MATH SCOPE AND SEQUENCE Math Essentials REAL NUMBERS … · 8.EE.A.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific

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MATH SCOPE AND SEQUENCE

Math Essentials ● 2019-2020

UNIT 1 – REAL NUMBERS AND FRACTIONS

Eureka Math Module 2, Topics A-D

(Approximately 17 Days ● 8/8/19 - 8/30/19)

Unit 1 Overview

In this unit, during Topic A, students find sums and differences of signed numbers and establish rules related to the addition and subtraction of rational numbers. Students begin by using a number line to count up and down. Eventually, students efficiently add integers using well-defined rules. When working with subtraction, students recognize that subtracting a signed number is the same as adding the opposite. They also understand that the distance between two signed numbers is the absolute value of their difference. Finally, students apply the properties of operations to add and subtract rational numbers. In this Unit, during Topic B, students extend their understanding of multiplication and division of whole numbers, decimals, and fractions to find the products and quotients of signed numbers. Students begin by conceptualizing multiplication as repeated addition. They use their understanding of repeated addition to justify the rules for multiplication of integers. The additive inverse and distributive property are used to show that (−1) (−1) = 1. Students use their understanding of division as the process of finding the missing factor of a product to justify that the rules for dividing signed numbers are consistent with that of multiplication, provided the divisor is not zero. Students extend the integer rules to include all rational numbers, provided the divisor is not zero. Finally, students convert fractions into decimals that either terminate in zeros or repeat. Lesson 13 (E): The content of this lesson is not aligned with the explicit expectations of the standards since it focuses on converting between fractions and decimals. However, the concepts and skills developed may prove to be advantageous for student’s long term. This lesson is an optional enrichment activity. Specifically, students will

find sums and differences of signed numbers and establish rules related to the addition and subtraction of rational numbers

extend their understanding of multiplication and division of whole numbers, decimals, and fractions to find the products and quotients of signed numbers. Students begin by conceptualizing multiplication as repeated addition.

convert fractions into decimals that either terminate in zeros or repeat.

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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.

7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram

Remediation Standard(s): 6.NS.C.6, 6.NS.C.7

7.NS.A.2 Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.


7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers


Focus Standards for Mathematical Practice

MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

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)

Additive Identity Additive Inverse

Multiplicative Identity Repeating Decimal

Expansion

Terminating Decimal Expansion

Familiar Terms (Tier 3 Vocabulary)

Equation Expression Integer Inverse

Negatives Opposites

Positives Rational Numbers

Cross-Curricular Terms (Tier 2 Vocabulary)

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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Suggested Tools Integer Cards, Equations

Expressions Integer Game (See explanation on page 11)

Number Line Tape Diagram

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

Unit 1: Real Numbers and Fractions 7th grade Module 2 Lesson 1

August 12th Unit 1: Real

Numbers and Fractions

7th grade Module 2 Lesson 2

Unit 1: Real Numbers and

Fractions 7th grade Module 2 Lesson 3


Fractions 7th grade Module 2

Lesson 5



Lesson 7



Lesson 8-9

August 19th

Flex





Lesson 11



Lesson 12



Lesson 13

August 26th Unit 1: Real

Numbers and Fractions






Lesson 16

FLEX FLEX

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September 2nd Labor Day (Holiday)

Unit Two begins

Additional Information

Remediation Support (LDOE Remediation Guide)

Module 1 lesson 4 and 6

Additional Lessons (Optional for remediation and enrichment)

Module 1 lesson 4 and 6

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

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

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UNIT 2 – INTEGER EXPONENTS AND SCIENTIFIC NOTATION WITH SUPPORTING LESSONS FOR EQUATIONS AND INEQUALITES

8th grade Eureka Math Module 1 Topics A


Unit 2 Overview

In this unit, during Topic A, students begin by learning the precise definition of exponential notation restricted to positive integer exponents. Students relate multiplication and division of expressions with the same base to combining like terms using the distributive property. They relate raising a power to a power to multiplying three factors using the associative property. Students expand their definition of exponential notation to include what it means to raise a nonzero number to a zero power and what it means to raise a positive integer to a negative exponent. Finally, students accept the properties of exponents as true for all integer exponents. Lesson 6 (E): The content in this lesson extends beyond the explicit expectations of the standards. This lesson is an optional enrichment activity. Specifically, students will

learn the precise definition of exponential notation restricted to positive integer exponents accept the properties of exponents as true for all integer exponents. relate multiplication and division of expressions with the same base to combining like terms using the distributive

property

Focus Standards


8.EE.A.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 32 × 3−5 = 3−3 = 1/33 = 1/27

Remediation Standards: 6.EE.A.1


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8.EE.A.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 × 108 and the population of the world as 7 × 109, and determine that the world population is more than 20 times large


8.EE.A.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notations are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology



MP.2 Reason abstractly and quantitatively. MP.6 Attend to precision. MP.7 Look for and make use of structure. MP.8 Look for and express regularity in repeated reasoning.

Unit Terms & Tools


Scientific Notation


Base, Exponent, Power ƒ Equivalent Fractions ƒ

ƒ Expanded Form (of decimal numbers)

Exponential Notation ƒ Integer ƒ

Square and Cube (of a number) ƒ

Whole Numbers


Suggested Tools Scientific Calculator and Rapid White Board Exchange

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.


September 2nd Labor Day (Holiday)

UNIT 2 – Integer Exponents and

Scientific Notation 8th grade Module 1

Lesson 1 and 2



Lesson 3 and 4



Lesson 5 and 6

FLEX

September 9th Unit 2: Supporting 7th grade Module 3

Lesson 1

Unit 2: Supporting 7th grade Module 3

Lesson 2


Lesson 3


Lesson 4 FLEX




Sprint and Fluency

Sprint and Fluency Packets (teacher edition)


. The mid-module assessment is designed to be given after completing Topic A. End of Module Assessments Topics A and B

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UNIT 3 – LINEAR EQUATIONS/INEQUALITIES

8th grade Eureka Math Module 4 Topics A and C


Unit 3 Overview

In this unit, during Topic A, students write and solve linear equations. They learn that a linear equation in 𝑥 is a statement of equality between two linear expressions in 𝑥. They also learn that an equation that contains a variable really is a question: Is there a value of 𝑥 that makes the linear equation true? Students begin using properties of equality to rewrite linear expressions, specifically using the distributive property to combine like terms. Further, students practice substituting numbers into equations to determine if a true number sentence is produced. Finally, students learn that not every linear equation has a solution. This leads to an understanding that linear equations either have a unique solution, no solution, or infinitely many solutions. In Topic C, students know that the slope of a line describes the rate of change of a line. Students first encounter slope by interpreting the unit rate of a graph (8. EE.B.5). In general, students learn that slope can be determined using any two distinct points on a line by relying on their understanding of properties of similar triangles from Module 3 (8. EE.B.6). Students verify this fact by checking the slope using several pairs of points and comparing their answers. In this topic, students derive 𝑦= mx+ 𝑏 for linear equations by examining similar triangles. Students generate graphs of linear equations in two variables first by completing a table of solutions and then by using information about slope and 𝑦-intercept. Once students are sure that every linear equation graphs as a line and that every line is the graph of a linear equation, students graph equations using information about 𝑥- and 𝑦-intercepts. Next, students learn some basic facts about lines and equations, such as why two lines with the same slope and a common point are the same line, how to write equations of lines given slope and a point, and how to write an equation given two points. With the concepts of slope and lines firmly in place, students compare two different proportional relationships represented by graphs, tables, equations, or descriptions. Finally, students learn that multiple forms of an equation can define the same line. In Topic B, students use linear equations and inequalities to solve problems (7. EE.B.4). They continue to use tape diagrams from earlier grades where they see fit, but will quickly discover that some problems would more reasonably be solved algebraically (as in the case of large numbers). Specifically, students will

use linear equations and inequalities to solve problems write and solve linear equations begin using properties of equality to rewrite linear expressions, specifically using the distributive property to combine

like term

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Focus Standards


8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

Remediation Standard(s) 6.EE.A.2 7.EE.B.4

8.EE.B.6 Use similar triangles to explain why the slope 𝑚𝑚 is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation 𝑦 = 𝑚 for a line through the origin and the equation 𝑦 = mx + 𝑏𝑏 for a line intercepting the vertical axis at 𝑏𝑏.

Remediation Standard(s) 6.EE.A.2 7.EE.B.4

8.EE.C.7 Solve linear equations in one variable Remediation Standard(s) 6.EE.A.2 7.EE.B.4


MP.1 Make sense of problems and persevere in solving them. SMP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics MP.7 Look for and make use of structure.

Unit Terms & Tools


Horizontal line Linear Equation non-vertical line

Rate of change Slope

Slope intercept Vertical line


Variable proportional relationships


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Suggested Tools Rapid White Board Exchange

Sample Calendar



September 16th District PD

(Student Holiday)

Unit 3: Linear Equations






FLEX

September 23rd Unit 3: Linear

Equations 8th grade Module 4

Lesson 4

Unit 3 Linear Equations 7th grade

Module 2 Lesson 17

Unit 3 Linear Equations 7th grade

Module 2 Lesson 22 and 23

Solving Multi-Step Equations

FLEX

September 30rd Unit 3: Linear Equations

8th grade Module 4 Lesson 5 and 6





FLEX Unit 3


October 7th Unit 3 7th grade Module 3 Lesson 14 and 15

Solving Multi-step Equations

FLEX Fall Break (Holiday)

Fall Break (Holiday)

October 14th Unit 3: Linear Equations










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October 21th Unit 3: Linear Equations




FLEX Unit 4 Beings




Lessons 1-2, 5, & 8-9 (E): The content in these lessons extends beyond the explicit expectations of the standards. These lessons are optional enrichment activities. LDOE Remediation Tool: The LDOE Eureka Remediation Tool provides additional support for this topic.


.

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UNIT 4 – SYSTEMS OF EQUATIONS

8th grade Eureka Math Module 4 Topics D


Unit 4 Overview

In this unit, Topic D: Simultaneous equations and their solutions are the focus of Topic D. Students begin by comparing the constant speed of two individuals to determine which has greater speed (8. EE.C.8c). Students graph simultaneous linear equations to find the point of intersection and then verify that the point of intersection is in fact a solution to each equation in the system (8. EE.C.8a). To motivate the need to solve systems algebraically, students graph systems of linear equations whose solutions do not have integer coordinates. Students learn to solve systems of linear equations by substitution and elimination (8. EE.C.8b). Students understand that a system can have a unique solution, no solution, or infinitely many solutions, as they did with linear equations in one variable. Finally, students apply their knowledge of systems to solve problems in real-world contexts, including converting temperatures from Celsius to Fahrenheit. Specifically, students will

graph simultaneous linear equations to find the point of intersection and then verify that the point of intersection is in fact a solution to each equation in the system

apply their knowledge of systems to solve problems in real-world contexts, including converting temperatures from Celsius to Fahrenheit.

Focus Standards


8.EE.C.8 Analyze and solve pairs of simultaneous linear equations. a. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

Remediation Standards: 6.EE.A.2 7.EE.A.1 7.EE.B.4


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b. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations. Solve simple cases by inspection. For example, 3𝑥+ 2𝑦 = 5 and 3𝑥 + 2𝑦 = 6 have no solution because 3𝑥 + 2𝑦 cannot simultaneously be 5 and 6. c. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.


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 MP.7 Look for and make use of structure.

Unit Terms & Tools


Linear System


Equivalent Equation Linear Equations

Constant Simultaneous linear

equations

Variable


Suggested Tools White board Exchanges

Sample Calendar


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October 21

Unit 4: System of Equations




October 28 Unit 4: System of Equations




FLEX



Unit 4: System of Equations 8th

grade Module 4 Lesson 28

November 4th Unit 4: System of Equations 8th

grade Module 4 Lesson 29

FLEX


Algebra I Module 1 Lesson 20



FLEX

November 11th Student Holiday Unit 5





. None

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UNIT 5 –LINEAR FUNCTIONS

8th grade Eureka Math Module 5 and 6 Topics A


Unit 4 Overview

In this unit, Module 5, Topic A, students learn the concept of a function and why functions are necessary for describing geometric concepts and occurrences in everyday life. The module begins by explaining the important role functions play in making predictions. For example, if an object is dropped, a function allows us to determine its height at a specific time. To this point, student work has relied on assumptions of constant rates; here, students are given data that show that objects do not always travel at a constant speed. Once the concept of a function is explained, a formal definition of function is provided. A function is defined as an assignment to each input, exactly one output (8.F.A.1). Students learn that the assignment of some functions can be described by a mathematical rule or formula. With the concept and definition firmly in place, students begin to work with functions in real-world contexts. For example, students relate constant speed and other proportional relationships (8. EE.B.5) to linear functions. In this unit, Module 6 Topic A examines the relationship between two variables using linear functions (8.F.B.4). Linear functions are connected to a context using the initial value and slope as a rate of change to interpret the context. Students represent linear functions by using tables and graphs and by specifying rate of change and initial value. Slope is also interpreted as an indication of whether the function is increasing or decreasing and as an indication of the steepness of the graph of the linear function (8.F.B.5). Specifically, students will

learn the concept of a function and why functions are necessary for describing geometric concepts and occurrences in everyday life.

begin to work with functions in real-world contexts. examines the relationship between two variables using linear functions examines the relationship between two variables using linear functions represent linear functions by using tables and graphs and by specifying rate of change and initial value

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

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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.

8.F.A.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

Remediation Standards:

8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed

8.F.B.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (𝑥, 𝑦) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

8.F.B.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.



Unit Terms & Tools


Linear Function Two-Way Frequency Table (description


Categorical variable Intercept or initial value

Numerical variable Slope

Cross-Curricular Terms


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(Tier 2 Vocabulary)


Sample Calendar



November 11th

Student Holiday

Unit 5: Linear Functions






FLEX

November 18th Unit 5: Linear Functions 8th grade Module 6 Lesson 1

Unit 5: Linear Functions 8th grade Module 6 Lesson 2

Unit 5: Linear Functions 8th grade Module 6 Lesson 3

Remediation FLEX

November 25 Thanksgiving Holiday

Thanksgiving Holiday








. None

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UNIT 6 – STATISTICS

6th grade Module 6 and Algebra I Module 2 Eureka Math

(Approximately 15 Days ● 12/2/19 -12/20/19)

Unit 6 Overview

In this unit, Topic A, students begin to think and reason statistically by first recognizing a statistical question as one that can be answered by collecting data (6. SP.A.1). Students learn that the data collected to answer a statistical question have a distribution that is often summarized in terms of center, variability, and shape (6. SP.A.2). Beginning in Topic A, and throughout the module, students see and represent data distributions using dot plots and histograms (6. SP.B.4). In Topics B and C, students study quantitative ways to summarize numerical data sets in relation to their context and to the shape of the distribution. The mean and mean absolute deviation (MAD) are used for data distributions that are approximately symmetric, and the median and interquartile range (IQR) are used for distributions that are skewed. Students apply their experience in writing, reading, and evaluating expressions in which letters stand for numbers (6. EE.A.2) as they learn to compute and interpret these statistical measures for center and spread. Specifically, students will

learn that the data collected to answer a statistical question have a distribution that is often summarized in terms of center, variability, and shape

study quantitative ways to summarize numerical data sets in relation to their context and to the shape of the distribution.

learn to compute and interpret these statistical measures for center and spread.

Focus Standards


6.SP.A.1 Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the

Remediation Standards:


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students in my school?” is a statistical question because one anticipates variability in students’ ages.

6.SP.A.2 Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

6.SP.B.4 Display numerical data in plots on a number line, including dot plots, histograms, and box plots.

6.SP.B.5 Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how

it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and

variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

d. Relating the choice of measures of center and variability to the shape of the data

distribution and the context in which the data were gathered



Unit Terms & Tools


histograms interquartile range

measures of center mean absolute deviation

plots



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Sample Calendar



November 25 Thanksgiving Holiday





December 2nd Unit 6: Statistics 6th grade Module 6

Lesson 1

Unit 6: Statistics 6th grade Module 6

Lesson 2


Lesson 3


Lesson 4

Unit 6: Statistics Algebra I Module 2

Lesson 1 December 9th Unit 6: Statistics



Lesson 3


Lesson 9


Lesson 10


Lesson 11 December 16

Flex Assessment Review for Exams Exams Exams





. None

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Documents

MATH SCOPE AND SEQUENCE Math Essentials REAL NUMBERS … · 8.EE.A.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific