## Extending the Digital Arm of Eureka Math / EngageNY

Support your core math program with our custom-built pathways corresponding to the themes, topics, and standards within Eureka Math and EngageNY. In addition to these custom pathway lessons, students will also have access to over 40 precursor lessons based on their TTM placement test and performance along their pathway.

## - JUMP TO EACH GRADE LEVEL -

## GRADE 3

**EUREKA MATH / ENGAGE NY TOPIC**

**THINK THROUGH MATH LESSON**

Visualizing Whole Numbers (Introductory Lesson)

Visualizing Place Value (Introductory Lesson)

Visualizing Addition (Introductory Lesson)

Visualizing Subtraction (Introductory Lesson)

## MODULE 1: Properties of Multiplication and Division and Solving Problems with Units of 2-5 and 10

**EUREKA MATH / ENGAGE NY TOPIC**

A: Multiplication and the Meaning of the Factors

B: Division as an Unknown Factor Problem

C: Multiplication Using Units of 2 and 3

D: Division Using Units of 2 and 3

E: Multiplication and Division Using Units of 4

F: Distributive Property and Problem Solving Using Units of 2–5 and 10

3.OA.1, 3.OA.2, 3.OA.3, 3.OA.4, 3.OA.5, 3.OA.6, 3.OA.7

**THINK THROUGH MATH LESSON** (CCSS)

Developing Fluency Using 2 as a Factor (3.OA.7)

Developing Fluency Using 5 or 10 as a Factor (3.OA.7)

Using Halves and Doubles to Solve Multiplication Problems (3.OA.7)

Concept of Multiplication – Grouping (3.OA.1)

Concept of Multiplication – Word Problems (3.OA.1)

Concept of Multiplication – Arrays (3.OA.1)

Concept of Division (3.OA.2)

Interpreting Division Problems (3.OA.2)

Constructing Division Problems (3.OA.2)

Relationship Between Multiplication and Division (3.OA.5)

Multiplication and Division Fact Families (3.OA.5, 3.OA.6, 3.OA.7)

Solving Multiplication and Division Equations (3.OA.4, 3.OA.6)

Division as an Unknown-Factor Problem (3.OA.4, 3.OA.6)

CCSS Addressed: ✓ 3.OA.1 | ✓ 3.OA.2 | ✓ 3.OA.3 * | ✓ 3.OA.4 | ✓ 3.OA.5 | ✓ 3.OA.6 | ✓ 3.OA.7

*✓ Standard Covered by TTM Lesson | * Standard Covered within Different Module on the Grade-level Pathway*

## MODULE 2: Place Value and Problem Solving with Units of Measure

**EUREKA MATH / ENGAGE NY TOPIC**

A: Time Measurement and Problem Solving

B: Measuring Weight and Liquid Volume in Metric Units

C: Rounding to the Nearest Ten and Hundred

D: Two- and Three-Digit Measurement Addition Using the Standard Algorithm

E: Two- and Three-Digit Measurement Subtraction Using the Standard Algorithm

3.NBT.1, 3.NBT.2, 3.MD.1, 3.MD.2

**THINK THROUGH MATH LESSON** (CCSS)

Adding and Subtracting Time (3.MD.1)

Reasoning About Place Value and Rounding (3.NBT.1)

Rounding the to the Nearest Ten and Hundred (3.NBT.1)

CCSS Addressed: ✓ 3.NBT.1 | ✓ 3.MD.1

*✓ Standard Covered by TTM Lesson | * Standard Covered within Different Module on the Grade-level Pathway*

## MODULE 3: Multiplication and Division with Units of 0, 1, 6-9, and Multiples of 10

**EUREKA MATH / ENGAGE NY TOPIC**

A: The Properties of Multiplication and Division

B: Multiplication and Division Using Units of 6 and 7

C: Multiplication and Division Using Units up to 8

D: Multiplication and Division Using Units of 9

E: Analysis of Patterns and Problem Solving Including Units of 0 and 1

F: Multiplication of Single-Digit Factors and Multiples of 10

3.OA.3, 3.OA.4, 3.OA.5, 3.OA.7, 3.OA.8, 3.OA.9, 3.NBT.3

**THINK THROUGH MATH LESSON** (CCSS)

Properties of Addition and Multiplication (3.OA.5)

Multiplication and Division Word Problems – Visual Models (3.OA.3)

Multiplication and Division Word Problems – Equations (3.OA.3)

Multiplication and Division Word Problems – Solutions (3.OA.3)

Multiplying by Multiples of Ten (3.NBT.3)

Additive and Multiplicative Patterns (3.OA.9)

CCSS Addressed: ✓ 3.NBT.3 | ✓ 3.OA.3 | ✓ 3.OA.4 * | ✓ 3.OA.5 | ✓ 3.OA.7 * | ✓ 3.OA.8 * | ✓ 3.OA.9

*✓ Standard Covered by TTM Lesson | * Standard Covered within Different Module on the Grade-level Pathway*

## MODULE 4: Multiplication and Area

**EUREKA MATH / ENGAGE NY TOPIC**

A: Foundations for Understanding Area

B: Concepts of Area Measurement

C: Arithmetic Properties Using Area Models

D: Applications of Area Using Side Lengths of Figures

3.MD.5, 3.MD.6, 3.MD.7

**THINK THROUGH MATH LESSON** (CCSS)

Unit Squares(3.MD.6)

Concept of Area (3.MD.5a, 3.MD.5b, 3.MD.6)

Area of Rectangles (3.MD.7a, 3.MD.7b, 3.MD.7c)

Recognizing Area as Additive (3.MD.7d)

Area of Basic Composite Figures (3.MD.7d)

Using Visual Models to Understand the Distributive Property (3.OA.5)

CCSS Addressed: ✓ 3.MD.5 | ✓ 3.MD.6 | ✓ 3.MD.7

## MODULE 5: Fractions as Numbers on the Number Line

**EUREKA MATH / ENGAGE NY TOPIC**

A: Partitioning a Whole into Equal Parts

B: Unit Fractions and Their Relation to the Whole

C: Comparing Unit Fractions and Specifying the Whole

D: Fractions on the Number Line

E: Equivalent Fractions

F: Comparison, Order, and Size of Fractions.

3.NF.1, 3.NF.2, 3.NF.3, 3.G.2

**THINK THROUGH MATH LESSON** (CCSS)

Understanding Fractions – Equal Areas (3.NF.1)

Understanding Fractions – Notation (3.G.2)

Unit Fractions on the Number Line (3.NF.2a)

Fractions on the Number Line (3.NF.2b)

Modeling Equivalent Fractions with Number Lines (3.NF.3a)

Visual Models of Equivalent Fractions (3.NF.3b)

Whole Numbers as Fractions (3.NF.3c)

Whole Numbers as Fractions on the Number Line (3.NF.3c)

Comparing Fractions with the Same Numerator or Denominator (3.NF.3d)

Recognizing Valid Fraction Comparisons I (3.NF.3d)

CCSS Addressed: ✓ 3.NF.1 | ✓ 3.NF.2 | ✓ 3.NF.3 | ✓ 3.G.2

## MODULE 6: Collecting and Displaying Data

**EUREKA MATH / ENGAGE NY TOPIC**

A: Generate and Analyze Categorical Data

B: Generate and Analyze Measurement Data

3.MD.3, 3.MD.4

**THINK THROUGH MATH LESSON** (CCSS)

Introduction to Data Displays (3.MD.3)

Line Plots and Length (3.MD.4)

CCSS Addressed: ✓ 3.MD.3 | ✓ 3.MD.4

## MODULE 7: Geometry and Measurement Word Problems

**EUREKA MATH / ENGAGE NY TOPIC**

A: Solving Word Problems

B: Attributes of Two-Dimensional Figures

C: Problem Solving with Perimeter

D: Recording Perimeter and Area Data on Line Plots

E: Problem Solving with Perimeter and Area

3.MD.4, 3.MD.8, 3.G.1

**THINK THROUGH MATH LESSON** (CCSS)

Solving Two-Step Word Problems (3.OA.8)

Modeling and Solving Two-Step Word Problems (3.OA.8)

Classifying Quadrilaterals I (3.G.1)

Perimeter (3.MD.8)

Line Plots and Length (3.MD.4)

CCSS Addressed: ✓ 3.MD.4 | ✓ 3.MD.8 | ✓ 3.G.1

## GRADE 4

**EUREKA MATH / ENGAGE NY TOPIC**

**THINK THROUGH MATH LESSON**

Visualizing Place Value Relationships (Introductory Lesson)

Visualizing Rounding (Introductory Lesson)

Visualizing Addition and Subtraction (Introductory Lesson)

Visualizing Multiplication and Division (Introductory Lesson)

## MODULE 1: Place Value, Rounding, and Algorithms for Addition and Subtraction

**EUREKA MATH / ENGAGE NY TOPIC**

A: Place Value of Multi-Digit Whole Numbers

B:Comparing Multi-Digit Whole Numbers

4.NBT.1, 4.NBT.2, 4.OA.1

**THINK THROUGH MATH LESSON** (CCSS)

Place Value Concepts (4.NBT.2)

Using Place Value Concepts to Compare Whole Numbers (4.NBT.2)

Understanding Place Value Relationships (4.NBT.1)

CCSS Addressed: ✓ 4.OA.1 | ✓ 4.NBT.1 | ✓ 4.NBT.2

C: Rounding Multi-Digit Whole Numbers

4.NBT.3

Rounding Whole Numbers (4.NBT.3)

Using Rounding in Problem Solving (4.NBT.3)

CCSS Addressed: ✓ 4.NBT.3

D: Multi-Digit Whole Number Addition

E: Multi-Digit Whole Number Subtraction

F: Addition and Subtraction Word Problems

4.OA.3, 4.NBT.4, 4.NBT.1, 4.NBT.2

Adding Whole Numbers (4.NBT.4)

Adding and Subtracting with the Standard Algorithm (4.NBT.4)

CCSS Addressed: ✓ 4.OA.3 * | ✓ 4.NBT.1 * | ✓ 4.NBT.2 * | ✓ 4.NBT.4

## MODULE 2: Unit Conversions and Problem Solving with Metric Measurement

**EUREKA MATH / ENGAGE NY TOPIC**

A: Metric Unit Conversions

B:Application of Metric Unit Conversions

4.MD.1, 4.MD.2

**THINK THROUGH MATH LESSON** (CCSS)

Units of Measure – Customary (4.MD.1)

Units of Measure – Metric (4.MD.1)

CCSS Addressed: ✓ 4.MD.1

## MODULE 3: Multi-digit Multiplication and Division

**EUREKA MATH / ENGAGE NY TOPIC**

A: Multiplicative Comparison Word Problems

B: Multiplication by 10, 100, and 1,000

4.OA.1, 4.OA.2, 4.MD.3, 4.OA.3, 4.NBT.5, 4.NBT.1

**THINK THROUGH MATH LESSON** (CCSS)

Multiplication as a Comparison – Equations (4.OA.1)

Multiplication as a Comparison – Word Problems (4.OA.2)

Area and Perimeter of Rectangles (4.MD.3)

CCSS Addressed: ✓ 4.OA.1 | ✓ 4.OA.2 | ✓ 4.OA.3 | ✓ 4.MD.3 * | ✓ 4.NBT.1 * | ✓ 4.NBT.5 *

C. Multiplication of up to Four Digits by Single-Digit Numbers

4.NBT.5, 4.OA.2, 4.NBT.1

Multiplying Whole Numbers (4.OA.1, 4.NBT.5)

CCSS Addressed: ✓ 4.OA.2 * | ✓ 4.NBT.1 * | ✓ 4.NBT.5

D. Multiplication Word Problems

4.OA.1, 4.OA.2, 4.OA.3, 4.NBT.5

Estimating Solutions to Multi-step Word Problems (4.OA.3)

CCSS Addressed: ✓ 4.OA.1 * | ✓ 4.OA.2 * | ✓ 4.OA.3 | ✓ 4.NBT.5 *

E. Division of Tens and Ones with Successive Remainders

4.NBT.6, 4.OA.3

Dividing Whole Numbers – One-digit Divisors (4.NBT.6)

Interpreting Remainders (4.OA.3)

CCSS Addressed: ✓ 4.OA.3 | ✓ 4.NBT.6

F. Reasoning with Divisibility

4.OA.4

Factors (4.OA.4)

Relating Factors and Multiples I (4.OA.4)

Relating Factors and Multiples II (4.OA.4)

CCSS Addressed: ✓ 4.OA.4

G. Division of Thousands, Hundreds, Tens, and Ones

4.NBT.6, 4.OA.3, 4.NBT.1

Dividing by Multiples of Ten (4.NBT.6)

CCSS Addressed: ✓ 4.OA.3 * | ✓ 4.NBT.1 * | ✓ 4.NBT.6

H. Multiplication of Two-Digit by Two-Digit Numbers

4.NBT.5, 4.OA.3, 4.MD.3

Multiplying Two-digit Numbers by Two-digit Numbers (4.NBT.5)

CCSS Addressed: ✓ 4.OA.3 * | ✓ 4.NBT.5 | ✓ 4.MD.3 *

## MODULE 4: Angle Measure and Plane Figures

**EUREKA MATH / ENGAGE NY TOPIC**

A. Lines and Angles

4.G.1

**THINK THROUGH MATH LESSON** (CCSS)

Identifying and Classifying Lines, Rays, and Segments (4.G.1)

CCSS Addressed: ✓ 4.G.1

B: Angle Measurement

C: Problem Solving with the Addition of Angle Measures

4.MD.5, 4.MD.5a, 4.MD.5b, 4.MD.6, 4.MD.7

Identifying and Comparing Angles (4.MD.5)

Angles (4.MD.5a, 4.MD.5b, 4.MD.6, 4.MD.7)

CCSS Addressed: ✓ 4.MD.5 | ✓ 4.MD.6 | ✓ 4.MD.7

D: Two-Dimensional Figures and Symmetry

4.G.1, 4.G.2, 4.G.3

Classifying Triangles (4.G.1, 4.G.2)

Classifying Quadrilateral II (4.G.1, 4.G.2)

Symmetry (4.G.3)

CCSS Addressed: ✓ 4.G.1 | ✓ 4.G.2 | ✓ 4.G.3

## MODULE 5: Fraction Equivalence, Ordering, and Operations

**EUREKA MATH / ENGAGE NY TOPIC**

A: Decomposition and Fraction Equivalence

B: Fraction Equivalence Using Multiplication and Division

4.NF.1 4.NF.3b, 4.NF.4a

**THINK THROUGH MATH LESSON** (CCSS)

Modeling Equivalent Fractions (4.NF.1)

Generating Equivalent Fractions (4.NF.1)

Reducing Fractions (4.NF.1)

CCSS Addressed: ✓ 4.NF.1 | ✓ 4.NF.3a * | ✓ 4.NF.3b * | ✓ 4.NF.4a *

C: Fraction Comparison

4.NF.2

Comparing Fractions – Visual Models (4.NF.2)

Comparing Fractions with Different Numerators and Different Denominators (4.NF.2)

Recognizing Valid Fraction Comparisons II (4.NF.2)

CCSS Addressed: ✓ 4.NF.2

D: Fraction Addition and Subtraction

4.NF.3a, 4.NF.3d

Adding and Subtracting Fractions with Like Denominators (4.NF.3a)

Adding and Subtracting Fractions with Like Denominators in Real-World Situations (4.NF.3a)

CCSS Addressed: ✓ 4.NF.1 * | ✓ 4.NF.3a | ✓ 4.NF.3d

E. Extending Fraction Equivalence to Fractions Greater than 1

4.NF.1, 4.NF.2, 4.NF.3, 4.NF.3a, 4.NF.3b, 4.NF.3c, 4.NF.3d, 4.MD.4, 4.NBT.6, 4.NF.4a

Decomposing Fractions and Mixed Numbers (4.NF.3b)

Writing Fractions as Mixed Numbers and Mixed Numbers as Fractions (4.NF.3b)

Understanding Fractions – Relationship Between Numerator and Denominator (4.NF.1)

CCSS Addressed: ✓ 4.NF.1 | ✓ 4.NF.2 * | ✓ 4.NF.3 | ✓ 4.NF.4a * | ✓ 4.NBT.6 * | 4.MD.4

F. Addition and Subtraction of Fractions by Decomposition

4.NF.3c, 4.NF.3d, 4.MD.4

Word Problems with Fractions and Mixed Numbers – Visual Models (4.NF.3d)

Word Problems with Fractions and Mixed Numbers – Estimation (4.NF.3d)

Adding and Subtracting Mixed Numbers with Like Denominators – Conceptual Strategies (4.NF.3c)

Adding and Subtracting Mixed Numbers with Like Denominators (4.NF.3c)

CCSS Addressed: ✓ 4.NF.3c | ✓ 4.NF.3d

G. Repeated Addition of Fractions as Multiplication

4.NF.4a, 4.NF.4c, 4.NF.4b, 4.MD.4, 4.MD.2, 4.NF.4, 4.OA.2

Multiplying Unit Fractions by Whole Numbers (4.NF.4a)

Multiplying Fractions by Whole Numbers (4.NF.4b)

Solving Word Problems with Multiplication of Fractions by Whole Numbers (4.NF.4c)

CCSS Addressed: ✓ 4.OA.2 | ✓ 4.NF.4

H. Exploring a Fraction Pattern

4.OA.5

Generating and Describing Number Patterns (4.OA.5)

CCSS Addressed: ✓ 4.OA.5

## MODULE 6: Decimal Fractions

**EUREKA MATH / ENGAGE NY TOPIC**

A: Exploration of Tenths

B: Tenths and Hundredths

4.NF.1, 4.NF.7, 4.NF.5, 4.NF.6, 4.NBT.1, 4.MD.1

**THINK THROUGH MATH LESSON** (CCSS)

Understanding Fractions with Denominators of 10 and 100 (4.NF.5)

Adding Fractions with Denominators of 10 and 100 (4.NF.5)

Comparing Decimal Fractions (4.NF.6)

Comparing and Ordering Decimal Fractions (4.NF.6)

Decimal Notation I (4.NF.6)

Decimal Notation II (4.NF.6)

Decimals to Hundredths (4.NF.7)

CCSS Addressed: ✓ 4.NBT.1 * | ✓ 4.NF.1 * | ✓ 4.NF.5 | ✓ 4.NF.6 | ✓ 4.NF.7 | ✓ 4.MD.1 *

C: Decimal Comparison

4.NF.7, 4.MD.1, 4.MD.2

Introduction to Comparing Decimals to Hundredths (4.NF.7)

Comparing Decimals to Hundredths (4.NF.7)

Recognizing Valid Decimal Comparisons (4.NF.7)

CCSS Addressed: ✓ 4.MD.1 * | ✓ 4.NF.7

D: Addition with Tenths and Hundredths

4.NF.5, 4.NF.6, 4.NF.3c, 4.MD.1

Fraction and Decimal Equivalents (4.NF.6)

Comparing Fractions and Decimals (4.NF.6)

CCSS Addressed: ✓ 4.NF.3c * | ✓ 4.NF.5 * | ✓ 4.NF.6 | ✓ 4.MD.1 *

E: Money Amount as Decimal Numbers

4.MD.2, 4.NF.5, 4.NF.6

N/A

CCSS Addressed: ✓ 4.NF.5 * | ✓ 4.NF.6 *

*TTM currently teaches money and decimals in the 5th grade as part of a lesson covering the addition and subtraction of decimals in real-world situations.*

## MODULE 7: Exploring Measurement with Multiplication

**EUREKA MATH / ENGAGE NY TOPIC**

A: Measurement Conversion Tables

B: Problem Solving with Measurement

C: Investigation of Measurements Expressed as Mixed Numbers

4.OA.1, 4.OA.2, 4.OA.3, 4.MD.1, 4.MD.2, 4.NBT.5, 4.NBT.6

**THINK THROUGH MATH LESSON** (CCSS)

Units of Measure – Customary (4.MD.1)

Units of Measure – Metric (4.MD.1)

CCSS Addressed: ✓ 4.OA.1 * | ✓ 4.OA.2 * | ✓ 4.OA.3 * | ✓ 4.NBT.5 * | ✓ 4.NBT.6 * | ✓ 4.MD.1

Year in Review

N/A

N/A

## Grade 5

**EUREKA MATH / ENGAGE NY TOPIC**

Warm-up Lesson

**THINK THROUGH MATH LESSON**

Operations with Whole Numbers – Mixed Practice (Review)

## MODULE 1: Place Value and Decimal Fractions

**EUREKA MATH / ENGAGE NY TOPIC**

A. Multiplicative Patterns on the Place Value Chart

5.NBT.1, 5.NBT.2, 5.MD.1

**THINK THROUGH MATH LESSON** (CCSS)

Understanding Place Value Relationships (4.NBT.1)

Place Value Relationships Within Whole Numbers and Decimals (5.NBT.1)

Multiplying by Powers of Ten (5.NBT.2)

Multiplying and Dividing by Powers of Ten (5.NBT.2)

CCSS Addressed: ✓ 5.NBT.1 | ✓ 5.NBT.2

B: Decimal Fractions and Place Value Patterns

5.NBT.3a, 5.NBT.3b

Decimals To Thousandths (5.NBT.3a)

Comparing Fractions and Decimals (5.NBT.3a)

Comparing Decimals to Thousandths (5.NBT.3b)

CCSS Addressed: ✓ 5.NBT.3

C: Place Value and Rounding Decimal Fractions

5.NBT.4

Rounding Decimals to the Nearest Tenth and Hundredth (5.NBT.4)

Reasoning About Rounding Decimals (5.NBT.4)

CCSS Addressed: ✓ 5.NBT.4

D. Adding and Subtracting Decimals

5.NBT.2, 5.NBT.3a, 5.NBT.3b, 5.NBT.7

Adding and Subtracting Decimals (5.NBT.7)

CCSS Addressed: ✓ 5.NBT.2 * | ✓ 5.NBT.3 * | ✓ 5.NBT.7

E. Multiplying Decimals

5.NBT.2, 5.NBT.3a, 5.NBT.3b, 5.NBT.7

Multiplying Decimals to Hundredths (5.NBT.7)

CCSS Addressed: ✓ 5.NBT.2 * | ✓ 5.NBT.3 * | ✓ 5.NBT.7

F: Dividing Decimals

5.NBT.3a, 5.NBT.3b, 5.NBT.7

Dividing Decimals to Hundredths (5.NBT.7)

CCSS Addressed: ✓ 5.NBT.3 * | ✓ 5.NBT.7

## MODULE 2: Multi-digit Whole Number and Decimal Fraction Operations

**EUREKA MATH / ENGAGE NY TOPIC**

A: Mental Strategies for Multi-Digit Whole Number Multiplication

5.NBT.1, 5.NBT.2, 5.OA.1

**THINK THROUGH MATH LESSON** (CCSS)

Multiplying by Powers of Ten (5.NBT.2)

Evaluating Simple Expressions (5.OA.1)

CCSS Addressed: ✓ 5.OA.1 | ✓ 5.NBT.1 * | ✓ 5.NBT.2

B: The Standard Algorithm for Multi-Digit Whole Number Multiplication

5.OA.1, 5.OA.2, 5.NBT.5

Multiplying Whole Numbers – Standard Algorithm (5.NBT.5)

CCSS Addressed: ✓ 5.OA.1 * | ✓ 5.OA.2 * | ✓ 5.NBT.5

C: Decimal Multi-Digit Multiplication

G: Partial Quotients and Multi-Digit Decimal Division

5.NBT.2, 5.NBT.7, 5.NBT.1, 5.OA.1, 5.OA.2

Using Reasoning and Estimation to Calculate with Decimals (5.NBT.7)

CCSS Addressed: ✓ 5.OA.1 * | ✓ 5.OA.2 * | ✓ 5.NBT.1 * | ✓ 5.NBT.2 * | ✓ 5.NBT.7

D: Measurement Word Problems with Whole Number and Decimal Multiplication

H: Measurement Word Problems with Multi-Digit Division

5.NBT.1, 5.NBT.2, 5.NBT.5, 5.NBT.6, 5.NBT.7, 5.MD.1

Adding and Subtracting Decimals in Real-World Situations (5.NBT.7)

Calculating with Decimals (5.NBT.7)

CCSS Addressed: ✓ 5.NBT.1 * | ✓ 5.NBT.2 * | ✓ 5.NBT.5 * | ✓ 5.NBT.6 * | ✓ 5.NBT.7

E: Mental Strategies for Multi-Digit Whole Number Division

F: Partial Quotients and Multi-Digit Whole Number Division

5.NBT.1, 5.NBT.2, 5.NBT.6

Dividing Whole Numbers – Two Digit Divisors (5.NBT.6)

CCSS Addressed: ✓ 5.NBT.1 * | ✓ 5.NBT.2 * | ✓ 5.NBT.6

## MODULE 3: Addition and Subtraction of Fractions

**EUREKA MATH / ENGAGE NY TOPIC**

A. Equivalent Fractions

4.NF.1

**THINK THROUGH MATH LESSON** (CCSS)

Modeling Equivalent Fractions (4.NF.1)

Generating Equivalent Fractions (4.NF.1)

Understanding Fractions – Relationship Between Numerator and Denominator (4.NF.1)

CCSS Addressed: ✓ 4.NF.1 | ✓ 4.NF.3c | ✓ 4.NF.3d

B: Making Like Units Pictorially

C: Making Like Units Numerically

5.NF.1, 5.NF.2

Adding Fractions (5.NF.1)

Subtracting Fractions (5.NF.1)

Adding and Subtracting Fractions (5.NF.1, 5.NF.2)

Adding and Subtracting Fractions – Multi-step Word Problems (5.NF.1, 5.NF.2)

CCSS Addressed: ✓ 5.NF.1 | ✓ 5.NF.2

D. Further Applications

5.NF.1, 5.NF.2

Adding Fractions – Estimation Strategies (5.NF.2)

Subtracting Fractions – Estimation Strategies (5.NF.2)

CCSS Addressed: ✓ 5.NF.1 * | ✓ 5.NF.2

## MODULE 4: Multiplication and Division of Fractions and Decimal Fractions

**EUREKA MATH / ENGAGE NY TOPIC**

A. Line Plots of Fraction Measurements

5.MD.2

**THINK THROUGH MATH LESSON** (CCSS)

Line Plots (5.MD.2)

CCSS Addressed: ✓ 5.MD.2

B. Fractions as Division

5.NF.3

Understanding Fractions as Division (5.NF.3)

CCSS Addressed: ✓ 5.NF.3

C: Multiplication of a Whole Number by a Fraction

D: Fraction Expressions and Word Problems

5.OA.1, 5.OA.2, 5.NF.4a, 5.NF.6

Multiplying Fractions by Whole Numbers to Solve Multi-step Problems (5.NF.4, 5.NF.6)

CCSS Addressed: ✓ 5.OA.1 * | ✓ 5.OA.2 * | ✓ 5.NF.4a | ✓ 5.NF.6

E: Multiplication of a Fraction by a Fraction

F: Multiplication with Fractions and Decimals as Scaling and Word Problems

5.NBT.7, 5.NF.4a, 5.NF.4b, 5.NF.5a, 5.NF.5b, 5.NF.6, 5.MD.1

Understanding Products with Fractions (5.NF.4, 5.NF.5a, 5.NF.5b)

Multiplying Fractions by Fractions (5.NF.4)

Fraction and Decimal Equivalents (5.NBT.3a)

CCSS Addressed: ✓ 5.NBT.7 * | ✓ 5.NF.4a | ✓ 5.NF.6 *

G. Division of Fractions and Decimal Fractions

5.OA.1, 5.NF.7a, 5.NF.7b, 5.NF.7c

Dividing Unit Fractions by Whole Numbers (5.NF.7a, 5.NF.7c)

Dividing Whole Numbers by Unit Fractions (5.NF.7b, 5.NF.7c)

CCSS Addressed: ✓ 5.OA.1 * | ✓ 5.NBT.7 * | ✓ 5.NF.7

H. Interpretation of Numerical Expressions

5.OA.1, 5.OA.2

Evaluating Simple Expressions (5.OA.1)

Writing Simple Expressions (5.OA.2)

Writing and Interpreting Simple Expressions (5.OA.2)

CCSS Addressed: ✓ 5.OA.1 | ✓ 5.OA.2

## MODULE 5: Addition and Multiplication with Volume and Area

**EUREKA MATH / ENGAGE NY TOPIC**

A. Concepts of Volume

5.MD.3a, 5.MD.3b, 5.MD.4

**THINK THROUGH MATH LESSON** (CCSS)

Volume of Rectangular Prisms I (5.MD.3a, 5.MD.3b, 5.MD.4)

CCSS Addressed: ✓ 5.MD.3 | ✓ 5.MD.4

B. Volume and the Operations of Multiplication and Addition

5.MD.3a, 5.MD.3b, 5.MD.5a, 5.MD.5b, 5.MD.5c

Volume of Rectangular Prisms II (5.MD.5a, 5.MD.5b, 5.MD.5c)

CCSS Addressed: ✓ 5.MD.3 * | ✓ 5.MD.5

C. Area of Rectangular Figures with Fractional Side Lengths

5.NF.4b, 5.NF.6

Multiplying with Fractions and Mixed Numbers (5.NF.6)

CCSS Addressed: ✓ 5.NF.4b * | ✓ 5.NF.6

D. Drawing, Analysis, and Classification of Two-Dimensional Shapes

5.G.3, 5.G.4

Classifying Quadrilaterals II (5.G.3, 5.G.4)

Classifying 2-Dimensional Figures (5.G.3, 5.G.4)

Classifying Triangles (5.G.4)

CCSS Addressed: ✓ 5.G.3 | ✓ 5.G.4

## MODULE 6: Problem Solving with the Coordinate Plane

**EUREKA MATH / ENGAGE NY TOPIC**

A. Coordinate Systems

5.G.1

**THINK THROUGH MATH LESSON** (CCSS)

Introduction to the Coordinate Plane (5.G.1)

CCSS Addressed: ✓ 5.G.1

B. Patterns in the Coordinate Plane and Graphing Number Patterns from Rules

5.OA.2, 5.OA.3, 5.G.1

Introduction to Scatter Plots (5.G.1)

CCSS Addressed: ✓ 5.OA.2 | ✓ 5.G.1 *

C. Drawing Figures in the Coordinate Plane

5.G.1, 5.G.2

N/A

*TTM does not currently have a fifth grade appropriate lesson covering the construction of parallel and perpendicular lines on the coordinate grid.*

CCSS Addressed: ✓ 5.G.1 * | ✓ 5.G.2 *

D. Problem Solving in the Coordinate Plane

5.G.2, 5.OA.3

Representing Real-World Quantities in the First Quadrant (5.G.2)

CCSS Addressed: ✓ 5.G.2 *

E. Multi-Step Word Problems

5.NF.2, 5.NF.3, 5.NF.6, 5.NF.7c, 5.MD.1, 5.MD.5, 5.G.2

Adding and Subtracting Fractions – Multi-step Word Problems (5.NF.1, 5.NF.2)

Multiplying Fractions by Whole Numbers to Solve Multi-step Problems (5.NF.4, 5.NF.6)

CCSS Addressed: ✓ 5.NF.2 | ✓ 5.NF.3 * | ✓ 5.NF.6 | ✓ 5.NF.7c * | ✓ 5.MD.5 * | ✓ 5.G.2 *

F. The Year in Review: A Reflection on “A Story of Units”

N/A

N/A

## Grade 6

## MODULE 1: Ratios and Unit Rates

A. Representing and Reasoning About Ratios

6.RP.1, 6.RP.3

Identifying Ratios (6.RP.1)

Ratios (6.RP.1, 6.RP.3)

Concept of Ratios and Rates (6.RP.1, 6.RP.2)

CCSS Addressed: ✓ 6.RP.1 | ✓ 6.RP.3a

B. Collections of Equivalent Ratios

6.RP.3.a

Using Ratios to Solve Problems (6.RP.3.a)

CCSS Addressed: ✓ 6.RP.3a

C. Unit Rates

6.RP.2, 6.RP.3.b, 6.RP.3.d

Identifying Unit Rates (6.RP.1, 6.RP.2)

Solving Problems with Unit Rates (6.RP.1, 6.RP.2, 6.RP.3.b)

Converting Units of Measure I (6.RP.3.d)

Converting Units of Measure II (6.RP.3.d)

Distance, Rate, and Time (6.RP.3.b)

CCSS Addressed: ✓ 6.RP.2 | ✓ 6.RP.3b | ✓ 6.RP.3d

D. Percent

6.RP.3.c

Percent Concepts (6.RP.3.c)

Reasoning with Percents (6.RP.3.c)

Calculations with Percent (6.RP.3.c)

CCSS Addressed: ✓ 6.RP.3c

## MODULE 2: Arithmetic Operations Including Division of Fractions

**EUREKA MATH / ENGAGE NY TOPIC**

A. Arithmetic Operations Including Dividing by a Fraction

6.NS.1

**THINK THROUGH MATH LESSON** (CCSS)

Using the Relationship Between Multiplication and Division to Divide Fractions (6.NS.1)

Dividing Fractions by Fractions (6.NS.1)

Using Division of Fractions to Represent and Solve Problems (6.NS.1)

Operations with Fractions – Mixed Practice (6.NS.1)

CCSS Addressed: ✓ 6.NS.1

B. Multi-Digit Decimal Operations – Adding, Subtracting, and Multiplying

C: Dividing Whole Numbers and Decimals

6.NS.2, 6.NS.3

Dividing Whole Numbers – Standard Algorithm (6.NS.2)

Adding and Subtracting Decimals (6.NS.3)

Adding and Subtracting Decimals in Real-World Situations (6.NS.3)

Using Reasoning and Estimation to Calculate with Decimals (6.NS.3)

Calculating with Decimals (6.NS.3)

CCSS Addressed: ✓ 6.NS.2 | ✓ 6.NS.3

D. Number Theory – Thinking Logically About Multiplicative Arithmetic

6.NS.4

Greatest Common Factor (6.NS.4)

Greatest Common Factor – Applications (6.NS.4)

Least Common Multiple (6.NS.4)

CCSS Addressed: ✓ 6.NS.4

## MODULE 3: Rational Numbers

**EUREKA MATH / ENGAGE NY TOPIC**

A. Understanding Positive and Negative Numbers on the Number Line

6.NS.5, 6.NS.6.a, 6.NS.6.c

**THINK THROUGH MATH LESSON** (CCSS)

Integer Concepts (6.NS.5, 6.NS.6.c)

Integer Concepts with a Number Line (6.NS.6.a, 6.NS.6.c)

CCSS Addressed: ✓ 6.NS.5 | ✓ 6.NS.6a | ✓ 6.NS.6c

B: Order and Absolute Value

C: Rational Numbers and the Coordinate Plane

6.NS.6.b, 6.NS.6.c, 6.NS.7, 6.NS.7.a, 6.NS.7.b, 6.NS.7.c, 6.NS.7.d 6.NS.8

Integers in the Coordinate Plane I (6.NS.6.b)

Integers in the Coordinate Plane II (6.NS.6.b)

Comparing Rational Numbers I (6.NS.6.c)

Comparing Rational Numbers II (6.NS.7.a, 6.NS.7.b)

Rational Numbers in the Coordinate Plane I (6.NS.6.c)

Rational Numbers in the Coordinate Plane II (6.NS.6.b, 6.RP.3.a, 6.NS.8)

Absolute Value I (6.NS.7.c)

Absolute Value II (6.NS.7.d)

CCSS Addressed: ✓ 6.NS.6b | ✓ 6.NS.6c | ✓ 6.NS.7 | ✓ 6.NS.8

## MODULE 4: Expressions and Equations

**EUREKA MATH / ENGAGE NY TOPIC**

A: Relationships of the Operations

B: Special Notations of Operations

C: Replacing Letters and Numbers

6.EE.1, 6.EE.2.c, 6.EE.3, 6.EE.4

**THINK THROUGH MATH LESSON** (CCSS)

Identifying and Generating Equivalent Expressions (6.EE.3, 6.EE.4)

Evaluating Simple Expressions (6.EE.2.c)

Evaluating Expressions with Two Operations (6.EE.2.c)

Understanding Exponents (6.EE.1)

Evaluating Expressions and Equations with Exponents (6.EE.1, 6.EE.2.c)

CCSS Addressed: ✓ 6.EE.1 | ✓ 6.EE.2c | ✓ 6.EE.3 | ✓ 6.EE.4

D: Expanding, Factoring, and Distributing Expressions

E: Expressing Operations in Algebraic Form

F: Writing and Evaluating Expressions and Formulas

6.EE.2.a, 6.EE.2.b, 6.EE.3, 6.EE.4, 6.EE.6

Evaluating Expressions with Real Numbers (6.ee.2.b)

Evaluating Expressions with the Distributive Property (6.EE.3)

Using the Distributive Property to Represent Real-World Situations (6.EE.3)

Introduction to the Language of Algebra (6.EE.2.a, 6.EE.6)

Combining Like Terms (6.EE.3, 6.EE.4)

CCSS Addressed: ✓ 6.EE.2a | ✓ 6.EE.2b | ✓ 6.EE.2c * | ✓ 6.EE.3 | ✓ 6.EE.4 | ✓ 6.EE.6

G: Solving Equations

H: Applications of Equations

6.EE.5, 6.EE.6, 6.EE.7, 6.EE.8, 6.EE.9

Reasoning About One-Step Equations (6.EE.5)

Writing and Solving One-Step Equations (6.EE.7)

Independent and Dependent Quantities (6.EE.9)

Introduction to the Language of Algebra (6.EE.2.a, 6.EE.6)

Introduction to Solving Word Problems with Algebra (6.EE.7)

Concept of Inequalities (6.EE.8)

CCSS Addressed: ✓ 6.EE.5 | ✓ 6.EE.6 | ✓ 6.EE.7 | ✓ 6.EE.8 | ✓ 6.EE.9

## MODULE 5: Area, Surface Area, and Volume Problems

**EUREKA MATH / ENGAGE NY TOPIC**

A. Area of Triangles, Quadrilaterals, and Polygons

6.G.1

**THINK THROUGH MATH LESSON** (CCSS)

Area of Parallelograms (6.G.1)

Area of Triangles (6.G.1)

Area of Trapezoids and Composite Figures (6.G.1)

CCSS Addressed: ✓ 6.G.1

B. Polygons on the Coordinate Plane

6.G.3

Distance on the Coordinate Plane I (6.G.3)

Distance on the Coordinate Plane II (6.NS.8)

CCSS Addressed: ✓ 6.G.3

C: Volume of Right Rectangular Prisms

D: Nets and Surface Area

6.G.2, 6.G.4

Surface Area and Volume of Rectangular Prisms (6.G.2, 6.G.4)

CCSS Addressed: ✓ 6.G.2 | ✓ 6.G.4

## MODULE 6: Statistics

**EUREKA MATH / ENGAGE NY TOPIC**

A. Understanding Distributions

6.SP.1, 6.SP.2, 6.SP.3, 6.SP.4, 6.SP.5b

**THINK THROUGH MATH LESSON** (CCSS)

Data Analysis (6.SP.1)

Measures of Spread – Range (6.SP.2, 6.SP.3)

Measures of Spread – Median (6.SP.2, 6.SP.5.c)

Measures of Center – Mean (6.SP.2, 6.SP.5.c)

Line Plots (5.MD.2)

Bar Graphs and Histograms (6.SP.4)

Circle Graphs (6.SP.4, 6.RP.3.c)

Stem-and-Leaf Plots (6.SP.2, 6.SP.4, 6.SP.5.c)

CCSS Addressed: ✓ 6.SP.1 | ✓ 6.SP.2 | ✓ 6.SP.4 | ✓ 6.SP.5b *

B: Summarizing a Distribution that is Approximately Symmetric Using the Mean and Mean Absolute Deviation

C: Summarizing a Distribution that is Skewed Using the Median and the Interquartile Range

D: Summarizing and Describing Distributions

6.SP.2, 6.SP.3, 6.SP.4, 6.SP.5, 6.SP.5a, 6.SP.5b, 6.SP.5c, 6.SP.5d

Understanding the Effects of Outliers on Mean and Median (6.SP.3)

Deviation from the Mean (6.SP.5.c, 6.SP.5.d)

Quartiles (6.SP.2, 6.SP.3)

Box Plots (6.SP.2, 6.SP.4, 6.SP.5.c)

Summarizing Data (6.SP.2, 6.SP.5.a, 6.SP.5.b, 6.SP.5.c, 6.SP.5.d)

CCSS Addressed: ✓ 6.SP.2 | ✓ 6.SP.3 | ✓ 6.SP.4 | ✓ 6.SP.5

## Grade 7

## MODULE 1: Ratios and Proportional Relationships

**EUREKA MATH / ENGAGE NY TOPIC**

A. Proportional Relationships

7.RP.2.a

**THINK THROUGH MATH LESSON** (CCSS)

Proportion Concepts (7.RP.2a, 7.RP.2c)

Proportional Relationships in Tables and Equations (7.RP.2a, 7.RP.2c)

CCSS Addressed: ✓ 7.RP.2a

B. Unit Rate and Constant of Proportionality

7.RP.2.b, 7.RP.2.c, 7.RP.2.d, 7.EE.4.a

Interpreting Unit Rates on Graphs (7.RP.2b)

Interpreting Points on Graphs of Proportional Relationships (7.RP.1, 7.RP.2d)

CCSS Addressed: ✓ 7.RP.2b | ✓ 7.RP.2c * | ✓ 7.RP.2d | ✓ 7.EE.4a *

C: Ratios and Rates Involving Fractions

D: Ratios of Scale Drawings

7.RP.1, 7.RP.2, 7.RP.2b 7.RP.3, 7.EE.4, 7.EE.4.a, 7.G.1

Using Proportions to Solve Problems (7.RP.3, 7.G.1)

Proportions in Scale Drawings (7.RP.3, 7.G.1)

Introduction to Similar Figures (7.RP.2c, 7.G.1)

Using Similar Figures to Solve Problems (7.RP.2c, 7.G.1)

Similarity (7.G.1)

CCSS Addressed: ✓ 7.RP.1 * | ✓ 7.RP.2b * | ✓ 7.RP.3 | ✓ 7.EE.4a * | ✓ 7.G.1

## MODULE 2: Rational Numbers

**EUREKA MATH / ENGAGE NY TOPIC**

A. Rational Numbers

7.NS.1.a

**THINK THROUGH MATH LESSON** (CCSS)

Adding and Subtracting Rational Numbers I (7.NS.1a, 7.NS.1b, 7.NS.1d)

Adding and Subtracting Rational Numbers II (7.NS.1c)

CCSS Addressed: ✓ 7.NS.1

B. Multiplication and Division of Integers and Rational Numbers

7.NS.2.a

Multiplying and Dividing Rational Numbers (7.NS.2a, 7.NS.2b, 7.NS.2c, 7.NS.2d)

Understanding and Multiplying with Negative Mixed Numbers (7.NS.2c)

CCSS Addressed: ✓ 7.NS.2

C: Applying Operations with Rational Numbers to Expressions and Equations

7.NS.3, 7.EE.2, 7.EE.4.a

Solving and Modeling Two-Step Problems (7.EE.4a)

Solving Equations with the Distributive Property (7.EE.4a)

Solving Equations with the Distributive Property in Context (7.EE.4a)

Writing and Interpreting Expressions with Rational Numbers (7.NS.3, 7.EE.3)

Operations with Rational Numbers I (7.NS.3)

Operations with Rational Numbers II (7.NS.3)

Solving Word Problems with Algebra (7.EE.2)

CCSS Addressed: ✓ 7.NS.3 | ✓ 7.EE.2 | ✓ 7.EE.4a

## MODULE 3: Expressions and Equations

**EUREKA MATH / ENGAGE NY TOPIC**

A: Use Properties of Operations to Generate Equivalent Expressions

7.EE.1, 7.EE.2

**THINK THROUGH MATH LESSON** (CCSS)

Common Factors in Polynomials (7.EE.1)

CCSS Addressed: ✓ 7.EE.1 | ✓ 7.EE.2 *

B: Solve Problems Using Expressions, Equations, and Inequalities

7.EE.3, 7.EE.4, 7.G.5

Angle Pairs (7.G.5)

Angles in a Polygon (7.G.5)

Writing and Interpreting Expressions with Rational Numbers (7.NS.3, 7.EE.3)

Concept of Inequalities II (7.EE.4b)

CCSS Addressed: ✓ 7.EE.3 | ✓ 7.EE.4 | ✓ 7.G.5

C: Use Equations and Inequalities to Solve Geometry Problems

7.G.4, 7.G.6

Circumference (7.G.4)

Area of Circles (7.G.4)

Area of Complex Composite Figures (7.G.6)

Surface Area of Cylinders (7.G.4, 7.G.6)

Surface Area of Pyramids (7.G.6)

Surface Area of Cones (7.G.4, 7.G.6)

Surface Area of Spheres (7.G.6)

Surface Area of Composite Solids (7.G.4, 7.G.6)

Surface Area and Volume of Rectangular Prisms (7.G.6)

CCSS Addressed: ✓ 7.G.4 | ✓ 7.G.6

## MODULE 4: Percent and Proportional Relationships

**EUREKA MATH / ENGAGE NY TOPIC**

A: Finding the Whole

C: Scale Drawings

7.RP.1, 7.RP.2, 7.RP.2b, 7.RP.2.c, 7.RP.3, 7.G.1

**THINK THROUGH MATH LESSON** (CCSS)

Interpreting Points on Graphs of Proportional Relationships (7.RP.1, 7.RP.2d)

Using Proportions to Solve Problems (7.RP.3, 7.G.1)

Proportions in Scale Drawings (7.RP.3, 7.G.1)

Introduction to Similar Figures (7.RP.2c, 7.G.1)

Using Similar Figures to Solve Problems (7.RP.2c, 7.G.1)

Similarity (7.G.1)

Using Division to Write Fractions as Decimals (7.NS.2d)

Percent and Percent Change (7.RP.3)

Percent and Percent Error (7.RP.3)

CCSS Addressed: ✓ 7.RP.1 | ✓ 7.RP.2b * | ✓ 7.RP.2c | ✓ 7.RP.3 | ✓ 7.G.1

B: Percent Problems Including More than One Whole

D: Population, Mixture, and Counting Problems Involving Percents

7.RP.1, 7.RP.2, 7.RP.2c, 7.RP.3, 7.EE.3

Fraction, Decimal, and Percent Equivalents (7.EE.3)

Simple Interest (7.RP.3)

CCSS Addressed: ✓ 7.RP.1 * | ✓ 7.RP.2 * | ✓ 7.RP.2c * | ✓ 7.RP.3 | ✓ 7.EE.3

## MODULE 5: Statistics and Probability

**EUREKA MATH / ENGAGE NY TOPIC**

A: Calculating and Interpreting Probabilities

B: Estimating Probabilities

7.SP.5, 7.SP.6, 7.SP.7, 7.SP.7a, 7.SP.7b 7.SP.8.a, 7.SP.8.b 7.SP.8c

**THINK THROUGH MATH LESSON** (CCSS)

Probability and Sample Spaces (7.SP.5, 7.SP.8b)

Simple Probability (7.SP.5, 7.SP.7b)

Compound Probability (7.SP.5, 7.SP.7a, 7.SP.8a, 7.SP.8b)

Simulations of Simple and Compound Events (7.SP.8c)

Making Predictions (7.SP.6)

CCSS Addressed: ✓ 7.SP.5 | ✓ 7.SP.6 | ✓ 7.SP.7 | ✓ 7.SP.8a | ✓ 7.SP.8b | ✓ 7.SP.8c

C: Random Sampling and Estimating Population Characteristics

D: Comparing Populations

7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4

Sampling (7.SP.2, 7.SP.4)

Comparing Data (7.SP.3)

CCSS Addressed: ✓ 7.SP.2 | ✓ 7.SP.3 | ✓ 7.SP.4

## MODULE 6: Geometry

**EUREKA MATH / ENGAGE NY TOPIC**

A. Unknown Angles

7.G.5

**THINK THROUGH MATH LESSON** (CCSS)

Angle Pairs (7.G.5)

Angles in a Polygon (7.G.5)

CCSS Addressed: ✓ 7.G.5

B: Constructing Triangles

7.G.2

Using Line Segments and Angles to Make Triangles (7.G.2)

CCSS Addressed: ✓ 7.G.2

C: Slicing Solids

7.G.3

N/A

*TTM does not currently cover 7.G.3*

D. Problems Involving Area and Surface Area

7.G.6

Circumference (7.G.4)

Area of Circles (7.G.4)

Area of Complex Composite Figures (7.G.6)

Surface Area of Cylinders (7.G.4, 7.G.6)

Surface Area of Pyramids (7.G.6)

Surface Area of Cones (7.G.4, 7.G.6)

Surface Area of Spheres (7.G.6)

Surface Area of Composite Solids (7.G.4, 7.G.6)

CCSS Addressed: ✓ 7.G.6

E. Problems Involving Volume

7.G.6

Surface Area and Volume of Rectangular Prisms (7.G.6)

Volume of Cylinders (8.G.9)

Volume of Pyramids and Cones (8.G.9)

Volume of Spheres (8.G.9)

Volume of Composite Solids (8.G.9)

CCSS Addressed: ✓ 7.G.6

## Grade 8

## MODULE 1: Integer Exponents and Scientific Notation

**EUREKA MATH / ENGAGE NY TOPIC**

A: Exponential Notation and Properties of Integer Exponents

8.EE.1

**THINK THROUGH MATH LESSON** (CCSS)

Understanding Properties of Integer Exponents (8.EE.1)

Applying Properties of Integer Exponents (8.EE.1)

CCSS Addressed: ✓ 8.EE.1

B: Magnitude and Scientific Notations

8.EE.3, 8.EE.4

Interpreting Numbers Written in in Scientific Notation (8.EE.3)

Operations with Numbers in Scientific Notation (8.EE.4)

CCSS Addressed: ✓ 8.EE.3 | ✓ 8.EE.4

## MODULE 2: The Concept of Congruence

**EUREKA MATH / ENGAGE NY TOPIC**

A: Definitions and Properties of the Basic Rigid Motions

B: Sequencing the Basic Rigid Motions

8.G.1, 8.G.1.a, 8.G.1.b, 8.G.1.c, 8.G.2

**THINK THROUGH MATH LESSON** (CCSS)

Translations (8.G.2, 8.G.3, 8.G.4)

Reflections (8.G.2, 8.G.3, 8.G.4)

Rotations (8.G.2, 8.G.3, 8.G.4)

Composition of Transformations (8.G.2, 8.G.3, 8.G.4)

CCSS Addressed: ✓ 8.G.2

C: Congruence and Angle Relationships

8.G.2, 8.G.5

Angles in a Polygon (8.G.5)

Parallel Lines and Transversals (8.G.5)

Congruence (8.G.2)

CCSS Addressed: ✓ 8.G.2 | ✓ 8.G.5

D: The Pythagorean Theorem (Optional)

8.G.6, 8.G.7

Understanding the Pythagorean Theorem (8.G.6)

Pythagorean Theorem – Hypotenuse (8.G.7)

Pythagorean Theorem – Legs (8.G.7)

Pythagorean Theorem – Mixed Problems (8.G.7)

Pythagorean Theorem – Distance Formula (8.G.7, 8.G.8)

CCSS Addressed: ✓ 8.G.6 | ✓ 8.G.7

## MODULE 3: Similarity

**EUREKA MATH / ENGAGE NY TOPIC**

A: Dilation

8.G.3

**THINK THROUGH MATH LESSON** (CCSS)

Dilations (8.G.3, 8.G.4)

CCSS Addressed: ✓ 8.G.3

B: Similar Figures

8.G.4, 8.G.5

Translations (8.G.2, 8.G.3, 8.G.4)

Reflections (8.G.2, 8.G.3, 8.G.4)

Rotations (8.G.2, 8.G.3, 8.G.4)

Composition of Transformations (8.G.2, 8.G.3, 8.G.4)

Angles in a Polygon (8.G.5)

CCSS Addressed: ✓ 8.G.4 | ✓ 8.G.5

C: The Pythagorean Theorem

8.G.6, 8.G.7

Understanding the Pythagorean Theorem (8.G.6)

Pythagorean Theorem – Hypotenuse (8.G.7)

Pythagorean Theorem – Legs (8.G.7)

Pythagorean Theorem – Mixed Problems (8.G.7)

Pythagorean Theorem – Distance Formula (8.G.7, 8.G.8)

CCSS Addressed: ✓ 8.G.6 | ✓ 8.G.7

## MODULE 4: Linear Equations

**EUREKA MATH / ENGAGE NY TOPIC**

A: Writing and Solving Linear Equations

8.EE.7, 8.EE.7.a, 8.EE.7.b

**THINK THROUGH MATH LESSON** (CCSS)

Solving Two-Step Equations (8.EE.7b)

Solving Equations with the Variable on Both Sides (8.EE.7b)

Analyzing Solution Sets to Linear Equations with the Variable on Both Sides (8.EE.7a)

CCSS Addressed: ✓ 8.EE.7

B: Linear Equations in Two Variables and Their Graphs

C: Slope and Equations of Lines

8.EE.5, 8.EE.6

Interpreting Slope (8.EE.5)

Slope (8.EE.6, 8.F.1, 8.F.2)

Slope-Intercept Form (8.EE.6, 8.F.4, 8.SP.3)

Solving a System of Linear Equations Graphically (8.EE.8, 8.EE.8a)

Solving a System of Linear Equations Algebraically (8.EE.8, 8.EE.8b)

Solving a System of Linear Equations – Applications (8.EE.8c)

CCSS Addressed: ✓ 8.EE.5 | ✓ 8.EE.6

D: Pythagorean Theorem

8.G.7, 8.EE.8, 8.EE.8.a, 8.EE.8.b, 8.EE.8.c

Understanding the Pythagorean Theorem (8.G.6)

Pythagorean Theorem – Hypotenuse (8.G.7)

Pythagorean Theorem – Legs (8.G.7)

Pythagorean Theorem – Mixed Problems (8.G.7)

Pythagorean Theorem – Distance Formula (8.G.7, 8.G.8)

CCSS Addressed: ✓ 8.EE.5 * | ✓ 8.EE.8

## MODULE 5: Examples of Functions from Geometry

**EUREKA MATH / ENGAGE NY TOPIC**

A: Functions

8.F.1, 8.EE.5, 8.EE.6, 8.F.3, 8.EE.8, 8.F.2, 8.G.9

**THINK THROUGH MATH LESSON** (CCSS)

Interpreting Slope (8.EE.5)

Slope (8.EE.6, 8.F.1, 8.F.2)

Slope-Intercept Form (8.EE.6, 8.F.4, 8.SP.3)

Point-Slope Form (8.F.3, 8.F.4)

CCSS Addressed: ✓ 8.F.1 | ✓ 8.F.2 | ✓ 8.F.3

B: Volume

8.G.9

Volume of Cylinders (8.G.9)

Volume of Pyramids and Cones (8.G.9)

Volume of Spheres (8.G.9)

CCSS Addressed: ✓ 8.G.9

## MODULE 6: Linear Functions

**EUREKA MATH / ENGAGE NY TOPIC**

A: Linear Functions

8.F.4, 8.F.5

**THINK THROUGH MATH LESSON** (CCSS)

Point-Slope Form (8.F.3, 8.F.4)

Interpreting Graphs or Real-World Situations (8.F.5)

Introduction to Sketching Graphs of Real-World Situations (8.F.5)

CCSS Addressed: ✓ 8.F.4 | ✓ 8.F.5

B: Bivariate Numerical Data

C: Linear and Nonlinear Models

8.SP.1, 8.SP.2, 8.SP.3

Direct Variation (8.SP.2, 8.SP.3)

Comparing Linear and Nonlinear Data (8.SP.1, 8.SP.2)

CCSS Addressed: ✓ 8.SP.1 | ✓ 8.SP.2 | ✓ 8.SP.3

D: Bivariate Categorical Data

8.SP.4

Patterns and Association in Data (8.SP.4)

CCSS Addressed: ✓ 8.SP.4

## MODULE 7: Linear Functions

**EUREKA MATH / ENGAGE NY TOPIC**

A: Square and Cube Roots

B: Decimal Expansions of Numbers

8.NS.1, 8.NS.2, 8.EE.2

**THINK THROUGH MATH LESSON** (CCSS)

Understanding Square and Cube Roots (8.EE.2)

Classifying and Ordering Real Numbers (8.NS.1)

Approximating Values of Irrational Numbers (8.NS.1, 8.NS.2)

CCSS Addressed: ✓ 8.NS.1 | ✓ 8.NS.2 | ✓ 8.EE.2

C. The Pythagorean Theorem

8.G.6, 8.G.7, 8.G.8

Pythagorean Theorem – Hypotenuse (8.G.7)

Pythagorean Theorem – Legs (8.G.7)

Pythagorean Theorem – Mixed Problems (8.G.7)

Pythagorean Theorem – Distance Formula (8.G.7, 8.G.8)

CCSS Addressed: ✓ 8.G.6 | ✓ 8.G.7 | ✓ 8.G.8

D. Applications of Radicals and Roots

8.G.7, 8.G.9

Volume of Pyramids and Cones (8.G.9)

Volume of Spheres (8.G.9)

Volume of Composite Solids (8.G.9)

CCSS Addressed: ✓ 8.G.7 * | ✓ 8.G.9

## Algebra

## MODULE 1: Relationships Between Quantities and Reasoning with Equations and Their Graphs

**EUREKA MATH / ENGAGE NY TOPIC**

A. Introduction to Functions Studied This Year – Graphing Stories

N.Q.1, N.Q.2, N.Q.3, A.CED.2

**THINK THROUGH MATH LESSON** (CCSS)

Using Units to Solve Problems (N.Q.1, N.Q.3)

Introduction to Nonlinear Models (F.LE.3)

CCSS Addressed: ✓ N.Q.1 | ✓ N.Q.3 | ✓ A.CED.2 *

B. The Structure of Expressions

A.SSE.2, A.APR.1

Identifying and Generating Equivalent Expressions (6.EE.A.3, 6.EE.A.4)

Adding and Subtracting Polynomials (A.APR.1)

Multiplying Polynomials (A.APR.1)

CCSS Addressed: ✓ A.SSE.2 * | ✓ A.APR.1

C. Solving Equations and Inequalities

D. Creating Equations to Solve Problems

A.CED.3, A.CED.4, A.REI.1, A.REI.3, A.REI.5, A.REI.6, A.REI.10, A.REI.12

N.Q.1, A.SSE.1, A.SSE.1a, A.SSE.1b, A.CED.1, A.CED.2, A.REI.3

Writing and Solving Linear Equations in One Variable (A.CED.3)

Solving Linear Equations in One Variable as a Reasoning Process (A.REI1, A.REI.3)

Writing and Graphing Linear Equations in Two or More Variables (A.CED.2)

Writing Linear Inequalities in One Variable (A.CED.1, A.CED.3)

Solving Linear Inequalities in One Variable (A.REI.3)

Solving Systems of Linear Equations (A.REI.6, A.REI.5)

Solving Linear Equations Graphically (A.REI.10, A.REI.11)

Graphing Linear Inequalities and Systems of Linear Inequalities in Real-World Situations (A.CED.3, A.REI.12)

Solving Literal Equations (A.CED.4)

Analyzing Solution Sets to Linear Equations with the Variable on Both Sides (8.EE.C.7a)

CCSS Addressed: ✓ N.Q.1 * | ✓ A.SSE.1 * | ✓ A.CED.1 | ✓ A.CED.2 | ✓ A.CED.3 | ✓ A.CED.4 | ✓ A.REI.1 | ✓ A.REI.3 | ✓ A.REI.5 | ✓ A.REI.6 | ✓ A.REI.10 | ✓ A.REI.12

## MODULE 2: Descriptive Statistics

**EUREKA MATH / ENGAGE NY TOPIC**

A. Shapes and Centers of Distributions

S.ID.1, S.ID.2, S.ID.3

**THINK THROUGH MATH LESSON** (CCSS)

Data Displays on the Real Number Line (S.ID.1)

Measures of Center – Mean (S.ID.A.3)

Measures of Center – Median (S.ID.A.3)

Understanding the Effects of Outliers on the Mean and Median (6.SP.A.3)

CCSS Addressed: ✓ S.ID.1 | ✓ S.ID.2 * | ✓ S.ID.3

B. Describing Variability and Comparing Distributions

S.ID.1, S.ID.2, S.ID.3

Deviation from the Mean (6.SP.B.5c, 6.SP.B.5d)

Quartiles (6.SP.A.2, 6.SP.A.3)

Comparing the Shape, Center, and Spread of Data Sets (S.ID.2, S.ID.3)

CCSS Addressed: ✓ S.ID.1 * | ✓ S.ID.2 | ✓ S.ID.3

D. Numerical Data on Two Variables

S.ID.6, S.ID.6.a, S.ID.6.b, S.ID.6.c, S.ID.7, S.ID.8, S.ID.9

Fitting Functions to Data (S.ID.6, S.ID.6a, S.ID.6b, S.ID.6c)

CCSS Addressed: ✓ S.ID.6 | ✓ S.ID.7 * | S.ID.8 | ✓ S.ID.9

C. Categorical Data on Two Variables

S.ID.5, S.ID.9

Summarizing and Interpreting Categorical Data (S.ID.5)

Data Analysis (6.SP.A.1)

Patterns of Association in Data (8.SP.A.4)

Correlation (S.ID.9, S.ID.7)

CCSS Addressed: ✓ S.ID.5 | ✓ S.ID.9

## MODULE 3: Linear and Exponential Functions

**EUREKA MATH / ENGAGE NY TOPIC**

A. Linear and Exponential Sequences

F.IF.1, F.IF.2, F.IF.3, F.IF.6, F.BF.1a, F.LE.2, F.LE.3, F.LE.1, F.LE.1b, F.LE.1c

**THINK THROUGH MATH LESSON** (CCSS)

Writing Geometric Sequences Using an Explicit Formula (F.BF.2)

Writing Geometric Sequences Recursively (F.BF.2)

Writing Arithmetic Sequences Explicitly and Recursively (F.BF.2)

Sequences as Functions (F.IF.3)

Modeling Exponential Relationships with Equations, Inequalities, and Graphs (A.CED.1, A.CED.2)

CCSS Addressed: ✓ F.IF.1 * | ✓ F.IF.2 * | ✓ F.IF.3 | ✓ F.IF.6 * | ✓ F.BF.1a * | ✓ F.LE.1 * | ✓ F.LE.2 * | ✓ F.LE.3 *

B. Functions and Their Graphs

F.IF.1, F.IF.2, F.IF.4, F.IF.5, F.IF.7a

Function Notation I (F.IF.1, F.IF.2)

Function Notation II (F.IF.1, F.IF.2)

Interpreting Graphs of Linear and Exponential Functions in Context (F.IF.4)

Sketching Graphs of Linear and Exponential Functions from a Context (F.IF.4)

Understanding the Domain of a Function (F.IF.5)

Sketching Graphs of Linear Functions from Symbolic Representations (F.IF.7a)

Sketching Graphs of Exponential Functions from Symbolic Representations (F.IF.7e)

Rate of Change for Linear and Exponential Functions (F.IF.6)

Comparing Functions Using Different Representations (F.IF.9)

Distinguishing Between Linear and Exponential Relationships (F.LE.1, F.LE.1a, F.LE.1b, F.LE.1c)

CCSS Addressed: ✓ F.IF.1 | ✓ F.IF.2 | ✓ F.IF.4 | ✓ F.IF.5 | ✓ F.IF.7a

C. Transformations of Functions

A.REI.11, F.IF.7a, F.BF.3

Transformations of Graphs of Linear and Exponential Functions (F.BF.3)

CCSS Addressed: ✓ A.REI.11 * | ✓ F.IF.7a * | ✓ F.BF.3

D. Using Functions and Their Graphs to Solve Problems

A.CED.1, A.SSE.3c, F.IF.6, F.IF.9, F.BF.1a, F.LE.2, F.LE.5, F.IF.4

Writing Linear and Exponential Functions from a Context (F.BF.1a)

Writing Linear and Exponential Functions Based on Different Representations (F.LE.2)

Interpreting the Structure of Linear and Exponential Expressions (A.SSE.1b)

Piecewise, Step, and Absolute Value Functions (F.IF.7b)

CCSS Addressed: ✓ A.CED.1 * | ✓ A.SSE.3c * | ✓ F.IF.4 * | ✓ F.IF.6 * | ✓ F.IF.9 * | ✓ F.BF.1a | ✓ F.LE.2

## MODULE 4: Polynomial and Quadratic Expressions, Equations, and Functions

**EUREKA MATH / ENGAGE NY TOPIC**

A. Quadratic Expressions, Equations, Functions, and Their Connection to Rectangles

A.SSE.1a, A.SSE.2, A.SSE.3a, A.APR.1, A.CED.1, A.CED.2, A.REI.4b, A.REI.11, F.IF.4, F.IF.5, F.IF.6, F.IF.7a

**THINK THROUGH MATH LESSON** (CCSS)

Factoring Expressions (A.SSE.B.3a)

Factoring Polynomials (F.IF.C.8a, A.SSE.A.2, A.SSE.B.3a)

Factoring Quadratic Expressions (A.SSE.3a)

Interpreting the Structure of Quadratic Expressions and Expressions with Rational Exponents (A.SSE.1a, A.SSE.1b)

Modeling Quadratic Relationships with Equations, Inequalities, and Graphs (A.CED.1, A.CED.2)

Writing Quadratic Functions from a Context (F.BF.1a, F.BF.1b)

Sketching Graphs of Quadratic Functions in Context (F.IF.4, F.IF.5, F.IF.6)

CCSS Addressed: ✓ A.SSE.1 | ✓ A.SSE.2 | ✓ A.SSE.3a | ✓ A.APR.1 * | ✓ A.CED.1 | ✓ A.CED.2 | ✓ A.REI.4b * | ✓ A.REI.11 * | ✓ F.IF.4 | ✓ F.IF.5 | ✓ F.IF.6 | ✓ F.IF.7a *

B. Using Different Forms of Quadratic Functions

N.RN.3, A.SSE.1, A.SSE.1a, A.SSE.1b, A.SSE.2, A.SSE.3, A.SSE.3a, A.APR.3, A.CED.1, A.CED.2, A.REI.4, A.REI.4a, A.REI.4b, F.IF.4, F.IF.6, F.IF.7, F.IF.7a, F.IF,8, F.IF.8a

Solving Quadratics – Completing the Square (A.REI.4a)

Writing Quadratic Functions From Their Graphs (F.BF.A.1, A.CED.A.2)

Solving Quadratic Equations Graphically (A.REI.D.10)

Rewriting Quadratics to Reveal Their Structure (A.SSE.3b, F.IF.8a)

Problem Solving with Quadratic Functions (A.REI.4b)

Using the Quadratic Formula (A.REI.4b)

CCSS Addressed: N.RN.3 | ✓ A.SSE.1 * | ✓ A.SSE.2 * | ✓ A.SSE.3a * | A.SSE.3b | A.APR.3 * | ✓ A.CED.1 * | ✓ A.CED.2 | ✓ A.REI.4 | ✓ F.IF.4 * | ✓ F.IF.6 * | ✓ F.IF.7a * | ✓ F.IF.8a

C. Function Transformations and Modeling

A.CED.2, F.IF.6, F.IF.7, F.IF.7b, F.IF.8, F.IF,8a, F.IF.9, F.BF.3

Sketching and Transforming Graphs of Quadratic Functions from Symbolic Representations (F.BF.3, F.IF.7a)

CCSS Addressed: ✓ A.CED.2 * | ✓ F.IF.6 * | ✓ F.IF.7b * | ✓ F.IF.8a * | ✓ F.IF.9 * | ✓ F.BF.3

## MODULE 5: A Synthesis of Modeling with Equations and Functions

**EUREKA MATH / ENGAGE NY TOPIC**

A. Elements of Modeling

B. Completing the Modeling Cycle

N.Q.2, A.CED.2, F.IF.4, F.IF.5, F.BF.1a, F.LE.1b, F.LE.1c, F.LE.2

N.Q.2, N.Q.3

**THINK THROUGH MATH LESSON** (CCSS)

*Elements of modeling are embedded throughout and not put into their own lessons.*

CCSS Addressed: ✓ N.Q.3 * | ✓ A.CED.1 * | ✓ A.CED.2 * | ✓ F.IF.4 * | ✓ F.IF.5 * | ✓ F.IF.6 * | ✓ F.BF.1a * | ✓ F.LE.1b * | ✓ F.LE.1c * | ✓ F.LE.2 *

## Geometry

## MODULE 1: Congruence, Proof, and Constructions

**EUREKA MATH / ENGAGE NY TOPIC**

A. Basic Construction

G.CO.1, G.CO.12, G.CO.13

**THINK THROUGH MATH LESSON** (CCSS)

Defining Basic Geometric Elements (G.CO.1)

Constructing Angles and Special Line Segments (G.CO.12)

Constructing Inscribed Figures (G.CO.13)

CCSS Addressed: ✓ G.CO.1 | ✓ G.CO.12 | ✓ G.CO.13

B. Unknown Angles

G.CO.9

What Is Proof? (G.CO.7, G.CO.9)

Proving Theorems About Lines and Angles (G.CO.9)

CCSS Addressed: ✓ G.CO.C.9

C. Transformations/Rigid Motions

G.CO.2, G.CO.3, G.CO.4, G.CO.5, G.CO.6, G.CO.7, G.CO.12

Defining Transformations (G.CO.4)

Rotational and Reflectional Symmetry (G.CO.3)

Representing Transformations with Algebra (G.CO.2)

Rigid Motion and Congruence (G.CO.5, G.CO.6)

CCSS Addressed: ✓ G.CO.2 | ✓ G.CO.3 | ✓ G.CO.4 | ✓ G.CO.5 | ✓ G.CO.6 | ✓ G.CO.7* | ✓ G.CO.12*

D. Congruence

G.CO.7, G.CO.8

Proving Theorems About Congruent Triangles (G.CO.8, G.CO.10)

Problem Solving with Congruent Triangles (G.SRT.5, G.CO.10)

Proving Theorems About Relationships in Triangles (G.CO.10)

CCSS Addressed: ✓ G.CO.7* | ✓G.CO.8

E. Proving Properties of Geometric Figures

G.CO.9, G.CO.10, G.CO.11

Proving Theorems About Parallelograms (G.CO.11)

CCSS Addressed: ✓ G.CO.9* | ✓ G.CO.10* | ✓ G.CO.11

F. Advanced Constructions

G.CO.13

N/A

CCSS Addressed: ✓ G.CO.13*

G. Axiomatic Systems

G.CO.1, G.CO.2, G.CO.3, G.CO.4, G.CO.5, G.CO.6, G.CO.7, G.CO.8, G.CO.9, G.CO.10, G.CO.11, G.CO.12, G.CO.13

N/A

CCSS Addressed: ✓ G.CO.1* | ✓ G.CO.2* | ✓ G.CO.3* | ✓ G.CO.4* | ✓ G.CO.5* | ✓ G.CO.6* | ✓ G.CO.7* | ✓ G.CO.8* | ✓ G.CO.9* | ✓ G.CO.10* | ✓ G.CO.11* | ✓ G.CO.12* | ✓ G.CO.13*

## MODULE 2: Similarity, Proof, and Trigonometry

**EUREKA MATH / ENGAGE NY TOPIC**

A: Scale Drawings

B: Dilations

G.SRT.1, G.SRT.1a, G.SRT.1b, G.SRT.4, G.MG.3

**THINK THROUGH MATH LESSON** (CCSS)

Proportions in Scale Drawings (7.RP.3, 7.G.1)

Properties of Dilations I (G.SRT.1b)

Properties of Dilations II (G.SRT.1a)

CCSS Addressed: ✓ G.SRT.1 | ✓ G.SRT.4*

C. Similarity and Dilations

G.SRT.2, G.SRT.3, G.SRT.5, G.MG.1

Transformations and Similarity (G.SRT.2, G.SRT.3)

Problem Solving with Transformations and Similarity (G.SRT.5)

CCSS Addressed: ✓ G.SRT.2 | ✓ G.SRT.3 | ✓ G.SRT.5

D. Applying Similarity to Right Triangles

G.SRT.4

Proving Theorems About Similar Triangles (G.SRT.4)

CCSS Addressed: ✓ G.SRT.4

E. Trigonometry

G.SRT.6, G.SRT.7, G.SRT.8, G.SRT.10, G.SRT.11

Similarity and Trigonometric Ratios (G.SRT.6)

Problem Solving with Similarity and Trigonometric Ratios (G.SRT.8)

Sine and Cosine of Complementary Angles (G.SRT.7)

Law of Sines and Law of Cosines (G.SRT.11)

CCSS Addressed: ✓ G.SRT.6 | ✓ G.SRT.7 | ✓ G.SRT.8 | ✓ G.SRT.11

## MODULE 3: Extending to Three Dimensions

**EUREKA MATH / ENGAGE NY TOPIC**

A: Area

B: Volume

G.GMD.1, G.GMD.2, G.GMD.3, G.GMD.4

**THINK THROUGH MATH LESSON** (CCSS)

Understanding Formulas for Curved Figures (G.GMD.1)

Cross Sections of 3-Dimensional Figures (G.GMD.4)

Volume of Cylinders (G.GMD.3)

Volume of Pyramids and Cones (G.GMD.3)

Volume of Spheres (G.GMD.3)

CCSS Addressed: ✓ G.GMD.1 | ✓ G.GMD.3 | ✓ G.GMD.4

## MODULE 4: Connecting Algebra and Geometry Through Coordinates

**EUREKA MATH / ENGAGE NY TOPIC**

A: Connecting Algebra and Geometry Through Coordinates

B: Perpendicular and Parallel Lines in the Cartesian Plane

G.MG.1, G.MG.3, G.GPE.4, G.GPE.5, G.GPE.7, A-REI.6, A-REI.12

**THINK THROUGH MATH LESSON** (CCSS)

Coordinates of Parallel and Perpendicular Lines (G.GPE.4, G.GPE.5)

Problem Solving with Coordinates of Parallel and Perpendicular Lines (G.GPE.4)

CCSS Addressed: ✓ G.GPE.4 | ✓ G.GPE.5 | ✓ G.GPE.7*

C: Perimeters and Areas of Polygonal Regions in the Cartesian Plane

D: Partitioning and Extending Segments and Parameterization of Lines

G.GPE.4, G.GPE.6, G.GPE.7

Dividing a Segment Proportionally (G.GPE.6)

Using Coordinates to Find Perimeters and Areas (G.GPE.7)

CCSS Addressed: ✓ G.GPE.4* | ✓ G.GPE.6 | ✓ G.GPE.7

## MODULE 5: Circles With and Without Coordinates

**EUREKA MATH / ENGAGE NY TOPIC**

A: Central and Inscribed Angles

B: Arcs and Sectors

C: Secants and Tangents

G.C.1, G.C.2, G.C.3, G.C.4, G.C.5

**THINK THROUGH MATH LESSON** (CCSS)

Tangents, Chords, Radii, and Angles in Circles (G.C.2, G.C.4)

Quadrilaterals Inscribed in Circles (G.C.3)

Radians and Area of Sectors (G.C.5)

CCSS Addressed: ✓ G.C.1* | ✓ G.C.2 | ✓ G.C.3 | ✓ G.C.4 | ✓ G.C.5

D: Equations for Circles and Tangents

E: Cyclical Quadrilaterals and Ptolemy’s Theorem

G.GPE.1, G.GPE.4, G.C.3

Equation of a Circle (G.C.1, G.GPE.1)

Problem Solving with the Equation of a Circle (G.GPE.1, G.GPE.4)

CCSS Addressed: ✓ G.GPE.1 | ✓ G.GPE.4 | ✓ G.C.3*