UNIT 1 RATIONAL NUMBERS Eureka Math Module 2, Topics A-C · 2019-08-05 · 1 UNIT 1 – RATIONAL...

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UNIT 1 – RATIONAL NUMBERS

Eureka Math Module 2, Topics A-C

(Approximately 21 Days ● 8/12/19-9/10/19)

Unit 1 Overview

In this unit, students will extend their understanding of rational numbers and operations with fractions to add, subtract, multiply, and divide rational numbers (including complex fractions). They will solve real-world and mathematical problems involving the four operations with rational numbers. While problem-solving with rational numbers, students will also deepen their understanding of solving equations. (Students will continue to expand their understanding of solving equations during Unit 2.) Specifically, students will: describe situations in which opposite quantities combine to make zero. show that a number and its opposite have a sum of zero and are called additive inverses. show that the distance between two rational numbers on a number line is the absolute value of their difference. understand how to add, subtract, multiply, and divide rational numbers. apply properties of operations to add, subtract, multiply, and divide rational numbers. convert a rational number to a decimal. solve real-world and mathematical problems involving addition, subtraction, multiplication, and division with rational numbers. use equations to solve word problems that include negative rational numbers.

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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.

a. Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

b. Understand 𝑝 + 𝑞 as the number located a distance |𝑞| from 𝑝, in the positive or negative direction depending on whether 𝑞 is positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts.

c. Understand subtraction of rational numbers as adding the additive inverse, 𝑝 − 𝑞 = 𝑝 + (−𝑞). Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

d. Apply properties of operations as strategies to add and subtract rational numbers.

Remediation Standard(s): 5.NF.A.1, 6.NS.C.5

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

a. Understand that multiplication is extended from fractions to rational numbers by requiring

that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (−1)(−1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.

b. Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If 𝑝 and 𝑞 are integers, then −(𝑝 𝑞⁄ ) = (−𝑝) 𝑞⁄ = 𝑝 (−𝑞)⁄ . Interpret quotients of rational numbers by describing real-world contexts.

c. Apply properties of operations as strategies to multiply and divide rational numbers. d. Convert a rational number to a decimal using long division; know that the decimal form of a

rational number terminates in 0s or eventually repeats.

Remediation Standard(s): 5.NF.B.3, 5.NF.B.4, 6.NS.A.1

7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational numbers. Please note, computations with rational numbers extend the rules for manipulating fractions to complex fractions.

Remediation Standard(s): 4.OA.A.3, 6.NS.B.3

7.EE.B.4a Solve word problems leading to equations of the form 𝑝𝑥 + 𝑞 = 𝑟 and 𝑝(𝑥 + 𝑞) = 𝑟, where 𝑝, 𝑞, and 𝑟 are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Remediation Standard(s): 6.EE.B.6, 6.EE.B.7

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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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.4 Model with mathematics. 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.

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, Formula for the Distance Between Two Numbers, Multiplicative Identity, Repeating Decimal Expansion, and Terminating Decimal Expansion

Familiar Terms (Tier 3 Vocabulary)

Absolute Value/Valor Absoluto, Associative Property (of Multiplication and Addition), Commutative Property (of Multiplication and Addition), Credit, Debit, Deposit, Distributive Property (of Multiplication Over Addition), Equation/Ecuación, Expression/Expresión, Integer, Inverse, Multiplicative Inverse, Negatives, Opposites, Overdraft, Positives, Rational Numbers, and Withdraw

Cross-Curricular Terms (Tier 2 Vocabulary)

Equal, Expression/Expresión, Evaluate/Evaluar, Identify/Identificar, Property/Propiedad, Opposite/Opuesto, Replace, and Rules

Suggested Tools Equations, Expressions, Integer Game, Number Line, and Tape Diagram

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Additional Information

Unit Notes Grade 7 begins in Module 2 since adding, subtracting, multiplying, and dividing rational numbers is the culmination of numerical work with the four basic operations. Because so much other work in Grade 7 depends on rational number arithmetic, fluency with rational number arithmetic is the goal in this grade. In order to meet this goal, it is important for students to be provided sufficient opportunities to practice. The state recommends that this module be addressed at the start of the school year. While Lesson 21 targets 7.NS.A.3, the lesson is not tightly aligned to any Grade 7 standard. The lesson should prove to be advantageous for students long term since it establishes properties of equality that will be used later to solve linear equations. Since the lesson is considered to be on grade level by the state, it is included in the sample calendar.

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 7.NS.A.1a, 7.NS.A.1b, 6.NS.C.6, 6.NS.C.7

2.2-A 7.NS.A.1b

2.3-A 7.NS.A.1b, 7.NS.A.1d

2.4-A 7.NS.A.1b, 7.NS.A.1d

2.5-A 7.NS.A.1c, 7.NS.A.1d

August 19th 2.6-A 7.NS.A.1c

2.7-A 7.NS.A.1a, 7.NS.A.1b, 7.NS.A.1c, 7.NS.A.1d, 7.NS.A.3

2.8-A 7.NS.A.1d

2.9-A 7.NS.A.1d

2.10-B 7.NS.A.2a

August 26th 2.11-B 7.NS.A.2a

2.12-B 7.NS.A.2b

2.14-B 7.NS.A.2d

2.15-B 7.NS.A.2a, 7.NS.A.2b, 7.NS.A.2c, 7.NS.A.3

2.16-B 7.NS.A.2c

September 2nd Labor Day (Holiday) 2.17-C 7.NS.A.3, 7.EE.B.4a

2.21-C 7.NS.A.3

2.22-C 7.EE.B.4a

2.23-C 7.EE.B.4a

September 9th FLEX FLEX Unit 2 Begins

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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. Lesson 13: The content in this lesson is not aligned to the explicit expectations of the standards. However, the concepts and skills developed during this lesson may prove to be advantageous for students long term. This lesson is an optional enrichment activity. Lessons 18-20: The content in these lessons is not tightly aligned with the explicit expectations of the standards. As a result, the use of these lessons may detract from the students’ pursuit of mastery. 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 7 TOPIC OF INSTRUCTION

REMEDIAL SKILL SUPPORT IN EUREKA MATH

Topic A Addition and subtraction of integers and rational numbers

Adding fractions with unlike denominators, including mixed numbers (5.NF.A.1)

Grade 5, Module 3, Topic B, Lessons 3-4

Subtracting fractions with unlike denominators, including subtracting mixed numbers (5.NF.A.1)


Understanding that positive and negative numbers are used together to describe quantities having opposite values and using positive and negative numbers to represent quantities in real-world contexts (6.NS.C.5)

Grade 6, Module 3, Topic A, Lessons 2-3

Understanding that opposite signs of numbers indicate locations on opposite sides of 0 on the number line (6.NS.C.6a)

Grade 6, Module 3, Topic A, Lessons 1 & 4-6

Finding and positioning rational numbers on horizontal and vertical number line diagrams (6.NS.C.6c)


Understanding which direction to move along the number line based on the sign of each number and interpreting statements of inequality (6.NS.C.7a)

Grade 6, Module 3, Topic B, Lessons 10 & 12

Understanding of absolute value as distance from zero on a number (6.NS.C.7c)


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

https://www.louisianabelieves.com/resources/library/k-12-math-year-long-planning

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Topic B Multiplication and division of integers and rational numbers

Understanding the various properties of multiplication (3.OA.B.5)


Interpreting a fraction as division of the numerator by the denominator (5.NF.B.3)


Using decimal notation for fractions with denominators 10 or 100 (4.NF.C.6)


Dividing multi-digit numbers using the standard algorithm (6.NS.B.2)

Grade 6, Module 2, Topic C, Lessons 12-13

Dividing multi-digit decimals using the standard algorithm (6.NS.B.3)


Multiplying multi-digit decimals using the standard algorithm (6.NS.B.3)


Dividing a unit fraction by a non-zero whole number (5.NF.B.7a), dividing a whole number by a unit fraction (5.NF.B.7b), and dividing a fraction by a fraction (6.NS.A.1)

Grade 5, Module 4, Topic G, Lessons 25-26 Grade 6, Module 2, Topic A, Lessons 3-4 & 7-8

Multiplying a fraction by a fraction, including multiplying mixed numbers (5.NF.B.4)

Grade 5, Module 4, Topic E, Lessons 13-15

Topic C Applying operations with rational numbers to expressions and equations

Solving multi-step word problems that use the four operations (4.OA.A.3.)

Grade 4, Module 3, Topic D, Lesson 12-13 Grade 4, Module 3, Topic G, Lessons 31-32

Creating expressions that arise when the total is not given and using variables to represent numbers in the expressions (6.EE.B.6)

Grade 6, Module 4, Topic F, Lessons 18-20

Modeling real-world and mathematical problems by writing and solving equations and interpreting the answer within the context of the problem (6.EE.B.7)

Grade 6, Module 4, Topic G, Lessons 26-29

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

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

GRADE 7 CONCEPT ENRICHMENT SUPPORT Adding, subtracting, multiplying, and dividing rational numbers (7.NS.A)

Knowing that numbers that are not rational are called irrational Understanding that every number has a decimal expansion (8.NS.A.1) Grade 8, Module 7, Topic B, Lessons 8 & 10 During the lesson, do not utilize the bullet/question that incorporates a square root symbol.

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 C. To ensure that the assessment tasks are aligned to the LSSM taught during Unit 1, it is suggested that teachers:

Omit question 2a since 7.EE.A.2 is only addressed during Lesson 19, which is considered an optional enrichment lesson. In place of question 2a, teachers should provide an expression for students to use when completing the remaining parts of the task.

Omit question 3 since the question addresses skills only covered in Lesson 20, which is considered an optional enrichment lesson.

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UNIT 2 – EXPRESSIONS AND EQUATIONS

Eureka Math Module 3, Topics A-B


Unit 2 Overview

In this unit, students will expand upon their understanding of equivalent expressions to write expressions in multiple forms. They will solve multi-step problems posed with rational numbers. They will also construct equations and inequalities to solve real-world and mathematical problems. Specifically, students will:

apply properties of operations to add, subtract, factor, and expand linear expressions with rational coefficients. understand that writing expressions in different forms in a problem context can shed light on the problem. solve multi-step problems posed with rational numbers and assess the reasonableness of answers. calculate with numbers in any form and convert between forms. construct and solve equations and inequalities. graph the solution set of an inequality and interpret the solution set in the context of the problem.

Focus Standards



7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients to include multiple grouping symbols (e.g., parentheses, brackets, and braces).

Remediation Standard(s): 6.EE.A.3, 6.EE.A.4

7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, 𝑎 + 0.05𝑎 = 1.05𝑎 means that “increase by 5%” is the same as “multiply by 1.05.”

Remediation Standard(s): None


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7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1 10⁄ of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 93 4⁄

inches long in the center of a door that is 271 2⁄ inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.

Remediation Standard(s): None

7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

a. Solve word problems leading to equations of the form 𝑝𝑥 + 𝑞 = 𝑟 and 𝑝(𝑥 + 𝑞) = 𝑟, where 𝑝, 𝑞, and 𝑟 are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

b. Solve word problems leading to inequalities of the form 𝑝𝑥 + 𝑞 > 𝑟, 𝑝𝑥 + 𝑞 ≥ 𝑟, 𝑝𝑥 + 𝑞 < 𝑟, or 𝑝𝑥 + 𝑞 ≤ 𝑟, where 𝑝, 𝑞, and 𝑟 are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the solutions.

Remediation Standard(s): 6.EE.B.6, 6.EE.B.7, 6.EE.B.8


SMP.2 Reason abstractly and quantitatively. SMP.4 Model with mathematics. 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.

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Expression in Expanded Form, Expression in Factored Form, Expression in Standard Form, Coefficient of a Term, and Term/Término


Distribute, Equation/Ecuación, Equivalent Expressions, Expression/Expresión, Factor, Identity, Inequality, Linear Expression, Number Sentence, Numerical Expression, Properties of Operations (Distributive, Commutative, and Associative), Term/Término, True or False Number Sentence, Truth Values of a Number Sentence, Value of a Numerical Expression, and Variable/Variable


Convert/Convertir, Describe/Describir, Negative/Negativo, Operation/Operacion, Rational, Value/Valor, and Values/Valores

Suggested Tools Area Model, Equations and Inequalities, Expressions, Number Line, and Tape Diagram

Sample Calendar



September 9th Unit 1 Ends 3.1-A 7.EE.A.1, 7.EE.A.2, 6.EE.A.3, 6.EE.A.4

3.2-A 7.EE.A.1, 6.EE.A.3, 6.EE.A.4

3.3-A 7.EE.A.1

September 16th District PD (Student Holiday)

3.4-A 7.EE.A.1

3.5-A 7.EE.A.1

3.6-A 7.EE.A.1, 7.EE.A.2

FLEX

September 23rd Benchmark 1 Assessment (Window provided for administration)

3.7-B 7.EE.B.3, 7.EE.B.4a, 6.EE.B.5

3.8-B 7.EE.B.3, 7.EE.B.4a

3.9-B 7.EE.B.3, 7.EE.B.4a, 8.EE.C.7b

FLEX

September 30th 3.12-B (No direct alignment to standard)

3.13-B 7.EE.B.4b

3.14-B 7.EE.B.4b

3.15-B 7.EE.B.4b

FLEX

October 7th FLEX Unit 3 Begins Fall Break (Holiday)

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Unit Notes The state recommends that the second unit of instruction in Grade 7 is Module 3 – Topics A and B. During Module 2, students added, subtracted, multiplied and divided rational numbers. They also began writing and solving equations. In this unit, students will continue to use the four operations with rational numbers as they solve real-life and mathematical problems. Students will also deepen their understanding of equations as they continue to construct equations to solve problems. Based on the state’s recommended year-long pacing, Topic C will be taught during Unit 6 since the lessons in this topic focus on standards from the Geometry domain. Since Lessons 10 and 11 from Topic B address 7.G.B.5, these lessons will also be taught during Unit 6. 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 topic and standard from Module 3 must be addressed prior to administering the assessment (suggested 9/23).

Topic A – Use properties of operations to generate equivalent expressions Standard – 7.EE.A.1

Although Lesson 12 does not align to any Grade 7 standard, it does establish the properties of inequality (using rational numbers) that will be used later to solve linear inequalities. The lesson should prove to be advantageous for students long term. The lesson is included in the sample calendar.


All lessons in Topics A and B (aside from Lessons 10 and 11) are taught during this module. As mentioned in the Unit Notes, Lessons 10 and 11 will be taught during Unit 6.





Topic A Use properties of operations to generate equivalent expressions

Applying properties of operations to generate equivalent expressions (6.EE.A.3)

Grade 6, Module 4, Topic D, Lessons 9-12

Determining if two expressions are equivalent (6.EE.A.4)

Grade 6, Module 4, Topic C, Lesson 8



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Topic B Solving problems using expressions, equations, and inequalities

Understanding of variables and using variables to represent numbers in expressions (6.EE.B.6)

Grade 6, Module 4, Topic F, Lessons 18-20

Solving single-step equations and inequalities (6.EE.B.7)

Grade 6, Module 4, Topic G, Lessons 26-29

Writing inequalities to represent a constraint or condition in a problem (6.EE.B.8)

Grade 6, Module 4, Topic G, Lesson 34


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

GRADE 7 CONCEPT ENRICHMENT SUPPORT Solving two-step equations fluently (7.EE.B.4a) Giving examples of linear equations in one variable

with one solution, infinitely many solutions, or no solutions Determining the number of solutions by transforming a given equation into simpler forms (8.EE.C.7a) Solving linear equations with rational number coefficients (8.EE.C.7b) Grade 8, Module 4, Topic A, Lessons 3-4 & 6-7


Tasks from the mid-module and end-of-module assessments are designed to be given after completing Topic B. To ensure the assessment tasks are aligned to the LSSM taught during Unit 2, it is suggested that teachers omit question 7 on the mid-module assessment and questions 3-7 on the end-of-module assessment. These questions target standards that will be addressed during Unit 6.

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UNIT 3 – RATIOS AND PROPORTIONAL RELATIONSHIPS

Eureka Math Module 1, Topics A-C


Unit 3 Overview

In this unit, students will build upon their reasoning of ratios, rates, and unit rates to develop an understanding of proportionality and the constant of proportionality. They will apply their understanding of proportionality to solve multi-step ratio problems. (Please note, Unit 3 focuses on multi-step ratio problems. Students will solve multi-step percent problems during Unit 4.) In addition, students will compute unit rates associated with ratios of fractions. Specifically, students will:

compute unit rates that include computations with complex fractions. determine if two quantities are in a proportional relationship. identify the constant of proportionality. represent proportional relationships by equations. explain what a point (𝑥, 𝑦) on the graph of a proportional relationship means. use proportional relationships to solve multi-step ratio problems.

Focus Standards



7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other quantities measured in like or different units. For example, if a person walks 1 2⁄ mile in each 1 4⁄

hour, compute the unit rate as the complex fraction 1 2⁄1 4⁄⁄ miles per hour, equivalently 2 miles per

hour.

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


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7.RP.A.2 Recognize and represent proportional relationships between quantities.

a. Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

b. Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

c. Represent proportional relationships by equations. For example, if total cost 𝑡 is proportional to the number 𝑛 of items purchased at a constant price 𝑝, the relationship between the total cost and the number of items can be expressed as 𝑡 = 𝑝𝑛.

d. Explain what a point (𝑥, 𝑦) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and (1, 𝑟) where 𝑟 is the unit rate.

Remediation Standard(s): 6,RP,A.2, 6.RP.A.3

7.RP.A.3 Use proportional relationships to solve multi-step ratio and percent problems of simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error. Please note, this unit focuses on multi-step ratio problems. Students will solve multi-step percent problems during Unit 4.

Remediation Standard(s): 6.RP.A.3

7.EE.B.4a Solve word problems leading to equations of the form 𝑝𝑥 + 𝑞 = 𝑟 and 𝑝(𝑥 + 𝑞) = 𝑟, where 𝑝, 𝑞, and 𝑟 are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

Remediation Standard(s): 6.EE.B.6, 6.EE.B.7


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.

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Constant of Proportionality, Miles per Hour, Proportional Relationship, and Proportional To


Equivalent Ratio, Rate, Ratio, Ratio Table, and Unit Rate


Constant/Constante, Determine/Determinar, Plot, Proportional/Proporcional, and Represent/Representar

Suggested Tools Ratio Table, Coordinate Plane, and Equations of the Form 𝑦 = 𝑘𝑥

Sample Calendar



October 7th Unit 2 Ends 1.1-A (Remediation)

1.2-A 7.RP.A.2a, 7.RP.A.2b, 7.RP.A.2c Marking Period Ends

Fall Break (Holiday) Fall Break (Holiday)

October 14th 1.3-A 7.RP.A.2a

1.4-A 7.RP.A.2a

1.5-A 7.RP.A.2a

1.6-A 7.RP.A.2a

FLEX

October 21st 1.7-B 7.RP.A.2b

1.8-B 7.RP.A.2b, 7.RP.A.2c

1.9-B 7.RP.A.2b, 7.RP.A.2c

1.10-B 7.RP.A.2a, 7.RP.A.2b, 7.RP.A.2c, 7.RP.A.2d

FLEX

October 28th 1.11-C 7.RP.A.1

1.12-C 7.RP.A.1

1.13-C (Not aligned to a specific standard)

1.14-C 7.RP.A.3

1.15-C 7.RP.A.2a, 7.RP.A.2b, 7.RP.A.2c, 7.RP.A.2d

November 4th FLEX LEAP 360 Interim 1A (Window provided for administration)

Unit 4 Begins

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Unit Notes Based on the state’s recommended year-long pacing, Topic D will be taught during Unit 6 since the lessons in this topic focus on standards from the Geometry domain. As seen in the sample calendar, the LEAP 360 Interim Form 1A takes place at the end of this unit (suggested 11/5). All skills addressed in Units 1-3 are eligible to be assessed on this interim. Lesson 1 is a remediation lesson since it is aligned to prior grade level standards. Some students may benefit from completing the lesson since it reviews the Grade 6 concepts related to ratios, rates, and unit rates. Teachers are encouraged to utilize the lesson and it is included in the sample calendar. The sample calendar also includes Lesson 13. Although this lesson is not tightly aligned to any Grade 7 standard, it does require students to use their understanding and skills developed in 7.RP.A.1 and 7.RP.A.2 to solve complex problems. This lesson should prove to be advantageous for students in their pursuit to master the 7.RP standards.


All lessons in Topics A-C are taught during this unit.





Topic A Proportional relationships

Identifying ratio relationships from a given description and writing ratio relationships between two quantities (6.RP.A.1)


Understanding the concept of a unit rate and using rate language in the context of a ratio relationship (6.RP.A.2)


Understanding the connection between ratios and the coordinate plane and plotting pairs of values on the coordinate plane (6.RP.A.3a)


Solving unit rate problems (6.RP.A.3b) Grade 6, Module 1, Topic C, Lessons 19-22



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Topic B Unit rate and the constant of proportionality

Understanding the concept of a unit rate and using rate language in the context of a ratio relationship (6.RP.A.2)


Making tables of equivalent ratios (6.RP.A.3a) Grade 6, Module 1, Topic B, Lessons 9-10 Solving unit rate problems (6.RP.A.3b) Grade 6, Module 1, Topic C, Lessons 20-23

Topic C Ratios and rates involving fractions

Creating equivalent fractions and explaining why two fractions are equivalent (4.NF.A.1)


Understanding fractions as division (5.NF.B.3) Grade 5, Module 4, Topic B, Lessons 2-5 Dividing fractions by fractions (6.NS.A.1) Grade 6, Module 2, Topic A, Lessons 3-5


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


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 C. To ensure the assessment tasks are aligned to the LSSM taught during Unit 3, it is suggested that teachers omit questions 2 and 4a-c. These questions target standards that will be addressed during Unit 6.

UNIT 1 RATIONAL NUMBERS Eureka Math Module 2, Topics A-C · 2019-08-05 · 1 UNIT 1 – RATIONAL...

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Transcript of UNIT 1 RATIONAL NUMBERS Eureka Math Module 2, Topics A-C · 2019-08-05 · 1 UNIT 1 – RATIONAL...