Alignment from Singapore Math to Engage New York

Alignment from Singapore Math to Engage New York Chapters Singapore Math/ Standards covered Engage New York- where to find the good stuff

Chapter 1: NBT-1 Recognize that in a multi-digit number, a digit in one place Module 1 Whole Numbers represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Topic A: Multiplicative Patterns on the Place Value Chart..... 1.A.1 Module 2 Topic A: Mental Strategies for Multi-Digit Whole Number Multiplication..... 2.A.1 Topic E: Multiplying Decimals...... 1.E.1 Chapter 2: NBT-1 Recognize that in a multi-digit number, a digit in one place Module 1: Whole Number represents 10 times as much as it represents in the place to its right Multiplication and 1/10 of what it represents in the place to its left. Topic A: Multiplicative Patterns on the Place Value Chart...... 1.A.1 and Division NBT- 2 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the Topic D: Adding and Subtracting Decimals ...... placement of the decimal point when a decimal is multiplied or 1.D.1 divided by a power of 10. Use whole-number exponents to denote powers of 10. Topic E: Multiplying Decimals...... 1.E.1

NBT-5 Fluently multiply multi-digit whole numbers using the Module 2: standard algorithm. NBT-6 Find whole-number quotients of whole numbers with up to Topic A: Mental Strategies for Multi-Digit Whole four-digit dividends and two-digit divisors, using strategies based on Number Multiplication..... 2.A.1 place value, the properties of operations, and/or the relationship Topic B: The Standard Algorithm for Multi-Digit between multiplication and division. Illustrate and explain the Whole Number Multiplication ... 2.B.1 calculation by using equations, rectangular arrays, and/or area models. Topic D: Measurement Word Problems with Whole Number and Decimal Multiplication ...... 2.D.1 OA-1 Use parentheses, brackets, or braces in numerical expressions, Topic E: Multiplying Decimals...... 1.E.1 and evaluate expressions with these symbols. Topic F: Partial Quotients and Multi-Digit Whole Number Division..... 2. F.1 OA-2 Write simple expressions that record calculations with Topic H: Measurement Word Problems with Multi- numbers, and interpret numerical expressions without evaluating Digit Division...... 2. H.1 them. Module 6: OA-3 Generate two numerical patterns using two given rules. Identify Topic B: Patterns in the Coordinate Plane and apparent relationships between corresponding terms. Form ordered Graphing Number Patterns from Rules ...... 6.B.1 pairs consisting of corresponding terms from the two patterns, and Topic D: Problem Solving in the Coordinate graph the ordered pairs on a coordinate plane. Plane ...... 6.D.1 Topic E: Multi-Step Word Problems ...... 6.E.1 Chapter 3: NF-1 Add and subtract fractions with unlike denominators Module 3: Fractions and (including mixed numbers) by replacing given fractions with Mixed Numbers equivalent fractions in such a way as to produce an equivalent sum Topic A: Equivalent Fractions 3.A.1 or difference of fractions with like denominators. For example, 2/3 + Topic B: Making Like Units Pictorially 3.B.1 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.) Topic C: Making Like Units Numerically 3.C.1

NF-2 Solve word problems involving addition and subtraction of Topic D: Further Applications 3.D.1 fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of Module 6: answers. Topic E: Multi-Step Word Problems ...... 6.E.1 NF-3 Interpret a fraction as division of the numerator by the denominator (a/b = a, b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. Chapter 4: NF-4a Interpret the product (a/b) x q as a parts of a partition of q Module 4: Multiplying and into b equal parts; equivalently, as the result of a sequence of Topic C: Multiplication of a Whole Number by a Dividing operations a x q ö b. Fraction ...... C.1 Fractions and Topic D: Fraction Expressions and Word Mixed Numbers Problems ...... 4.D.1 NF-4b Apply and extend previous understandings of Topic E: Multiplication of a Fraction by a multiplication to multiply a fraction or whole number by a Fraction ...... 4.E.1 fraction. B: Find the area of a rectangle with fractional side Topic F: Multiplication with Fractions and Decimals lengths by tiling it with unit squares of the appropriate unit as Scaling and Word Problems…. 4.F.1 fraction side lengths, and show that the area is the same as would Topic G: Division of Fractions and Decimal be found by multiplying the side lengths. Multiply fractional side Fractions ...... 4.G.1 lengths to find areas of rectangles, and represent fraction products as rectangular areas. NF-5a Comparing the size of a product to the size of one factor Module 5: on the basis of the size of the other factor, without performing Topic C: Area of Rectangular Figures with Fractional the indicated multiplication. Side Lengths ...... 5.C.1

NF-5b Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a Module 6: familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given Topic E: Multi-Step Word Problems ...... 6.E.1 number; and relating the principle of fraction equivalence a/b = (n x a)/ (n x b) to the effect of multiplying a/b by 1. NF-6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

NF -7a Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. NF-7b Interpret division of a whole number by a unit fraction, and compute such quotients. NF- 7c Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. Chapter 5: OA-1 Use parentheses, brackets, or braces in Module 2: Algebra numerical expressions, and evaluate expressions with Topic A: Mental Strategies for Multi-Digit Whole these symbols. Number Multiplication..... 2.A.1 OA-2 Write simple expressions that record Topic B: The Standard Algorithm for Multi-Digit calculations with numbers, and interpret numerical Whole Number Multiplication ... 2.B.1 expressions without evaluating them. Module 4: Topic D: Fraction Expressions and Word Problems ...... 4.D.1 Topic G: Division of Fractions and Decimal Fractions ...... 4.G.1 Topic H: Interpretation of Numerical Expressions ...... 4.H.1

Module 6: Topic B: Patterns in the Coordinate Plane and Graphing Number Patterns from Rules ...... 6.B.1 Chapter 6: NF-4a Interpret the product (a/b) x q as a parts of a partition of q into b Module 4: Area of Triangle equal parts; equivalently, as the result of a sequence of operations a x q ö b. Topic C: Multiplication of a Whole Number by a Fraction ...... C.1 Topic D: Fraction Expressions and Word Problems ...... 4.D.1 G- 3 Understand that attributes belonging to a category of two Topic E: Multiplication of a Fraction by a dimensional figures also belong to all subcategories of that Fraction ...... 4.E.1 category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles G-4 Classify two-dimensional figures in a hierarchy based on Module 5: properties. Topic C: Area of Rectangular Figures with Fractional Side Lengths ...... 5.C.1 Topic D: Drawing, Analysis, and Classification of Two-Dimensional Shapes...... 5.D.1

Chapter 7: NF.5a- Interpret multiplication as scaling (resizing) by: comparing Module 4: Ratio the size of a product to the size of one factor on the basis of the size Topic F: Multiplication with Fractions and Decimals of the other factor, without performing the indicated multiplication. as Scaling and Word Problems…. 4.F.1 Chapter 8: NBT-1 Recognize that in a multi-digit number, a digit in one place Module 1: Decimals represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left. Topic A: Multiplicative Patterns on the Place Value Chart ...... 1.A.1 NBT.3a-Read, write, and compare decimals to thousandths. Read Topic B: Decimal Fractions and Place Value and write decimals to thousandths using base- ten numerals, number Patterns ...... 1.B.1 names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 Topic C: Place Value and Rounding Decimal + 3 x 1/10 + 9 x 1/100 + 2 x 1/1000. Fractions ...... 1.C.1 NBT.3b- Compare two decimals to thousandths based on meaning of Topic D: Adding and Subtracting Decimals ...... the digits in each place, using >, =, <, symbols to record the results 1.D.1 of comparisons. Topic E: Multiplying Decimals...... 1.E.1 NBT.4- Use place value understanding to round decimals to any Topic F: Dividing Decimals...... 1.F.1 place. NBT.7- Add, subtract, multiply, and divide decimals to hundredths, Module 2: using concrete models or drawings and strategies based on place Topic A: Mental Strategies for Multi-Digit Whole value, properties of operations, and/or the relationship between Number Multiplication..... 2.A.1 addition and subtraction; relate the strategy to a written method and Topic C: Decimal Multi-Digit Multiplication...... explain the reasoning used. [From cluster: Perform operations with 2.C.1 multi-digit whole numbers and with decimals to hundredths] Topic D: Measurement Word Problems with Whole Number and Decimal Multiplication ...... 2.D.1 Topic E: Multiplying Decimals...... 1.E.1 Topic G: Partial Quotients and Decimal Multi-Digit Division ...... 2.G.1 Topic H: Measurement Word Problems with Multi- Digit Division...... 2. H.1 Module 4: Topic E: Multiplication of a Fraction by a Fraction ...... 4.E.1 Topic G: Division of Fractions and Decimal Fractions ...... 4.G.1 Chapter 9: NBT-1 Recognize that in a multi-digit number, a digit in one Module 1: Multiplying and place represents 10 times as much as it represents in the place Dividing to its right and 1/10 of what it represents in the place to its Topic A: Multiplicative Patterns on the Place Value Decimals left. Chart...... 1.A.1 NBT- 2 Explain patterns in the number of zeros of the Topic C: Place Value and Rounding Decimal product when multiplying a number by powers of 10, and Fractions ...... 1.C.1 explain patterns in the placement of the decimal point when a Topic D: Adding and Subtracting Decimals ...... decimal is multiplied or divided by a power of 10. Use 1.D.1 whole-number exponents to denote powers of 10. Topic E: Multiplying Decimals...... 1.E.1

NBT.4- Use place value understanding to round decimals to any place.

NBT.7- Add, subtract, multiply, and divide decimals to Module 2: hundredths, using concrete models or drawings and strategies Topic A: Mental Strategies for Multi-Digit Whole based on place value, properties of operations, and/or the Number Multiplication..... 2.A.1 relationship between addition and subtraction; relate the Topic C: Decimal Multi-Digit Multiplication...... strategy to a written method and explain the reasoning used. 2.C.1 [From cluster: Perform operations with multi-digit whole Topic D: Measurement Word Problems with Whole numbers and with decimals to hundredths] Number and Decimal Multiplication ...... 2.D.1 Topic G: Partial Quotients and Decimal Multi-Digit Division ...... 2.G.1 Topic H: Measurement Word Problems with Multi- Digit Division...... 2. H.1

Chapter 10: Percent Chapter 11: G-1 Use a pair of perpendicular number lines, called axes, to define a Module 1: Graph and coordinate system, with the intersection of the lines (the origin) arranged Probability to coincide with the 0 on each line and a given point in the plane locatedTopic A: Multiplicative Patterns on the Place Value by using an ordered pair of numbers, called its coordinates. UnderstandChart...... 1.A.1 that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names ofModule 2: the two axes and the coordinates correspond (e.g., x-axis and x- coordinate, y-axis and y-coordinate). Topic D: Measurement Word Problems with Whole Number and Decimal Multiplication ...... 2.D.1

G-2 Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret Module 4: coordinate values of points in the context of the situation. Topic A: Line Plots of Fraction Measurements ...... 4.A.1 MD-1 Convert among different-sized standard measurement units Topic E: Multiplication of a Fraction by a within a given measurement system (e.g., convert 5 cm to 0.05 m), and Fraction ...... 4.E.1 use these conversions in solving multi-step, real world problems.

MD-2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Module 6: Topic A: Coordinate Systems ...... 6.A.1 Topic B: Patterns in the Coordinate Plane and Graphing Number Patterns from Rules ...... 6.B.1 Topic C: Area of Rectangular Figures with Fractional Side Lengths ...... 5.C.1 Topic D: Problem Solving in the Coordinate Plane ...... 6.D.1 Topic E: Multi-Step Word Problems ...... 6.E.1

Chapter 12: Angles Chapter 13: Module 5: Properties of G- 3 Understand that attributes belonging to a category Topic D: Drawing, Analysis, and Classification of Triangles and 4 of two dimensional figures also belong to all Two-Dimensional Shapes...... 5.D.1 Sided Figures subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles G-4 Classify two-dimensional figures in a hierarchy based on properties.

Chapter 14: Three Dimensional Shapes Chapter 15: Module 1: Surface Area and NBT.5- Fluently multiply multi-digit whole numbers using the Volume Topic A: Multiplicative Patterns on the Place Value standard algorithm. Chart...... 1.A.1 MD-1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world Module 2: problems. Topic B: The Standard Algorithm for Multi-Digit MD3a- Recognize volume as an attribute of solid figures and Whole Number Multiplication ... 2.B.1 understand concepts of volume measurement. A cube with side Topic D: Measurement Word Problems with Whole length 1 inch, called a "unit cube," is said to have "one cubic unit" Number and Decimal Multiplication ...... 2.D.1 of volume, and can be used to measure volume. Module 4: Topic E: Multiplication of a Fraction by a MD.5a- Relate volume to the operations of multiplication and Fraction ...... 4.E.1 addition and solve real world and mathematical problems involving volume. Find the volume of a right rectangle prism with whole number side lengths by packing it with unit cubes, and show Module 5: that the volume is the same as would be found by multiplying the Topic A: Concepts of Volume ...... 5.A.1 edge lengths, equivalently by multiplying the height by the area of Topic B: Volume and the Operations of the base. Represent threefold whole-number products as volumes, Multiplication and Addition ...... 5.B.1 e.g., to represent the associative property. Module 6: MD.5b- Apply the formulas V = l x w x h and V= b x h for Topic E: Multi-Step Word Problems ...... 6.E.1 rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving real world and mathematical problems MD.5c- Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping parts, applying this technique to solve real world problems.

Module 1:

Topic A: Multiplicative Patterns on the Place Value Chart...... 1. A.1 Topic B: Decimal Fractions and Place Value Patterns ...... 1.B.1 Topic C: Place Value and Rounding Decimal Fractions ...... 1.C.1 Topic D: Adding and Subtracting Decimals ...... 1.D.1 Topic E: Multiplying Decimals...... 1.E.1 Topic F: Dividing Decimals...... 1.F.1

Module 2:

Topic A: Mental Strategies for Multi-Digit Whole Number Multiplication..... 2.A.1 Topic B: The Standard Algorithm for Multi-Digit Whole Number Multiplication ... 2.B.1 Topic C: Decimal Multi-Digit Multiplication...... 2.C.1 Topic D: Measurement Word Problems with Whole Number and Decimal Multiplication ...... 2.D.1 Topic E: Mental Strategies for Multi-Digit Whole Number Division.... 2.E.1 Topic F: Partial Quotients and Multi-Digit Whole Number Division..... 2. F.1 Topic G: Partial Quotients and Decimal Multi-Digit Division ...... 2.G.1 Topic H: Measurement Word Problems with Multi-Digit Division...... 2. H.1

Module 3: Topic A: Equivalent Fractions...... 3.A.1 Topic B: Making Like Units Pictorially...... 3.B.1 Topic C: Making Like Units Numerically ...... 3.C.1 Topic D: Further Applications..3. D.1

Module 4: Topic A: Line Plots of Fraction Measurements ...... 4.A.1 Topic B: Fractions as Division ...... 4.B.1 Topic C: Multiplication of a Whole Number by a Fraction ...... C.1 Topic D: Fraction Expressions and Word Problems ...... 4.D.1 Topic E: Multiplication of a Fraction by a Fraction ...... 4.E.1 Topic F: Multiplication with Fractions and Decimals as Scaling and Word Problems…. 4.F.1 Topic G: Division of Fractions and Decimal Fractions ...... 4.G.1 Topic H: Interpretation of Numerical Expressions ...... 4.H.1

Module 5: Topic A: Concepts of Volume ...... 5.A.1 Topic B: Volume and the Operations of Multiplication and Addition ...... 5.B.1 Topic C: Area of Rectangular Figures with Fractional Side Lengths ...... 5.C.1 Topic D: Drawing, Analysis, and Classification of Two-Dimensional Shapes...... 5.D.1

Module 6: Topic A: Coordinate Systems ...... 6.A.1 Topic B: Patterns in the Coordinate Plane and Graphing Number Patterns from Rules ...... 6.B.1 Topic C: Drawing Figures in the Coordinate Plane ...... 6.C.1 Topic D: Problem Solving in the Coordinate Plane ...... 6.D.1 Topic E: Multi-Step Word Problems ...... 6.E.1 Topic F: The Years In Review: A Reflection on A Story of Units ...... 6.F.1