St. Louis Public Schools Mathematics - Grade 5 st Quarter ...

St. Louis Public Schools

Mathematics - Grade 5

1st Quarter Pacing Guide - August 11

th – October 10th

, 2014 Grade 5 Mathematics Overview: Fifth grade mathematics is about (1) 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); (2) extending division to two-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; and (3) developing understanding of volume. Key Areas of Focus for 3-5: Multiplication and division of whole numbers and fractions – concepts, skills and problem solving Required Fluency: 5.NBT.5 Multi-digit multiplication 1

st Quarter Overarching Learning Goals

Unit 1: Decimal Place Value, Arithmetic and Numerical Patterns (Approx. 18-22 days) Number and Operations in Base Ten

• Understand the place value system. (5.NBT.3, 5.NBT.3a, 5.NBT.3b, 5.NBT.4) • Perform operations with multi-digit whole numbers and with decimals to hundredths. (5.NBT.7)

Operations and Algebraic Thinking • Write and interpret numerical expressions. (5.OA.1, 5.OA.2) • Analyze patterns and relationships. (5.OA.3)

Unit 2: Developing Fluency with Whole Number Multiplication and Division (Approx. 20-25 days) Number and Operations in Base Ten

• Perform operations with multi-digit whole numbers and with decimals to hundredths. (5.NBT.5, 5.NBT.6)

Assessment: Formative assessment strategies will be used frequently in every lesson to gauge students' understanding and make adjustments to instruction accordingly. Summative assessment strategies will be used at the end of each lesson and unit to gauge students’ mastery of standards and to plan for reteaching/intervention.

Standards for Mathematical Practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.




th – October 10th

, 2014

Adapted from A Story of Units: A Curriculum Overview for Grade P-5 from EngageNY and commoncore.org Adapted from Mathematics Common Core Scope and Sequence – Grade 3 from Long Beach Unified School District Objectives and Resources/Materials adapted from enVision Math --- Copyright 2009 Pearson Education (St. Louis Public Schools holds valid license for Pearson enVision Math resources) Additional Resources from Missouri Department of Elementary and Secondary Education @ www.dese.mo.gov (MLS’s crosswalks and mathematics model curriculum units.) * enVision math lessons with a capital letter behind the number i.e. 1-5A are additional lessons created for transition to Common Core – these lessons are available online (not part of the 2011 enVision text.) **Strikethrough indicates not addressing that part of the standard.

Unit 1: Decimal Place Value, Arithmetic and Patterns (Approx. 15-18 days) Time Frame

Missouri Learning Standards (Common Core Standards)

Content Objectives (numbers correspond with resources) Students will be able to…

Mathematical Practices

Resources/Materials (numbers correspond with objectives)

Assessment Students will be able to demonstrate mastery of the standards by…

3-5 days 5.NBT.3 Read, write and compare decimals to the thousandths. 5.NBT.3a Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x

100 + 4 x 10 + 7 x 1 + 3 x ( ) + 9 x ( ) + 2 x (

). 5.NBT.3b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 5.NBT.4 Use place value understanding to round decimals to any place.

(1) write the standard, expanded, and word forms of whole numbers in billions, and identify the value of digits in whole numbers. (Prepares for 5.NBT.1, not a 5th grade MLS) (2) write decimals in expanded, standard, and word form through millionths. (5.NBT.3, 5.NBT.3a) (3) compare and order decimals through thousandths. (5.NBT.3, 5.NBT.3a, 5.NBT.3b) (4) round whole numbers through millions and decimals through thousandths. (5.NBT.4)

1, 2, 4, 6, 8 enVision Math Lesson Sequence: (1) 1-1: Place Value pp. 4-5 (2) 1-3: Decimal Place Value pp. 10-11 (3) 1-4: Comparing and Ordering Decimals pp. 12-13 (4) 2-2: Rounding Whole Numbers and Decimals pp. 28-29 Manipulatives: Place value blocks Teaching Tools: decimal place-value chart, Problem Solving Recording Sheet

enVision Formative Assessments: Quick Check 1-1 Quick Check 1-3 Quick Check 1-4 Quick Check 2-2

3-5 days 5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

(1) add and subtract decimals in tenths and hundredths using models. (5.NBT.7) (2) compute sums of decimals involving tenths, hundredths, and thousandths. (5.NBT.7) (3) compute differences of decimals involving tenths, hundredths, and thousandths. (5.NBT.7) (4) use multiple steps to solve a variety of problems. (5.NBT.7)

1, 3, 4, 5, 6, 7 enVision Math Lesson Sequence: (1) 2-6A**: Modeling Addition and Subtraction of Decimals (2) 2-6: Adding Decimals pp. 42-43 (3) 2-7: Subtracting Decimals pp. 44-45 (4) 2-8: Problem Solving: Multi-Step Problems pp. 46-49 Manipulatives: 10X10 grids, place-value blocks, crayons or markers (optional) Teaching Tools: centimeter grid paper, Problem Solving Recording Sheet

enVision Formative Assessments: Quick Check 2-6A Quick Check 2-6 Quick Check 2-7 Quick Check 2-8




th – October 10th

, 2014


Unit 1: Decimal Place Value, Arithmetic and Patterns (Approx. 15-18 days) Time Frame






6-7 days 5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. http://illustrativemathematics.org/illustrations/555 5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 x (8 + 7). Recognize that 3 x (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. http://illustrativemathematics.org/illustrations/139 http://illustrativemathematics.org/illustrations/556 http://illustrativemathematics.org/illustrations/590 5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

(1) translate words into algebraic expressions. (5.OA.2) (2) use patterns to show relationships and solve algebraic expressions.(5.OA.2) (3) extend patterns in a table using given rules and will then look for the relationship between corresponding terms in the sequences. (5.OA.3) (4) use the Distributive Property to simply expressions and solve equations. (5.OA.1, 5.NBT.5) (5) use given values for variables to evaluate numerical or algebraic expressions with three or more numbers and tow or more operations. (5.OA.1) (6) use the order of operations to evaluate expressions with whole numbers and decimals. (5.OA.1) (7) Students will study completed tables to determine a rule and write an addition or subtraction expression. (5.OA.3) (8) Students will study completed tables to determine a rule and write a multiplication or division expression. (5.OA.3)

1, 2, 5, 7, 8 enVision Math Lesson Sequence: (1) 6-1: Variables and Expressions pp. 146-147 (2) 6-3 More Patterns and Expressions pp. 152-155 (3) 6-4A*: Patterns: Extending Tables (4) 6-4: Distributive Property pp. 156-157 (5) 6-5: Order of Operations pp. 158-161 (6) 6-6A*: Evaluating Expressions (7) 6-6B*: Addition and Subtraction Expressions (8) 6-6C*:Multiplication and Division Expressions Manipulatives: counters, place-value blocks Teaching Tools: Problem Solving Recording Sheet

enVision Formative Assessments: Quick Check 6-1 Quick Check 6-2 Quick Check 6-4A Quick Check 6-4 Quick Check 6-5 Quick Check 6-6A Quick Check 6-6B Quick Check 6-6C Summative: Unit 1 assessment (Use Pearson Success Net or Acuity to create a unit assessment based on the Missouri Learning Standards covered in Unit 1)

http://illustrativemathematics.org/illustrations/555







th – October 10th

, 2014


Unit 2: Developing Fluency with Whole Number Multiplication and Division (Approx. 20-25 days) Time Frame






4-5 days 5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

Multiplying Whole Numbers (1) use partial products or the traditional algorithm to multiply multi-digit numbers by a one-digit number. (5.NBT.5) (2) multiply two-digit numbers by two-digit numbers. (5.NBT.5) (3) multiply two-digit numbers by factors with more than two-digits. (5.NBT.5) (4) use diagrams and write equations to solve problems. (5.NBT.5, 5.OA.2)

1, 3, 4, 5, 6, 7 enVision Math Lesson Sequence: (1) 3-4: Multiplying by 1-Digit Numbers pp. 64-67 (2) 3-5: Multiplying by 2-Digit Numbers pp. 68-69 (3) 3-6: Multiplying Greater Numbers pp. 70-71 (4) 3-8: Problem Solving: Draw a Picture and Write an Equation pp. 74-77 Manipulatives: straightedges, colored pencils or crayons Teaching Tools: small grid paper, Problem Solving Recording Sheet

enVision Formative Assessments: Quick Check 3-4 Quick Check 3-5 Quick Check 3-6 Quick Check 3-8

5-8 days 5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Dividing by 1-Digit Divisors (1) find the quotient of a division problem whose dividend is a multiple of 10, where division involves a basic fact. (5.NBT.6) (2) use rounding and compatible numbers to estimate quotients of whole numbers. (5.NBT.6) (3) find quotients using the model of sharing money. (5.NBT.6) (4) divide three-digit whole numbers by one-digit divisors. (5.NBT.6) (5) divide with zeros in the quotient. (5.NBT.6)

1, 3, 4, 5, 6, 7 enVision Math Lesson Sequence: (1) 4-1: Dividing Multiples of 10 and 100 pp. 84-85 (2) 4-2: Estimating Quotients pp. 86-87 (3) 4-4: Connecting Models and Symbols pp. 92-93 (4) 4-5: Dividing by 1-Digit Divisors pp. 94-97 (5) 4-6: Zeros in the Quotient pp. 98-101 Manipulatives: number cubes, bills and coins, centimeter grid paper or color tiles Teaching Tools: multiplication table, Problem Solving Recording Sheet

enVision Formative Assessments: Quick Check 4-1 Quick Check 4-2 Quick Check 4-4 Quick Check 4-5 Quick Check 4-6




th – October 10th

, 2014


Unit 2: Developing Fluency with Whole Number Multiplication and Division (Approx. 20-25 days) Time Frame






10-12 days

5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm. 5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Dividing by 2-Digit Divisors (1) find the quotients of division problems whose dividends and divisors are multiples of 10, where the dividend involves a basic fact. (5.NBT.6) (2) use estimation to find approximate solutions to quotients with two-digit divisors using compatible numbers. (5.NBT.6) (3) use arrays and area models to model division. (5.NBT.6) (4) find the hidden question or questions to solve multiple-step problems. (5.NBT.5, 5.NBT.6) (5) find quotients with a two-digit divisor that is a multiple of ten. (5.NBT.6) (6) find one-digit quotients where the divisor is a two-digit number. (5.NBT.6) (7) divide a three-digit number by a two-digit number to find a two-digit quotient. (5.NBT.6) (8) solve problems involving division of numbers with 4 or 5 digits by 2-digit divisors with an estimate or by using a calculator when the exact answer is needed. (5.NBT.6) (9) determine which information is missing and identify extraneous information in problems. (5.NBT.5, 5.NBT.6)

1, 2, 3, 4, 5, 6, 7, 8

enVision Math Lesson Sequence: (1) 5-1: Using Patterns to Divide pp. 122-123 (2) 5-2: Estimating Quotients with 2-Digit Divisors pp. 124-125 (3) 5-3A*: Connecting Models and Symbols (4) 5-3: Problem Solving: Multiple-Step Problems pp. 126-127 (5) 5-4: Dividing by Multiples of 10 pp. 128-129 (6) 5-5: 1-Digit Quotients pp. 130-133 (7) 5-6: 2-Digit Quotients pp. 134-135 (8) 5-7: Estimating and Dividing with Greater Numbers pp. 136-137 (9) 5-8 Problem Solving: Missing or Extra Information pp. 138-139 Manipulatives: calculator (optional), bills and coins, Teaching Tools: grid paper, Problem Solving Recording Sheet Click here for Lesson Plans

enVision Formative Assessments: Quick Check 5-1 Quick Check 5-2 Quick Check 5-3A Quick Check 5-3 Quick Check 5-4 Quick Check 5-5 Quick Check 5-6 Quick Check 5-7 Quick Check 5-8 Summative: Unit 2 assessment (Use Pearson Success Net or Acuity to create a unit assessment based on the Missouri Learning Standards covered in Unit 2)

http://www.slps.org/Page/24109

2014-‐2015 Mathematics Scope and Sequence – Grade 5 -‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐-‐

Sequence of Grade 5 Mathematics Units Aligned with Missouri Learning Standards 1st Quarter

Aug 11 – Oct 10 (43 days) 2nd Quarter

Oct 13 – Dec 19 (44 days) 3rd Quarter

Jan 5 – March 6 (42 days) 4th Quarter

March 9 – May 22 (47 days) Unit 1: Decimal Place Value, Arithmetic and Patterns (Approx. 18 – 22 days)

Unit 3: Multiplying and Dividing Decimals & Relating Decimals and Fractions (Approx. 18 – 20 days)

Unit 5: Multiplying and Dividing Fractions and Mixed Numbers (Approx. 10 – 15 days)

Unit 7: Problem Solving with Data and Measurement (Approx. 15 – 20 days)

Missouri Learning Standards

enVision Lessons/ Resources







5.NBT.3 5.NBT.3.a 5.NBT.3.b 5.NBT.4 5.OA.1 5.OA.2 5.OA.3

1-‐1 1-‐3 1-‐4 2-‐2 2-‐6A* 2-‐6 2-‐7 2-‐8 6-‐1 6-‐3 6-‐4A*

6-‐4 6-‐5 6-‐6A* 6-‐6B* 6-‐6C*

5.NBT.1 5.NBT.2 5.NBT.3.a 5.NBT.7 5.NF.3

7-‐1 7-‐2 7-‐3 7-‐4A* 7-‐4B* 7-‐4 7-‐5 7-‐6A* 7-‐6 7-‐7 7-‐8

9-‐2 9-‐3 9-‐8 9-‐9 9-‐10

5.NF.4 5.NF.4.a 5.NF.4.b 5.NF.5 5.NF.5.a 5.NF.5.b 5.NF.6 5.NF.7 5.NF.7.a 5.NF.7.b 5.NF.7.c

11-‐1 11-‐2A* 11-‐2 11-‐3A* 11-‐3 11-‐4A* 11-‐4 11-‐5A*

5.MD.1 5.MD.2

12-‐1 12-‐2 14-‐1 14-‐2 14-‐3 14-‐4 14-‐5 DESE**3 18-‐2A* 18-‐2B 18-‐2

Unit 2: Developing Fluency with Whole Number Multiplication and Division (Approx. 18-‐ 22 days)

Unit 4: Adding and Subtracting Fractions (Approx. 22 – 25 days)

Unit 6: Understanding Concepts of Volume (Approx. 22 – 28 days)

Unit 8: Coordinate Planes and Classifying Two-‐Dimensional Figures (Approx. 20 – 25 days)









5.NBT.5 5.NBT.6 5.OA.2

3-‐4 3-‐5 3-‐6 3-‐8 4-‐1 4-‐2 4-‐4 4-‐5 4-‐6 5-‐1

5-‐2 5-‐3A* 5-‐3 5-‐4 5-‐5 5-‐6 5-‐7 5-‐8

5.NF.1 5.NF.2

10-‐1A* 9-‐7 10-‐1 10-‐2 10-‐3 10-‐4 10-‐5A* 10-‐6 10-‐7A* DESE**1

5.MD.3 5.MD.3.a 5.MD.3.b 5.MD.4 5.MD.5 5.MD.5.a 5.MD.5.b 5.MD.5.c

13-‐4 13-‐5A* 13-‐5 13-‐6A* 13-‐6 13-‐7 DESE**2

5.G.1 5.G.2 5.G.3 5.G.4 5.OA.3

17-‐2 17-‐3 17-‐4A* 17-‐4B* 17-‐4C* DESE**4 8-‐3 8-‐4 8-‐5

8-‐6A* 8-‐6B* 8-‐6

* enVision math lessons with a capital letter behind the number i.e. 1-‐5A are additional lessons created for transition to Common Core – these lessons are available online (not part of the 2011 student text.) **Missouri Department of Elementary and Secondary Education – Model Curriculum Units https://k12apps.dese.mo.gov/webapps/ModelCurriculum/findunit.aspx (1) Select 5th Grade à math à Adding and Subtracting Fractions (2) Select 5th Grade à math à Build It Volume (3) Select 5th Grade à math à Converting Like Measurement Units within a Given Measurement System (4) Select 5th Grade à math à Graphing Points on the Coordinate Plane

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