Grade 4 Mathematics, Quarter 4, Unit 4.3 Using Place Value to Add and Subtract Whole Numbers to the Millions. Overview

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1 Whole Numbers to the Millions Overview Number of instruction days: 7 9 (1 day = 90 minutes) Content to Be Learned Round multi-digit whole numbers using understanding of place value. Recognize that the value of digits in a whole number increases by a power of 10 as you move to the left. Fluently add and subtract multi-digit whole numbers using the standard algorithm Solve multi-step word problems using whole numbers. Represent word problems with an equation using a letter standing for the unknown quantity. Mathematical Practices to Be Integrated 1 Make sense of problems and persevere in solving them. Analyze the relationships that place value creates in our number system. Check for the reasonableness of an answer by estimating, using your knowledge that the value of the digits in a number increases or decreases by powers of Model with mathematics. Solve addition and subtraction word problems using bar diagrams to find the unknown quantity. Interpret results and revise if necessary. Essential Questions How can you compose and decompose the same number in different ways? What strategy do you use to round a given number? How can you use place value to round numbers? How can you use the standard algorithm to add/subtract? Explain the process. How can you use a letter to represent an unknown quantity when solving an equation? Providence Public Schools D-105

2 Version 4 Whole Numbers to the Millions (7 9 days) Standards Common Core State Standards for Mathematical Content Number and Operations in Base Ten 2 2 Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000, NBT Generalize place value understanding for multi-digit whole numbers. 4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place. Use place value understanding and properties of operations to perform multi-digit arithmetic. 4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm. Operations and Algebraic Thinking 4.OA Use the four operations with whole numbers to solve problems. 4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. 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. Common Core State Standards for Mathematical Practice 1 Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, Does this make sense? They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. 4 Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. D-106 Providence Public Schools

3 Grade 4 Mathematics, Quarter 4, Unit 4.3 Whole Numbers to the Millions (7 9 days) Version 4 Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Clarifying the Standards Prior Learning In Grade 2, students compared 2 three-digit numbers. In Grade 3, students rounded whole numbers to the nearest hundred. Place value was an additional rather than a major cluster according to the PARCC document. Adding and subtracting multi-digit whole numbers was also an additional cluster according to the PARCC document. Students learned to 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. Current Learning In Grade 4, place value is one of the major clusters according to the PARCC document; therefore, it requires more emphasis and time throughout the year. In Quarter 1, students understand, compare, and round up to six-digit numbers. In Quarter 2, students extend this learning to seven-digit numbers. Adding and subtracting is also a major cluster in Grade 4 according to PARCC. In Quarter 1, students add and subtract multi-digit whole numbers up to the hundred-thousands place using the standard algorithm. In Quarter 2, students add and subtract multi-digit whole numbers to the millions place using the standard algorithm. By the end of Grade 4, students add and subtract fluently to the millions place. Future Learning In Grade 5, students will extend their knowledge of the place value system to decimals and division based on base ten numbers. The extension of the place value system is a major intellectual accomplishment, involving understanding and skill with base ten units. The Number and Operations in Base Ten: Place Value System domain does not appear in grades 6 and beyond. It is expected that students will understand and apply place value in all mathematics. In Grade 5, students will perform the four operations with multi-digit whole numbers and with decimals to the hundredths. Additional Findings Conceptual understanding of and procedural fluency with multi-digit numbers and decimal fractions require that students understand and use the base ten quantities represented by number words and number notation. Research indicates that much of students difficulty with decimal fractions stems from their failure to understand the base ten representations. (Adding It Up, p. 417) To read numerals between 1,000 and 1,000,000, students need to understand the roles of commas. Each sequence of three digits made by commas is read as hundreds, tens, and ones, followed by the name of the appropriate base-thousand unit. (Progressions for the Common Core State Standards in Mathematics: K 5, Number and Operations in Base Ten, p. 12) Providence Public Schools D-107

4 Version 4 Whole Numbers to the Millions (7 9 days) By the end of this grade band (3 5), students should be computing fluently with whole numbers. Computational fluency refers to having efficient and accurate methods for computing. Students exhibit computational fluency when they demonstrate flexibility in the computational methods they choose, understand and can explain these methods, and produce accurate answers efficiently. (Principles and Standards for School Mathematics, p. 152). Assessment When constructing an end-of-unit assessment, be aware that the assessment should measure your students understanding of the big ideas indicated within the standards. The CCSS for Mathematical Content and the CCSS for Mathematical Practice should be considered when designing assessments. Standards-based mathematics assessment items should vary in difficulty, content, and type. The assessment should comprise a mix of items, which could include multiple choice items, short and extended response items, and performance-based tasks. When creating your assessment, you should be mindful when an item could be differentiated to address the needs of students in your class. The mathematical concepts below are not a prioritized list of assessment items, and your assessment is not limited to these concepts. However, care should be given to assess the skills the students have developed within this unit. The assessment should provide you with credible evidence as to your students attainment of the mathematics within the unit. Round multi-digit whole numbers. Explain the pattern that occurs in the value of digits in a whole number as you move to the left. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Solve multi-step word problems and represent the situation with an equation using a letter standing for the unknown quantity. Use estimation to show that your answer is reasonable. Instruction Learning Objectives Students will be able to: Round multi-digit whole numbers using understanding of place value. Explain that the value of digits in a whole number increases by a power of ten as you move to the left. Fluently add and subtract multi-digit whole numbers using the standard algorithm. Solve multi-step word problems using whole numbers. Represent word problems using an equation with a letter standing for the unknown quantity. Use estimation to show that your answer is reasonable. Demonstrate understanding of the concepts and skills in this unit. D-108 Providence Public Schools

5 Grade 4 Mathematics, Quarter 4, Unit 4.3 Whole Numbers to the Millions (7 9 days) Version 4 Resources envision Math Grade 4, Pearson Education, Inc., 2009 Topic 1, Numeration, Teacher Edition Also see Section I, Supplemental Materials Lesson 1.3A, Place Value Relationships Topic 2, Adding and Subtracting Whole Numbers, Teacher Edition Teacher Resource Masters Student Edition Investigations in Numbers, Data, and Space, Grade 4, Pearson Education, Inc., 2008 Implementing Investigations in Grade 4- Implementation Guide Unit 5; Landmarks and Large Numbers, Teacher Edition Investigation 2: Adding It Up Investigation 4: Subtraction Also see Section I, Supplemental Materials Session 3.6A, Larger Place Values Session 4.4A, Studying the U.S. Algorithm for Subtraction Teacher Resources Binder Pearson Online Success Net, Implementing Investigations Site, Exam View Assessment Suite Note: The district resources may contain content that goes beyond the standards addressed in this unit. See the Planning for Effective Instructional Design and Delivery and Assessment sections for ample resources to refer to when planning your unit and individual lessons. Materials Place-value blocks, place-value chart Instructional Considerations Key Vocabulary millions demonstrate word form expanded form standard form associative property of addition commutative property of addition decompose identity property of addition Providence Public Schools D-109

6 Version 4 Whole Numbers to the Millions (7 9 days) Planning for Effective Instructional Design and Delivery In Unit 1.1 and 1.2, students were working with place value and adding and subtracting whole numbers up to the hundred thousands place. This unit extends their learning to the millions place. Throughout this unit, some parts of the resources will need to be repurposed and reused because this is an extension of the previous units. When planning with the resources, focus on practice with the numbers in the millions place. Students should be developing fluency using the standard algorithm. When planning the unit, refer to envisions Topics 1 and 2 for the Math Background for Teachers on pages 2A, 2B, 26A, and 26B. Also refer to the Investigations Unit 5 TE in the Teacher Notes pages , , and the Dialogue Box pages , Students should have a deep understanding of place value and number sense and be able to 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. This is the first grade level in which students are expected to be proficient at using the standard algorithm to add and subtract. However, other previously learned strategies are still appropriate for students to use. After much practice with using place value to justify their steps, they will develop fluency with the algorithm. As stated in the progression document, the standard algorithm is the culminations of a long progression of reasoning about quantities, the base-ten system, and the properties of operations. According to the progressions, students in grade 3 begin the step to formal algebraic language by using a letter for the unknown quantity in expressions or equations for one and two step problems. The symbols for arithmetic, multiplication and division continue to be used in grades 3, 4, and 5. Students use estimation to assess the reasonableness of their answers. Estimation skills include identifying when estimation is appropriate, determining the level of accuracy needed, selecting the appropriate method of estimation, and verifying solutions or determining the reasonableness of situations using various estimation strategies. Incorporate Ten Minute Math Activities, the Problem of the Day, and the Daily Spiral Review that are aligned to The Common Core State Standards for Mathematics. EnVision Center Activities and Investigations Activities offer additional practice for student learning and support small group differentiated instruction. Use teacher created common tasks as formative assessments to monitor student progress and understanding of critical content and essential questions. Use data from formal and informal assessments to guide your instruction and planning. For planning considerations, read through the teacher editions for suggestions about scaffolding techniques, using additional examples, and differentiated instruction as suggested by the envision and Investigations resources, particularly the Algebra Connections and Teacher Notes section. D-110 Providence Public Schools

7 Grade 4 Mathematics, Quarter 4, Unit 4.3 Whole Numbers to the Millions (7 9 days) Version 4 Notes Providence Public Schools D-111

8 Version 4 Whole Numbers to the Millions (7 9 days) D-112 Providence Public Schools

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