Common Core Standards Plus – Mathematics – Grade 5 with Common Core ELD Standard Alignment

Domain Lesson Focus Standard(s) ELD Standards 1 Place Value Patterns 5.NBT.1: Recognize that in a multi‐digit 2 Place Value Patterns number, a digit in one place represents 10 times as much as it represents in the place ELD..5.5: Listening actively and 3 Place Value Patterns asking/ answering questions about what to its right and 1/10 of what it represents was heard. 4 Place Value Patterns in the place to its left.

E1 Evaluation ‐ Place Value Patterns 5 Powers of Ten 5.NBT.2: Explain patterns in the number of zeros of the product when multiplying a 6 Multiply by Powers of Ten number by powers of 10, and explain patterns in the placement of the ELD.PI.5.5: Listening actively and 7 Divide by Powers of Ten asking/ answering questions about what point when a decimal is multiplied or was heard. 8 Multiply & Divide by Powers of Ten divided by a power of 10. Use whole‐ ELD.PI.5.10: Composing/writing number exponents to denote powers of literary and informational texts. E2 Evaluation ‐ Powers of Ten 10.

P1 Performance Lesson #1 Power of Ten (5.NBT.1, 5.NBT.2)

5.NBT.7 Word Form of

‐ 9 5.NBT.3: Read, write, and compare 10 Expanded Form of Decimals decimals to thousandths. ELD.PI.5.5: Listening actively and Ten

5.NBT.3a: Read and write decimals to asking/ answering questions about what

5.NBT.1 Standard Form of Decimals thousandths using base‐ten numerals, was heard. 11 number names, and expanded form, e.g., ELD.PI.5.10: Composing/writing Base 12 Decimal Forms 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × literary and informational texts. in

(1/10) + 9 × (1/100) + 2 × (1/1000). E3 Evaluation ‐ Decimal Forms Standards

13 Compare Decimals 5.NBT.3b: Compare two decimals to

Ten thousandths based on meanings of the digits

in each place, using >, =, and < symbols to 14 Compare Decimals record the results of comparisons. Base

ELD.PI.5.5: Listening actively and Operations in asking/ answering questions about what 15 Round Decimals 5.NBT.4: Use place value understanding to was heard. round decimals to any place. ELD.PI.5.10: Composing/writing and Round Decimals

16 literary and informational texts. E4 Evaluation – Compare, Round Decimals 5.NBT.3b, 5.NBT.4 Operations

P2 Performance Lesson #2 Working with Decimals (5.NBT.3, 5.NBT.3a‐b, 5.NBT.4) and Number

17 Multiply Whole Numbers

Multiply Whole Numbers

Number 18 5.NBT.5: Fluently multiply multi‐digit ELD.PI.5.5: Listening actively and 19 Multiply Whole Numbers whole numbers using the standard asking/ answering questions about what algorithm. was heard. 20 Multiply Whole Numbers E5 Evaluation ‐ Multiply Whole Numbers 21 Divide Whole Numbers 5.NBT.6: Find whole‐number of whole numbers with up to four‐digit 22 Divide Whole Numbers dividends and two‐digit , using strategies based on place value, the ELD.PI.5.5: Listening actively and 23 Divide Whole Numbers properties of operations, and/or the asking/ answering questions about what relationship between and was heard. 24 Divide Whole Numbers . Illustrate and explain the calculation ELD.PI.5.10: Composing/writing by using equations, rectangular arrays, literary and informational texts. E6 Evaluation‐Divide Whole Numbers and/or area models. P3 Performance Lesson #3 Multiplication and Division (5.NBT.5, 5.NBT.6)

1 Common Core Standards Plus – Mathematics – Grade 5 with Common Core ELD Standard Alignment

Domain Lesson Focus Standard(s) ELD Standards 25 Add Decimals 5.NBT.7: Add, subtract, multiply, and divide 26 Add Decimals decimals to hundredths, using concrete models or drawings and strategies based on ELD.PI.5.5: Listening actively and 27 Subtract Decimals place value, properties of operations, and/or asking/ answering questions about what the relationship between and was heard. 28 Subtract Decimals ; relate the strategy to a written method and explain the reasoning used. E7 Evaluation ‐ Add and Subtract Decimals

5.NBT.7 ‐ 29 Multiply Decimals Ten 30 Multiply Decimals

5.NBT.1 ELD.PI.5.5: Listening actively and 5.NBT.7 asking/ answering questions about what Base 31 Multiply Decimals was heard. in 32 Multiply Decimals Standards

E8 Evaluation ‐ Multiply Decimals Ten 33 Multiply Decimals Multiply Decimals Base 34

Operations

ELD.PI.5.5: Listening actively and

in th 35 Divide Whole Numbers by 1/10 5.NBT.7 asking/ answering questions about what was heard. and 36 Divide Whole Numbers by 1/100th E9 Evaluation‐Multiply and Divide Decimals Operations

& 37 Divide a Decimal by a Whole Number Number 38 Divide a Decimal by a Whole Number ELD.PI.5.5: Listening actively and

Number 39 Divide a Whole Number by a Decimal 5.NBT.7 asking/ answering questions about what was heard. 40 Divide Decimals to Hundredths ELD.PI.5.10: Composing/writing literary and informational texts. E10 Evaluation ‐ Division with Decimals P4 Performance Lesson #4 Operations with Decimals (5.NBT.7)

5.NF.1: Add & subtract with unlike denominators (including mixed numbers) by

1 Add Fractions replacing given fractions with equivalent

5.NF.7c fractions to produce an equivalent sum or ‐ difference of fractions with like denominators. ELD.PI.5.5: Listening actively and asking/ answering questions about what Add Fractions in Context 5.NF.2: see below 5.NF.1 2 was heard. ELD.PI.5.6: Reading closely and Fractions 3 Add Mixed Numbers 5.NF.1 explaining interpretations/ideas from reading.

Standards Add Mixed Numbers in Context 5.NF.2

4 Evaluation – Add Fractions; Mixed 5.NF.1, 5.NF.2 E1 Numbers Fractions Operations

– 5.NF.1 5 Subtract Fractions and 6 Subtract Fractions in Context 5.NF.2 ELD.PI.5.5: Listening actively and asking/ answering questions about what Subtract Mixed Numbers 5.NF.1 was heard.

Operations 7 ELD.PI.5.6: Reading closely and & explaining interpretations/ideas from 8 Subtract Mixed Numbers in Context 5.NF.2 Number reading. Evaluation – Subtract Fractions; Mixed 5.NF.1, 5.NF.2 Number E2 Numbers

2 Common Core Standards Plus – Mathematics – Grade 5 with Common Core ELD Standard Alignment

Domain Lesson Focus Standard(s) ELD Standards

9 Add/Estimate Problems 5.NF.2: Solve word problems involving addition and subtraction of fractions ELD.PI.5.5: Listening actively and 10 Add/Estimate Fraction Problems referring to the same whole, including asking/ answering questions about what cases of unlike denominators, e.g., by was heard. ELD.PI.5.6: Reading closely and using visual fraction models or equations 11 Subtract/Estimate Fraction Problems explaining interpretations/ideas from to represent the problem. Use benchmark reading. 12 Subtract/Estimate Fraction Problems fractions and number sense of fractions to ELD.PI.5.10: Composing/writing estimate mentally and assess the literary and informational texts. E3 Evaluation – Solving Fraction Problems reasonableness of answers.

13 Interpret Fractions as Division 5.NF.3: Interpret a fraction as division of the numerator by the denominator (a/b = 14 Interpret Fractions as Division ELD.PI.5.5: Listening actively and a ÷ b). Solve word problems involving asking/ answering questions about what division of whole numbers leading to 15 Solve Problems with Fractions was heard. answers in the form of fractions or mixed ELD.PI.5.6: Reading closely and

numbers, e.g., by using visual fraction explaining interpretations/ideas from 16 Solve Problems with Mixed Numbers models or equations to represent the reading. problem. ELD.PI.5.10: Composing/writing literary and informational texts. 5.NF.7c E4 Evaluation – Solving Fraction Problems ‐ Performance Lesson #5 Add & Subtract Fractions and Mixed Numbers (5.NF.1, P5

5.NF.1 5.NF.2, 5.NF.3)

17 Multiply Fractions Fractions 5.NF.4: Apply and extend previous

understandings of multiplication to Multiply Fractions 18 multiply a fraction or whole number by ELD.PI.5.5: Listening actively and Standards a fraction. 5.NF.4a: Interpret the asking/ answering questions about what 19 Multiply Fractions was heard. product (a/b) × q as a parts of a partition ELD.PI.5.10: Composing/writing of q into b equal parts; equivalently, as 20 Multiply Fractions literary and informational texts. Operations Fractions

the result of a sequence of operations a – × q ÷ b. E5 Evaluation ‐ Multiply Fractions and

21 Multiply Fractions 5.NF.4, 5.NF.4b: Find the area of a rectangle with fractional side lengths by ELD.PI.5.5: Listening actively and Operations 22 Multiply Fractions to Find Area tiling it with unit squares of the asking/ answering questions about what &

was heard. Number appropriate unit fraction side lengths, and ELD.PI.5.6: Reading closely and Multiply Fractions to Find Area show that the area is the same as would 23 explaining interpretations/ideas from be found by multiplying the side lengths. reading.

Number 24 Multiply Fractions to Find Area Multiply fractional side lengths to find ELD.PI.5.10: Composing/writing areas of rectangles, and represent fraction literary and informational texts. Evaluation‐Multiply Fractions to Find products as rectangular areas. E6 Area 5.NF.5: Interpret multiplication as scaling 25 Interpret Multiplication as Scaling (resizing), by: 5.NF.5a: Comparing the size of a product to the size of one factor on the Interpret Multiplication as Scaling basis of the size of the other factor, without 26 performing the indicated multiplication. ELD.PI.5.5: Listening actively and asking/ answering questions about what 5.NF.5, 5.NF.5b: Explain why multiplying a given was heard. 27 Interpret Multiplication as Scaling number by a fraction greater than 1 results in a ELD.PI.5.6: Reading closely and product greater than the given number; explain explaining interpretations/ideas from why multiplying a given number by a fraction reading. less than 1 results in a product smaller than the ELD.PI.5.10: Composing/writing Interpret Multiplication as Scaling given number; relate the principle of fraction literary and informational texts. 28 equivalence a/b = (n×a) /(n×b) to the effect of multiplying a/b × 1. Evaluation‐Interpret Multiplication as 5.NF.5, 5.NF.5a, 5.NF.5b E7 Scaling

3 Common Core Standards Plus – Mathematics – Grade 5 with Common Core ELD Standard Alignment

Domain Lesson Focus Standard(s) ELD Standards 29 Fraction Multiplication Problems

30 Fraction Multiplication Problems 5.NF.6: Solve real world problems ELD.PI.5.5: Listening actively and involving multiplication of fractions and asking/ answering questions about what 31 Fraction Multiplication Problems mixed numbers, e.g., by using visual was heard. fraction models or equations to ELD.PI.5.6: Reading closely and 32 Fraction Multiplication Problems explaining interpretations/ideas from represent the problem. reading. Evaluation‐Fraction Multiplication ELD.PI.5.10: Composing/writing E8 Problems literary and informational texts. Performance Lesson #6 Multiplying Fractions (5.NF.4, 5.NF.4a, 5.NF.5, 5.NF.5b,

P6 5.NF.6) 33 Divide a Fraction by a Whole Number 5.NF.7c

‐ 5.NF.7: Apply and extend previous 34 Divide a Fraction by a Whole Number understandings of division to divide unit ELD.PI.5.5: Listening actively and fractions by whole numbers and whole asking/ answering questions about what 5.NF.1 35 Divide a Fraction by a Whole Number numbers by unit fractions. 5.NF.7a: was heard. Interpret division of a unit fraction by a ELD.PI.5.10: Composing/writing Fractions 36 Divide a Fraction by a Whole Number non‐zero whole number, and compute literary and informational texts. such quotients. Standards

Evaluation‐Divide a Fraction by a Whole E9 Number 37 Divide a Whole Number by a Fraction Operations Fractions

–

38 Divide a Whole Number by a Fraction ELD.PI.5.5: Listening actively and and

5.NF.7b: Interpret division of a whole asking/ answering questions about what 39 Divide a Whole Number by a Fraction number by a unit fraction, and compute was heard. such quotients. ELD.PI.5.10: Composing/writing literary and informational texts. Operations 40 Divide a Whole Number by a Fraction &

Number Evaluation‐Divide a Whole Number by a E10 Fraction

Number 41 Solve Real World Fraction Problems

5.NF.7c: Solve real world problems 42 Solve Real World Fraction Problems ELD.PI.5.5: Listening actively and involving division of unit fractions by non‐ asking/ answering questions about what zero whole numbers and division of whole 43 Solve Real World Fraction Problems was heard. numbers by unit fractions, e.g., by using ELD.PI.5.6: Reading closely and visual fraction models and equations to explaining interpretations/ideas from 44 Solve Real World Fraction Problems represent the problem. reading. ELD.PI.5.10: Composing/writing Evaluation‐Real World Fraction literary and informational texts. E11 Problems P7 Performance Lesson#7 Real World Fraction Problems (5.NF.7, 5.NF.7a‐5.NF.7c)

1 Converting Metric Units 5.MD.5c ‐

Data ELD.PI.5.5: Listening actively and 2 Converting Metric Units 5.MD.1: Convert among different‐sized asking/ answering questions about what &

5.MD.1 standard measurement units within a was heard.

given measurement system (e.g., convert 5 ELD.PI.5.6: Reading closely and 3 Converting Customary Units

Stand. explaining interpretations/ideas from cm to 0.05 m), and use these conversions in solving multi‐step, real world problems. reading. Data ELD.PI.5.10: Composing/writing & 4 Converting Customary Units literary and informational texts.

Measurement Evaluation ‐ Converting Measures within Measure. E1 the Same System

4 Common Core Standards Plus – Mathematics – Grade 5 with Common Core ELD Standard Alignment

Domain Lesson Focus Standard(s) ELD Standards 5 Fractional Data Sets

6 Fractional Data Sets 5.MD.2: Make a line plot to display a data ELD.PI.5.5: Listening actively and set of measurements in fractions of a unit asking/ answering questions about what 7 Fractional Data Sets (1/2, 1/4, 1/8). Use operations on fractions was heard. for this grade to solve problems involving ELD.PI.5.6: Reading closely and explaining interpretations/ideas from 8 Fractional Data Sets information presented in line plots. reading. Evaluation ‐ Solving Problems with ELD.PI.5.10: Composing/writing literary and informational texts. E2 Fractional Data Sets P8 Performance Lesson #8 Measurement Units & Line Plots (5.MD.1, 5.MD.2)

9 Measure with Cubic Units 5.MD.3: Recognize volume as an attribute of solid figures and understand concepts 10 Measure with Cubic Units of volume measurement. ELD.PI.5.5: Listening actively and asking/ answering questions about what was heard. 11 Measure with Cubic Units 5.MD.4: Measure volumes by counting ELD.PI.5.6: Reading closely and unit cubes, using cubic cm, cubic in, cubic explaining interpretations/ideas from 12 Measure with Cubic Units ft, and improvised units. reading.

E3 Evaluation ‐ Measure with Cubic Units 5.MD.3, 5.MD.4 5.MD.5c ‐

Find Volume by Multiplying Edge 5.MD.5: Relate volume to the operations 13 Lengths of multiplication and addition and solve Find Volume by Multiplying Edge real world and mathematical problems Data 5.MD.1

involving volume. 5.MD.5a: Find the 14 Lengths volume of a right rectangular prism with ELD.PI.5.5: Listening actively and asking/ answering questions about what and Find Volume by Multiplying Edge whole‐number side lengths by packing it 15 Lengths was heard. with unit cubes, and show that the volume ELD.PI.5.10: Composing/writing

Standards is the same as would be found by Find Volume by Multiplying Edge literary and informational texts. 16 Lengths multiplying the edge lengths, equivalently

Data by multiplying the height by the area of Evaluation‐Find Volume by Multiplying E4 the base. Represent threefold whole‐

and Edge Lengths

number products as volumes.

Measurement 17 Apply the Formulas for Volume ELD.PI.5.5: Listening actively and 5.MD.5b: Apply the formulas V = l × w × 18 Apply the Formulas for Volume asking/ answering questions about what h and V = b × h for rectangular prisms to was heard.

Measurement Apply Volume Formulas to Solve 19 find volumes of right rectangular prisms ELD.PI.5.6: Reading closely and Problems with whole number edge lengths in the explaining interpretations/ideas from Apply Volume Formulas to Solve context of solving real world and reading. ELD.PI.5.10: Composing/writing 20 mathematical problems. Problems literary and informational texts. Evaluation‐Apply Volume Formulas to E5 Solve Problems Volume of Non‐overlapping Right 21 Rectangular Prisms Volume of Non‐overlapping Right 5.MD.5c: Recognize volume as additive. 22 ELD.PI.5.5: Listening actively and Rectangular Prisms Find volumes of solid figures composed of asking/ answering questions about what Solving Volume Problems by two non‐overlapping right rectangular 23 was heard. Decomposing Prisms prisms by adding the volumes of the non‐ ELD.PI.5.6: Reading closely and Solving Volume Problems by overlapping parts, applying this technique explaining interpretations/ideas from 24 Decomposing Prisms to solve real world problems. reading. ELD.PI.5.10: Composing/writing E6 Evaluation ‐ Solving Volume Problems literary and informational texts. Performance Lesson #9 All About Volume (5.MD.3, 5.MD.4, 5.MD.5, 5.MD.5a‐ P9 5.MD.5c)

5 Common Core Standards Plus – Mathematics – Grade 5 with Common Core ELD Standard Alignment

Domain Lesson Focus Standard(s) ELD Standards 1 Evaluating Expressions

2 Evaluating Expressions 5.OA.1: Use parentheses, brackets, or ELD.PI.5.5: Listening actively and 3 Evaluating Expressions braces in numerical expressions, and asking/ answering questions about what evaluate expressions with these symbols. was heard. 4 Evaluating Expressions

E1 Evaluation‐Evaluating Expressions

5 Writing Numerical Expressions

6 Writing Numerical Expressions ELD.PI.5.5: Listening actively and 5.OA.2: Write simple expressions that asking/ answering questions about what 7 Writing Numerical Expressions record calculations with numbers, and was heard. interpret numerical expressions without ELD.PI.5.6: Reading closely and evaluating them. explaining interpretations/ideas from 8 Writing Numerical Expressions reading.

5.OA.3 Evaluation‐Writing Numerical

‐ E2 Expressions 9 Interpret Numerical Expressions 5.OA.1

Thinking Interpret Numerical Expressions ELD.PI.5.5: Listening actively and

10 5.OA.2: Write simple expressions that asking/ answering questions about what 11 Interpret Numerical Expressions record calculations with numbers, and was heard. Standards

interpret numerical expressions without ELD.PI.5.6: Reading closely and evaluating them. explaining interpretations/ideas from 12 Interpret Numerical Expressions reading. Algebraic Evaluation‐Interpret Numerical ELD.PI.5.10: Composing/writing Thinking

literary and informational texts. E3 Expressions and

P10 Performance Lesson #10 Expressions (5.OA.1, 5.OA.2) Algebraic 13 Generating Arithmetic Patterns and

5.OA.3: Generate two numerical patterns 14 Pattern Relationships using two given rules. Identify apparent ELD.PI.5.5: Listening actively and Operations relationships between corresponding asking/ answering questions about what 15 Pattern Relationships terms. Form ordered pairs consisting of was heard. corresponding terms from the two ELD.PI.5.10: Composing/writing Operations literary and informational texts. 16 Pattern Relationships patterns, and graph the ordered pairs on a coordinate plane. E4 Evaluation‐Pattern Relationships

17 Pattern Relationships 5.OA.3: Generate two numerical patterns 18 Pattern Relationships using two given rules. Identify apparent relationships between corresponding ELD.PI.5.5: Listening actively and 19 Graphing Patterns terms. Form ordered pairs consisting of asking/ answering questions about what corresponding terms from the two was heard. 20 Graphing Patterns patterns, and graph the ordered pairs on a ELD.PI.5.10: Composing/writing coordinate plane. literary and informational texts. E5 Evaluation‐Pattern Relationships

P11 Performance Lesson #11 Patterns (5.OA.3)

6 Common Core Standards Plus – Mathematics – Grade 5 with Common Core ELD Standard Alignment

Domain Lesson Focus Standard(s) ELD Standards 5.G.1: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with Plotting Points on a Coordinate Grid the intersection of the lines (the origin) 1 arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of 2 Plotting Points on a Coordinate Grid one axis, and the second number indicates how far to travel in the direction of the second axis, ELD.PI.5.5: Listening actively and with the convention that the names of the two asking/ answering questions about what axes and the coordinates correspond. was heard. 5.G.2: Represent real world and ELD.PI.5.10: Composing/writing 3 Graphing and Interpreting Points mathematical problems by graphing points literary and informational texts.

5.G.4) in the first quadrant of the coordinate ‐ 4 Graphing and Interpreting Points plane, and interpret coordinate values of points in the context of the situation. 5.G.1 Evaluation‐Understanding and 5.G.1, 5.G.2 E1 Interpreting Coordinate Systems P12 Performance Lesson #12 Graph It! (5.G.1, 5.G.2) Standards

Geometry 5.G.3: Understand that attributes belonging to a category of two‐ Understanding Attributes of Triangles 5 dimensional figures also belong to all subcategories of that category. (Geometry 5.G4: Classify two‐dimensional figures in a ELD.PI.5.5: Listening actively and Creating a Hierarchy of Triangles 6 hierarchy based on properties. asking/ answering questions about what was heard. Understanding Attributes of 7 5.G.3 ELD.PI.5.6: Reading closely and Quadrilaterals explaining interpretations/ideas from reading. 8 Creating a Hierarchy of Quadrilaterals 5.G.4 ELD.PI.5.10: Composing/writing literary and informational texts. Evaluation‐Two Dimensional Shapes – 5.G.3, 5.G.4 E2 Classifying and Hierarchy P13 Performance Lesson #13 Just Plane Hierarchy (5.G.3, 5.G.4)

7