Overview. Essential Questions. Grade 2 Mathematics, Quarter 1, Unit 1.2 Understanding and Comparing Three-Digit Numbers Using Place Value

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1 Numbers Using Place Value Overview Number of instruction days: 6 8 (1 day = 90 minutes) Content to Be Learned Understand that 100 is a bundle of 10 tens. Understand that the three digits of a three-digit number represent the amounts of hundreds, tens, and ones in the number. Read and write numbers using base-ten numerals, number names, and expanded form. Use place value to compare 2 three-digit numbers and use symbols to represent the comparisons. Mathematical Practices to Be Integrated 7 Look for and make use of structure. Recognize and use the structure of the base-ten number system to read and write numbers. Use the structure of the base-ten number system to compare numbers. 8 Look for and express regularity in repeated reasoning. Recognize that just as a bundle of 10 ones is a ten and 2 tens is a twenty, a bundle of 10 tens is a hundred and 2 hundreds is 200 and so on Essential Questions What strategies can you use to compare 2 three-digit numbers? How many bundles of 100 are in (a given three-digit number)? Using what you have learned about place value, how can you represent this three-digit number in three different ways? Look at the three-digit number. How many tens are there? How many hundreds? How many ones? How can you represent the three-digit number using expanded form? How can you compare two numbers and record the results? Providence Public Schools D-7

2 Version 5 Numbers Using Place Value (6 8 days) Standards Common Core State Standards for Mathematical Content Number and Operations in Base Ten 2.NBT Understand place value. 2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: a. 100 can be thought of as a bundle of ten tens called a hundred. b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones). 2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. 2.NBT.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. Common Core State Standards for Mathematical Practice 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. 8 Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y 2)/(x 1) = 3. Noticing the regularity in the way terms cancel when expanding (x 1)(x + 1), (x 1)(x 2 + x + 1), and (x 1)(x 3 + x 2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results. D-8 Providence Public Schools

3 Grade 2 Mathematics, Quarter 1, Unit 1.2 Numbers Using Place Value (6 8 days) Version 5 Clarifying the Standards Prior Learning Students in Grade 1 expanded their knowledge of place value. They began to think of the numbers between 10 and 100 in terms of tens and ones. They worked on comparing 2 two-digit numbers and used appropriate notation to record those comparisons. Current Learning Extending understanding of the base-ten system is a critical area in second grade. Students build upon their Grade 1 work with tens and ones and extend that knowledge of bundling to groups of 100. Students recognize that numbers such as 300 refer to 3 hundreds and 0 tens and 0 ones. They refine their skills in reading and representing three-digit numbers using numerals, words, and expanded form. Students have opportunities to apply this knowledge of numbers in order to compare three-digit numbers. They use the symbols <, >, and = to record the results of the comparisons. Place value is a critical area in Grade 2. Future Learning In Grade 3, students will apply what they know about place value to round whole numbers to the nearest 10 or 100. They will use algorithms with larger numbers in computation, which requires a deep understanding of place value. Additional Findings According to Principles and Standards in School Mathematics, it is absolutely essential that students develop a solid understanding of the base-ten numeration system and place value concepts by the end of grade 2 (p. 81). Students should have opportunities to practice and apply their knowledge of place value in a variety of ways, such as developing computation strategies and comparing numbers (Curriculum Focal Points, p. 14; Principles and Standards in School Mathematics, p. 82). Mastery of K 2 aspects of the base-ten system (or whole numbers) is essential for students conceptual and procedural knowledge of the larger multi-digit numbers and decimals (Adding It Up, pp ). Providence Public Schools D-9

4 Version 5 Numbers Using Place Value (6 8 days) 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. Demonstrate understanding place value in that three digits of a three-digit number represent the amounts of hundreds, ten and ones. Read and write numbers using base ten numerals, number names and expanded form. Use place value to compare two three-digit numbers and use symbols to represent the comparisons. Instruction Learning Objectives Students will be able to: Understand that 100 is a bundle of ten tens Explain that the digits of a three-digit number represent the amounts of hundreds, ten and ones. Read and write numbers using number names. Read and write numbers using base ten numerals and expanded form. Use place value to compare two three-digit numbers and use symbols to represent the comparisons. Demonstrate understanding of the concepts and skills learned in this unit. Resources Investigations in Number, Data, and Space Grade 2, Pearson Education, Inc., 2008 Implementing Investigations in Grade 2 Implementation Guide Unit 6 Teacher Edition, Counting Coins and Combinations Investigation 5A, Working with 3-Digit Numbers Section I, Supplemental Materials, Sessions 5A.1 5A.5 Teacher Resources Binder D-10 Providence Public Schools

5 Grade 2 Mathematics, Quarter 1, Unit 1.2 Numbers Using Place Value (6 8 days) Version 5 envision Math Grade 2, Pearson Education, Inc., 2009 Topic 17 Teacher Edition, Subtraction Facts to 18 Resource Masters Student Pages See Supplemental Section in the Curriculum Framework for CCSS Aligned Lessons Lesson 5A.1-5A.5, Working with 3-Digit Numbers, Invest. (Unit 6) Lesson 5A.3-5A.4, Working with 3-Digit Numbers, Invest. (Unit 8) 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 information and resources to refer to when planning your unit and individual lessons. Materials Place value blocks, connecting cubes, digit cards. Instructional Considerations Key Vocabulary place value digit bundle expanded form symbol greater than less than Planning for Effective Instructional Design and Delivery This unit is a continuation of the kinds of place value work that was started in first grade under the cluster heading of Understand Place Value, where bundling ten groups of a multiple of ten demonstrates the mathematics of our number system. When students have a deep understanding of how our number system works, they will be able to be successful in working with any numbers whether they are small or large - or whole or fractional and so on. This knowledge base will also give them a level of flexibility. Practice with reading, speaking and writing a smaller range of numbers (i.e. 4-6, 40 60, ) within a hundreds chart or number line can help connect the language patterns to the digit and numeral patterns. Students need to see representations that go beyond the expected norm of what is often presented in texts. The PARCC assessment will present tasks that are rigorous and require an in depth understanding of place value concepts. For example, students instructed in how to find what number is composed by 12 Providence Public Schools D-11

6 Version 5 Numbers Using Place Value (6 8 days) tens, 2 hundreds, and 15 ones will be better prepared for a variety of assessment tasks and computation in later grades. When comparing numbers, concrete models are essential. Various manipulatives can be used. In terms of scaffolding, number lines that represent a range of numbers not typically represented will help students situate those numbers and connect them to place value concepts, e.g. a number line that shows various numbers between 699 and 855. In this unit the language of comparison plays a role in students ability to demonstrate an understanding of the standards addressed. Opportunities for students to speak, read and write about these comparisons should be a part of this unit as well. The use of SIOP/ELL/academic language objectives would be very efffective here and in every lesson where a certain precision of language is required. Continue to use the Investigations routine Today s Number. Also, in envision Topic 17 teachers can refer to the activity for below-level students in the Meeting Individual Needs section. This activity may help students who need support in developing an understanding of the symbols < and >. Notes D-12 Providence Public Schools