Mathematical Practices Overview: Mathematical Practices MP.1: Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3: Construct viable arguments and critique the reasoning of others. MP.4: Model with mathematics. MP.5: Use appropriate tools strategically. MP.6: Attend to precision. MP.7: Look for and make use of structure. MP.8: Look for and express regularity in repeated * Refer to EnVision Mathematical Handbook for the practices and examples for students. On the pearsonrealize.com website there are student friendly videos for each practice. 1
Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. Student Friendly Language I can try many times to understand and solve a math problem. 2. Reason abstractly and quantitatively. I can think about the math problem in my head first. 3. Construct viable arguments and critique the reasoning of others. I can make a plan, called a strategy, to solve the problem and discuss other students strategies too. 4. Model with mathematics. I can use math symbols and numbers to solve the problem. 5. Use appropriate tools strategically. I can use math tools, pictures, drawings, and objects to solve the problem. 6. Attend to precision. I can check to see if my strategy and calculations are correct. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. I can use what I already know about math to solve the problem. I can use a strategy that I used to solve another math problem. 2
* Below is a table from the EnVision Overview and Implementation Guide (p.17). The Topic bands on the curriculum map have been color coded to indicate if the topic is a Priority Cluster (green) or Supporting Cluster (blue). Priority Clusters 5.NBT.A: Understand the place value system. 5.NBT.B: Analyze patterns and relationships. 5.NF.A: Use equivalent fractions as a strategy to add and subtract fractions. 5.NF.B: Apply and extend previous understanding of multiplication and division to multiply and divide fractions. 5.MD.C: Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.. Supporting Clusters 5.OA.A: Understand the place value system. 5.OA.B: Perform operations with multi-digit whole numbers and with decimals to hundredths. 5. MD.A: Convert like measurement units within a given measurement system. 5.MD.B: Represent and interpret data. 5.G.A: Graph point on the coordinate plane to solve realworld and mathematical problems. 5.G.B: Classify two-dimensional figures into categories based on their properties. 3
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Topic 1 Place Value Extending division to 2 digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations. Domain: Number and Operations in Base Ten Cluster: Understand the place value system. 5.NBT.A.1 5.NBT.A.3a 5.NBT.A.3b Topic 1 Daily Pacing Chart 7-8 days 3-4 days 12 days Date Lesson # Lessons Page Vocabulary Materials/Resources 8/29 Establish routines and procedures (use of manipulatives, math tools, online resources, and centers). Administer optional beginning of the year assessments. 8/31 9/1 to 9/19 Topic Opener 2 1.1 Place Value Relationships 6A Digits, value Place-value blocks (or Teachign Tools 8 and 9) 1.2 Tenths and Hundredths 8A Fraction Models: Strips (Teaching Tool 5) 1.3 Thousandths 12A 10 x 10 x 10 cube 1.4 Decimal Place Value 14A standard form, expanded form, word form, equivalent decimals Place-value chart (Teaching Tool 6) 1.5 Comparing and Ordering Decimals 16A Comparing and Ordering Decimals (Teaching Tool 7) 1.6 Problem Solving: Look for a Pattern 18A Problem Solving: Look for a 5
Pattern (Teaching Tool 8) Reteach Reteaching 22 Assessment Topic 1 test, Alternate Topic 1 Test, Online Topic 1 Test 24 Scoring Rubric in T.E. on p. 26 Assessment Performance Assessment 26 Assessment Placement Test 26A Assessment Basic Facts Timed Tests 26B Topic 2 Adding and Subtracting Decimals Extending division to 2 digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations. Domain: Operations and Algebraic Thinking Clusters: Understand the place value system. Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.A.4 5.NBT.B.7 Topic 2 Daily Pacing Chart 9-10 days 1-2 days 11 days Date Lesson # Lessons Page Vocabulary Materials/Resources 9/20 to 10/04 Topic Opener 27 2.1 Mental Math 30A commutative property, associative property, compatible numbers, compensation Place value materials, Teaching Tool 9 6
Due in OARS or Assess Online by 10/14 2.2 Rounding Decimals 34A rounding Teaching Tool 10 2.3 Estimating Sums and Differences 36A Teaching Tool 11 2.4 Modeling Addition and Subtraction of Decimals 2.5 Adding Decimals 44A 2.6 Subtracting Decimals 46A 2.7 Problem Solving: Multiple Step Problems 48A Reteach Reteaching 52 Assessment Topic 2 Test, Alternate Topic 2 Test, or Online Topic 2 Test (Due in OARS or Assess Online) Assessment Performance Assessment (Due in OARS) 40A Teaching Tool 12 (per student)/ Teaching Tool 31 (optional); Teaching Tool 24 (optional); colored pencils, crayons, or markers, scissors (per group) 56 58 Scoring Rubric in T. E. p. 58 7
Topic 3 Multiplying Whole Numbers Extending division to 2 digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations. Domain: Number and Operations in Base Ten Clusters: Understand the place value system. Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.A.2 5.NBT.B.5 5.NBT.B.7 5.OA.A.2 Topic 3 Daily Pacing Chart 8 days 2 days 10 days Date Lesson # Lessons Page Vocabulary Materials/Resources 10/04 to 10/18 Topic Opener 59 3.1 Multiplication Properties 62A commutative property of multiplication, associative property of multiplication, identity property of multiplication, zero property of multiplication 3.2 Multiplying by Powers of 10 64A base, exponent, exponential notation, factors, multiple, power, product 3.3 Multiplying 2 Digit Numbers by Multiples of 10 66A 3.4 Multiplying 2 Digit by 2 Digit Numbers 3.5 Multiplying Greater Numbers 70A Two-color Counters (Teaching Tool 13) ¼- inch grid paper (Teaching Tool 10) 68A partial products Straightedges, Small Grid Paper (Teaching Tool 16) 8
3.6 Problem Solving: Draw a Picture and Write an Equation 72A Problem-Solving Recording Sheet (Teaching Tool 1), 1 per student Reteach Reteaching 74 Assessment Topic 3 test, Alternate Topic 3 Test, 76 Online Topic 3 Test Assessment Performance Assessment 78 Scoring Rubric in T.E. p. 78 Topic 4 Dividing by 1-Digit Divisors Extending division to 2 digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations. Domain: Number and Operations in Base Ten Cluster: Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.B.6 5.OA.A.2 Topic 4 Daily Pacing Chart 6-7 days 2-3days 9 days 9
Date Lesson # Lessons Page Vocabulary Materials/ Resources 10/19 Topic 79 to 11/02 Opener 4.1 Dividing Multiples of 10 and 100 82A dividend, divisor, quotient 4.2 Estimating Quotients 84A Multiplication Table (Teaching Tool 17) (per pair) 4.3 Problem Solving: Reasonableness 86A 4.4 Dividing by 1 Digit Divisors 88A Four number cubes (2 labeled 1-6, 2 labeled 4-9) (per group) 4.5 Zeros in the Quotient 92A Bills and Coins or Teaching Tool 18: four $100 bills, five $10 bills, twenty $1 bills 4.6 More Dividing by 1 Digit Divisors 96A 4.7 Problem Solving: Draw a Picture and 98A Write an Equation Problem-Solving Recording Sheet (Teaching Tool 1) (per student) Bills and Coins (Teaching Tool 18) (optional) Reteach Reteaching 100 Assessment Topic 4 Test, or Alternate Test, or Online Topic 4 Test 102 Assessment Performance Assessment 104 Scoring Rubric in T.E. p. 104 Assessment Benchmark Test Topics 1-4 104A 10
Topic 5 Dividing by 2-Digit Divisors Extending division to 2 digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations. Domain: Number and Operations in Base Ten Cluster: Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.B.6 Topic 5 Daily Pacing Chart 10 days 2 days 12 days 11
Date Lesson # Lessons Page Vocabulary Materials/Resources 11/02 Topic Opener 105 to 5.1 Using Patterns to Divide 108A 11/18 5.2 Estimating Quotients with 2 Digit Divisors 110A 5.3 Connecting Models and Symbols 112A Grid Paper 5.4 Dividing by Multiples of 10 114A 5.5 1-Digit Quotients 116A 5.6 2-Digit Quotients 120A 5.7 Dividing with Greater Numbers 122A Calculator 5.8 Problem Solving: Missing or Extra Information 124A Problem-Solving Recording Sheet (Teaching Tool 1) Reteach Reteaching 126 Assessment Topic 5 test, Alternate Topic 5 test, Online Topic 5 test 128 Scoring Rubric in T.E. p. 130 Assessment Performance Assessment 130 12
Topic 6 Multiplying Decimals Extending division to 2 digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations. Domain: Number and Operations in Base Ten Clusters: Perform operations with multi-digit whole numbers and with decimals to hundredths. Understand the place value system. 5.NBT.A.1 5.NBT.A.2 5.NBT.B.7 Topic 6 Daily Pacing Chart 10 days 2 days 12 days Date Lesson # Lessons Page Vocabulary Materials/Resources 11/21 131 to 12/12 6.1 Multiplying Decimals by 10, 100, or 1,000 134A Multiplying Decimals by 10, 100, or 1,000 6.2 Estimating the Product of a Decimal and a Whole Number 136A (Teaching Tool 19) Estimating the Product of a Decimal and a Whole Number (Teaching Tool 20) 6.3 Number Sense: Decimal Multiplication 138A 6.4 Models for Multiplying Decimals 140A Decimal Grids (Teaching Tool 21), Color pencils 6.5 Multiplying a Decimal by a Whole Number 144A Multiplying a Whole Number and 13
Due in OARS or Assess Online by 12/16 a Decimal (Teaching Tool 41) 6.6 Multiplying Two Decimals 146A Multiplying Two Decimals (Teaching Tool 22) Reteach Reteaching 150 Assessment Topic 6 test Topic 6 Test, Alternate Topic 6 Test, or Online Topic 6 Test ( Due in OARS or Assess 152 Assessment Online) Performance Assessment (Due in OARS or Assess Online) 154 Scoring Rubric in T.E. p. 154 Topic 7 Dividing Decimals Extending division to 2 digit divisors, integrating decimal fractions into the place value system and developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations. Domain: Number and Operations in Base Ten Clusters: Perform operations with multi-digit whole numbers and with decimals to hundredths. Understand the place value system. 5.NBT.A.1 5.NBT.A.2 5.NBT.B.7 14
Topic 7 Daily Pacing Chart 11 days 2 days 11 days Date Lesson # Lessons Page Vocabulary Materials/Resources 12/13 to 1/11 Topic Opener 155 7.1 Dividing Decimals by 10, 100, or 1,000 158A 7.2 Estimating Decimal Quotients 160A 7.3 Number Sense: Decimal Division 162A 7.4 Dividing by a Whole Number 164A Decimal Models (Teaching Tool 23), scissors 7.5 Dividing a Whole Number by a Decimal 166A Decimal Grids (Teaching Tool 21), scissors 7.6 Dividing a Decimal by a Decimal 168A Decimal Grids (Teaching Tool 21), 7.7 Problem Solving: Multiple Step Problems 170A Problem-Solving Recording Sheet (Teaching Tool 1) Reteach Reteaching 172 Assessment Topic 7 Test, Alternate Topic 7 Test, Online Topic 7 Test 174 Assessment Performance Assessment 176 Scoring Rubric in T.E. p. 176 Topic 8 Numerical Expressions, Patterns, and Relationships 15
Domain: Operations and Algebraic Thinking Clusters: Analyze patterns and relationships. 5.OA.A.1 5.OA.A.2 5.OA.B.3 Topic 8 Daily Pacing Chart 8 days 3 days 11 days Date Lesson # Lessons Page Vocabulary Materials/Resources 1/12 to 1/30 Topic Opener 8.1 Variables and Expressions 180A algebraic expression, numerical expression, variable 8.2 Order of Operations 182A order of operations 8.3 Evaluating Expressions 186A 8.4 Addition and Subtraction Expressions 188A Place-Value Blocks (or Teaching Tool 24) 8.5 Multiplication and Division Expressions 190A Place-Value Blocks (or Teaching Tool 24) 8.6 Patterns: Extending Tables 192A corresponding, sequence, term Counters (optional) 8.7 Problem Solving: Use Reasoning 194A Color tiles: 10 red, 10 green, and 10 yellow per group/ Problem- Solving Recording Sheet Reteach Reteaching 196 Assessment Topic 8 Test, Alternate Topic 8 Test, Online Topic 8 Test 198 Assessment Performance Assessment 200 Scoring Rubric in T.E. p. 200 16
Assessment Benchmark Test Topics 5-8 200A Topic 9 Adding and Subtracting Fractions Developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions.) Domain: Number and Operations-Fractions Cluster: Use equivalent fractions as a strategy to add and subtract fractions. 5.NF.A.1 5.NF.A.2 5.OA.A.2.1 Topic 9 Daily Pacing Chart 10 days 2 days 12 days 17
Date Lesson # Lessons Page Vocabulary Materials/Resources 1/31 to 2/15 Topic Opener 9.1 Prime Factorization 201 204A prime number, composite number, prime factorization 9.2 Finding Prime Factors 206A prime factorization, factor tree 9.3 Problem Solving: Writing to Explain 208A benchmark fraction 9.4 Estimating Sums and Differences of Fractions 210A Number lines (Teaching Tool 26), fraction models: strips (ore Teaching Tool 5), Due in OARS or 9.5 Adding Fractions with Unlike Denominators 212A least common, denominator (LCD) 9.6 Subtracting Fractions with Unlike Denominators 214A scissors (per pair) Fraction models: strips (or Teaching Tool 5), scissors (per pair) Fraction models: strips (or Teaching Tool 5), scissors (per pair) 9.7 More Adding and Subtracting Fractions 216A Fraction models: circle (Teching Tool 28), scissors (per pair) Fraction Models: Strips (Teaching Tool 5) (optional) 9.8 Problem Solving: Draw a Picture and Write an Equation Reteach Reteaching 222 Assessment Topic 9 Test, Alternate Topic 9 Test, Online 224 218A 18
Assess Online by 3/3 Assessment Topic 9 Test (due in OARS or assess online) Performance Assessment (due in OARS) 226 Scoring Rubric in T.E. p. 226 Topic 10 Adding and Subtracting Mixed Numbers Developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions.) Domain: Number and Operations - Fractions Cluster: Use equivalent fractions as a strategy to add and subtract fractions. 5.NF.A.1 5.NF.A.2 Topic 10 Daily Pacing Chart 8-9 days 2 days 11 days 19
Date Lesson # Lessons Page Vocabulary Materials/Resources 2/16 Topic Opener 227 to 3/07 10.1 Estimating Sums and Differences of Mixed 230A mixed number Numbers 10.2 Modeling Addition and Subtraction of Mixed Numbers 232A Fraction models: strips (or Teaching Tool 5) (per pair) 10.3 Adding Mixed Numbers 236A Fraction models: strips (or Teaching Tool 5) (per pair) 10.4 Subtracting Mixed Numbers 238A Fraction models: strips (or Teaching Tool 5) (per pair) 10.5 More Adding and Subtracting Mixed Numbers 10.6 Problem Solving: Draw a Picture and Write an Equation 240A 242A Reteach Reteaching 244 Assessment Topic 10 Test, Alternate Topic 10 Test, Online Topic 10 Test 246 Assessment Performance Assessment 248 Scoring Rubric in T.E. p. 248 Topic 11 Multiplying and Dividing Fractions and Mixed Numbers Developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions.) 20
Domain: Number and Operations - Fractions Cluster: Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 5.NF.B.3, 5.NF.B.4a, 5.NF.B.4b, 5.NF.B.5a, 5.NF.B.5b, 5.NF.B.6, 5.NF.B.7a, 5.NF.B.7b, 5.NF.B.7c Topic 11 Daily Pacing Chart 12 days 2 days 14 days Date Lesson # Lessons Page Vocabulary Resources/Materials 3/08 Topic Opener 249 to 11.1 Multiplying Fractions and Whole 252A 3/28 Numbers 11.2 Multiplication as Scaling 254A resizing, scaling 11.3 Estimating Products 258A 11.4 Multiplying Two Fractions 260A Paper 11.5 Area Models 264A Centimeter Grid Paper (Teaching Tool 31) 11.6 Multiplying Mixed Numbers 266A Multiplying Mixed Numbers (Teaching Tool 30) 11.7 Problem Solving: Multiple Step 268A Problems 11.8 Fractions and Division 270A Scissors; Circle Patterns (Teaching Tool 29) 3 same-size circles per group 11.9 Fractions, Mixed Numbers, and 272A Decimals as Quotients 11.10 Dividing Whole Numbers by Unit Fractions 274A reciprocal Four 81/2 x 11 sheets of paper, scissors (per pair) 21
11.11 Dividing Unit Fractions by Non-Zero Whole Numbers 276A 11.12 Problem Solving: Draw a Picture and 278A Write an Equation Reteach Reteaching 280 Assessment Topic 11 Test, Alternate Topic 11 Test, Online Topic 11 Test Assessment Performance Assessment 284 Fraction Models: Circles (Teaching Tool 28), optional Paper 282 Scoring Rubric in T.E. p. 284 Topic 12 Volume of Solids Developing understanding of volume. Domain: Measurement and Data Cluster: Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 5.MD.C.3a, 5MD.C.3b, 5.MD.C.4 5.MD.C.5a, 5.MD.C.5b, 5.MD.C.5c 22
Topic 12 Daily Pacing Chart 5 days 2 days 7 days Date Lesson # Lessons Page Vocabulary Materials/Resources 3/29 to 4/07 Topic Opener 12.1 Modeling Addition of Fractions 285 288A volume, cubic unit, cube, edge Due in OARS or Assess Online by 4/14 Unit cubes (30 per student), manila folder (per pair) 12.2 Adding Fractions with Like Denominators 290A prism Unit cubes (40 per group) 12.3 Modeling Subtraction of Fractions 292A Combining volumes (Teaching Tool 32), markers in 2 colors 12.4 Subtracting Fractions with Like Denominators 294A Unit cubes (4 per group), Problem- Solving Recording Sheet (Teaching Tool 1) Reteach Reteaching 298 Assessment Topic 12 test, Alternate Topic 12 Test, Online Topic 12 Test (due in OARS or Assess online) Assessment Performance Assessment (due in OARS) Assessment Benchmark Test Topics 9-12 302A 300 302 Scoring Rubric in T.E. p. 302 23
Topic 13 Volume of Solids Domain: Measurement and Data Cluster: Convert like measurement units within a given measurement system. 5.MD.A.1 Topic 13 Daily Pacing Chart 9 days 2 days 11 days 24
Date Lesson # Lessons Page Vocabulary Materials/ Resources 4/10 Topic Opener 303 to 13.1 Converting Customary Units of Length 306A 5/1 Inch and yardstick rulers (or Teaching Tool 33), 2 different colored markers, strips of paper 1 yard long (1 per group 13.2 Converting Customary Units of Capacity 308A Teaching Tool 34, (optional); liquid measuring cup, empty containers (pint, quart, ½ gallon, and gallon size), water 13.3 Converting Customary Units of Weight 310A 13.4 Converting Metric Units of Length 312A Centimeter rulers marked in millimeters (or Teaching Tool 35) (per group) 13.5 Converting Metric Units of Capacity 314A (optional) Liquid measuring cup (shows ml), empty liter container, water (per group) 13.6 Converting Metric Units of Mass 316A 13.7 Problem Solving: Multiple Step 318A Problems Reteach Reteaching 320 Assessment Topic 13 Test, Alternate Topic 13 Test, 322 Problem-Solving Recording Sheet (Teaching Tool 1) 25
or Online Topic 13 Test Assessment Performance Assessment 324 Scoring Rubric in T.E. p. 324 Topic 14 Data Cluster: Represent and interpret data 5.MD.B.2 5.G.A.2 Domain: Measurement and Data Topic 14 Daily Pacing Chart 7 days 2 days 10 days 26
Date Lesson # Lessons Page Vocabulary Materials/ Resources 5/2 Topic Opener 325 to 5/16 14.1 Line Plots 328A line plot, outlier 14.2 Data from Surveys 330A survey, data, sample, frequency table, line plot 14.3 Making Line Plots 332A 14.4 Measurement Data 334A Problem- Solving: Look for a Pattern (Teaching Tool 8, optional) 14.5 Problem Solving: Writing to Explain 336A Reading Time, Teaching Tool 36 (1 per student) Reteach Reteaching 338 Assessment Topic 14 Test, Alternate Topic 14 Test, 340 Online Topic 14 Test Assessment Performance Assessment 342 Scoring Rubric in T.E. p. 342 27
Topic 15 Classifying Plane Figures Domain: Geometry Cluster: Classify two-dimensional figures into categories based on their properties. 5.G.B.3 5.G.B.4 Topic 15 Daily Pacing Chart 8 days 2 days 9 days 28
Date Lesson # Lessons Page Vocabulary Materials/Resources 5/17 Topic Opener 343 to 5/31 15.1 Polygons 346A Polygon, regular polygon, triangle, Wooden sticks or straws quadrilateral, pentagon, hexagon, octagon 15.2 Triangles 348A Equilateral triangle, isosceles triangle, scalene triangle, right triangle, acute triangle, obtuse triangle 15.3 Attributes of Quadrilaterals 350A Parallelogram, Teaching Tool 37 trapezoid, rectangle, rhombus, square 15.4 Special Quadrilaterals 352A 15.5 Classifying Quadrilaterals 354A Teaching Tool 38, scissors, paper 15.6 Problem Solving: Make and Test 356A generalization Generalizations Reteach Reteaching 358A Assessment Topic 15 Test, Alternate Topic 15, Online Topic 15 Test 360 Assessment Performance Assessment 362 Scoring Rubric in T.E. p. 362 29
Topic 16 Coordinate Geometry Domain: Geometry Cluster: Graph points on the coordinate plane to solve real-world and mathematical problems. 5.G.A.1 5.G.A.2 5.OA.B.3 Topic 16 Daily Pacing Chart 8 days 2 days 10 days Date Lesson # Lessons Page Vocabulary Materials/Resources 6/1 to 6/10 Topic Opener 16.1 Ordered Pairs 366A Coordinate grid, x-axis, y-axis, origin, ordered pair, x-coordinate, y-coordinate Coordinate grids (Teaching Tool 39) (1 per student) 16.2 Patterns and Graphing 370A Grid Paper 16.3 More Patterns and Graphing 372A Grid Paper 16.4 Graphing Number Patterns 374A Grid Paper 16.5 Problem Solving: Work Backward 376A Reteach Reteaching 378 Assessment Topic 16 Test, Alternate Topic 16 Test, Or Online Topic 16 Test opic 16 test 380 Assessment Performance Assessment 382 Scoring Rubric in T.E. p. 382 Assessment Benchmark Test Topics 13-16 382A 30
6/6 to 6/10 Assessment End of Year Test 382B Step up Lessons Step up Lessons to 6 th grade 383 31