Common Core State Standards 2nd Edition Math Pacing Guide Third Grade—1stNine Week Period 2nd Edition: Viola Sanchez, Marita Lindbeck, Jennifer Russell `````````````````````````````````````````````````````````````````````````````````````` Mr. Stan Rounds, Superintendent Dr. Steven Sanchez, Deputy Superintendent Prepared By: Lydia Polanco, Coordinator of Elementary Instruction st
1 Edition Developed by: Jennifer Russell, Viola Sanchez, Felicity Valle, and Marita Lindbeck st
Third Grade—1 Nine Week Period 1 Math Pacing Guide Las Cruces Public Schools Understanding Mathematics: The standards define what students should understand and be able to do in their study of mathematics. Asking a student to understand something means asking a teacher to assess whether the student has understood it.1 Mathematical understanding and procedural skill are equally important.2 Description of the Pacing Guide: A pacing guide is an interval based description of what teachers teach in a particular grade or course; the order in which it is taught, and the amount of time dedicated to teaching the content. Purpose of a Pacing Guide: The purpose of a pacing guide is to ensure that all of the standards are addressed during the academic year. Each pacing guide is nine weeks in duration. Components of the Pacing Guide: • Critical Areas-­‐ Each grade level has identified Critical Areas. These areas are woven throughout the standards and should receive additional time and attention. • Mathematical Practice Standards (8)-­‐ Based on the NCTM Process Standards, these standards describe the variety of "processes and proficiencies" students should master while working with the Grade Level Content Standards. • Domains are larger groups of related Content Standards. Standards from different domains may sometimes be closely related.3 • Clusters are groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a connected subject.4 • Grade level standards define what students should know and be able to do by the end of each grade level. • Unpacked standards provide a clear picture for the teacher as he/she implements the CCSS • Resources—includes but not limited to current district core resources • Depth of Knowledge — (DOK) Criteria for systematically analyzing the alignment between standards and standardized assessments 1
www.corestandards.org, Mathematics, Introduction, p. 4
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www.corestandards.org, Mathematics, Introduction, p. 5
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Third Grade—1 Nine Week Period 2 STANDARDS-­‐BASED, LCPS Pacing Guides STANDARDS-­‐DRIVEN Other Resources Common Core State Standards Core Program enVision Math Supplemental Technology Based program to prepare for PARCC (First in Math, FASTT Math, etc.) st
Third Grade—1 Nine Week Period 3 Grade Level: Third Grade Quarter: 1st Nine Weeks Standard Q1 Q2 Q3 Q4 3.OA.1 I/P P R R Domain: Operations and Algebraic Thinking Cluster: Represent and solve problems involving multiplication and division. Critical Areas: #1: Strong Connection #2 #3 #4 Grade Level Content Standard Mathematical Practice Standard 3. OA.1 Interpret products of whole numbers, e.g., Interpret 5 × 7 as MP.1 Make sense of problems and persevere in solving them. the total number of objects in 5 groups of 7 objects each. • Plan a solution pathway instead of jumping to a solution. • Continually ask themselves, “Does this make sense?” Can For example, describe a context in which a total number of objects can understand various approaches to solutions. be expressed as 5 × 7. • Monitor their progress and change the approach if necessary. MP.4 Model with mathematics. • Apply the mathematics they know to solve everyday problems. • Ask themselves, “How can I represent this mathematically?” MP. 7 Look for and make use of structure • Look for the overall structure and patterns in mathematics. Unpacked Content Standard 3. OA.1 In the 1st Quarter, students were introduced to the idea that multiplication requires them to think in terms of “groups of” instead of individual things. Students learned that the multiplication symbol “x” means groups of and problems such as 5 x 7 refers to 5 groups of 7. Students should practice and apply in this quarter. Special Note: arrays should be rows x columns. Vocabulary 3.OA.1 groups of, total, factor, product, each, interpret, object(s), array, associative property, rows, columns, repeated addition, number sentence, multiplication sentence, equation, expression Resources Depth of Knowledge 3 OA 1 Other Resources/Tools3.OA.1 (DOK 1) enVision Resources: Which two number sentences are true about the array shown National Council of Teachers of Mathematics, below? Topic 4 Illuminations: Exploring equal sets ********* Lessons: • http://illuminations.nctm.org/LessonDetail. ********* 4-­‐1, 4-­‐5 a. 2 + 9 = 11 and 9 x = 18 aspx?ID=L317 b. 9 + 9 = 18 and 9 + 18 = 17 Interactive Digital Path: c. 2 x 9 = 18 and 9 + 9 = 18 Ixl.com-­‐
Meanings of Multiplication http://www.ixl.com/math/standards/common-­‐
d. 9 x 9 = 81 and 9 + 9 + 18 core/grade-­‐3 (DOK 2) • Multiplication: Multiplication sentences st
Third Grade—1 Nine Week Period 4 •
(Third grade -­‐ E.1) Properties: Relate addition and multiplication (Third grade -­‐ J.7) k-­‐5mathteachingresources.com-­‐ • Array Picture Cards-­‐activity Possible Read Alouds-­‐ • 100 Hungry Ants • Six Dinner Sid • Amanda Beans' Amazing Dream • The Doorbell Rang Tools: • Set of counters • Number lines to skip count and relate to multiplication (Common Core State Standards for Mathematics) Everyday objects that come in groups What is another way to show the exact same amount as the two addition sentences below? 4+4+4+4+4+4=24 and 8+8+8=24 (6 x 4 = 24) and (3 X 8 = 24) st
Third Grade—1 Nine Week Period 5 Grade Level: Third Grade Quarter: 1st Nine Weeks Standard 3.OA.9 Domain: Operations and Algebraic Thinking Critical Areas: #1: Strong Connection Grade Level Content Standard Q1 I/P Q2 Q3 Q4 I/P R R Cluster: Represent and solve problems involving multiplication and division. #2 #3 #4 Mathematical Practice Standard MP.1 Make sense of problems and persevere in solving them. 3. OA.9 Identify arithmetic patterns (including patterns in the • See relationships between various representations. addition table or multiplication table), and explain them using MP.2 Reason abstractly and quantitatively properties of operations. • Understand the meaning of quantities and are flexible in the use of operations and their properties. For example, observe that 4 times a number is always even, and MP.7 Look for and make use of structure explain why 4 times a number can be decomposed into two equal • Apply general mathematical rules to specific situations addends. • Look for the overall structure and patterns in mathematics 1st Quarter-­‐ Identify arithmetic patterns 2nd Quarter-­‐Identify arithmetic patterns and explain them using properties of operations. Unpacked Content Standard 3. OA.9 For the 1st Quarter, students will only be identifying arithmetic patterns. It is not until the 2nd Quarter that students will explain the patterns they have identified using properties of operations; this ties to working on 3 OA 5 in the 2nd Quarter. This standard should be introduced and practiced through a daily routine. Daily routines could include, but are not limited to, Ten Minute Math, Math Calendar, and/or Problem of the Day. See Appendix 2 of this Pacing Guide for in depth ideas for Daily Routines. This standard calls for students to examine arithmetic patterns involving both addition and multiplication. Arithmetic patterns are patterns that change by the same rate, such as adding the same number. Students need ample opportunities to observe and identify important numerical patterns related to operations. They should build on their previous experiences with properties related to addition and subtraction. Students investigate addition and multiplication tables in search of patterns and explain why these patterns make sense mathematically. Vocabulary: 3.OA.9 assess, estimation, equation, reasonableness, rounding, operation, parenthesis, quantity, represent, pattern, relationship, arithmetic, properties, addition, multiplication, identify, Identity Property of Multiplication, Zero Property of Multiplication Resources Depth of Knowledge 3 OA 9 (DOK1) Other Resources/Tools 3.OA.9 enVision Resources: What rule does the patterns of numbers below follow? National Council of Teachers of Mathematics, Topic: 5 4,8,12,16,20 (Increases by 4 every time) Illuminations: st
Third Grade—1 Nine Week Period 6 Lessons 5-­‐2, 5-­‐3, 5-­‐4, 5-­‐5 Interactive Digital Path: Multiplication Facts: Use Patterns • http://illuminations.nctm.org/Activities.aspx?grade=2 Ixl.com-­‐http://www.ixl.com/math/standards/common-­‐
core/grade-­‐3 • Multiplication: Multiplication input/output tables (Third grade -­‐ E.13) • Addition: Addition input/output tables -­‐ up to three digits (Third grade -­‐ C.2) k-­‐5mathteachingresources.com-­‐ • Using Number Patterns to Describe Multiples • Increasing and Decreasing Number Patterns • Two Step Number Patterns • Patterns in the Addition Table • Patterns in the Multiplication Table Possible Read Alouds-­‐ • 100 Hungry Ants • Six Dinner Sid • Amanda Beans' Amazing Dream • The Doorbell Rang • Two of Everything • Math-­‐terpieces: The Art of Problem Solving Tools: • Set of counters/ Cubes • Number lines to skip count and relate to multiplication (Common Core State Standards for Mathematics) • Everyday objects that come in groups • Chart Paper (DOK2) Why can any number times four be decomposed into two equal addends? st
Third Grade—1 Nine Week Period 7 Grade Level: Third Grade Quarter: 1st Nine Weeks Standard 3.NBT.1 3.NBT.2 Domain: Number and Operations in Base Ten Q1 I/P P Q2 R P Q3 R R Q4 R R Cluster: Use place value understanding and properties of operations to perform multi-­‐digit arithmetic.4 Critical Areas: #1: Connection #2 No Connection #3 No Connection #4 No Connection Grade Level Content Standard Mathematical Practice Standard 3. NBT.1 Use place value understanding to round whole numbers to MP. 5. Use appropriate tools strategically the nearest 10 or 100. • Use estimation and other mathematical knowledge to detect 3. NBT.2 Fluently add and subtract within 1000 using strategies and possible errors. algorithms based on place value, properties of operations, and/or the MP.7 Look for and make use of structure relationship between addition and subtraction • Apply general mathematical rules to specific situations. st
• Look for the overall structure and patterns in mathematics. 1 Quarter 100 nd
MP.8.Look for and express regularity in repeated reasoning. 2 Quarter 1000 • Continually evaluate the reasonableness of their intermediate results Unpacked Content Standard 3. NBT.1 This standard should be introduced and practiced through a daily routine. Daily routines could include, but are not limited to, Ten Minute Math, Math Calendar, and/or Problem of the Day. See Appendix 2 of this Pacing Guide for in depth ideas for Daily Routines. This standard refers to place value understanding, which extends beyond an algorithm or procedure for rounding. The expectation is that students have a deep understanding of place value and number sense and can explain and reason about the answers they get when they round. Students should have numerous experiences using a number line and a hundreds chart as tools to support their work with rounding. Students learn when and why to round numbers. As students’ understanding of place value increases, the strategies for rounding are valuable for estimating, justifying and predicting the reasonableness of solutions in problem-­‐solving. 3. NBT.2This standard refers to fluently, which means accuracy, efficiency (using a reasonable number of steps and time), and flexibility (using strategies such as the distributive property).Problems should include both vertical and horizontal forms, including opportunities for students to apply the commutative and associative properties. Students explain their thinking and show their work by using strategies and algorithms, and verify that their answer is reasonable. Vocabulary 3.NBT.1: Place value, rounding, whole numbers, nearest (10-­‐100), digits, standard form, expanded form Vocabulary 3.NBT.2: Fluently, add, subtract, strategies, algorithms, place value, properties, operations, relationship Resources Depth of Knowledge (DOK1) 3 NBT 1 Other Resources/Tools 3.NBT.1 st
Third Grade—1 Nine Week Period 8 enVision Resources: Topic 1 Lessons: 1-­‐1, 1-­‐2, 1-­‐3 1-­‐4, 1-­‐5, 1-­‐6, 1-­‐7 Interactive Digital Path: Numeration Number Sense National Council of Teachers of Mathematics, Illuminations: • http://illuminations.nctm.org/Activities.aspx?g
rade=2 Ixl.com-­‐
http://www.ixl.com/math/standards/common-­‐
core/grade-­‐3 • Estimation and rounding: Rounding (Third grade -­‐ L.1) k-­‐5mathteachingresources.com-­‐ • Round Up or Down? • Round to the Nearest Ten • Round to the Nearest 100 Possible Read Alouds-­‐ • 100 Hungry Ants • Six Dinner Sid • Amanda Beans' Amazing Dream • The Doorbell Rang • Two of Everything • Math-­‐terpieces: The Art of Problem Solving Tools: • Set of counters/ Cubes • Number lines to skip count and relate to multiplication (Common Core State Standards for Mathematics) • Everyday objects that come in groups • Chart Paper • Base Ten Blocks(ones, tens, hundreds) Round 120 to the nearest 100. (DOK2) Round 153 to the nearest 10 and nearest 100. st
Third Grade—1 Nine Week Period 9 3 NBT 2 enVision Resources: Topic 8 Lesson 1-­‐3 Interactive Digital Path: Numeration Number Sense: Addition and Subtraction Other Resources/Tools 3.NBT.2 National Council of Teachers of Mathematics, Illuminations: • http://illuminations.nctm.org/Activities.aspx?g
rade=2 Ixl.com-­‐
http://www.ixl.com/math/standards/common-­‐
core/grade-­‐3 • Properties: Properties of addition (Third grade -­‐ J.3) • Properties: Solve using properties of addition (Third grade -­‐ J.4) k-­‐5mathteachingresources.com-­‐ • 3 Digit Addition Split • Doubling to 1000 Possible Read Alouds-­‐ • 100 Hungry Ants • Six Dinner Sid • Amanda Beans' Amazing Dream • The Doorbell Rang • Two of Everything • Math-­‐terpieces: The Art of Problem Solving Tools: • Set of counters/ Cubes • Number lines to skip count and relate to multiplication (Common Core State Standards for Mathematics) • Everyday objects that come in groups • Chart Paper Base Ten Blocks(ones, tens, hundreds) 3 NBT 2 (DOK1) 529-­‐113=416 so, 416 + ____=529 (DOK2) 753-­‐642=______ 700-­‐600=______ 50-­‐40=_____ 3-­‐2=_____ So, 753-­‐642=_____ (DOK3) 744 + 233 =_____ _____ +______=______ _____ +______=______ _____ +______=______ So, 744 + 233 =________ Explain a way to check your math on the above problem. st
Third Grade—1 Nine Week Period 10 Appendices 1. Grade Level 3-­‐ Pacing Guide st
Third Grade—1 Nine Week Period 11 st
Third Grade—1 Nine Week Period 12 Appendices 2 Grade Level 3-­‐ Daily Math Routines Daily math routines are possible ideas to be used in conjunction with everyday instruction in order for students to be exposed to content that is addressed in the following content standards. Domain: Operations and Algebraic Thinking (OA) Standard:3.OA.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. Cluster: Solve problems involving the four operations, and identify and explain patterns in Possible Daily Math Routine 1. The students will identify arithmetic patterns using addition table, multiplication table, and hundreds chart. Given the tables, in small groups, students will discover and explain their patterns, then share them with the whole group and or a shoulder partner. 2. Incorporate arithmetic patterns while during a class meeting/ calendar time. Students should start looking for any patterns they might see. If students have a difficult time identifying patterns, try to prompt them by asking them the following questions… Domain: Number and Operations in Base Ten 3. NBT. 1: Use place value understanding to round whole numbers to the nearest 10 or 100. •
What patterns do you find within the hundreds chart? •
Can we find patterns by adding or multiplying? •
How do you know if something is a pattern? Cluster: Use place value understanding and properties to perform multi-­‐digit arithmetic. Possible Daily Math Routine 1. Place the numbers 1-­‐200 into a small bucket. Everyday have a small group of students take turns choosing numbers from the bucket at random. After a student has chosen a number he or she may round the number to the nearest 10 or 100 or may st
Third Grade—1 Nine Week Period 13 3.NBT.3 Multiply one-­‐digit whole numbers by multiples of 10 in the range 10-­‐90 (e.g., 9×80, 5×60) using strategies based on place value and properties of operations. choose to have the class practice rounding the number together. 2. Teacher may also choose for students to play” Round Up or Down? “as a morning warm up. Directions: • Choose one of the following numbers and write it above the first mark on the number line: 100, 200, 300, 400, 500, 600, 700, 800, 900 2. Count on by 10s from your starting number to complete the missing numbers on the number line. • Write 12 different numbers in the boxes on this page that fall between the smallest and largest numbers on your number line. 4. Cut out the boxes. • Round each number to the nearest hundred and place them on the appropriate side of the number line. • Have a friend check your work. Possible Daily Math Routine 1. Teacher may also choose for students to play Multiples of Ten Multiply as a morning warm up. Materials: Numeral Cards (1-­‐ 9), counters, Multiples of Ten gameboard Directions: 1. Work with a partner. Take turns to turn over two numeral cards and add a zero to your second number to make a multiple of 10. 2. Multiply your two factors and complete the math talk sentence. Example: Tom turns over two cards: He adds a zero to the 5, multiplies the factors and says, “The product of 8 and 50 is 400.” st
Third Grade—1 Nine Week Period 14 3. If you have the largest product for the round, place a counter in your circle on the game-­‐board. 4. Keep going until one of you has 10 counters in your circle. Domain: Measurement and Data 3. MD.1 Tell and write time to the nearest minute and measure timeintervals in minutes. Solve word problems involving addition andsubtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram. Cluster: Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects. Possible Daily Math Routine 1. Give each student a “Judy” clock. Write a time on the board or smart-­‐board and have students practice setting their clocks. 2. Teachers might choose to work through a math word problem as a class or have students work to solve in partners. st
Third Grade—1 Nine Week Period 15 Appendices 3 Grade Level 3-­‐ Practice Standards st
Third Grade—1 Nine Week Period 16 Appendices 5 Grade Level 3-­‐ Pacing Guide st
Third Grade—1 Nine Week Period 17 Balanced Assessment Strategies Selected Response Constructed Response Performance Assessment Informal Assessment Multiple Choice Fill-­‐in-­‐the-­‐blank (words, phrases) Presentation Oral questioning True–False Essay Movement Observation Matching Short answer (sentences, paragraphs) Exhibition Interview Diagram Model Conference Web Dramatization Process description Concept Map Enactment Checklist Flowchart Project Rating scale Graph Table Debate Journal sharing Thinking aloud process Matrix Student self-­‐assessment Illustration Peer review st
Third Grade—1 Nine Week Period 18