DRAFT Curriculum Map s1
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DRAFT Curriculum Map Grade 3
Vision for Assessment and Instruction As a community of learners, we strive to implement a rigorous thinking curriculum that utilizes an inquiry-based, formative assessment process in order to provide opportunities for students to develop academic maturity as disciplinary thinkers.
______This document was created to support instructional design and delivery of Grade 2 mathematics using enVision Math from Pearson as a resource.
Math Grade 3: Year-at-a-Glance Month Units Content Standards Unit #1 Place Value and Problem Solving with Addition and Subtraction (Topics 1-3) In this unit, students will use place 3.NBT.1 September* 3.NBT.2 *envisions Benchmark Topic 1-3 value understanding, properties of addition and subtraction, and 3.OA.8 estimation strategies to solve problems involving addition and subtraction.
Unit #2 Represent, Understand, and Problem Solve with Multiplication and Division 3.OA.1 3.OA.6 (Topics: 4, 7, 5, 6, 8) 3.OA.2 3.OA.7 In this unit, students will develop Sept/Oct-Dec 3.OA.3 3.OA.8 understanding of, interpreting, 3.OA.4 3.OA.9 representing, and solving problems 3.OA.5 3.NBT.3 involving multiplication and division.
Unit #3 Developing Understanding of 3.NF.1 Fractions 3.NF.2 Jan-Feb (Topics: 9-10) 3.NF.3 In this unit, students will develop 3.G.2 understanding of fractions as 3.MD.4 numbers.
March- April Unit #4 3.MD.1 3.MD.5 Measurement and Data 3.MD.2 3.MD.6 (Topics: 12, 15, 13, 14) 3.MD.7 3.MD.8 In this unit, students will read, write, 3.G.2 measure, and solve word problems involving addition and subtraction of time intervals; work with metric units of capacity and mass; and understand the concept of perimeter and area measurements.
Grade 3 Page 2 Grade ____ Math Grade 3: Year-at-a-Glance Month Units Content Standards
Unit #5 Representing and Interpreting Data (Topic 16) In this unit, students will draw, read, 3.MD.3 May and analyze scaled picture graphs 3.MD.4 and bar graphs that represent a data set and use those graphs to solve word problems.
Unit #6 Geometric Figures and Problem Solving Involving Perimeter and Area (Topic 11) 3.G.1 June In this unit, students will 3. MD 7a & 7d categorize shapes based on their 3.MD.8 attributes and recognize that measurements of perimeter and area as attributes of plane figures.
Grade 3 Page 3 Grade ____ Grade 3
Unit 1: Place Value and Problem Solving with Addition and Subtraction (Approx. 2-3 weeks*) (*Do enVision Benchmark to decide how long to spend on these Supporting Standards needed for Unit 2. enVision Benchmark answer key) In this unit, students will use place value understanding, properties of addition and subtraction, and estimation strategies to solve problems involving addition and subtraction.
Over-Arching Essential Questions for Unit 1: How does understanding place value help you round whole numbers?
How does place value and properties of operations help you add and subtract?
In this unit students will: Use place value to round whole numbers to the nearest 10 or 100. Add and subtract within 1000 using addition and subtraction methods/strategies developed in grade two.
NY Culminating Task: Check and Post Assessments – from engage , Module 2 Tasks 1-5 Gr 3_Unit 2_Mid-Post Assessments.pdf
Standards
Common Core State Standards-Mathematics: (Supporting Standards) Number and Operations in Base Ten 3.NBT Use place value understanding and properties of operations to perform multi-digit arithmetic. 1. Use place value understanding to round whole numbers to the nearest 10 or 100. 2. Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. Operations and Algebraic Thinking 3.OA Solve problems involving the four operations, and identify and explain patterns in arithmetic. 8. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. Standards for Mathematical Practice: SMP 1 Make sense of problems and persevere in solving SMP 2 Reason abstractly and quantitatively. Students reason them. Students use the concept of rounding and place value abstractly and quantitatively as they translate word problem understanding to solve addition and subtraction word situations into equations and use the equations to answer problems. They may use concrete manipulatives, pictorial questions about those situations. representations, and/or mental mathematics to conceptualize and solve a problem. SMP 3 Construct viable arguments and critique the reasoning SMP 4 Model with mathematics. Students represent problem of others. As students participate in investigating patterns on situations in multiple ways using numbers, words Grade 3 Page 4 Grade ____ the hundreds charts they construct arguments to explain why (mathematical language), objects, and math drawings. They the pattern makes sense. Students also listen to others’ use models to represent both equations and story problems explanations, decide if they make sense and ask appropriate and can explain their thinking. They evaluate their results in questions. the context of the situation and reflect on whether the results make sense. SMP 5 Use appropriate tools strategically. Students may use SMP 6 Attend to precision. Students communicate clearly, a number line and/or the hundreds chart to visualize the using grade-level-appropriate vocabulary accurately and placement of numbers and find the halfway point when precise explanations and reasoning to explain their processes rounding, and place-value blocks to solve problems. and solutions. Students consider if their answers are reasonable and check their work to ensure the accuracy of solution. SMP 7 Look for and make use of structure. Students use patterns in counting sequences of whole numbers on a number line, mental math strategies based on patterns (making ten, fact families, doubles), and the structure of place value to solve problems.
ELD Standards to Support Unit: Part I: Interacting in Meaningful Ways A. Collaborative 1. Exchanging information and ideas with others through oral collaborative conversations on a range of social and academic topics 2. Interacting with others in written English in various communicative forms (print, communicative technology, and multimedia 3. Offering and supporting opinions and negotiating with others in communicative exchanges 4. Adapting language choices to various contexts (based on task, purpose, audience, and text type) B. Interpretive 5. Listening actively to spoken English in a range of social and academic contexts 6. Reading closely literary and informational texts and viewing multimedia to determine how meaning is conveyed explicitly and implicitly through language 7. Evaluating how well writers and speakers use language to support ideas and opinions with details or reasons depending on modality, text type, purpose, audience, topic, and content area 8. Analyzing how writers and speakers use vocabulary and other language resources for specific purposes (to explain, persuade, entertain, etc.) depending on modality, text type, purpose, audience, topic, and content area C. Productive 9. Expressing information and ideas in formal oral presentations on academic topics 11. Supporting own opinions and evaluating others’ opinions in speaking and writing 12. Selecting and applying varied and precise vocabulary and language structures to effectively convey ideas Part II. Learning About How English Works A. Structuring Cohesive Texts 1. Understanding text structure 2. Understanding cohesion B. Expanding and Enriching Ideas 5. Modifying to add details C. Connecting and Condensing Ideas 6. Connecting ideas 7. Condensing ideas
Grade 3 Page 5 Grade ____ Social and Emotional Learning Standards for Mathematical Practice: SMP. 1 Make sense of problems and persevere in solving them SMP. 2 Reason abstractly and quantitatively SMP. 3 Construct viable argument and critique the reasoning of others SMP. 4 Model with mathematics SMP. 6 Attend to precision SMP. 7 Look for and make use of structure SMP. 8 Look for and express regularity in repeated reasoning SEL Competencies: Self-awareness Self-management Social awareness Relationship skills Responsible decision making
Grade 3 Page 6 Grade ____ Unit 1: Place Value and Problem Solving with Addition and Subtraction (Approx. 2-3 weeks) Math: Standards 3.NBT.1, 3.NBT.2, 3.NBT.3, 3.OA.8 Assessments for Learning Note: These assessments are suggested, not required, and can be used Essential Questions as lessons.
1. 1. enVision, Quick Check Master 1-1, 1-7 How can you use place value understanding to represent numbers? How does making an organized list help you solve addition and subtraction problems?
3.NBT.1 2. 2. enVision, Quick Check Master 1-3 What is a number line? What is an interval? How can we use a number line to represent numbers? 3.NBT. 1 3. How can we use place value to round numbers to 3. enVision, Quick Check Master 1-4 the nearest 10?How can we use place value to round numbers to the nearest 10? 3.NBT.1 4. enVision, Quick Check Master 1-6
4. From NC Wikispace: How can we use place value to round numbers to the nearest 100? “Comparing Heights” 3.NBT.1 Task 2 . “All About Rounding”3.NBT.1 Task 3 How can a number line help me round? . “Cafeteria Lunch Orders” 3.NBT.1 Task 1 How do you select an appropriate interval for a number line? From Illustrative Mathematics: “Rounding to the Nearest Ten and 3.NBT.1 Hundreds”
. “Rounding to 50 or 500”From NC Wikispace: “All About Rounding”3.NBT.1 Task 3 5. 5. From Illustrative Mathematics: In what kinds of situations is it appropriate to estimate? Why? . “Classroom Supplies” Why does place value play a significant role when From NC Wikispace: using the properties of operations to solve addition
Grade 3 Page 7 Grade ____ and subtraction word problems? “From 100 to 0” 3.NBT.2 Task 3 How can models be used to solve problems “Mrs. Snyder’s Game Board” involving addition and subtraction? 3.NBT.2 Task 1 What mental strategies can be used to add and subtract numbers reasonably quickly and accurately? 3.NBT.2 & 3.OA.8 Sequence of Learning Outcomes Students will be able to…in order to… Resources:
1. Students will use place value to read and write 3 digit enVision, Topic 1: “Numeration” numbers. Lessons 1-1, 1-7 Strategies for Teaching and Learning: Prior to implementing rules for rounding students need to have opportunities to investigate place value. A strong understanding of place value is essential for the development of number sense and the subsequent work that involves rounding numbers. Use and draw place value blocks (base ten blocks). Make an organized list. 2. Students will be able to place numbers on a number enVision, Topic 1: “Numeration” line. Lessons 1-2, 1-3 Strategies for Teaching and Learning: Use a number line as tools to support students’ understanding of place value.
3. Students will be able to use place value to round enVision, Topic 1: “Numeration” numbers to the nearest 10 on a number line. 3.NBT.1 Lessons 1-4, 1-5
Strategies for Teaching and Learning: Using a number line, plot decade numbers to identify the halfway point between two possible answers on a number line Use a number line or a hundreds chart as tools to support students’ understanding of place value. 4. Use place value to round numbers to the nearest 100 on enVision, Topic 1: “Numeration” a number line. 3.NBT. 1 Lessons 1-5, 1-6 From NC Wikispace: NOTE: Students will learn WHEN and WHY to round “Cafeteria Lunch Orders” 3.NBT.1 Task 1 numbers and extend their understanding of place value to From Illustrative Mathematics: include whole numbers with four digits. “Rounding to 50 or 500” Strategies for Teaching and Learning: Using a number line, plot decade numbers to identify the halfway point between two possible answers on a number line Use a number line or a hundred number chart as tools to support students’ understanding of place value. 5. Solve math problems involving three digit numbers enVision, Topic 2: “Number Sense: Addition using estimation to check for reasonableness in the and Subtraction” solution. Use strategies and algorithms based on place Lessons 2-1, 2-2, 2.3, 2.4, 2.5, 2.6, 2.7 Grade 3 Page 8 Grade ____ value, properties of operations, and/or the relationship enVision, Topic 3: “Using Place Value to Add between addition and subtraction. and Subtract” 3.NBT.2 , 3.OA.8 Lessons 3-1, 3-2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 3.10, 3-11, 3-12, 3-13 NOTE: The content of this standard 3.NBT.2 is a review of all the Addition and Subtraction methods/strategies used in solving all 12 problem types (12) from grade 2. Now in grade three, students will use some of those methods to generalize to larger numbers.
"Choose Three Ways" is a handout for recording multiple methods when problem- solving.
Strategies for Teaching and Learning: * Use and draw place value blocks (base ten blocks). Make an organized list. Using a number line. A hundred number chart as tools to support students’ understanding of place value. Mental strategies that support the development of addition and subtraction fluency in addition to the understanding of place value include: o Counting on o Making tens o Decomposing a number leading to a ten o Related facts o Relationship between addition and subtraction o Equivalent but easier or known sums o Doubles o Doubles plus one
Additional Resources Differentiation (e.g. Special Education, EL, GATE) enVisions, Topic 1: “Math Background” pp.2G-2H Use of math journals for differentiation and enVision, Topic 2: “Math Bacjkground” pp. 27A-27B formative assessment (use link below) https://www.teachingchannel.org/videos/math General Strategy Support for Unit: From the CA -journals Mathematics Framework “Instructional Strategies” chapter provides Flexible grouping: research-based strategies for teaching math, K-12 Content “ Supporting High Quality Common Interest Core Instruction” chapter addresses the development, Project/product implementation, and maintenance of high-quality, Level (Heterogeneous/ standards-based mathematics instructional programs Homogeneous)
Grade 3 Page 9 Grade ____ CCSS Support for the Unit: Tiered: CA Mathematics Framework “3rd Grade” Independent Management Plan (Must p. 1-5 “What students Learn in Grade Do/May Do) Three” Grouping p. 135-146 Number and Operations in Base Ten domain o Content p. 10-14 Operations and Algebraic Thinking o Rigor w/in the concept p. 2734-2937 “Essential Learning for Next Grade” o Project-based learning KS Assoc. of Teachers of Mathematics FLIPBOOKS Scroll o Homework rd down to 3 grade to view the pdf version. Provide o Grouping illustrated examples, instructional strategies, additional o Formative Assessment resources/tools and misconceptions by standard. p. 13 Operations and Algebraic domain Anchor Activities: p. 43 Number and Operations in Base Ten domain Content-related NC Unpacking Documents Tasks for early finishers Scroll down to “3rd grade Unpacking Document”. o Game Provide illustrated examples, instructional strategies, o Investigation additional resources/tools and misconceptions by o Partner Activity standard. o Stations p. 13-14 Operations and Algebraic Thinking domain Depth and Complexity Prompts/Icons: p. 18-19 Number and Operations in Base Ten Depth domain o Language of the Discipline Progressions for CCSS-M o Patterns Narrative documents describing the progression of a o Unanswered Questions topic across a number of grade levels, informed both by o Rules research on children's cognitive development and by the o Trends logical structure of mathematics. o Big Ideas p. 2-4, 11 Number and Operations in Base Ten o Complexity domain p. 2-3, 27-28 Counting and Cardinality and http://scusd- Operations and Algebraic Thinking domains math.wikispaces.com/home enVisions, Topic 1: “Math Background” pp.2G-2H Click here for: "Differentiation Resources" - Teaching Student-Centered Mathematics SCUSD Wikispaces Developmentally Appropriate Instruction for Grades 3-5 * Ch. 8 “Exploring Number and Operation Sense”, pages 100-107. Ch. 9 “Helping Children Master the Basic Facts”, pages 127 – 137. Ch.10 “Developing Whole-Number Place Value Concepts” , pages 151-170. Ch. 11 “Building Strategies for Whole-Number Computation”, pages 171-180.
Grade 3 Page 10 Grade ____ Unit 2: Represent, Understand, and Problem Solving with Multiplication and Division (Approx. 12 weeks)) In this unit, students will develop understanding of, interpreting, representing, and solving problems involving multiplication and division.
Over-Arching Essential Questions for Unit 2: How does understanding the properties and relationships between multiplication and division help solve problems involving the four operations?
In this unit students will: Develop understanding of multiplication and it’s properties Develop understanding of division and it’s properties Develop strategies for multiplication & division Identify relationships between multiplication & division
Culminating Task: Unit 1 Post Assessment modified from GA DOE “Ice Cream Scoops,” Part II “Multiplication and Division” only, pp. 156-162 and/ or Mid-point Check and Post Assessments- from engageNY, Module 3, All Tasks Gr 3_Unit 3_Mid & Post Assessments.pdf Standards Common Core State Standards-Mathematics: (Major Standards) Operations and Algebraic Thinking 3.OA Represent and solve problems involving multiplication and division 1. Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7. 2. Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a context in which a number of shares or a number of groups can be expressed as 56 ÷ 8. 3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawing and equations with a symbol for the unknown number to represent the problem. 4.Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations8x? =48,5=□÷3,6x6=?. Understand properties of multiplication and the relationship between multiplication and division. 5. Apply properties of operations as strategies to multiply and divide (students need not use formal terms Grade 3 Page 11 Grade ____ for these properties). Examples: If 6 x 4 is known, then 4 x 6 = 24 is also known (Commutative property of multiplication.). 3 x 5 x 2 can be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 3 x 10 = 30 (Associative property of multiplication). Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x 2) = 40 + 16 = 56 (Distributive property). 6. Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. Multiply and divide within 100. 7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers. Solve problems involving the four operations, and identify and explain patterns in arithmetic. 8. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding (this standard is limited to problems posed with whole numbers and having whole-number answers; students should know how to perform operations in the conventional order when there are no parentheses to specify a particular order {Order of Operations}). 9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. Number and Operations in Base Ten 3.NBT Use place value understanding and properties of operations to perform multi-digit arithmetic (a range of algorithms may be used). 3. Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 x 80, 5 x 60) using strategies based on place value and properties of operations. ELD Standards to Support Unit: Part I: Interacting in Meaningful Ways A. Collaborative 1 1. Exchanging information and ideas with others through oral collaborative conversations on a range of social and academic topics 2 2. Interacting with others in written English in various communicative forms (print, communicative technology, and multimedia 3 3. Offering and supporting opinions and negotiating with others in communicative exchanges 4 4. Adapting language choices to various contexts (based on task, purpose, audience, and text type) B. Interpretive 1 5. Listening actively to spoken English in a range of social and academic contexts 2 6. Reading closely literary and informational texts and viewing multimedia to determine how meaning is conveyed explicitly and implicitly through language 3 7. Evaluating how well writers and speakers use language to support ideas and opinions with details or reasons depending on modality, text type, purpose, audience, topic, and content area 4 8. Analyzing how writers and speakers use vocabulary and other language resources for specific purposes (to explain, persuade, entertain, etc.) depending on modality, text type, purpose, audience, topic, and content area C. Productive 9. Expressing information and ideas in formal oral presentations on academic topics 11. Supporting own opinions and evaluating others’ opinions in speaking and writing 12. Selecting and applying varied and precise vocabulary and language structures to effectively convey ideas Part II. Learning About How English Works A. Structuring Cohesive Texts 1. Understanding text structure 2. Understanding cohesion B. Expanding and Enriching Ideas Grade 3 Page 12 Grade ____ 5. Modifying to add details C. Connecting and Condensing Ideas 6.Connecting ideas 7.Condensing ideas Standards for Mathematical Practice: SEL SMP. 1 Make sense of problems and persevere in Self-awareness solving them Self-management SMP. 2 Reason abstractly and quantitatively Social awareness SMP. 3 Construct viable argument and critique the reasoning of others Relationship skills SMP. 4 Model with mathematics Responsible decision making SMP. 5 Use appropriate tools strategically SMP. 6 Attend to precision SMP. 7 Look for and make use of structure SMP. 8 Look for and express regularity in repeated reasoning
Unit 2: Represent, Understand, and Problem Solving with Multiplication and Division (Approx. 12 weeks*) * This Unit needs more lessons than what enVision provides. Look at “Resource” column for additional lessons.) Math: Standards 3.OA.1-4, 3.OA.5, 3.OA.6, 3.OA.7, 3.OA.8, 3.OA.9, 3.NBT.3
Assessments for Learning Note: These assessments are suggested, not required, and can be used as Essential Questions: lessons.
1. 1. NC Wikispace, 3 rd Grade Tasks How can I relate what I know about skip counting to multiply? What patterns can be used to find certain multiplication facts? How are addition and multiplication related? 2. What is the relationship between factors and 2. From Illustrative Mathematics: “Fish Tanks” products? “ Markers in Boxes” 3. 3. NC Wikispace, 3 rd Grade Tasks How can multiplication be represented? What strategies can be used to find the factors or products? 4. 4. NC Wikispace, 3 rd Grade Tasks How can division be represented? From Illustrative Mathematics: How can I use what I know about subtraction, “ Two Interpretations of Division” equal sharing and forming equal groups to “ Gifts from Grandma” Variation1 solve division problems?
Grade 3 Page 13 Grade ____ How are subtraction and division related? “ Finding the unknown in a division equation”
5. 5. NC Wikispace, 3 rd Grade Tasks How can the same array model represent multiplication and division? How can I use the array model to explain multiplication and division? How can I model division? How are multiplication and division alike and different? 6. 6. NC Wikispace, 3 rd Grade Tasks How can I use the array model to explain multiplication and division? From Illustrative Mathematics: How can I use known facts to find unknown “ Analyzing Word Problems Involving Multiplication” facts? 7. 7. NC Wikispace, 3 rd Grade Tasks How multiplication and division related How can different strategies be helpful when solving problems? 8. 8. From NC Wikispace: How can I model multiplication? 3.OA.3 Task 3: Raking Leaves When can you use multiplication and division in real life? How is the commutative property of multiplication evident in an array model, but not in subtraction or division? 9. 9. From NC Wikispace: What is an associative property in 3.OA.5 Task 1: Patterns on the Multiplication multiplication? Chart How is the associative property of 3.OA.5 Task 2: Prove It! multiplication used in solving a problem? 10. How does decomposing numbers help you 10. From Illustrative Mathematics: solve multiplication problems? Valid Equalities? (Part 2)
11. From NC Dept. of Public Instruction 11. How are multiplication and division related? "Prove it!"
12. 12. From NC Dept. of Public Instruction: How does using an area model help "Sharing Pencils" understand multiplication and division? How does the model (array) help us think about the different ways to decompose a number(factors or products) to solve multiplication and division problems?
Grade 3 Page 14 Grade ____ 13. 13. From Illustrative Mathematics: What strategies can be used to solve “ Two Interpretations of Division” multiplication problems? What strategies can be used to solve real- world division problems? 14. 14. From Illustrative Mathematics “Finding the What patterns can be used to find certain Unknown in a Division Equation” multiplication facts? Why is the multiplication table symmetric about its diagonal? What strategies can be used to learn multiplication facts? 15. From Illustrative Mathematics 15. “ The Stamp Collection” How do the properties of operations enable “ you to solve problems? The Class Trip” What strategies can be used to solve From NC Dept. of Public Instruction multiplication problems? "Mario's Designs" From Illustrative Mathematics: 16. Why does place value play a significant role Addition Patterns when using the properties of operations to solve Patterns in a Mulitiplication Table problems? Symmetry of the Addition Table Making a Ten 17. 17. From Illustrative Mathematics: How is place value related to multiples of How Many Colored Pencils? ten? How is multiplying by ten related to palce value? What happens to a number when it is multiplied by ten? Sequence of Learning Outcomes Resources: Students will be able to…in order to…
1. 1. Recognize multiplication as finding the total enVision, Topic 4: “Meanings of Multiplication” number of objects in a certain number of equal- Lessons 4-1, 4-3, 4-4, 4-5 sized groups. Provide students context (story problems) as they learn equal groupings. 3.OA.1 Strategies for Teaching and Learning: The standard defines multiplication of whole numbers a x b as finding the total number of objects in a groups of b objects. Use the terms “number of objects in each group”(3 x __ = 18 and 18 ÷ 3 = __) or “number of groups” (__ x 6 = 18 and 18 ÷ 6 = __) with students. Number bond can be used as a visual representation of this skip counting strategy. Draw pictures to represent equal groups Grade 3 Page 15 Grade ____ May use a variety of models (tile squares, counters, linking cubes, beans, etc.) for students to manipulate equal groups 2. Interpret factors as the size of the group or the enVision, Topic 5: “Multiplication Facts: Use number of groups. Show with models “a number Patterns” Lessons 5-1, 5-2, 5-3, 5-4, 5-5, 5-6, 5-7 of groups of a certain number of object (or size)” enVision, Topic 6: “Multiplication Facts: Use Known when the language of “groups of” is presented Facts” Lessons 6-1, 6-2, 6-3, 6-4, 6-5, 6-6, 6-7, 6-8, 6- with various terms (for example, “piles of,” 9 “stacks of,” “rows of,” “cups of,” “teams of,” CA Mathematics Framework “3 rd Grade” pg. 9 chart etc.). 3.OA.1 Flipbook from KS Assoc. of Teacher of Mathematics, pg. 4-5 NC Unpacking, pg. 4 From engageny Downloadable Resources PDF, Module 1, Topic A “Mulitplcation and the Meaning of the Factors”, pg. 1.A.1-1.A.40 Strategies for Teaching and Learning: Use context to help students determine the factors. Use number lines to show equal groups
3. Represent multiplication with the array to show enVision, Topic 4: “Meanings of Multiplication” the relationship among all the numbers involved Lessons 4-2 (factor x factor = product). Use context so CA Mathematics Framework “3 rd Grade” pg. 9 chart students will be able to visualize “rows/columns Flipbook from KS Assoc. of Teacher of Mathematics, of” a particular group. 3.OA.1 pg. 4-5 NC Unpacking, pg. 4 From engageny Downloadable Resources PDF, Module 1, Topic A “Mulitplcation and the Meaning of the Factors”, pg. 1.A.1-1.A.40 Video on Word Problems with tape Diagrams Strategies for Teaching and Learning: Build rectangular arrays using “rows of.” Describe arrays in terms of equal groups (by rows or by columns). For example, 4 x 5: “There are 4 rows of 5 chairs.” which is different from 5 rows of 4 chairs where the meaning and representation are different. The product is the same. Partition arrays into smaller arrays (concept of decomposition) Use tape diagrams 4. Recognize division in two different situations – enVision, Topic 7: “Meanings of Division” equal sharing (e.g., how many are in each Lessons 7-1, 7-2, 7-3, 7-5, 7-6 group?), and determining how many groups (e.g., CA Mathematics Framework “3 rd Grade” pg. 9 chart how many groups can you make?) Flipbook from KS Assoc. of Teacher of Mathematics, 3.OA.2 pg. 6 NC Unpacking, pg. 4 From engageny Downloadable Resources PDF, Module 1, Topic B “Division as an Unknown Factor Problem”,
Grade 3 Page 16 Grade ____ pg. 1.B.1-1.B.35 Strategies for Teaching and Learning: Use the terms “number of objects in a group”(3 x __ = 18 and 18 ÷ 3 = __) or “number of groups” (__ x 6 = 18 and 18 ÷ 6 = __) with students rather than “partitive division” or “quotitive division.” Use the array model to determine the unknown in division. 5. Model the relationship between enVision, Topic 8: “Division Facts” multiplication and division by using a variety Lessons 8-1, 8-2, 8-3, 8-4, 8-6, 8-7, 8-8 of methods, such as bar modeling, number line, CA Mathematics Framework “3 rd Grade” pg. 9 chart arrays, etc. 3.OA.3 Flipbook from KS Assoc. of Teacher of Mathematics, pg. 7-9 NC Unpacking, pg. 5-6 From engageny Downloadable Resources PDF, Module 1, Topic A “Mulitplcation and the Meaning of the Factors”, pg. 1.A.1-1.A.40 Topic B “Division as an Unknown Factor Problem”, pg. 1.B.1-1.B.35 Lesson from LearnZillion: “Solve Multiplication and Division Problems: Using a Diagram”
Strategies for Teaching and Learning: Model division as the unknown factor in multiplication in multiple ways (for example, bar modeling, number line, arrays, etc.). 6. Use multiplication and division within 100 to enVision, Topic 8: “Division Facts” solve word problems in situations involving Lessons 8-5, 8-9 equal groups, arrays, and measurement CA Mathematics Framework “3 rd Grade” pg. 9 chart quantities. 3.OA.3 Flipbook from KS Assoc. of Teacher of Mathematics, pg. 7-9 NC Unpacking, pg. 5-6 From engageny Downloadable Resources PDF, Module 1, Topic A “Mulitplcation and the Meaning of the Factors”, pg. 1.A.1-1.A.40 Topic B “Division as an Unknown Factor Problem”, pg. 1.B.1-1.B.35 Strategies for Teaching and Learning: Model problems using pictorial representations and manipulatives. 7. Determine the unknown whole number in a enVision, Topic 7: “Meanings of Division” multiplication or division equation relating Lessons 7-4 three whole numbers to make the equation CA Mathematics Framework “3 rd Grade” pg. 9 chart true. 3.OA.4 Flipbook from KS Assoc. of Teacher of Mathematics, pg. 10-11, and 24 NC Unpacking, pg. 7
engageny Downloadable Resources PDF, Module 1,
Grade 3 Page 17 Grade ____ Topic B “Division as an Unknown Factor Problem”, pg. 1.B.1-1.B.35
Strategies for Teaching and Learning: Use manipulatives, pictures, words, and/or equations to represent the problem and explain thinking process 8. Understand and apply the commutative enVision, Topic 4: “Meanings of Multiplication” property of multiplication as a strategy to Taught in 4-3 so use Quick Check 4-3 p.103A & multiply when solving word problems. 3.OA.5 “Differentiated Instruction” On-Level Center Activity p. 103B Mathematics International, Unit 1 “Multiplication” Section 1, “Properties of Mutliplication” o Lesson 1, p.A5-7 Teaching Student-Centered Mathematics: Grades 3-5 “The Order Property in Multiplication,” p.66 engageNY, Module 3 “Multiplication and Division with Units of 0, 1, 6-9, and 10” Topic 1, Lesson 1 CA Framework p. 10-11 Flipbook p. 12-15 NC Unpacking, p. 9-10 Strategies for Teaching and Learning: Students use the array, drawings, manipulatives, etc. to justify why the commutative property only applies to addition and multiplication, but not to subtraction or division. Skip counting on the array model can be used to practice multiplication facts. Spend time interpreting rows and columns by rotating array by 90˚. 9. Understand and apply the associative property enVision, Topic 6: “Multiplication Facts” of multiplication as a strategy to multiply when Taught in 6-6 so use Quick Check 6-6 p.153A & solving word problems. “Differentiated Instruction” On-Level Center 3.OA.5 Activity p. 153B Mathematics International, Unit 1 “Multiplication” Section 1, “Properties of Multiplication” Lesson 2, p.A8 CA Framework p. 10-11 Flipbook p. 12-15 NC Unpacking, p. 9-10 Strategies for Teaching and Learning: Have students use drawings, arrays, etc. to justify why multiplying “three or more whole numbers without using any parentheses will yield the same result regardless of how we group the factors.” (NCTM, Multiplication and Division, Grade 3-5, p.30). Students use other methods (area model, partial products, calculator, etc.) to justify their reasoning from applying decomposition and the associative property.
Grade 3 Page 18 Grade ____ 10. Decompose and re-compose numbers to apply enVision, Topic 6: “Multiplication Facts” the associative property to solve multiplication Taught in topic 6 so use “Math Background” word problems. 3.OA.5 p.154A as a model, then see Strategies below Mathematics International, Unit 1 “Multiplication” Section 1, “Properties of Multiplication” Lesson 2, p. A8 Strategies for Teaching and Learning: Students solve 7 × 6 by decomposing the 6 as two 3s (2 × 3) to get 7 × 2 × 3. They apply the associative property to solve (7 × 2) and then × 3 (7 × 2) × 3 (refer to the Progression Document K, Counting and Cardinality, K-5, Operations and Algebraic Thinking, p.26). Have students use other methods (area model, partial products, calculator, etc.) to justify their reasoning from applying decomposition and the associative property. 11. Use an area model to understand and apply enVision, Topic 6: “Multiplication Facts” the distributive property of multiplication(as a Taught in 6-7 so use Quick Check 6-7 p.155A strategy) to multiply and divide. Students begin using the conventional order of operations (multiplication and division are done before addition and subtraction). 3.OA.5 Strategies for Teaching and Learning: Students need opportunities to continue to decompose numbers in order to apply the distributive property {for example, 32 x 7 = (30 + 2) x 7 = (30 x 7) + (2 x 7)} (refer to North Carolina’s Unpack Content, p. 9-10). Students are learning and understanding the concept of distributive property; they do not need to use the formal terms. Use the area model to guide students to understand the relationship between the distributive property and decomposition of numbers. 12. Use an area model to apply the distributive Teaching Student-Centered Mathematics: property of multiplication over addition as a Grades 3-5 strategy to solve products they do not know “The Distributive Property,” p.66 (for example, 3 × 5 is 15, so 3 × 6 is 15 + 3 more o “Slice It Up” activity 2.27 is 18) to solve word problems. 3.OA.5 “Strategies for Multiplication Facts” “If You Didn’t Know” activity 3.9, p.92 & 98-99 Strategies for Teaching and Learning: Students may decompose other factor pairs and use the area model/diagram to support their reasoning. Ask students if they see a pattern (refer to the Progression document K-5, Operations and Algebraic Thinking p.26).
Grade 3 Page 19 Grade ____ 13. Use the relationship between Taught in envision, Topic 7 Lesson 7-3 & 8 Lessons multiplication and division to solve 8-1, 8-8 division word problems as an Mathematics International, Unit 3 “Division” unknown factor problem (48 ÷ 8 = ? Section 1 “Calculations for Finding How Many 8 × ? = 48). 3.OA.6 for 1 Person” o Lesson 1, p.A25-27 o Lesson 2, p.A28 Section 2, “Calculations for fidning the Number of People We Can Divide Something Into” o Lesson 1, p.A29=31 o Lesson 2, p.A31-32 o Lesson 3, p.A33 Strategies for Teaching and Learning: Interpret the unknown in division using the array model. Students solve word problems that involve unknown product, group size unknown, and number of groups unknown. 14. Develop multiplication and division Taught in envision, Topic 8 Lessons 8-2, 8-3, 8-4 facts by studying patterns and Mathematics International, Unit 3 “Division” relationships in multiplication facts “Power Builder,” p.A36 and relating multiplication and “Mastery Problems, p.A37 division. Students record the patterns after using arrays, drawings, hundreds chart, manipulatives, etc. and justify their reasoning. 3.OA.7 Strategies for Teaching and Learning: Strategies for learning multiplication facts include: Patterns General strategies Other strategies Strategies for learning division facts include: Unknown factors Related facts (For further details, refer to CA Mathematics Framework, p.12) Grade 3 Page 20 Grade ____ Students need the opportunity to practice multiplying and dividing within 100 and know all products of 2 one-digit numbers from memory throughout the school year. 15. Solve two-step word problems using enVision, Topic 5: Taught in lesson 5-7 so use the four operations. Represent these Quick Check 5-7 p.131A problems using equations with a letter Math Background, pp. 113A-113B standing for the unknown quantity by Interactive Learning, pp. 114-115 using tape diagrams. 3.OA.8 enVision, Topic 6: Taught in lesson 6-9 so use Quick Check -9 p.161A Math Background, pp. 137A-137B Interactive Learning, pp. 138-139 enVision, Topic 8: Taught in lesson 8-5 so use Quick Check 8-5 p.201A & Enrichment Master p.201B Math Background, pp. 187A-187B Interactive Learning, pp. 188-189 CA Framework p. 13-14 Flipbook p. 19-21 NC Unpacking, p. 14-15 Strategies for Teaching and Learning: Students should have opportunities to assess the reasonableness of their answers using mental computation and estimation strategies including rounding. Students should have opportunities to use visual representations, such as, part-part-whole, bar models, tape diagrams to solve problems (refer to CA Mathematics Framework, p.14) 16. Identify arithmetic patterns and enVision, Topic 5: Taught in lesson 5-2, 5-3, 5-4, explain the patterns using properties 5-5 so use Quick Check 5-1 p.119A of operations. 3.OA.9 Math Background, pp. 113A-113B Interactive Learning, pp. 114-115 CA Framework p. 14-15 Flipbook p. 22-23 NC Unpacking, p. 16-18
“ Discover Number Patterns with Skip Counting” Video from the Teaching Channel Mathematics International, Unit 3 “Division” Section 3 “Calculations for Finding Times as Much” o Lesson 1, p.A35-36 Strategies for Teaching and Learning: Students need paper or white boards to model: For example, that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends (4 x 7 can be thought of as double 2 x 7). 17. Use decomposition of factors of ten enVision, Topic 5: Taught in lesson 5-6 and properties of operations to Math Background, pp. 113A-113B multiply one-digit whole numbers by Interactive Learning, pp. 114-115 multiples of ten (10 – 90). Recognize CA Framework p. 15-16
Grade 3 Page 21 Grade ____ and explain patterns when Flipbook p. 30 multiplying by multiples of ten. NC Unpacking, p. 21 3.NBT.3 Mathematics International, Unit 9 “Multiplication Algorithm,” Part 1 Section 1 “Multiplication by 10 and 100” o Lesson 1, p.A91-92 o Lesson 2, p.A92 Section 2, “Mulitplication of 2-Digit by 1-Digit Numbers” o Lesson 1, p.A93-95 o Lesson 2, p.A96 o Lesson 3, p.A97 o Lesson 4, p.A98 Strategies for Teaching and Learning: Give students the opportunity to develop the conceptual understanding before teaching the standard algorithm. This skill will support students’ later learning of standard algorithm for multiplication of multi-digit numbers. For example, 40 × 3 can be interpreted as 3 groups of 4 tens or 12 tens. Twelve tens equals 120 (refer to Mathematics Framework, p.16). Additional Resources Differentiation (e.g. Special Education, EL, GATE) CA Mathematics Framework “3 rd Grade” pg. 9 chart Differentiation Support for Unit: Flipbook from KS Assoc. of Tchr of Mathematics, pg. Use of math journals for differentiation and 4-5 formative assessment (use link below) NC Unpacking, pg. 4 https://www.teachingchannel.org/videos/math- Video from engageny Number bond journals From engageny Downloadable Resources PDF, Module Flexible grouping: 1, Topic A “Mulitplcation and the Meaning of the Content Factors”, pg. 1.A.1-1.A.40 Interest enVision, Topic 4: Project/product Math Background, pp. 95A-95B Level (Heterogeneous/ Homogeneous) Interactive Learning, pp. 96-97 Tiered: Independent Management Plan (Must Do/May Do) Grouping o Content o Rigor w/in the concept o Project-based learning o Homework o Grouping o Formative Assessment
Anchor Activities: Content-related
Grade 3 Page 22 Grade ____ Tasks for early finishers o Game o Investigation o Partner Activity o Stations
Depth and Complexity Prompts/Icons: Depth o Language of the Discipline o Patterns o Unanswered Questions o Rules o Trends o Big Ideas o Complexity
From GA DOE, Differentiation via Math Centers (Tubs)
Unit 3: Developing Understanding of Fractions (about 8 weeks) In this unit, students will develop understanding of fractions as numbers.
Over-Arching Essential Questions for Unit 2:
Grade 3 Page 23 Grade ____ What is a fraction? How can I use fractions to name parts of a whole?
In this unit students will: Develop understanding of a fraction 1/b as the quality formed by 1 part when the whole is portioned into b equal parts Develop understanding of a fraction a/b as the quality formed by a parts of size 1/b Understanding and representing fractions on a number line Explain how two fractions are equal Compare fractions by their size
Culminating Task Mid-point Check and Post Assessments- from engageNY, Module 5 Tasks 1-4 Gr 3_Unit 5_Mid & Post Assessments.pdf Standards Common Core State Standards-Mathematics: Number and Operations -- Fractions 3.NF Develop understanding of fractions as numbers 1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b. 2. Understand a fraction as a number on the number line; represent fractions on a number line diagram. a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line. b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line. 3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same endpoint on a number line. b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/2; recognize that 6/1 = 6; locate 4/4 and 1 at the same point on a number line diagram. d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a fraction model.
ELD Standards to Support Unit: Part I: interacting in Meaningful Ways A. Collaborative 1. Exchanging information and ideas with others through oral collaborative conversations on a range of social and academic topics 2. Interacting with others in written English in various communicative forms (print, communicative technology, and multimedia 3. Offering and supporting opinions and negotiating with others in communicative exchanges 4. Adapting language choices to various contexts (based on task, purpose, audience, and text type) B. Interpretive 5. Listening actively to spoken English in a range of social and academic contexts Grade 3 Page 24 Grade ____ 6. Reading closely literary and informational texts and viewing multimedia to determine how meaning is conveyed explicitly and implicitly through language 7. Evaluating how well writers and speakers use language to support ideas and opinions with details or reasons depending on modality, text type, purpose, audience, topic, and content area 8. Analyzing how writers and speakers use vocabulary and other language resources for specific purposes (to explain, persuade, entertain, etc.) depending on modality, text type, purpose, audience, topic, and content area C. Productive 9. Expressing information and ideas in formal oral presentations on academic topics 11. Supporting own opinions and evaluating others’ opinions in speaking and writing 12. Selecting and applying varied and precise vocabulary and language structures to effectively convey ideas Part II. Learning About How English Works A. Structuring Cohesive Texts 1. Understanding text structure 2. Understanding cohesion B. Expanding and Enriching Ideas 5. Modifying to add details C. Connecting and Condensing Ideas 6. Connecting ideas 7. Condensing ideas Standards for Mathematical Practice SEL Competencies: SMP. 2 Reason abstractly and quantitatively Self-awareness SMP. 3 Construct viable argument and critique the Self-management reasoning of others Social awareness SMP. 4 Model with mathematics Relationship skills SMP. 5 Use appropriate tools strategically Responsible decision making SMP. 8 Look for and express regularity in repeated reasoning Unit 3: Developing Understanding of Fractions (Topics 9-10) Standards: 3.NF1, 3.NF2, 3.NF.3 Essential Questions: Assessments for Learning Note: These assessments are suggested, not required, and can be used as lessons. 1. 1. “Naming the Whole for a Fraction” What is a whole? "Geometric Pictures of One Half" What does equal parts mean? "Representing Half of a Circle" How can I represent fractions of different "Selling Bubble Gum" sizes? 2. 2. "Equal Shares" What are the important features of a unit of "Making a Scarf" fraction? Why is the denominator important to the unit fractions? 3. 3. enVision, Quick Check 9-1 Why is the size of the whole important? What is the relationship between a unit fraction and a unit of 1? Grade 3 Page 25 Grade ____ 4. “ Locating Fractions Less than One on the How can I represent fractions of different Number Line” lengths? “ Locating Fractions Greater than One on the How can the numbers 0 and 1 on a number Number Line” line help you compare fractions? “ Find 1” 5. 5. How can I compare fractions? "Sharing Pie" How can I compare fractions when they have "Comparing Fractions" the same numerators? “ Closest to 1/2” How can I compare fractions when they have illustrative math “Comparing Fractions” the same denominators? When we compare two fractions, how do we know which has the greater value?
6. 6. "Halves, Thirds, and Sixths" What are equivalent fractions? What equivalent groups of fractions can I discover using Fraction Strips? What equivalent groups of fractions can I discover using a number line? 7. 7. "All the Jumps" How can we represent whole numbers as fractions? What is the difference between 2/1 and 2/2, 3/1 and 3/3? 8. How are fractions used in problem Solving 8. "Distances Swam" situations? Sequence of Learning Outcomes Resources: Students will be able to…in order to… Note: enVision, Topic 9, Lessons 9-3, 9-4 address 4th grade standards. Recommended to skip. 1. Partition, or divide, a whole (line segments, enVision, Topic 9: “Understanding Fractions” rectangles, circles, etc.) into equal-sized parts and Math Background, pp. 217A-217B describe each part as “halves, thirds, fourths, Interactive Learning, pp. 290-291 sixths, or eighths” (depending on the number of Lesson 9-1 partitions. Count the number of equal-sized parts , Module 5 “Fracions as Numbers on the Number that make up the whole (“1 third, 2 thirds, 3 Line” thirds and 3 thirds make a whole” …). 3.NF.1 Topic A: “Partitioning a Whole into Equal Parts” Topic B: “Unit Fractions and Their Relation to the Whole” Topic C: “Comparing Unit Fractions and Specify the Whole” Topic D: “Fractions on the Number Line” Topic E: “Equivalent Fractions”
Grade 3 Page 26 Grade ____ Topic F: “Comparison, Order, and Size of Fractions” Mathematics International, Unit 14: “Fractions” Section B: “Meaning of fractions and their representation” o Lesson 1-3, p.B43-46 o Lesson “Using Mathematics”, p.B47-49
Teaching Student-Centered Mathematics, Grades 3-5, Ch. 5 “Exploring Fraction Concepts,” p. 131-155
CA Framework p. 16-23, 30-32 Flipbook p. 32-37, 54-55 NC Unpacking, p. 21-25, 45 Strategies for Teaching and Learning: Note: (Understanding that a fraction is a quantity formed by part of a whole is essential to number sense with fractions. Fractional parts are the building blocks for all fraction concepts, in the same sense that the number 1 is the basic building block of the whole numbers.) Students should continue to build upon their 1st & 2nd grade prior knowledge /experience related to partitioning circles and rectangles into two, three, or four equal shares and use the words: halves, half of, thirds, a third of, fourth, fourth of, quarter of. They can further explore concepts of fractions using other concrete models such as pattern blocks. Have students practice counting with fractions just as they counted with whole numbers. Counting equalized parts will help them determine the number of parts it takes to make a whole and recognize fractions that are equivalent to whole numbers. “ Example of Instruction”: 3.NF.1 & 3.G.2
Common Misconception: Students may think that all shapes can be divided the same way. Students may not understand that when partitioning a whole shape, number line, or a set into unit fractions, the interval must be equal. 2. Use fraction bars and geometric shapes to enVision, Topic 9: “Understanding Fractions” partition the whole into where b represents Lesson 9-2 the number of equal-sized parts. Understand CA Framework p. 16-23, 30-32 and describe each fractional part of a whole is Flipbook p. 32-37, 54-55 called a unit fraction. Read, count, and label NC Unpacking, p. 21-25, 45 unit fractions using words and numbers . 3.NF.1 Strategies for Teaching and Learning: Students will need many opportunities to analyze and discuss fractional parts using concrete models to develop familiarity and understanding of fractions. Students need to practice recognizing and representing that the numerator is the top number (term) of a fraction and that it represents the number of equal-sized parts of a whole. Students can reason about fractional parts using decomposition strategy and/or number bond representation (e.g., is the same as and , and , or and). Students to practice writing the denominator as the bottom number (term) of a fraction and that it Grade 3 Page 27 Grade ____ represents the total number of equal-sized parts. Common Misconception: Students see the numbers in fractions as two unrelated whole numbers separated by a line. 3. Understand that the size of a fractional part is enVision, Topic 9: “Understanding Fractions” relative to the size of a whole. 3.NF.1 Lesson 9-8 CA Framework p. 16-23 Flipbook p. 32-37 NC Unpacking, p. 21-25
Strategies for Teaching and Learning: (Use real-world objects) Students need to recognize that of the liquid in a small bottle could be less liquid than of the liquid in a larger bottle, but of a ribbon is longer than of the same ribbon because when the ribbon is divided into 3 equal parts, the parts are longer than when the ribbon is divided into 8 equal parts. 4. Use number lines to understand that the whole is enVision, Topic 9: “Understanding Fractions” the unit interval, measured by length from one Lesson 9-5, 9-6, 9-7 number to another number. Using the understanding of consecutive whole numbers, CA Framework p. 16-23 create unit fractions on number lines, focusing on Flipbook p. 32-37 halves, thirds, fourths, sixths, and eighths. NC Unpacking, p. 21-25 3.NF.2 Whole numbers on a number line:
Unit fractions on a number line:
Strategies for Teaching and Learning: Divide a shape into equal parts and represent this relationship on a number line, where the equal parts are between two whole numbers, starting with partitioning equal lengths between 0 and 1. They then work with number lines that have endpoints other than o and 1, or that include multiple whole number intervals. Students should plot fractions on a number line, by using the meaning of the fraction (e.g., to plot on a number line, there are 6 equal parts with 4 copies of one of the 6 equal parts). Common Misconception: Students do not count correctly on the number line. For example, students may count the hash mark at zero as the first unit fraction 5. enVision, Topic 10: “Fraction Comparison and Understand and explain the concept that the Equivalence”
Grade 3 Page 28 Grade ____ larger the denominator, the smaller the size Math Background, pp. 241A-241B of the piece. 3.NF.1 Interactive Learning, pp. 242-243 Represent and compare common fractions Lesson 10-1, 10-2, 10-3, 10-4 with like numerators or denominators and tell why one fraction is greater than, less CA Framework p. 16-23 than, or equal to the other by using concrete Flipbook p. 32-37 and pictorial models. 3.NF.3d NC Unpacking, p. 21-25 Strategies for Teaching and Learning: Students should practice decomposing fraction bars or shapes into equal shares to visual the pieces getting smaller as the denominator gets larger. Students can use fraction bars that show the same sized whole as models to compare fractions. They can also use Venn diagrams to organize and compare fractions to determine the relative size of the fractions, such as more than , exactly or less than . Encourage students to write the results of the comparisons with the symbols >, =, or <, and justify the conclusions with a model. Common Misconception: Students may not understand fractions can be greater than 1 6.Create simple equivalent fractions, (e.g., = , = ) 6. enVision, Topic 10: “Fraction Comparison…” and explain why the fractions are equivalent by using Lesson 10-5, 10.6 a visual fraction model. CA Framework p. 16-23 Flipbook p. 32-37 NC Unpacking, p. 21-25
3.NF.3b
Strategies for Teaching and Learning: Students need to use fraction strips and number lines to understand that two equivalent fractions are two ways of describing the same amount by using different-sized fractional parts. For example, in the fraction , if the eighths are taken in twos, then each pair of eighths is a fourth. Sixth-eighths then can be seen as equivalent to three-fourths. (Resource: Van de Walle) 7. Read and understand whole numbers as fractions, enVision, Topic 10: “Fraction Comparison…” and recognize fractions that are equivalent to the Lesson 10-7 whole numbers. Examples: Express 3 in the form of ; CA Framework p. 16-23 recognize that = 6; locate and 1 at the same point Flipbook p. 32-37 on a number line diagram. 3.NF.3c NC Unpacking, p. 21-25
Strategies for Teaching and Learning: Students need to use fraction strips and number lines to understand how to express whole number fractions on the number line when the unit interval is 1. Use a number line to help students notice that the difference between and , or and , and that these fractions is even greater and continue to grow as the numbers go higher.
Grade 3 Page 29 Grade ____ 8. Solve real-world problems that involve comparing enVision, Topic 10: “Fraction Comparison…” fractions by using visual fraction models and Lesson 10-8 strategies based on noticing equal numerators or “ Jon and Charlie’s Run” denominators. 3.NF.3d “ Snow Day” Strategies for Teaching and Learning: Have models available for student use such as fraction strips and number lines(scratch paper available to create their own.) so students can experience fractions across many constructs, such as the following three categories of models: area (e.g., of a garden), length (e.g., of an inch), and set or quantity (e.g., of the class). Partitioning and iterating are ways for students to understand the meaning of fractions, especially numerator and denominator. Additional Resources Differentiation (e.g. Special Education, EL, GATE) General Strategy Support for Unit: Use of math journals for differentiation and From the CA Mathematics Framework formative assessment (use link below) “ Instructional Strategies” chapter provides https://www.teachingchannel.org/videos/math- research-based strategies for teaching math, K-12 journals “ Supporting High Quality Common Core Flexible grouping: Instruction” chapter addresses the development, Content implementation, and maintenance of high-quality, Interest standards-based mathematics instructional programs Project/product Level (Heterogeneous/ Homogeneous) “ Universal Design for Learni n g” from CAST, the Tiered: Center for Applied Special Technology Independent Management Plan (Must Do/May Do) Grouping o Content o Rigor w/in the concept o Project-based learning o Homework o Grouping o Formative Assessment Anchor Activities: Content-related Tasks for early finishers o Game o Investigation o Partner Activity o Stations Depth and Complexity Prompts/Icons: Depth o Language of the Discipline o Patterns o Unanswered Questions o Rules o Trends Grade 3 Page 30 Grade ____ o Big Ideas o Complexity
http://scusd-math.wikispaces.com/home
Unit #4 Measurement and Data (about 6-8 weeks) In this unit, students will
Over-Arching Essential Questions for Unit 1: Grade 3 Page 31 Grade ____ See (Topics: 12, 15, 13, 14)
In this unit students will:
Culminating Task:
Standards
Math Common Core State Standards- Mathematics: 3.MD.1 3.MD.5 3.MD.2 3.MD.6 3.MD.7 3.G.2
ELD Standards to Support Unit: Part I: interacting in Meaningful Ways A. Collaborative 1. Exchanging information and ideas with others through oral collaborative conversations on a range of social and academic topics 2. Interacting with others in written English in various communicative forms (print, communicative technology, and multimedia 3. Offering and supporting opinions and negotiating with others in communicative exchanges 4. Adapting language choices to various contexts (based on task, purpose, audience, and text type) B. Interpretive 5. Listening actively to spoken English in a range of social and academic contexts 6. Reading closely literary and informational texts and viewing multimedia to determine how meaning is conveyed explicitly and implicitly through language 8. Analyzing how writers and speakers use vocabulary and other language resources for specific purposes (to explain, persuade, entertain, etc.) depending on modality, text type, purpose, audience, topic, and content area C. Productive 9. Expressing information and ideas in formal oral presentations on academic topics 11. Supporting own opinions and evaluating others’ opinions in speaking and writing 12. Selecting and applying varied and precise vocabulary and language structures to effectively convey ideas Part II. Learning About How English Works A. Structuring Cohesive Texts 1. Understanding text structure 2. Understanding cohesion B. Expanding and Enriching Ideas 5. Modifying to add details C. Connecting and Condensing Ideas 6. Connecting ideas 7. Condensing ideas Standards for Mathematical Practice: SEL Competencies: SMP 1 Make sense of problems and persevere in Self-awareness solving them Self-management SMP 2 Reason abstractly and quantitatively Social awareness SMP 3 Construct viable argument and critique the Relationship skills reasoning of others Responsible decision making Grade 3 Page 32 Grade ____ SMP 4 Model with mathematics SMP 5 Use appropriate tools strategically SMP 6 Attend to precision SMP 7 Look for and make use of structure
Grade 3 Page 33 Grade ____