GeoGebra

Sample Calendar





November 25 Thanksgiving Holiday

December 2

Module 5 Lesson 1 and 2 A1: N-Q.A.1 A1: F-IF.B.4, A1: F-IF.B.5, A1: F-IF.B.6, A1: F-BF.A.1a, A1: F-BF.B.3*,

Module 5 Lesson 3 and 4 A1: N-Q.A.1*, A1: F-BF.A.1a, A1: F-BF.B.3*, A1: F-LE.A.2

Module 5 Lesson 5 and 6 A1: N-Q.A.1*, A1: A-REI.C.6 A1: F-BF.A.1a, A1: F-BF.A.1a, A1: F-LE.A.1b, A1: F-LE.A.1c,

Module 5 Lesson 7 and 8 A1: N-Q.A.3, A1: F-IF.B.4, A1: F-IF.B.5, A1: F-IF.B.6, A1: S-ID.B.6a, A1: S-ID.B.6c,

Module 5 Lesson 9

45

A1: F-LE.A.2 LEAP 2025 Testing Window Begins

, A1: F-LE.A.2

A1: S-ID.C.8

December 9 FLEX Review for LEAP 2025 Algebra I Testing or LEAP 2025 Algebra I Testing

December 16

Review for Final Exam LEAP Testing window closed

Review for Algebra I Final Exam Final Algebra I Exam





Use to help students struggling with mastery of Lessons 1 and 2 (F-LE.A.1) 8.F.A.3*, 8.F.B.4*

Grade 8 Module 5 Lesson 2 and 3



The end-module assessment is designed to be given after completing Topic B. .




46

Unit 13– LEAP 2025 Review

Eureka Math Module 1-5, Topics A – D or E --- (Depending on Topics)


Unit 13 Overview

The fundamental purpose of this course is to formalize and extend the mathematics that students learned in the middle grades. Because it is built on the middle grades standards, this is a more ambitious version of Algebra I than has generally been offered. The modules deepen and extend understanding of linear and exponential relationships by contrasting them with each other and by applying linear models to data that exhibit a linear trend, and students engage in methods for analyzing, solving, and using quadratic functions. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations

Summary of the Years Topic:

Module 1: Relationships Between Quantities and Reasoning with Equations and Their Graphs Module 2: Descriptive Statistics Module 3: Linear and Exponential Functions Module 4: Polynomial and Quadratic Expressions, Equations, and Functions Module 5: A Synthesis of Modeling with Equations and Functions

Sample Calendar





47

December 9 FLEX Review for LEAP 2025 Algebra I Testing or LEAP 2025 Algebra I Testing

December 16

Review for Final Exam LEAP Testing window closed

Review for Algebra I Final Exam Final Algebra I Exam


Remediation Support



Additional Lessons



Modules 1-5

Topics: A-E.



unit 1 solving equations and inequalities · unit 1 – solving equations and inequalities eureka...

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