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UNIT 1 – ARITHMETIC OPERATIONS

Eureka Math Module 2, Topics A-D

(Approximately 17 Days ● 8/12/19-9/4/19)

Unit 1 Overview

During this unit, students will apply and extend their understanding of the four operations (addition, subtraction, multiplication, and division) to include division of whole numbers, division of a fraction by a fraction, and operations on multi-digit decimals. This expanded understanding serves to complete their study of the four operations with positive rational numbers. In addition, students will find the greatest common factor of two whole numbers and the least common multiple of two whole numbers. Specifically, students will:

interpret and compute quotients of fractions. solve word problems involving division of fractions by fractions and use visual fraction models and equations to represent the problems. fluently divide multi-digit numbers using the standard algorithm. fluently add, subtract, multiply, and divide multi-digit decimals. find the greatest common factor and least common multiple of two whole numbers. use the distributive property to rewrite an expression that involves two whole numbers with a common factor (GCF).

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.

6.NS.A.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2 3⁄ ) ÷ (3 4⁄ ) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2 3⁄ ) ÷ (3 4⁄ ) = 8 9⁄ because 3 4⁄ of 8 9⁄ is 2 3⁄ . (In general, (𝑎 𝑏⁄ ) ÷ (𝑐 𝑑⁄ ) = 𝑎𝑑 𝑏𝑐⁄ .) How much chocolate will each person get if 3 people share 1 2⁄ lb of chocolate equally? How many 3 4⁄ -cup servings are in 2 3⁄ of a cup of yogurt? How wide is a rectangular strip of land with length 3 4⁄ mi and area 1 2⁄ square mi?

Remediation Standard(s): 3.OA.B.6, 5.NF.B.7

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6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm. Remediation Standard(s): 5.NBT.B.6

6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

Remediation Standard(s): 5.NBT.B.5, 5.NBT.B.6, 5.NBT.B.7

6.NS.B.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4(9 + 2).

Remediation Standard(s): 4.OA.B.4, 5.OA.A.2

Focus Standards for Mathematical Practice

SMP.1 Make sense of problems and persevere in solving them. Aligned ELP Connector(s): ELPC 6-8.1, ELPC 6-8.2, ELPC 6-8.3, ELPC 6-8.5, ELPC 6-8.6, ELPC 6-8.8, ELPC 6-8.9

SMP.2 Reason abstractly and quantitatively. SMP.6 Attend to precision.

Aligned ELP Connector(s): ELPC 6-8.2, ELPC 6-8.3, ELPC 6-8.4, ELPC 6-8.7, ELPC 6-8.10

SMP.7 Look for and make use of structure. SMP.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)

Greatest Common Factor (GCF), Least Common Multiple (LCM), and Multiplicative Inverses

Familiar Terms (Tier 3 Vocabulary)

Algorithm, Composite Number/Número Compuesto, Distributive Property, Dividend/Dividendo, Divisor/Divisor, Estimate/Estimar, Factors/Factores, Multiples/Múltiplos, Prime Number/Número Primo, and Reciprocal

Cross-Curricular Terms (Tier 2 Vocabulary)

Apply/Aplicar, Determine/Determinar, Explain/Explicar, Identify/Identificar, Order/Ordenar and Orden, Represent/Representar, Table/Tabla, and Value/Valor

Suggested Tools Counters, Fraction Tiles, Tape Diagrams, and Area Models

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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)

LEAP 360 Diagnostic (Window provided for administration)

August 12th 2.1-A (Remediation)

2.2-A (Remediation)

2.3-A 6.NS.A.1

2.4-A 6.NS.A.1

2.7-A 6.NS.A.1

August 19th 2.8-A 6.NS.A.1

FLEX 2.9-B 6.NS.B.3

2.10-B 6.NS.B.3

2.11-B 6.NS.B.3

August 26th FLEX

2.12-C 6.NS.B.2

2.13-C 6.NS.B.2

2.14-C 6.NS.B.2, 6.NS.B.3

FLEX

September 2nd Labor Day (Holiday) 2.18-D 6.NS.B.4

FLEX Unit 2 Begins

Additional Information

Unit Notes Grade 6 begins in Module 2 since students apply and extend their previous understanding of the four operations (addition, subtraction, multiplication, and division) to now include:

fluently dividing multi-digit numbers using the standard algorithm. fluently adding, subtracting, multiplying, and dividing multi-digit decimals using the standard algorithm for

each operation. interpreting and computing quotients of fractions and solving word problems involving division of fractions

by fractions. Since this unit focuses on culminating standards for several years’ worth of work and heavily builds on prior grade level skills, the state recommends that the module be addressed at the start of the year. Lessons 1 and 2 are aligned to prior grade level standards. Since these lessons incorporate numerous division models, teachers are encouraged to utilize the lessons. These lessons are included in the sample calendar.

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Additional Lessons (Optional for remediation and enrichment)

The following lessons are not included in the sample calendar. The decision to include these lessons should be made at the teacher level. Lessons 5-6, 15-17, and 19: The content in these lessons is not aligned to the explicit expectations of the standards or goes beyond the explicit expectations of the standards. These lessons are optional enrichment activities.

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 the 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 Remediation Guides and Tools.

GRADE 6 TOPIC OF INSTRUCTION

REMEDIAL SKILL SUPPORT IN EUREKA MATH

Topic A Dividing fractions by fractions

Understanding of division as an unknown factor problem (3.OA.B.6)

Grade 3, Module 1, Topic B, Lessons 4-6

Understanding division of a fraction by a whole number and how a number smaller than 1 can be split into group sizes larger than 1 (5.NF.B.7a)

Grade 5, Module 4, Topic G, Lesson 26

Determining the contextual meaning of a whole number being divided by a unit fraction (5.NF.B.7b)

Grade 5, Module 4, Topic G, Lesson 25

Understanding division of a whole number by a fraction and division of a fraction by a whole number within real-world contexts (5.NF.B.7c)

Grade 5, Module 4, Topic G, Lesson 27

Topic B Multi-digit decimal operations – adding, subtracting, and multiplying

Using place value strategies to add decimals (5.NBT.B.7)

Grade 5, Module 1, Topic D, Lesson 9

Using place value strategies to subtract decimals (5.NBT.B.7)

Grade 5, Module 1, Topic D, Lesson 10

Relating the standard algorithm of decimal multiplication to the standard algorithm of whole-number multiplication (5.NBT.B.7)

Grade 5, Module 1, Topic E, Lessons 11-12

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Topic C Dividing whole numbers and decimals

Subtracting multi-digit whole numbers using the standard algorithm (4.NBT.B.4)

Grade 4, Module 1, Topic E, Lessons 13-15

Multiplying multi-digit whole numbers using the standard algorithm (5.NBT.B.5)

Grade 5, Module 2, Topic B, Lessons 5-8

Finding quotients (including multi-digit divisors and dividends) using models (4.NBT.B.6, 5.NBT.B.6)

Grade 4, Module 3, Topic E, Lessons 15-18 Grade 5, Module 2, Topic F, Lessons 20-23

Connecting the standard algorithm of division to place value (5.NBT.A.1)

Grade 5, Module 1, Topic A, Lessons 1-2

Topic D Number theory – thinking logically about multiplicative arithmetic (greatest common factor and least common multiple)

Finding factor pairs (4.OA.B.4a) Grade 4, Module 3, Topic F, Lesson 22 Distinguishing between a factor and a multiple (4.OA.B.4c)

Grade 4, Module 3, Topic F, Lesson 24

Understanding prime and composite numbers (4.OA.B.4d)

Grade 4, Module 3, Topic F, Lessons 22-23

Enrichment Support for Honors Classes (Incorporating Above Grade Level Skills)

Incorporating above grade level skills is not recommended during this unit.

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

Tasks from the mid-module assessment are designed to be given after completing Topic B. Tasks from the end-of-module assessment are designed to be given after completing Topic D. To ensure the assessment tasks are aligned to the LSSM taught during Unit 1, it is suggested that teachers omit question 5 since Euclid’s Algorithm, a component of this task, is not an explicit expectation of 6.NS.A.4.

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UNIT 2 – EXPRESSIONS AND EQUATIONS

Eureka Math Module 4, Topics A-H

(Approximately 30 Days ● 9/5/19-10/22/19)

Unit 2 Overview

During this unit, students will extend their arithmetic work to include using variables to represent numbers in expressions and equations. They will evaluate expressions with whole number exponents. Students will understand the relationships of operations and use these relationships to generate equivalent expressions. They will also solve equations and inequalities that represent real-world and mathematical problems. Specifically, students will: write and evaluate expressions that include whole number exponents. read and write expressions in which letters stand for numbers. use mathematical terms to identify parts of an expression. evaluate expressions at specific values of their variables. apply properties of operations, including the distributive property, to write and identify equivalent expressions. identify the value(s) that when substituted for the variable will make a given equation or inequality true. create expressions that use variables when solving real-world problems. create and solve equations and inequalities that are based on real-world situations and use the number line to represent inequalities. analyze the relationship between the dependent and independent variables in an equation.

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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.

6.EE.A.1 Write and evaluate numerical expressions involving whole-number exponents. Remediation Standard(s): 4.OA.B.4, 5.NBT.A.2

6.EE.A.2 Write, read, and evaluate expressions in which letters stand for numbers.

a. Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract 𝑦 from 5” as 5 − 𝑦.

b. Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

c. Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas 𝑉 = 𝑠3 and 𝐴 = 6𝑠2 to find the volume and surface area of a cube with sides of length 𝑠 = 1 2⁄ .

Remediation Standard(s): 5.OA.A.2, 5.OA.B.3

6.EE.A.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + 𝑥) to produce the equivalent expression 6 + 3𝑥; apply the distributive property to the expression 24𝑥 + 18𝑦 to produce the equivalent expression 6(4𝑥 + 3𝑦); apply properties of operations to 𝑦 + 𝑦 + 𝑦 to produce the equivalent expression 3𝑦.

Remediation Standard(s): 1.OA.B.3, 3.OA.B.5, 5.OA.A.2

6.EE.A.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions 𝑦 + 𝑦 + 𝑦 and 3𝑦 are equivalent because they name the same number regardless of which number 𝑦 stands for.

Remediation Standard(s): 1.OA.B.3, 3.OA.B.5, 5.OA.A.2

6.EE.B.5 Understand solving an equation or inequality as a process of answering a question; which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

Remediation Standard(s): None

6.EE.B.6 Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

Remediation Standard(s): None

6.EE.B.7 Solve real-world and mathematical problems by writing and solving equations and inequalities of the form 𝑥 + 𝑝 = 𝑞 and 𝑝𝑥 = 𝑞 for cases in which 𝑝, 𝑞, and 𝑥 are all nonnegative rational numbers. Inequalities will include >,<,≤, and ≥.

Remediation Standard(s): 5.NF.A.1, 5.NF.B.4

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6.EE.B.8 Write an inequality of the form 𝑥 > 𝑐 or 𝑥 < 𝑐 to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form 𝑥 > 𝑐 or 𝑥 < 𝑐 have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

Remediation Standard(s): None

6.EE.C.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation 𝑑 = 65𝑡 to represent the relationship between distance and time.

Remediation Standard(s): 5.OA.B.3

Focus Standards for Mathematical Practice

SMP.2 Reason abstractly and quantitatively. SMP.6 Attend to precision.

Aligned ELP Connector(s): ELPC 6-8.2, ELPC 6-8.3, ELPC 6-8.4, ELPC 6-8.7, ELPC 6-8.10

SMP.7 Look for and make use of structure. SMP.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)

Equation/Ecuación, Equivalent Expressions, Exponential Notation for Whole Number Exponents, Expression/Expresión, Linear Expression, Number Sentence, Numerical Expression, Solution of an Equation, Truth Values of a Number Sentence, Value of a Numerical Expression, and Variable/Variable

Familiar Terms (Tier 3 Vocabulary)

Distribute, Expand, Factor, Number Sentence, Product, Properties of Operations (Distributive, Commutative, and Associative), Quotient/Cociente, Sum/Suma, Term/Término, True or False Number Sentence, and Variable/Variable or Unknown Number

Cross-Curricular Terms (Tier 2 Vocabulary)

Diagram/Diagrama, Explain/Explicar, Expression/Expresión, Evaluate/Evaluar, Problems/Problemas, Property/Propiedad, Reasoning/Razonar, Represent/Representar, and Substitution/Sustitución

Suggested Tools Bar Model, Geometric Figures, and Protractors

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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

September 2nd Labor Day (Holiday) Unit 1 Ends 4.3-A 6.EE.A.3

4.5-B 6.EE.A.1

September 9th 4.6-B 6.EE.A.1

4.7-C 6.EE.A.2c

4.8-C 6.EE.A.4

4.9-D 6.EE.A.2a, 6.EE.A.3

4.10-D 6.EE.A.2b, 6.EE.A.3

September 16th District PD (Student Holiday)

4.11-D 6.EE.A.2c, 6.EE.A.3

4.12-D 6.EE.A.3, 6.EE.A.4

4.13-D & 4.14-D 6.EE.A.2a, 6.EE.A.2b

Benchmark 1 Assessment (Window provided for administration)

September 23rd 4.15-E 6.EE.A.2b

4.16-E & 4.17-E 6.EE.A.2a, 6.EE.A.2a

4.18-F 6.EE.A.2c, 6.EE.B.6

4.19-F 6.EE.A.2c, 6.EE.B.6

4.20-F 6.EE.A.2c, 6.EE.B.6

September 30th FLEX (Recommended 4.21-F if time allows) 6.EE.A.2c

4.22-F 6.EE.A.1, 6.EE.A.2c, 6.EE.B.6

4.23-G 6.EE.B.5

4.24-G 6.EE.B.5

4.25-G 6.EE.B.5

October 7th 4.26-G 6.EE.B.7

4.27-G 6.EE.B.7

4.28-G 6.EE.B.7 Marking period ends

Fall Break (Holiday) Fall Break (Holiday)

October 14th 4.29-G 6.EE.A.3, 6.EE.B.7

4.30-H 6.EE.B.7

4.31-H 6.EE.C.9

4.32-H 6.EE.C.9

4.33-H 6.EE.B.5

October 21st 4.34-H 6.EE.B.7, 6.EE.B.8

FLEX Unit 3 Begins

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Additional Information

Lesson Notes The state recommends that Module 4 is the second unit of instruction in Grade 6. In Module 1, students reason about equations when using ratio and rate reasoning to solve real-world and mathematical problems. Therefore, some students may benefit from discussing expressions and equations (Module 4) before working with ratios and rates (Module 1). As seen in the sample calendar, the Benchmark 1 Assessment takes place during this unit. The assessment will address skills from Unit 1 and Unit 2 (Part A). To ensure students are prepared for the assessment, the following topics and standards from Module 4 must be addressed prior to administering the assessment (suggested 9/20).

Topic A – Relationships of the operations Topic B - Special notations of operations Topic C – Replacing letters and numbers Topic D – Expanding, factoring, and distributing expressions Standards – 6.EE.A.1, 6.EE.A.2c, 6.EE.A.3, and 6.EE.A.4

According to the lesson notes, Lessons 13 and 14 are part of a two-day lesson (Lesson 13 is Part A and Lesson 14 is Part B). To allow for an extra FLEX day during this unit, it is recommended that these lessons be taught during the same class period. It is also recommended that Lessons 16 and 17 be combined since they cover the same skills. These suggestions are included in the sample calendar. The sample calendar also includes Lesson 21 as an optional, yet recommended, lesson. The content in this lesson extends beyond the explicit expectations of the standards. Since this lesson heavily emphasizes analyzing relationships between two values in a table, it may support some students in mastering 6.EE.C.9. It is included as an optional activity on a FLEX day. According to the state, students will need additional practice recognizing that inequalities of the form 𝑥 > 𝑐 or 𝑥 < 𝑐 have infinitely many solutions (portion of 6.EE.B.8). Teachers are encouraged to promote this understanding when students are representing solutions of such inequalities on number line diagrams (also part of 6.EE.B.8).

Additional Lessons (Optional for remediation and enrichment)

The following lessons are not included in the sample calendar. The decision to include these lessons should be made at the teacher level. Lessons 1-2 & 4: The content in these lessons is not aligned to the explicit expectations of the standards. These lessons are optional enrichment activities.

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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 the 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 Remediation Guides and Tools.

GRADE 6 TOPIC OF INSTRUCTION

REMEDIAL SKILL SUPPORT IN EUREKA

Topic A Relationships of the operations

Understanding the relationship between inverse operations of addition and subtraction to generate equivalent expressions (1.OA.B.3)

Grade 1, Module 2, Topic A, Lessons 2 & 6

Understanding the relationships between inverse operations of multiplication and division and division as repeated subtraction (3.OA.B.5)

Grade 3, Module 3, Topic E, Lessons 1 & 9

Topic B Special notations of operations

Using exponents to name place value units and using exponents to denote powers of 10 (5.NBT.A.2)

Grade 5, Module 1, Topic A, Lessons 3-4

Topic D Expanding, factoring, and distributing expressions

Writing numerical expressions (5.OA.A.2) Grade 5, Module 2, Topic B, Lessons 3-4 Interpreting numerical expressions (5.OA.A.2) Grade 5, Module 2, Topic B, Lessons 3-4 Understanding of the distributive property (3.OA.B.5)

Grade 3, Module 3, Topic A, Lesson 2 Grade 3, Module 3, Topic B, Lesson 6 Grade 3, Module 3, Topic C, Lesson 10

Topic E Expressing operations in algebraic form

Writing simple expressions (5.OA.A.2) Grade 5, Module 4, Topic H, Lesson 32

Topic G Solving equations

Adding and subtracting fractions with unlike denominators (5.NF.A.1)

Grade 5, Module 3, Topic B, Lessons 3-6

Understanding the relationship between multiplication of fractions and division (5.NF.B.4a)

Grade 5, Module 4, Topic C, Lesson 7

Multiplying fractions by fractions (5.NF.B.4b) Grade 5, Module 4, Topic E, Lessons 13-15

Topic H Applications of equations

Forming ordered pairs, plotting points on a coordinate plane, and generating two numerical patterns using two given rules (5.OA.B.3)

Grade 5, Module 6, Topic B, Lesson 7

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Enrichment Support for Honors Classes (Incorporating Above Grade Level Skills)

If students exhibit proficiency on the following concepts, teachers may consider incorporating the recommended above grade level skills.

GRADE 6 CONCEPT ENRICHMENT SUPPORT Applying properties of operations to generate equivalent expressions and identifying when two expressions are equivalent (6.EE.A.3 & 6.EE.A.4)

Applying properties of operations as strategies to add, subtract, factor, and expand linear expressions (7.EE.A.1) Grade 7, Module 3, Topic A, Lessons 1-4 Teachers should choose questions that include positive rational numbers only.

Solving one-step equations (6.EE.B.7) Solving two-step equations (7.EE.B.4a) Grade 7, Module 2, Topic C, Lessons 22-23 Teachers should choose questions that include positive rational numbers only.

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

Tasks from the mid-module assessment are designed to be given after completing Topic E. Tasks from the end-of-module assessment are designed to be given after completing Topic H.