Curriculum Guide Grade 5

Transcription

1 2016/2017 Elementary Mathematics 1 st Quarter Curriculum Guide Grade 5 Page 1 of 61

2 Duration 8/15/16 9/13/16 21 Days 5 th Grade Year at a Glance Quarter 1 Quarter 2 Quarter 3 Quarter 4 9/14/16 10/14/16 23 Days 10/17/16 11/16/16 22 Days 11/17/16 12/22/16 22 Days 1/9/17 1/26/17 12 Days 1/27/17 2/28/17 22 Days 3/1/17 3/16/17 12 Days 3/27/17 4/11/17 11 Days 4/12/17 5/10/17 19 Days 5/11/17 6/2/17 16 Days Modules Math Florida Standards Module 1: Place Value and Decimal Fractions Number and Operations in Base Ten 5.NBT NBT NBT.1.4 Measurement and Data 5.MD.1.1 : Multi Digit Whole Number and Decimal Fraction Operations Operations and Algebraic Thinking 5.OA OA.1.1 Number and Operations in Base Ten 5.NBT NBT NBT.2.6 Module 3: Addition and Subtraction of Fractions Number and Operations Fractions 5.NF NF.1.2 Module 4: Multiplication and Division of Fractions and Decimal Fractions Operations and Algebraic Thinking 5.OA OA.1.2 Number and Operations Fractions 5.NF NF.2.4a 5.NF NF NF.2.7 Measurement and Data 5.MD MD.2.2 Module 5: Addition and Multiplication with Volume and Area Number and Operations Fractions 5.NF.2.4b Measurement and Data 5.MD MD MD.3.5 Geometry 5.G G.2.4 Module 6 Part 1: Problem Solving with the Coordinate Plane Operations and Algebraic Thinking 5.OA OA.2.3 Number and Operations Fractions Geometry 5.G G.1.2 Review, Remediation, Enrichment Standards will vary per teacher Module 6 Part 2: Problem Solving with the Coordinate Plane Part 2 Number and Operations Fractions 5.NF NF NF NF.2.7c Measurement and Data 5.MD MD.3.5 Geometry 5.G G.1.2 Measurement and Data 5.MD.1.1 *Standards that are not bold are embedded in Modules throughout the year and thus should not be fully taught the first time they are addressed. Extending Application of Grade 5 Focus Standards: Place Value, Multi Digit Multiplication, and Division Number and Operations in Base Ten 5.NBT NBT NBT NBT.2.6 Page 2 of 61

3 Elementary Mathematics 5 th Grade Testing Calendar Required (The following assessments have been scheduled for you in your grade level curriculum guides. Please note: these assessments are required to be administered within the testing window provided. Please refer to the Optional Testing calendar for additional assessments that have been developed for you to administer should you choose to. Required assessments are subject to change. Please refer to the district testing calendar for testing window and details) Quarter Assessment Approximate Testing Dates Duration 1 i Ready Fall 8/17 8/31 2 days 2 Mid Year Scrimmage 12/1 12/18 2 days i Ready Winter 12/5 12/16 2 days 3 FSA 4/10 5/5 2 days 4 i Ready Spring 5/1 5/12 2 days Elementary Mathematics 5 th Grade Testing Calendar Page 3 of 61

4 Optional (The following assessments have been developed and scheduled in your grade level Curriculum Guides. Please note: these assessments are optional, should you choose to administer them. Please refer to the required assessment calendar for required testing for your grade level). Quarter Assessment Approximate Duration Testing Dates 1 Assess/Performance Task 8/19 Mid Module 1 8/31 1 day End of Module 1 9/12 1 day Assess/Performance Task 9/23 5.NBT.2.5 Mid 9/30 1 day End of 10/13 1 day 2 Assess/Performance Task 5.NF NF /25 Mid Module 3 11/4 1 day End of Module 3 11/15 1 day Assess/Performance Task 11/30 5.NF.2.4a Mid Module 4 12/13 1 day Assess/Performance Task 12/15 5.NF Assess/Performance Task 1/10 5.NF.2.5 Assess/Performance Task 5.NF.2.7a 1/24 End of Module 4 1/30 1 day Mid Module 5 2/8 1 day Assess/Performance Task 2/16 5.NF.2.4b End of Module 5 2/28 1 day 4 Mid Module 6 1 day Assess/Performance Task 4/25 5.G.1.1, 5.G.1.2 End of Module 6 5/15 1 day Page 4 of 61

5 August 5th Grade Notes Mon Tues Wed Thu Fri Notes Day 1 22 Day 6 Module 1 Lesson 5 29 Day 11 Module 1, Lesson 7 16 Day 2 Mod 1 Lesson 1 23 Day 7 i-ready Diagnostic 30 Day 12 Module 1, Lesson 8 PRE PLANNING WEEK 17 Day 3 Module1 Lesson 2 I-ready testing window begins on this day. There are two days allotted as flex for accommodating testing days. 24 Day 8 i-ready Diagnostic 31 ERD Day 13 Mid-Module 1 Assessment Topics A-C 18 Day 4 Module 1 Lesson 3 25 Day 9 Module 1 Lesson5 19 Day 5 Module 1 Lesson 4 26 Day 10 Module 1 Lesson 6 *Please Note: This calendar was developed with recommendations from the CG. Teachers may not be on the exact day, based on class needs. Page 5 of 61

6 September 5 th Grade Notes Mon Tues Wed Thu Fri Notes 1 Day 14 Module 1, Lessons Day 15 Module 1 Lesson 11 5 Labor Day 6 Day 16 Module 1 Lesson 12 7 Day 17 Module 1 Lesson 13 8 Day 18 Module 1 Lesson 14 9 Day 19 Module 1 Lesson Day 20 End-of Module 1 Assessment 19 Day 25 Lesson 3 13 Day 21 Review and Remediate previous taught standards 20 Day 26 Lesson 5 14 ERD Day 22 Lesson 1 21 Day 27 Lesson 6 15 Day 23 Lesson 2 22 Day 28 Lesson 7 16 Day 24 PEMDAS 23 Day 29 Lesson 9 26 Day 30 Lesson Day 31 Lesson ERD Day 32 Lesson Day 33 Lesson Day 34 Mid- Assessment *Please Note: This calendar was developed with recommendations from the CG. Teachers may not be on the exact day, based on class needs. Page 6 of 61

7 October 5 th Grade Notes Mon Tues Wed Thu Fri Notes 3 Day 35 Lesson Day 40 Lesson 22 4 Day 36 Lesson Day 41 Lesson 23 5 Day 37 Divide Whole Numbers Ready Common Core Lesson 6 12 ERD Day 42 Divide Decimals Ready Common Core Lesson 9 6 Day 38 Lesson Day 43 End-of-Module 2 Assessment 7 Day 39 Lesson Day 44 Review and Remediate previous taught standards Quarter 1 Ends 17 Day 45 Module 3 Lesson 1 18 Day 46 Module 3 Lesson 2 19 Day 47 Module 3 Lesson 3 20 Day 48 Module 3 Lesson 4 21 Planning Day Quarter 2 Begins 24 Day 49 Module 3 Lesson 5 25 Day 50 Module 3 Lesson 6 26 ERD Day 51 Module 3 Lesson 7 27 Day 52 Module 3 Lesson 8 28 Day 53 Module 3 Lesson 9 31 Day 54 Module 3 Lesson 10 *Please Note: This calendar was developed with recommendations from the CG. Teachers may not be on the exact day, based on class needs Page 7 of 61

8 DUVAL COUNTY PUBLIC SCHOOLS Math Curriculum Lesson Guide Quarter 1 Module 1 Course: Unit # Dates/Pacing: Grade 5 Math Module 1: Place Value and Decimal Fractions 08/15/ /13/2016, 21 Days Numbers and Operations in Base Ten 5.NBT.1.1 Recognize that in a multi digit number, a digit in one place 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. Cognitive Complexity: Level 2 Basic Application of Skills and Concepts Explain patterns in the number of zeroes of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10. Cognitive Complexity: Level 2 Basic Application of Skills and Concepts 5.NBT.1.3 Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using base ten numerals, number names, and expanded form, e.g., = (1/10) + 9 (1/100) + 2 (1/1000). MAFS b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Cognitive Complexity: Level 2 Basic Application of Skills and Concepts 5.NBT.1.4 Use place value understanding to round decimals to any place. Cognitive Complexity: Level 1 Recall 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. Cognitive Complexity: Level 2 Basic Application of Skills and Concepts Measurement and Data 5.MD.1.1 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 problems. Cognitive Complexity: Level 1 Recall Page 8 of 61

9 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. Standards for 5 th Grade ly proficient students in grade 5 should solve problems by applying their understanding of operations with whole numbers, decimals, and fractions including mixed numbers. They solve problems related to volume and measurement conversions. Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may check their thinking by asking themselves, What is the most efficient way to solve the problem?, Does this make sense?, and Can I solve the problem in a different way?. ly proficient students in grade 5 should recognize that a number represents a specific quantity. They connect quantities to written symbols and create a logical representation of the problem at hand, considering both the appropriate units involved and the meaning of quantities. They extend this understanding from whole numbers to their work with fractions and decimals. Students write simple expressions that record calculations with numbers and represent or round numbers using place value concepts. In fifth grade mathematical proficient students may construct arguments using concrete referents, such as objects, pictures, and drawings. They explain calculations based upon models and properties of operations and rules that generate patterns. They demonstrate and explain the relationship between volume and multiplication. They refine their mathematical communication skills as they participate in mathematical discussions involving questions like How did you get that? and Why is that true? They explain their thinking to others and respond to others thinking ly proficient students in grade 5 experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures, using objects, making a chart, list, or graph, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should be able to use all of these representations as needed. Fifth graders should evaluate their results in the context of the situation and whether the results make sense. They also evaluate the utility of models to determine which models are most useful and efficient to solve problems. ly proficient fifth graders consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be helpful. For instance, they may use unit cubes to fill a rectangular prism and then use a ruler to measure the dimensions. They use graph paper to accurately create graphs and solve problems or make predictions from real world data. ly proficient students in grade 5 continue to refine their mathematical communication skills by using clear and precise language in their discussions with others and in their own reasoning. Students use appropriate terminology when referring to expressions, fractions, geometric figures, and coordinate grids. They are careful about specifying units of measure and state the meaning of the symbols they choose. For instance, when figuring out the volume of a rectangular prism they record their answers in cubic units. In fifth grade mathematically proficient students look closely to discover a pattern or structure. For instance, students use properties of operations as strategies to add, subtract, multiply and divide with whole numbers, fractions, and decimals. They examine numerical patterns and relate them to a rule or a graphical representation. Page 9 of 61

10 8. Look for and express regularity in repeated reasoning. ly proficient fifth graders use repeated reasoning to understand algorithms and make generalizations about patterns. Students connect place value and their prior work with operations to understand algorithms to fluently multiply multi digit numbers and perform all operations with decimals to hundredths. Students explore operations with fractions with visual models and begin to formulate generalizations. Content Standard MAFS.5.NBT.1.1 Item Specifications Recognize that in a multi digit number, a digit in one place represents 10 times as much as it represents in the place to its right and of what it represents in the place to its left. Assessment Limit Item Types Context Items may require a comparison of the values of digits across multiple place values, including whole numbers and decimals from millions to thousandths. Editing Task Choice Equation Editor Hot Text Multiple Choice Multiselect Open Response Allowable Complexity Level Level: 1 Recall Achievement Level Descriptions Level 2 Level 3 Level 4 Level 5 recognizes that a digit in one place represents 10 times as much as it represents in the place to its right, or 1/10 of what it represents in the place to its left recognizes that a digit in one place 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 across multiple place values explains, using multiplicative comparison, the relationship between the values of digits across multiple place values [intentionally left blank] Page 10 of 61

11 Content Standard MAFS. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole number exponents to denote powers of 10. Assessment Limit Items may contain whole numbers and decimals from millions to thousandths. Items may contain whole number exponents with bases of 10. Item Types Editing Task Choice Equation Editor GRID Hot Text Multiple Choice Multiselect Open Response Context No Context Complexity Level Level: 2 Basic Application of Skills & Concepts Achievement Level Descriptions Level 2 Level 3 Level 4 Level 5 recognizes patterns in the number of zeroes of products when multiplying a number by powers of 10; uses whole number exponents greater than zero to denote powers of 10 explains patterns in the number of zeroes of the product when multiplying a number by powers of 10, and explains patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10; uses whole number exponents to denote powers of 10 interprets a multiplication problem to identify the factor of 10 by which one number is greater or lesser than another [intentionally left blank] Page 11 of 61

12 Content Standard MAFS.5.NBT.1.3 Read, write, and compare decimals to thousandths. MAFS.5.NBT.1.3a Read and write decimals to thousandths using base ten numerals, number names, and expanded form, e.g., = ( ) + 9 ( ) + 2 ( ) MAFS.5.NBT.1.3b Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Assessment Limit Items may contain decimals to the thousandths with the greatest place value within 1,000,000. Item Types Context Complexity Level Equation Editor GRID Matching Item Multiple Choice Multiselect Allowable Level: 2 Basic Application of Skills & Concepts Achievement Level Descriptions Level 2 Level 3 Level 4 Level 5 reads and writes decimals using baseten numerals and number names reads and writes decimals using expanded form; compares two decimals, using >, =, and < symbols to record the results of comparisons writes decimals in expanded form or base ten numerals in multiple formats compares two decimals that are written in different formats Page 12 of 61

13 Content Standard MAFS.5.NBT.1.4 Use place value understanding to round decimals to any place. Assessment Limit Item Types Context Complexity Level Items may contain decimals to the thousandths with the greatest place value within 1,000,000. The least place value a decimal may be rounded to is the hundredths place. Equation Editor Matching Item Multiple Choice Multiselect Table Item Allowable Level: 1 Recall Achievement Level Descriptions Level 2 Level 3 Level 4 Level 5 uses place value understanding of decimals to round to the nearest whole number uses place value understanding to round multi digit numbers between millions and thousands place to any place uses rounding strategies in real world situations determines a number that falls between two numbers of different place values Page 13 of 61

14 Content Standard MAFS. 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. Assessment Limit Items may only use factors that result in decimal solutions to the thousandths place (e.g., multiplying tenths by hundredths). Items may not include multiple different operations within the same expression (e.g., x 8.55). Expressions may have up to two procedural steps of the same operation. Item Types Editing Task Choice Equation Editor GRID Hot Text Multiple Choice Multiselect Open Response Context Allowable Complexity Level Level: 2 Basic Application of Skills & Concepts Achievement Level Descriptions Level 2 Level 3 Level 4 Level 5 adds and subtracts decimals to the hundredths place, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction multiplies and divides decimals to the hundredths place, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relates the strategy to a written method and explains the reasoning used adds, subtracts, multiplies, and divides decimals to the hundredths place to solve multistep problems determines the error in the computation of a problem involving decimals, and justifies the reasoning Page 14 of 61

15 Content Standard MAFS.5.MD.1.1 Convert among different sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi step, real world problems. Assessment Limit Measurement values may be whole, decimal, or fractional values. Conversion is within the same system. Acceptable units are limited to those given in standard. Item Types Context Equation Editor GRID Multiple Choice Multiselect Open Response Table Item Allowable Complexity Level Level: 2 Basic Application of Skills & Concepts Achievement Level Descriptions Level 2 Level 3 Level 4 Level 5 converts among different sized standard measurement units within a given measurement system uses one conversion to solve multistep, real world problems uses multiple conversions to solve multistep, real world problems analyzes a conversion problem to identify an error Page 15 of 61

16 New or Recently Introduced Terms Thousandths (related to place value) Exponents (how many times a number is to be used in a multiplication sentence) Millimeter (a metric unit of length equal to one thousandth of a meter) Equation (statement that two mathematical expressions have the same value, indicated by use of the symbol =; e.g., 12 = 4 x 2 + 4) Teacher Academic Language Familiar Terms and Symbols Centimeter (cm, a unit of measure equal to one hundredth of a meter) Tenths (as related to place value) Hundredths (as related to place value) Place value (the numerical value that a digit has by virtue of its position in a number) Base ten units (place value units) Digit (a numeral between 0 and 9) Standard form (a number written in the format: 135) Expanded form (e.g., = 135) Unit form (e.g., 3.21 = 3 ones 2 tenths 1 hundredth) Word form (e.g., one hundred thirty five) Number line (a line marked with numbers at evenly spaced intervals) Bundling, making, renaming, changing, regrouping, trading Unbundling, breaking, renaming, changing, regrouping, trading >, <, = (greater than, less than, equal to) Number sentence (e.g., = 7) Page 16 of 61

17 Place Value and Decimal Fractions In Module 1, students understanding of the patterns in the base ten system are extended from Grade 4 s work with place value of multi digit whole numbers and decimals to hundredths to the thousandths place. In Grade 5, students deepen their knowledge through a more generalized understanding of the relationships between and among adjacent places on the place value chart, e.g., 1 tenth times any digit on the place value chart moves it one place value to the right (5.NBT.1.1). Toward the module s end students apply these new understandings as they reason about and perform decimal operations through the hundredths place. Topic A opens the module with a conceptual exploration of the multiplicative patterns of the base ten system using place value disks and a place value chart. Students notice that multiplying by 1000 is the same as multiplying by 10 x 10 x 10. Since each factor of 10 shifts the digits one place to the left, multiplying by 10 x 10 x 10 which can be recorded in exponential form as 10 3 () shifts the position of the digits to the left 3 places, thus changing the digits relationships to the decimal point (). Application of these place value understandings to problem solving with metric conversions completes Topic A (5.MD.1.1). Topic B moves into the naming of decimal fraction numbers in expanded, unit (e.g., 4.23 = 4 ones 2 tenths 3 hundredths), and word forms and concludes with using like units to compare decimal fractions. Now in Grade 5, students use exponents and the unit fraction to represent expanded form, e.g., 2 x (1/10) + 4 (1/100) = (5.NBT.1.3). Further, students reason about differences in the values of like place value units and expressing those comparisons with symbols (>, <, and =). Students generalize their knowledge of rounding whole numbers to round decimal numbers in Topic C initially using a vertical number line to interpret the result as an approximation, eventually moving away from the visual model (5.NBT.1.4). In the latter topics of Module 1, students use the relationships of adjacent units and generalize whole number algorithms to decimal fraction operations (). Topic D uses unit form to connect general methods for addition and subtraction with whole numbers to decimal addition and subtraction, e.g., 7 tens + 8 tens = 15 tens = 150 is analogous to 7 tenths + 8 tenths = 15 tenths = 1.5. Topic E bridges the gap between Grade 4 work with multiplication and the standard algorithm by focusing on an intermediate step reasoning about multiplying a decimal by a one digit whole number. The area model, with which students have had extensive experience since Grade 3, is used as a scaffold for this work. Topic F concludes Module 1 with a similar exploration of division of decimal numbers by one digit whole number divisors. Students solidify their skills with and understanding of the algorithm before moving on to long division involving two digit divisors in. The mid module assessment follows Topic C. The end of module assessment follows Topic F Suggested Methods of Instructional Delivery Directions for Administration of Sprints Sprints are designed to develop fluency. They should be fun, adrenaline rich activities that intentionally build energy and excitement. A fast pace is essential. During Sprint administration, teachers assume the role of athletic coaches. A rousing routine fuels students motivation to do their personal best. Student recognition of increasing success is critical, and so every improvement is celebrated. One Sprint has two parts with closely related problems on each. Students complete the two parts of the Sprint in quick succession with the goal of improving Page 17 of 61

18 on the second part, even if only by one more. With practice the following routine takes about 8 minutes. Sprint A Pass Sprint A out quickly, face down on student desks with instructions to not look at the problems until the signal is given. (Some Sprints include words. If necessary, prior to starting the Sprint quickly review the words so that reading difficulty does not slow students down.) T: You will have 60 seconds to do as many problems as you can. T: I do not expect you to finish all of them. Just do as many as you can, your personal best. (If some students are likely to finish before time is up, assign a number to count by on the back.) T: Take your mark! Get set! THINK! (When you say THINK, students turn their papers over and work furiously to finish as many problems as they can in 60 seconds. Time precisely.) After 60 seconds: T: Stop! Circle the last problem you did. I will read just the answers. If you got it right, call out Yes! and give a fist pump. If you made a mistake, circle it. Ready? T: (Energetically, rapid fire call the first answer.) S: Yes! T: (Energetically, rapid fire call the second answer.) S: Yes! Repeat to the end of Sprint A, or until no one has any more correct. If need be, read the count by answers in the same way you read Sprint answers. Each number counted by on the back is considered a correct answer. T: Fantastic! Now write the number you got correct at the top of your page. This is your personal goal for Sprint B. T: How many of you got 1 right? (All hands should go up.) T: Keep your hand up until I say the number that is 1 more than the number you got right. So, if you got 14 correct, when I say 15 your hand goes down. Ready? T: (Quickly.) How many got 2 correct? 3? 4? 5? (Continue until all hands are down.) Optional routine, depending on whether or not your class needs more practice with Sprint A: T: I ll give you one minute to do more problems on this half of the Sprint. If you finish, stand behind your chair. (As students work you might have the person who scored highest on Sprint A pass out Sprint B.) T: Stop! I will read just the answers. If you got it right, call out Yes! and give a fist pump. If you made a mistake, circle it. Ready? (Read the answers to the first half again as students stand.) Movement To keep the energy and fun going, always do a stretch or a movement game in between Sprint A and B. For example, the class might do jumping jacks while skip counting by 5 for about 1 minute. Feeling invigorated, students take their seats for Sprint B, ready to make every effort to complete more problems this Page 18 of 61

19 time. Sprint B Pass Sprint B out quickly, face down on student desks with instructions to not look at the problems until the signal is given. (Repeat the procedure for Sprint A up through the show of hands for how many right.) T: Stand up if you got more correct on the second Sprint than on the first. S: (Students stand.) T: Keep standing until I say the number that tells how many more you got right on Sprint B. So if you got 3 more right on Sprint B than you did on Sprint A, when I say 3 you sit down. Ready? (Call out numbers starting with 1. Students sit as the number by which they improved is called. Celebrate the students who improved most with a cheer.) T: Well done! Now take a moment to go back and correct your mistakes. Think about what patterns you noticed in today s Sprint. T: How did the patterns help you get better at solving the problems? T: Rally Robin your thinking with your partner for 1 minute. Go! Rally Robin is a style of sharing in which partners trade information back and forth, one statement at a time per person, for about 1 minute. This is an especially valuable part of the routine for students who benefit from their friends support to identify patterns and try new strategies. Students may take Sprints home. RDW or Read, Draw, Write (a Number Sentence and a Statement) Mathematicians and teachers suggest a simple process applicable to all grades: 1) Read. 2) Draw and Label. 3) Write a number sentence (equation). 4) Write a word sentence (statement). The more students participate in reasoning through problems with a systematic approach, the more they internalize those behaviors and thought processes. What do I see? Can I draw something? What conclusions can I make from my drawing? Page 19 of 61

20 Module Specific This Module focuses on the specific aspects of MAFS. 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 and will cover the remainder of this standard in. One flex day is included in this module. For purposes of this document, it has been placed on Day 21, after the End of Module Assessment, but can be used at any time throughout the module. Resources Math Studio Talk: Common Core Instruction for 5.NBT (, 1.3, also covers 2.5, 2.7) studiotalk common core instruction 5nbt How to use sprints to build fluency november 2012 rigor breakdown sprints fluency in action Module Materials (S) Personal white boards (S) Personal place value mats, place value disks, markers (S) Meter strip, markers (T/S)Number lines (a variety of templates) and a large one for the back wall of the classroom Additional Aligned Activities MATH INVESTIGATIONS Unit 3, Session 1.3 Close to NBT.1.1 Unit 6, Session 1.4 Decimals in Between 5.NBT.1.3a, 1.3b Unit 6, Session 2.1 Fill Two 5.NBT.1.3a, 1.3b Page 20 of 61

21 Standards Topics and Objectives 5.NBT MD.1.1 A Multiplicative Patterns on the Place Value Chart Lesson 1: Reason concretely and pictorially using place value understanding to relate adjacent base ten units from millions to thousandths. Lesson 2: Reason abstractly using place value understanding to relate adjacent base ten units from millions to thousandths. Lesson 3: Use exponents to name place value units and explain patterns in the placement of the decimal point. Lesson 4: Use exponents to denote powers of 10 with application to metric conversions. 5.NBT.1.3 B Decimal Fractions and Place Value Patterns Lesson 5: Name decimal fractions in expanded, unit, and word forms by applying place value reasoning. Lesson 6: Compare decimal fractions to the thousandths using like units and express comparisons with >, <, =. 5.NBT.1.4 C Place Value and Rounding Decimal Fractions Lesson 7: Round a given decimal to any place using place value understanding and the vertical number line. Lesson 8: Round a given decimal to any place using place value understanding and the vertical number line. Mid Module Assessment: Topics A C 5.NBT NBT NBT.1.3 D E F Adding and Subtracting Decimals Lesson 9 10: Add decimals using place value strategies and relate those strategies to a written method. Subtract decimals using place value strategies and relate those strategies to a written method. *Combine lessons 9 10 into 1 lesson: Add and Subtract Multiplying Decimals Lesson 11: Multiply a decimal fraction by single digit whole numbers, relate to a written method through application of the area model and place value understanding, and explain the reasoning used. Lesson 12: Multiply a decimal fraction by single digit whole numbers, including using estimation to confirm the placement of the decimal point. Dividing Decimals Lesson 13: Divide decimals by single digit whole numbers involving easily identifiable multiples using place value understanding and relate to a written method. Lesson 14: Divide decimals with a remainder using place value understanding and relate to a written method. Lesson 15: Divide decimals using place value understanding including remainders in the smallest unit. Page 21 of 61

22 Lesson 16: Solve word problems using decimal operations.(optional: can be used as enrichment or omitted for remediation) End of Module Assessment: Topics A F Topic A: Place Value and Decimal Fractions Topic A begins with a conceptual exploration of the multiplicative patterns of the base ten system. This exploration extends the place value work done with multi digit whole numbers in Grade 4 to larger multi digit whole numbers and decimals. Students use place value disks and a place value chart to build the place value chart from millions to thousandths. They compose and decompose units crossing the decimal with a view toward extending their knowledge of the 10 times as large and 1/10 as large relationships among whole number places to that of adjacent decimal places. This concrete experience is linked to the effects on the product when multiplying any number by a power of ten. For example, students notice that multiplying 0.4 by 1,000 shifts the position of the digits to the left three places, changing the digits relationships to the decimal point and producing a product with a value that is as large (400.0) (). Students explain these changes in value and shifts in position in terms of place value. Additionally, students learn a new and more efficient way to represent place value units using exponents (e.g., 1 thousand = 1,000 = 10 3 ) (). Conversions among metric units such as kilometers, meters, and centimeters give students an opportunity to apply these extended place value relationships and exponents in a meaningful context by exploring word problems in the last lesson of Topic A (5.MD.1.1). Date/ Day of the school year 08/15/2016 Day: 1 Objective/ Essential Question Students will be able to describe and practice the rituals and routines of the mathematics classroom. How can I describe and practice the rituals and routines of the mathematics classroom? Math Florida Standards/ Practice MP1 MP2 MP3 MP4 MP5 MP6 MP7 MP8 Academic Language Interactive Journal Sprints Concept Development Anchor Chart Practice Accountable Talk Manipulatives White Board CHAMPs Gradual Release Model Lesson Rituals and Routines Interactive Journals Centers Introduce Sprints Accountable Talk Manipulatives During Centers Time: Rituals and Routines Lesson Assessment / Performance Tasks During your 30 minute centers block, use this time to deliver the Ritual and Routine lessons using the 8. They are designed to be short 30 minute activities that introduce students to the Standards for and effective modeling of strategies. Page 22 of 61

23 08/16/2016 Day: 2 Students will reason concretely and pictorially using place value understanding to relate adjacent base ten units from millions to thousandths. How can I use what I know about place value to relate adjacent base ten units using pictures or manipulatives? 5.NBT NBT NBT NF NF.3.6 Adjacent Digit Number disk Number line Ones Place value chart Tenths Thousandths Module 1 Topic A Lesson 1: Reason concretely and pictorially using place value understanding to relate adjacent base ten units from millions to thousandths. Materials Need For Lesson: (S) Personal white boards (S) Personal place value mats, disks, and markers MP4 MP7 MP8 Students can see expression without x, 2(3+2). It's the same as 2 x (3+2). During your 30 minute centers block, use this time to deliver the Ritual and Routine lessons using the 8. They are designed to be short 30 minute activities that introduce students to the Standards for and effective modeling of strategies. 08/17/2016 Day: 3 Students will reason abstractly using place value understanding to relate adjacent base ten units from millions to thousandths. How can I use what I know about place value to relate adjacent base ten units? 5.NBT OA.1.4, 2.5, NBT NBT NBT.1.1 MP2 MP3 MP7 Module 1 Topic A Lesson 2: Reason abstractly using place value understanding to relate adjacent base ten units from millions to thousandths. (S) Personal white boards During your 30 minute centers block, use this time to deliver the Ritual and Routine lessons using the 8. They are designed to be short 30 minute activities that introduce students to the Standards for and effective modeling of strategies. This lesson is the concrete foundation for understanding that as digits move on the place value chart, their value changes. After students understand this concept, you eventually want to move them to the abstract movement of the decimal point. Page 23 of 61

24 08/18/2016 Day: 4 Students will use exponents to name place value units and explain patterns in the placement of the decimal point. How can I use exponents to name place value units and explain patterns in the placement of the decimal point? 5.NBT OA.3.7 MP7 Base number Exponents Powers of ten Module 1 Topic A Lesson 3: Use exponents to name place value units and explain patterns in the placement of the decimal point. (S) Personal white boards. During your 30 minute centers block, use this time to deliver the Ritual and Routine lessons using the 8. They are designed to be short 30 minute activities that introduce students to the Standards for and effective modeling of strategies. After students understand the shift of the digits on the place value chart, you eventually want to move them to the abstract movement of the decimal point. 08/19/2016 Day: 5 Students will use exponents to denote powers of ten with application to metric conversions. How can I apply what I know about powers of ten in order to solve metric conversion problems? 5.NBT MD NBT MD.1.1 MP3 MP4 MP5 Conversion Metric conversion Metric system Module 1 Topic A Lesson 4: Use exponents to denote powers of 10 with application to metric conversions. (S) Personal white boards. (S) Meter strip, markers CPALMS Task: The Error During your 30 minute centers block, use this time to deliver the Ritual and Routine lessons using the 8. They are designed to be short 30 minute activities that introduce students to the Standards for and effective modeling of strategies. Page 24 of 61

25 Topic B: Decimal Fractions and Place Value Patterns Naming decimal fractions in expanded, unit, and word forms in order to compare decimal fractions is the focus of Topic B (5.NBT.1.3). Familiar methods of expressing expanded form are used, but students are also encouraged to apply their knowledge of exponents to expanded forms (e.g., 4, = /100). Place value charts and disks offer a beginning for comparing decimal fractions to the thousandths but are quickly supplanted by reasoning about the meaning of the digits in each place, noticing differences in the values of like units and expressing those comparisons with symbols (>, <, and =). Date/ Day of the school year 08/22/2016 Day: 6 08/23/2016 Day: 7 Objective/ Essential Question Students will name decimal fractions in expanded, unit, and word forms by applying place value reasoning. How can I use what I know about place value to read and write decimals to the thousandths using base ten numerals, number names and expanded form? Students will complete I ready Diagnostic. Math Florida Standards/ Practice 5.NBT.1.3a 5.MD.1.1 MP7 Academic Language Expanded form Standard form Unit form Lesson Module 1 Topic B Lesson 5: Name decimal fractions in expanded, unit, and word forms by applying place value reasoning. (S) Personal white boards. (S) Personal white board with place value chart Assessment / Performance Tasks During your 30 minute centers block, use this time to deliver the Ritual and Routine lessons using the 8. They are designed to be short 30 minute activities that introduce students to the Standards for and effective modeling of strategies. This lesson has been given two days because the standard addresses reading and writing decimals in expanded, standard, and word form. Keep in mind this content doesn t reappear as the targeted standard later in the curriculum; ensure this is taught to the full depth of the standard and item specifications. Flex Day: I Ready Diagnostic Testing. This day is added as a flex day to accommodate for I Ready testing. Please move this date to accommodate for the testing window and continue to move forward with the pacing of the curriculum guide as necessary. i Ready Diagnostic Recommendation: Curriculum Associates minute sessions, not a continuous 90 minute session. Page 25 of 61

26 08/24/2016 Day: 8 Students will complete I ready Diagnostic. Flex Day: I Ready Diagnostic Testing. This day is added as a flex day to accommodate for I Ready testing. Please move this date to accommodate for the testing window and continue to move forward with the pacing of the curriculum guide as necessary. i Ready Diagnostic 08/25/2016 Day: 9 08/26/2016 Day: 10 Students will name decimal fractions in expanded, unit, and word forms by applying place value reasoning. How can I use what I know about place value to read and write decimals to the thousandths using base ten numerals, number names and expanded form? Students will compare decimal fractions to the thousandths using like units and express comparisons with <, >, and =. How can I compare decimals to the thousandths and express the comparison with a symbol? 5.NBT.1.3a 5.MD.1.1 MP7 Expanded form Standard form Unit form Recommendation: Curriculum Associates minute sessions, not a continuous 90 minute session. Module 1 Topic B Continue Lesson 5: Name decimal fractions in expanded, unit, and word forms by applying place value reasoning. (S) Personal white boards. (S) Personal white board with place value chart During your 30 minute centers block, use this time to deliver the Ritual and Routine lessons using the 8. They are designed to be short 30 minute activities that introduce students to the Standards for and effective modeling of strategies. This lesson has been given two days because the standard addresses reading and writing decimals in expanded, standard, and word form. Keep in mind this content doesn t reappear as the targeted standard later in the curriculum; ensure this is taught to the full depth of the standard and item specifications. 5.NBT.1.3b 5.NBT NBT NBT.1.3a Compare Equal to Greater than Inequality Less than Module 1 Topic B Lesson 6: Compare decimal fractions to the thousandths using like units and express comparisons with >, <, =. (S) Personal white boards During your 30 minute centers block, use this time to deliver the Ritual and Routine lessons using the 8. They are designed to be short 30 minute activities that introduce students to the Standards for and effective modeling of strategies. Page 26 of 61

27 Topic C: Place Value and Rounding Decimal Fractions In Topic C, students generalize their knowledge of rounding whole numbers to round decimal numbers to any place. In Grades 3 and 4, vertical number lines provided a platform for students to round whole numbers to any place. In Grade 5, vertical number lines again provide support for students to make use of patterns in the base ten system, allowing knowledge of whole number rounding (4.NBT.1.3) to be easily applied to rounding decimal values (5.NBT.1.4). The vertical number line is used initially to find more than or less than halfway between multiples of decimal units. In these lessons, students are encouraged to reason more abstractly as they use place value understanding to approximate by using nearest multiples. Naming those nearest multiples is an application of flexibly naming decimals using like place value units. To round 3.85 to the nearest tenth, students find the nearest multiples, 3.80 (38 tenths 0 hundredths) and 3.9 (39 tenths 0 hundredths), and then decide that 3.85 (38 tenths 5 hundredths) is exactly halfway between and, therefore, must be rounded up to 3.9. Date/ Day of the school year 08/29/2016 Day: 11 Objective/ Essential Question Students will round a given decimal to any place using place value understanding and the vertical number line. How can I use what I know about place value and a number line to round decimals? Math Florida Standards/ Practice 5.NBT NBT NBT.1.3b MP6 Academic Language Nearest Number line Round Vertical number line decompose Lesson Module 1 Topic C Lesson 7: Round a given decimal to any place using place value understanding and the vertical number line. (S) Personal white boards, place value charts, markers Assessment / Performance Tasks 08/30/2016 Day: 12 Students will round a given decimal to any place using place value understanding and the vertical number line. How can I use a number line and what I know about place value to round decimals? 5.NBT NBT NBT.1.4 Maximum Minimum Module 1 Topic C Lesson 8: Round a given decimal to any place using place value understanding and the vertical number line. (S) Personal white boards (S) Personal place value boards Page 27 of 61

28 08/31/2016 Day: 13 Students will show mastery of standards introduced in Module 1 Topics A C. 5.NBT NBT NBT.1.4 Module 1 Mid Module Assessment Topics A C Module 1 Mid Module Assessment Topics A C How can I use strategies I ve learned to help me as a mathematician? Page 28 of 61

29 Topic D: Adding and Subtracting Decimals Topics D through F mark a shift from the opening topics of Module 1. From this point to the conclusion of the module, students begin to use base ten understanding of adjacent units and whole number algorithms to reason about and perform decimal fraction operations addition and subtraction in Topic D, multiplication in Topic E, and division in Topic F (). In Topic D, unit form provides the connection that allows students to use what they know about general methods for addition and subtraction with whole numbers to reason about decimal addition and subtraction (e.g., 7 tens + 8 tens = 15 tens = 150 is analogous to 7 tenths + 8 tenths = 15 tenths = 1.5). Place value charts and disks (both concrete and pictorial representations) and the relationship between addition and subtraction are used to provide a bridge for relating such understandings to a written method. Realworld contexts provide opportunities for students to apply their knowledge of decimal addition and subtraction as well in Topic D. Date/ Day of the school year 09/01/2016 Day: 14 Objective/ Essential Question Add and subtract decimals using place value strategies and relate those strategies to a written method. Math Florida Standards/ Practice 5.NBT.1.3 Academic Language Add Algorithm Equation Subtract Lesson Module 1 Topic D Lessons 9 and 10: Add and subtract decimals using place value strategies and relate those strategies to a written method. Assessment / Performance Tasks How can I use place value strategies to add and subtract decimals and relate those strategies to a written method? 5.NBT NBT NBT2.7 (S) Personal white boards (S) Place value chart, place value disks The teacher should use addition and subtraction strategies from both lessons 9 and 10 in today s lesson. Page 29 of 61

30 Topic E: Multiplying Decimals A focus on reasoning about the multiplication of a decimal fraction by a one digit whole number in Topic E provides the link that connects Grade 4 multiplication work and Grade 5 fluency with multi digit multiplication. Place value understanding of whole number multiplication coupled with an area model of the distributive property is used to help students build direct parallels between whole number products and the products of one digit multipliers and decimals (). Once the decimal has been placed, students use an estimation based strategy to confirm the reasonableness of the product through place value reasoning. Word problems provide a context within which students can reason about products. Date/ Day of the school year 09/02/2016 Day: 15 09/06/2016 Day: 16 Objective/ Essential Question Students will multiply a decimal fraction by single digit whole numbers, relate to a written method through the application of the area model and place value understanding, and explain the reasoning used. What are strategies for multiplying a decimal fraction by a whole number? Students will multiply a decimal fraction by single digit whole numbers, including using estimation to confirm the placement of the decimal point. Math Florida Standards/ Practice 5.NBT NBT.1.1 MP7 5.NBT.1.3 Academic Language Partial product evaluate Lesson Module 1 Topic E Lesson 11: Multiply a decimal fraction by single digit whole numbers, relate to a written method through application of the area model and place value understanding, and explain the reasoning used. (S) Personal white boards with place value charts, number disks Estimation Module 1 Topic E Lesson 12: Multiply a decimal fraction by single digit whole numbers, including using estimation to confirm the placement of the decimal point. (S) Personal white boards Assessment / Performance Tasks Page 30 of 61

31 How can I use estimation to confirm that my product is reasonable when using multiplication? MP8 Topic F: Dividing Decimals Topic F concludes Module 1 with an exploration of division of decimal numbers by one digit whole number divisors using place value charts and disks. Lessons begin with easily identifiable multiples such as and move to quotients that have a remainder in the smallest unit (through the thousandths). Written methods for decimal cases are related to place value strategies, properties of operations, and familiar written methods for whole numbers (). Students solidify their skills with an understanding of the algorithm before moving on to division involving two digit divisors in. Students apply their accumulated knowledge of decimal operations to solve word problems at the close of the module. Date/ Day of the school year 09/07/2016 Day: 17 Objective/ Essential Question Students will divide decimals by single digit whole numbers involving easily identifiable multiples using place value understanding and relate it to a written method. How can I use what I know about multiples and place value to divide decimals and relate it to a written method? Math Florida Standards/ Practice 3.NF.1.3d Academic Language Dividend Divisor Quotient Lesson Module 1 Topic F Lesson 13: Divide decimals by single digit whole numbers involving easily identifiable multiples using place value understanding and relate to a written method. (S) Personal white boards (S) Number disks Assessment / Performance Tasks Page 31 of 61