Overview. Essential Questions. Grade 4 Mathematics, Quarter 1, Unit 1.1 Applying Place Value Up to the 100,000s Place

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1 to the 100,000s Place Overview Number of instruction days: 8 10 (1 day = 90 minutes) Content to Be Learned Compare whole numbers within 1,000,000 using >, <, or = symbols. Round whole numbers within 1,000,000. Recognize that the value of digits in a whole number increases by a power of ten as you move to the left. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. 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 recognizing that the value of the digits in a number increases or decreases by powers of Look for and make use of structure. Identify patterns within the number system by recognizing that the value of the digits in a number increases or decreases by powers of 10. Essential Questions How can you compose and decompose the same number in different ways? What are strategies for comparing and ordering numbers? What strategy do you use to round a given number? How can you use place value to round numbers? How can symbols be used to record the results of comparisons of whole numbers? Providence Public Schools D-1

2 Version 4 to the 100,000s Place (8 10 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.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that = 10 by applying concepts of place value and division. 4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place. 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. 7 Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 8 equals the well remembered , in preparation for learning about the distributive property. In the expression x 2 + 9x + 14, older students can see the 14 as 2 7 and the 9 as They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 3(x y) 2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. D-2 Providence Public Schools

3 Grade 4 Mathematics, Quarter 1, Unit 1.1 to the 100,000s Place (8 10 days) Version 4 Clarifying the Standards Prior Learning In grade 2, students compared 2 three-digit numbers to the hundred. Third-grade students rounded whole numbers to the nearest hundred. In Grade 3, place value was an additional rather than a major cluster according to the PARCC document. Current Learning Place value is a major cluster in grade 4 according to the PARCC document; therefore the study of place value requires more emphasis and time throughout the year. In grade 4 Quarter 1, students understand, compare, and round up or down up to six-digit numbers. In quarter 2, students extend this learning to seven-digit numbers. Future Learning In grade 5, students will extend their knowledge of the place value system into decimals and division based on base-10 numbers. Although the Place Value: Number and Operations in Base Ten domain does not appear beyond grade 6, it is expected that students will understand and apply place value in all mathematics. Additional Findings Conceptual understanding and procedural fluency with multidigit 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-10 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. 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. Providence Public Schools D-3

4 Version 4 to the 100,000s Place (8 10 days) 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. Explain how to compare whole numbers within 1,000,000. Compare whole numbers within 1,000,000 and record using >, <, or = symbols. Explain how to round whole numbers within 1,000,000. Apply concepts of place value to show understanding that the value of digits in a whole number increases by a power of ten as you move to the left. Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Learning Objectives Instruction Students will be able to: Compare whole numbers within 1,000,000 using >, <, or = symbols to record. Round whole numbers within 1,000,000. Read and write multi-digit whole numbers using base ten numerals, number names, and expanded form. Understand that the value of the digits in a whole number increase by a power of ten as you move to the left. Demonstrate understanding of the concepts and skills in this unit. Resources envision Math Grade 4, Pearson Education, Inc., 2009 Topic 1, Numeration, Teacher Edition Section I, Supplemental Resources Lesson 1-3A Place Value Relationships 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 1; Factors, Multiples, and Arrays, Teacher Edition Investigation 1: Representing Multiplication with Arrays Unit 5; Landmarks and Large Numbers, Teacher Edition D-4 Providence Public Schools

5 Grade 4 Mathematics, Quarter 1, Unit 1.1 to the 100,000s Place (8 10 days) Version 4 Section I Supplemental Resources Lesson 3-6A Larger Place Value Unit 6; Fraction Cards and Decimal Squares, Teacher Edition Investigation 1: Parts of Rectangles 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 Instructional Considerations Key Vocabulary demonstrate word form expanded form standard form Planning for Effective Instructional Design and Delivery As you plan for instruction throughout the year, you will notice many resource choices within each unit. It may not be necessary to use all components of the materials when planning for instruction. The materials may support core instruction, opportunities for practice, scaffolding and differentiation. This purposeful planning will ensure alignment to the standards in each unit. Place value is not new to this grade level, so use this time to review place value and continue to deepen their understanding and extend to within 1,000,000. In Lesson 1-1 (TE, page 4B), use nonlinguistic representations by having students represent numbers using place-value blocks (physical models). At the beginning of the lesson, pose the problem of an airplane that flies at 1,358 feet. Students work in pairs to represent their knowledge of numbers using place-value blocks and discuss their representations. Then ask students to find other ways to represent 1,358. Expanded form in the CCSS is expressed more in a way that represents place value. Expressing expanded form this way would deepen the students understanding of the place value system. Ex. 4,628= 4 x x x x 1. One way to increase the rigor and to really see if the students understand place value is to give them some problems to solve using the following form, Write the following number in standard form: 16 tens, 31 ones and 4 hundreds. This will challenge the students and encourage checking their work and attending to precision. Providence Public Schools D-5

6 Version 4 to the 100,000s Place (8 10 days) In addition to writing numbers in standard form and expanded form, be sure that students are composing and decomposing numbers in different ways. For example, 1,256 could be written as = 1,256 or 1, = 1,256, there are many Ten Minute Activities in the Investigations Units 1 and Unit 6 that will give the students practice in this area. In Lesson 1-4, students should do only the problems that involve numbers within 1,000,000. They do not need to do every problem on the student page. Ask students to create their own examples of comparing and ordering numbers within 1,000,000. 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. Notes D-6 Providence Public Schools

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