Grade 5 Unit 1 Developing Fluency With Multiplication And Division Mathematics

Transcript

Grade 5 Unit 1 Developing Fluency with Multiplication and Division Mathematics Unit Goals – Stage 1 Number of Days: 35 Traditional: September 2 – October 21, Track B: September 2 – October 21, 2015 Unit Description: In Unit 1 students build on their work from previous grade levels to refine their strategies for multiplication and division in order to reach fluency in multiplication. Students reason about dividing whole numbers with two-digit divisors to build strategies for accurate computations. Students continue to develop more sophisticated strategies for division to become flexible and efficient with the standard algorithm in Grade 6. Materials: Good Questions for Math Teaching (Referred to as Good Questions, given to teachers at Tri 2 training 2014-2015), Implementing the Common Core State Standards through Mathematical Problem Solving Grades 3 – 5 (Referred to as “Problem Solving - Grades 3-5” in Unit Guide, given to teachers at Tri 3 training 2014-2015), “Multiple Markers” for class number line, base-ten blocks, place-value chart, graph paper, GoMath! MathBoard or whiteboard Standards for Mathematical Practice SMP.1 SMP.2 SMP.3 SMP.4 SMP.5 SMP.6 SMP.7 SMP.8 Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Standards for Mathematical Content Clusters Addressed Operations and Algebraic Thinking 5.OA.A Write and interpret numerical expressions. Numbers and Operations in Base Ten: 5.NBT.A Understand the place value system. 5.NBT.B Perform operations with multi-digit whole numbers. LONG BEACH UNIFIED SCHOOL DISTRICT Transfer Goals Students will be able to independently use their learning to…  Make sense of never-before-seen problems and persevere in solving them.  Construct viable arguments and critique the reasoning of others. Making Meaning UNDERSTANDINGS ESSENTIAL QUESTIONS Students will understand that… Students will keep considering…  The position of a digit determines its value.  What is the underlying pattern?  The place value system is based on powers  How can estimating help us when solving of 10. problems?  Multiplication and division calculations of  What are some ways to represent the whole numbers can be solved and explained quantities and/or solve the problem? in many ways. Acquisition KNOWLEDGE SKILLS Students will know… Students will be skilled at and/or be able to…  The definitions of the academic vocabulary  Evaluate expressions with parentheses. words such as exponent, numerical  Write and interpret numerical expressions. expression, parentheses, powers of 10,  Use the standard algorithm to fluently multiply evaluate and compatible numbers. multi-digit whole numbers.  Use mental strategies for multi-digit whole  Use efficient strategies to divide multi-digit number operations. whole numbers. 1 Posted 6/10/15 Grade 5 Unit 1 Developing Fluency with Multiplication and Division Mathematics Assessed Grade Level Standards Standards for Mathematical Practice SMP.1 SMP.2 SMP.3 SMP.4 SMP.5 SMP.6 SMP.7 SMP.8 Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning. Standards for Mathematical Content Operations and Algebraic Thinking [a] 5.OA.A Write and interpret numerical expressions. 5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. Number and Operations in Base Ten [m] 5.NBT.A Understand the place value system. 5.NBT.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. 5.NBT.2 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. [m] 5.NBT.B Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm. 5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Key: [m]= major clusters; [s] = supporting clusters; [a] = additional clusters LONG BEACH UNIFIED SCHOOL DISTRICT 2 Posted 6/10/15 Grade 5 Unit 1 Developing Fluency with Multiplication and Division Mathematics Evidence of Learning – Stage 2 Assessment Evidence Unit Assessment Students will complete selected response and constructed response items to indicate level of mastery/understanding of the unit standards as outlined in this guide. [a] 5.OA.A  The student writes or identifies a numerical expression that records a calculation represented with words.  The student interprets numerical expressions in words without evaluating them.  The student evaluates numerical expressions with grouping symbols. [m] 5.NBT.A  The student represents powers of 10 by using whole-number exponents. [m] 5.NBT.B  The student adds or subtracts multi-digit whole numbers in non-contextual mathematics problems.  The student multiplies multi-digit whole numbers.  The student determines whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. For selected content, students will need to…  Solve complex problems in pure and applied mathematics, making productive use of knowledge and problem solving strategies.  Clearly and precisely construct viable arguments to support their own reasoning and critique the reasoning of others. Other Evidence Formative Assessment Opportunities  Opening Tasks  Go Math! Show What You Know  Classroom Challenges  Go Math! Performance Task  Homework (Go Math! Standards Practice Book)  Go Math! Getting Ready for the Smarter Balance  Go Math! Chapter Test (Assessment Guide)  Go Math! Chapter Review / Test – Student Book Exit slips Extension Menus It’s All About the Facts Supplemental materials In-class projects Recorded Teacher Observations Writing activities Quizzes SBAC Interim Assessment Block (IAB)          Access Using Formative Assessment for Differentiation for suggestions. Located on the LBUSD website – “M” Mathematics – Curriculum Documents. LONG BEACH UNIFIED SCHOOL DISTRICT 3 Posted 6/10/15 Grade 5 Unit 1 Developing Fluency with Multiplication and Division Mathematics Learning Plan – Stage 3 Suggested Sequence of Key Learning Events and Instruction Days Daily Daily Metas de Aprendizaje Aprenderé las operaciones básicas de matemáticas… Expectations    Utilizaré estrategias de matemática mental para sumar y restar…  90 minutes per week (Schools/ grades with ST Math) Perseveraré en la resolución de problemas mientras juego juegos interactivos para ayudarme a entender las matemáticas…  1 Puedo trabajar en grupos cooperativos…       2 Puedo agregar a las ideas de los demás y expresar ideas claramente…    Core Resources: Go Math! http://www-k6.thinkcentral.com  Maintaining Fluency Through Fact Families, pp. 1 –10, 13 28  Review Properties of Addition and Multiplication, Lesson 1.3 pp. 13 - 16 Saying facts orally. Writing fact families. Using the Properties of Addition and Multiplication. Participating in daily Number Talks. Communicating my reasoning.  Developing long term problem solving skills. Visualizing math concepts. Making connections between concepts and across grades. Playing interactive games. ST Math Objectives  Whole numbers  Multi-Digit Multiplication  Multi-Digit Division Optional  Addition and Subtraction with Regrouping Setting the Classroom Culture/Mindset – “Mistakes are Embraced.” Setting roles for each member of the group.  Asking thoughtful questions. Listening attentively and respectfully to others. Appropriately challenging others’ LONG BEACH UNIFIED SCHOOL DISTRICT Number Talks Strategies and Problem Sets, Grades 2-5 (also found on intranet in Instructional Tools)  4 Pyramid Cup Challenge (more activities found in Instructional Tools Normbuilding Activities) Talk Moves Posters (Instructional Tools Classroom Discussion Resources) Supplemental Resources: Books, Internet and Curriculum Intranet (LBUSD Math Intranet th Instructional Tools – Elementary – 5 Grade)     Diagnostic Basic Facts Tests (Assessments) It’s All About the Facts Supplemental Materials (Instructional Tools) Basic Facts Game: “Tic Tac Toe Sums“ http://www.youcubed.org/task/ti c-tac-toe-sums/ Calendar Math ST Tip  Assure your login to stmath.com (Teacher Console)  Utilize your STMath Start Up guide (2015 – 2016 version)  Create LBUSD/ST Math ticket to JiJi (from pdf in startup guide)    Setting up Positive Norms in Math Class (Instructional Tools Classroom Discussion Resources) SMP Posters (Instructional Tools Standards for Mathematical Practice) Math Talk Bookmarks (Instructional Tools - Classroom Discussion Resources) Posted 6/10/15 Grade 5 Unit 1 Developing Fluency with Multiplication and Division Mathematics Learning Plan – Stage 3 Suggested Sequence of Key Learning Events and Instruction Days Metas de Aprendizaje Expectations   3 4 Puedo utilizar las herramientas apropiadas de manera estratégica… Puedo formar un número de múltiples dígitos…   Core Resources: Go Math! http://www-k6.thinkcentral.com  Math Conversation Guide Table Tent (Instructional Tools -Classroom Discussion Resources) ideas. Being thoroughly prepared for classroom discussions. Effectively following set behaviors and norms for discussion. Participating in daily Multiple Markers routine. Effectively following set behaviors and norms for using manipulatives. OPENING TASK – “Math Detective”  Using clues about place value. Supplemental Resources: Books, Internet and Curriculum Intranet (LBUSD Math Intranet th Instructional Tools – Elementary – 5 Grade)   Multiple Markers for 100 Days Go Math! Manipulatives   Prompts for Multiple Markers Shapes for Multiple Markers  Ch. 1 “Math Detective” p. 3 Ch. 1 “Show What You Know” and Vocabulary Builder” pp. 3 –4  See www.illustrative mathematics.org/5 for tasks and videos to be used throughout the unit. Engage, Explore, Evaluate Problems (to use throughout the unit)   Note: These activities should be used as a formative assessment for this unit. 5-7 Puedo explicar la relación de los dígitos en diferentes lugares de un número de múltiples dígitos…     8 - 10 Puedo usar exponentes para mostrar las potencias de 10…   Building numbers with base-ten blocks. Using a place-value chart. Comparing the value of different digits by using phrases such as, “__ is 10 times as much as __” and “__ is 1/10 of __.” Writing multi-digit numbers in standard form, word form and expanded form.  Using base-ten blocks. Explaining the pattern for how the number of zeroes in a product  LONG BEACH UNIFIED SCHOOL DISTRICT   5 Lesson 1.1: Investigate Place Value and Patterns Lesson 1.2: Place Value of Whole Numbers  Lesson 1.4: Powers of 10 and Exponents Lesson 1.5: Algebra -   Problem Solving - Grades 3-5, Task 3.7 “Selling Stickers” pp. 5254 Good Questions, p. 36 #1, 2 and p. 39 #2 Problem Solving - Grades 3-5, Task 3.4 “Buying Tickets at the School Fair” pp. 44-46 Posted 6/10/15 Grade 5 Unit 1 Developing Fluency with Multiplication and Division Mathematics Learning Plan – Stage 3 Suggested Sequence of Key Learning Events and Instruction Days Metas de Aprendizaje Expectations   11 - 12 Puedo resolver problemas del mundo real relacionados con la multiplicación y división…  relates to the power of 10. Multiplying a whole number by a power of 10. Using a basic fact and a pattern to multiply mentally by multiples of 10, 100, and 1000. Illustrating and explaining my calculations using equations, rectangular arrays, and/or area models. Core Resources: Go Math! http://www-k6.thinkcentral.com Multiplication Patterns  Ch. 1 Mid-Chapter Checkpoint pp. 25 – 26  Lesson 1.9: Problem Solving - Multiplication and Division o “Think Smarter” p. 42 Supplemental Resources: Books, Internet and Curriculum Intranet (LBUSD Math Intranet th Instructional Tools – Elementary – 5 Grade)  *Adapting for Grade 5 on p. 46 Good Questions, p. 36 #3  Good Questions, p. 44 #4, 7  Match the Expression cards  Problem Solving - Grades 3-5, Task 2.9 “Wacky Parentheses” pp. 29-30 Good Questions, p. 45 #10 Note: This lesson should be used as a formative assessment for students’ multiplication and division strategies. What type of strategies are being used? Are the students using invented strategies or going straight to the standard algorithm? Can they explain their strategy or the algorithm used? What are the common misconceptions? 13 - 14 15 - 16 Puedo escribir e interpretar las expresiones numéricas… Puedo evaluar las expresiones numéricas…     Matching a numerical expression to words. Writing an expression to match a calculation that is described verbally.  Performing the operations in parentheses first. Placing parentheses in an expression to equal a given value.  LONG BEACH UNIFIED SCHOOL DISTRICT  6 Suggestion: Start with Match the Expression p. 45 #13. Use Lesson 1.10: Numerical Expressions Lesson 1.11: Evaluate Numerical Expressions  Posted 6/10/15 Grade 5 Unit 1 Developing Fluency with Multiplication and Division Mathematics Learning Plan – Stage 3 Suggested Sequence of Key Learning Events and Instruction Days 17 - 21 Metas de Aprendizaje Puedo conceptualizar y resolver problemas de multiplicación que contienen números enteros… Expectations     22 Puedo explicar la relación que existe entre la multiplicación y la división… 23 - 24 Puedo resolver problemas del mundo real… 25 - 32 Puedo conceptualizar y resolver problemas de división que contienen números enteros con dividendos de hasta cuatro dígitos y divisores de dos dígitos… Core Resources: Go Math! http://www-k6.thinkcentral.com  Lesson 1.3: Algebra – Properties o The Distributive Property pp. 14-16  Lesson 1.6: Multiply by 1Digit Numbers  Lesson 1.7: Multiply by 2Digit Numbers Estimating products to check the reasonableness of my solution. Using various strategies connecting place value, arrays, area models and the Distributive Property to partial products. Fluently using the standard algorithm. Explaining the standard algorithm for multiplication of multi-digit numbers. Supplemental Resources: Books, Internet and Curriculum Intranet (LBUSD Math Intranet th Instructional Tools – Elementary – 5 Grade)     Maintaining Fluency Through Fact Families, pp. 13 – 32 Problem Solving - Grades 3-5, Task 2.6 “Kevin and Glenn Estimate” pp. 22-23 Good Questions, p. 43 #2 and p. 44 #5, 6 Factor Bingo Task Using arrays, the area model, and the Distributive Property to solve division problems with multiplication.  Lesson 1.8: Relate Multiplication to Division FORMATIVE ASSESSMENT LESSON City Park  Using my understanding of multiplication and division of whole numbers.  Communicating my reasoning.  Checking to see if my answers make sense.  FAL, City Park (Assessment)  City Park - FAL, Differentiated Activities Using patterns and basic facts and/or compatible numbers to help estimate. Using inverse operations to check a division problem. Modeling with base-10 blocks and drawing quick pictures. Using partial quotients to find and  Ch. 2 “Math Detective” p. 61 “Show What You Know” and Vocabulary Builder” pp. 61-62 Lesson 2.1 Place the First Digit Lesson 2.2: Divide by 1-Digit Divisors  Maintaining Fluency Through Fact Families, pp. 13 - 32 Good Questions, p. 43 #1 & 2, p. 44 #8, p. 45 #9 Whole Numbers Quiz      LONG BEACH UNIFIED SCHOOL DISTRICT 7      Posted 6/10/15 Grade 5 Unit 1 Developing Fluency with Multiplication and Division Mathematics Learning Plan – Stage 3 Suggested Sequence of Key Learning Events and Instruction Days Metas de Aprendizaje Expectations  Core Resources: Go Math! http://www-k6.thinkcentral.com  Lesson 2.3: Division with 2Digit Divisors  Lesson 2.4: Partial Quotients  Lesson 2.5: Estimate with 2Digit Divisors  Lesson 2.6: Divide by 2-Digit Divisors  Lesson 2.7 Interpret the Remainder  Lesson 2. 8 Adjust Quotients subtract multiples of the divisor. Using the standard algorithm (note: Students are not expected to be fluent with the standard algorithm until Grade 6). Supplemental Resources: Books, Internet and Curriculum Intranet (LBUSD Math Intranet th Instructional Tools – Elementary – 5 Grade) Note: Some multiplication and division lessons from Go Math! may need to be done during the 30 minute Facts Fluency time or merged depending on the needs of your students. 33 34 35 Puedo resolver problemas de comparación del mundo real…  Using bar models when quantities are multiples of each other.  Lesson 2.9: Problem Solving Division Unit Assessment Ch. 2 Performance Task – “Feature Presentation” (Assessment Guide, pp. AG108 – AG112D) We would appreciate feedback on this unit. You can copy and paste this link into your browser or go on the math internet to Curriculum Documents - Unit Guide. Click on the link at the top of the page. http://goo.gl/forms/8U03MFVbCP LONG BEACH UNIFIED SCHOOL DISTRICT 8 Posted 6/10/15