Investigations. Investigations and the Common Core State Standards GRADE. in Number, Data, and Space. Complicated Kris Northern

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1 GRADE Complicated Kris Northern 2 Investigations in Number, Data, and Space INV12_TEG02_FM_TitleCR.indd 1 Investigations and the Common Core State Standards This image illustrates some of the best qualities of fractals infinity, reiteration, and self similarity. Kris Northern 4/27/11 6:58 AM

2 This work is protected by United States copyright laws and is provided solely for the use of teachers and administrators in teaching courses and assessing student learning in their classes and schools. Dissemination or sale of any part of this work (including the World Wide Web) will destroy the integrity of the work and is not permitted. Glenview, Illinois Boston, Massachusetts Chandler, Arizona Upper Saddle River, New Jersey The Investigations curriculum was developed by TERC, Cambridge, MA. This material is based on work supported by the National Science Foundation ( NSF ) under Grant No.ESI Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. ISBN-13: ISBN-10: Copyright 2012 Pearson Education, Inc., or its affiliates. All Rights Reserved. Printed in the United States of America. This publication is protected by copyright, and permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. The publisher hereby grants permission to reproduce pages C2 C129, in part or in whole, for classroom use only, the number not to exceed the number of students in each class. Notice of copyright must appear on all copies. For information regarding permissions, write to Pearson Curriculum Group Rights & Permissions, One Lake Street, Upper Saddle River, New Jersey Pearson, Scott Foresman, and Pearson Scott Foresman are trademarks in the U.S. and/or other countries, of Pearson Education, Inc., or its affiliates. Common Core State Standards: Copyright National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved V

3 Contents A B O U T T H I S G U I D E Overview New Program Components Understanding This Guide Grade 2 Pacing Understanding the Unit Instructional Plans iv iv v v vi C O M M O N C O R E S T A T E S T A N D A R D S Overview: Standards for Mathematical Practice Correlation: Standards for Mathematical Practice Correlation: Standards for Mathematical Content viii x xiv Instructional Plans U N I T 1 Counting, Coins, and Combinations CC1 Sessions Resource Masters U N I T 2 Shapes, Blocks, and Symmetry CC5 CC9 C2 U N I T 3 Stickers, Number Strings, and Story Problems CC17 CC21 C23 U N I T 4 Pockets, Teeth, and Favorite Things CC26 CC28 C34 U N I T 5 How Many Floors? How Many Rooms? CC40 C46 U N I T 6 How Many Tens? How Many Ones? CC43 CC47 C57 U N I T 7 Parts of a Whole, Parts of a Group CC76 CC78 C80 U N I T 8 Partners, Teams, and Paper Clips CC83 CC87 C83 U N I T 9 Measuring Length and Time CC112 CC116 C110 Contents

4 About This Guide Overview Investigations in Number, Data, and Space is a focused and coherent K 5 curriculum, which was intentionally designed and sequenced to promote a deep understanding of mathematics. The curriculum units at each grade level represent a cohesive whole. Each successive unit builds on the previous unit, both within and across strands, and across grades. The geometry and measurement, data, and patterns and functions units focus on foundational mathematical ideas and practices and also support work in the number and operations units. By teaching the Investigations curriculum as written, teachers enable students to go deeply into mathematical practices and content. Most of the Common Core State Standards (CCSS) are met by teaching the Grade 2 units in order and as written. Investigations and the Common Core State Standards in Grade 2 provides additional content to fully satisfy all Common Core State Standards. In this guide, new sessions build on existing content. New Math and Teaching Notes and adaptations to Classroom Routines address language, vocabulary, notation, and/or levels of fluency specific to the Common Core State Standards. New Program Components In addition to the components below, the resource masters are available online in Spanish. For Te acher s For Student s GRADE 2 Student Activity Book Investigations Common Core Edition in number, Data, and Space Common Core Edition SPACE Investigations and the Common Core State Standards in Grade 2 iv 9 2 Student Activity Book IN NUMBER, DATA, AND Investigations and the Common Core State Standards Investigations ISBN-13: ISBN-10: _G2_SE_SAB_FSD.indd 1 Snap-In Tabs for Instructional Plans Student Activity Book Common Core Edition 6/9/11 11:50 AM About This Guide INV12_TE02_FM_ATG.indd 4 6/22/11 2:11 PM

5 Understanding This Guide This guide includes Unit Instructional Plans, new daily sessions, and Resource Masters. The front section of this guide includes Instructional Plans and new session pages. The back section has the Resource Masters. Both sections are organized by unit. There are four main functions of the Unit Instructional Plan charts: Daily pacing guide New session numbers and titles Adaptations to existing sessions Correlation to Common Core State Standards The pacing guide identifies which content can be skipped in the Investigations curriculum as well as which new sessions need to be included for coverage of all CCSS content. All new sessions follow the format of the existing program. New session pages are immediately after the Unit Instructional Plan. Related student pages are included in the Student Activity Book Common Core Edition at point of use. In addition, Student Activity Book pages are included as Resource Masters at the back of this guide. The Instructional Plan also provides various adaptations to existing sessions that you will want to incorporate when planning and preparing for the daily class. These adaptations include the following: 1) adjustments, 2) additions, or 3) replacements to existing content in a session. The correlation cites all Mathematical Practices and Mathematical Content Standards for the session and the Classroom Routines. Grade 2 Pacing In order to accommodate the new sessions that have been written for Grade 2, it is necessary to skip some of the existing sessions. This material can be included at the end of the school year if time permits. Unit Original Sessions New Sessions Skipped Sessions Total Sessions Total About This Guide v

6 Understanding the Unit Instructional Plans Common Core Common Core State Standard Domains for the unit are listed in the tab for easy reference. Pacing Guide Each session is planned for one day. Sessions These new sessions build on existing content to introduce new ideas. Math and Teaching Notes These brief notes should be read prior to doing the activity or discussion. On occasion, these notes contain additional discussion points that should be used in order to fully satisfy a standard. Classroom Routines These adaptations should be read prior to doing the Classroom Routine activity. Family Letters When necessary, family letters have been revised to match the content adjustments. Grade 2, Unit 2 Instructional Plan vi About This Guide

7 Common Core Standards Every session is correlated to Common Core State Standards and Mathematical Practices. Math Workshop New and/or existing games or activities may be added to existing Math Workshops to provide additional practice. Homework and Daily Practice Homework may be assigned for some sessions that did not previously have homework. Occasionally, a Homework assignment may be replaced with a new assignment due to content changes. When appropriate, additional Daily Practice pages have been added to provide ongoing review of new content. End-of-Unit Assessments These sessions are sometimes revised to include content in new sessions or reflect skipped sessions within the unit. Grade 2, Unit 2 Instructional Plan About This Guide vii

8 Overview S t a n d a r d s f o r M a t h e m a t i c a l P r a c t i c e While the Common Core State Standards for Mathematical Content describe what mathematics students should be able to understand and do, the Standards for Mathematical Practice describe how students should engage with these mathematical concepts and skills. These standards are closely aligned with the six major goals that guided the development of the Investigations curriculum: Support students to make sense of mathematics and learn that they can be mathematical thinkers. Focus on computational fluency with whole numbers as a major goal of the elementary grades. Provide substantive work in important areas of mathematics rational numbers, geometry, measurement, data, and early algebra and connections among them. Emphasize reasoning about mathematical ideas. Communicate mathematics content and pedagogy to teachers. Engage the range of learners in understanding mathematics. never encountered. They learn mathematical content and develop fluency and skill that is well grounded in meaning. Students learn that they are capable of having mathematical ideas, applying what they know to new situations, and thinking and reasoning about unfamiliar problems. (Grades K 5, Unit 1, p. 6) These two practices are embedded in most sessions in Investigations. Students are expected to make sense of, and solve, problems, and to reason mathematically about the problems posed. For example, in Unit 6 of Grade 3, students create a 12-cube train composed of a repeating pattern of red, blue, and green cubes. Numbers are associated with the elements of the pattern, and students are asked to determine the element of the pattern associated with a particular counting number Grade 3, Unit 6, page 58 Green Number Sequence MP1 Make sense of problems and persevere in solving them. MP2 Reason abstractly and quantitatively. The first two Mathematical Practices are the foundation of the Investigations curriculum. They support the expectation that all students can, and do, make sense of and reason about mathematics. The first principle that guided the development of Investigations states: Students have mathematical ideas. Students come to school with ideas about numbers, shapes, measurements, patterns, and data. If given the opportunity to learn in an environment that stresses making sense of mathematics, students build on the ideas they already have and learn about new mathematics they have Red Number Sequence Blue Number Sequence Grade 3, Unit 6, page 71 Through discussion, students determine that all green cubes in the pattern are multiples of 3. Students discuss how they found the color of the 53rd cube, without counting by 1s. viii Overview: Standards for Mathematical Practice

9 MP4 Model with mathematics. MP5 Use appropriate tools strategically. MP6 Attend to precision. Choosing appropriate tools and representations, and the ability to accurately solve problems and communicate those solutions to others, are critical components of the mathematical work in Investigations. Whole group discussions often make explicit regularities about numbers and operations by focusing students attention on these regularities, and encouraging argument based on mathematical reasoning. In Investigations sessions, students are expected to accurately solve problems and communicate their thinking to others. For example, in Unit 8 of Grade 1, students figure out how many hands there are in a group of 8 people. To solve this problem, students use drawings, cubes, and numerical reasoning. A. B. 1, 2 3, 4 5, 6 7, 8 9, 10 11, 12 13, 14 15, MP3 Construct viable arguments and critique the reasoning of others. MP7 Look for and make use of structure. MP8 Look for and express regularity in repeated reasoning. In Investigations classrooms, students are expected to make sense of the mathematics, and reason about what they notice. As students develop strategies for solving problems, they are involved in three major tasks: understanding the structure of the problem, developing strategies for solving the problem, and communicating their solutions and strategies orally and in writing. (Grade 2, Unit 1, p. 197) Investigations students are constantly asked what they notice about the way numbers and/or operations behave and to articulate, represent, and justify generalizations about numbers and operations. For example, in Unit 1 of Grade 4, students reason about numbers and their factors. Students use what they notice to make representations that show that a factor of a number is also a factor of its multiples. Students use these representations to communicate with, and convince, classmates that all the factors of 16 (e.g., 4, 8) are also factors of 48. C , 10 11, 12 13, 14 15, 16 D E. 4 people have 8 hands 8 people have hands = = 16 Grade 1, Unit 8, page 57 In a whole group discussion, the teacher asks students to explain their solutions. As students explain their solutions, the teacher records the information on a chart, demonstrating ways to record their work = 48 Grade 4, Unit 1, page 109 The Investigations curriculum is intentionally designed to promote a deep understanding of mathematics and develop mathematically proficient students who can think, reason, model, and solve problems. Virtually every session satisfies one or more of these Mathematical Practices. Overview: Standards for Mathematical Practice ix

10 Correlation S t a n d a r d s f o r M a t h e m a t i c a l P r a c t i c e MP1 Make sense of problems and persevere in solving them. MP2 Reason abstractly and quantitatively. 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. A major goal of Investigations in Number, Data, and Space is to support students to make sense of mathematics and learn that they can become mathematical thinkers. To this end, students create, use, and share contexts and representations to make sense of problems. Classroom discussions highlight different ways of interpreting a problem, solving it, and using representations to communicate the pertinent mathematical ideas. Students persevere in solving problems by investigating and practicing problem-solving strategies. Throughout the program, see the following examples in Grade 2: U6 Sessions 1.1, 1.2, 1.3, 1.4 U7 Sessions 1.1, 1.2, 2.1, 2.2, 2.3, 2.4 U8 Sessions 1.1, 1.2 Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Another major goal of Investigations is to provide a curriculum that emphasizes reasoning about mathematical ideas. Students move between concrete examples with specific quantities, objects, or data and generalizations about what works in similar situations. They express these generalizations in words, with variables, and with various representations including contexts, diagrams, and manipulatives. Abstract and quantitative reasoning are reinforced in strategically challenging games as well as Classroom Routines (Grades K 2) and Ten-Minute Math (Grades 3 5). Students flexibly use different properties of operations to solve problems. Throughout the program, see the following examples in Grade 2: U3 Sessions 4.1, 4.2, 4.3, 4.4, 4.5 U4 Sessions 1.2, 1.3A U5 Sessions 1.5, 2.1, 2.2 U6 Sessions 2.1, 2.3 U1 U9 Classroom Routines: Today s Number x Correlation: Standards for Mathematical Practice

11 Grade 2 Curriculum Units U1 Counting, Coins, and Combinations U2 Shapes, Blocks, and Symmetry U3 Stickers, Number Strings, and Story Problems U4 Pockets, Teeth, and Favorite Things U5 How Many Floors? How Many Rooms? U6 How Many Tens? How Many Ones? U7 Parts of a Whole, Parts of a Group U8 Partners, Teams, and Paper Clips U9 Measuring Length and Time MP3 Construct viable arguments and critique the reasoning of others. MP4 Model with mathematics. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and if there is a flaw in an argument explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. The program provides ongoing opportunities for students to express and defend mathematical arguments. Students use a variety of representations, contexts, and examples to prove their conclusions and provide feedback about the arguments made by their classmates. The program emphasizes that there is often more than one strategy for solving a problem. Students defend their strategies as they listen to and evaluate the choices made by others. Students strategies are often recorded on a chart and posted so that all students can analyze, review, and use their classmates ideas. Throughout the program, see the following examples in Grade 2: U2 Sessions 1.3, 2.2, 2.3, 2.4 U3 Sessions 3.1, 3.2 U4 Sessions 2.2, 2.5 U5 Sessions 2.2, 2.3, 2.4 U7 Sessions 1.2, 1.3, 1.4 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. 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. Throughout the curriculum, students use representations and contexts to visualize, describe, and analyze mathematical relationships. Using these models allows students to express and further develop their ideas and to engage in the ideas of others. They develop a repertoire of models they know well and can apply when faced with unfamiliar problem situations. Students use representations and contexts judiciously and with purpose. Throughout the program, see the following examples in Grade 2: U1 Sessions 2.1, 4.1 U3 Sessions 2.1, 2.2, 2.3, 2.4 U4 Sessions 1.1, 1.7 U8 Sessions 3.1, 3.2, 3.3, 3.4, 3.5 Correlation: Standards for Mathematical Practice xi

12 MP5 Use appropriate tools strategically. MP6 Attend to precision. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Students have access to an array of tools, such as connecting cubes, pattern blocks, 100 charts, and technology. Students use other tools, such as drawings, the number line, or a rectangular array. Mathematical tools are introduced that are useful for a whole class of problems and can be extended to accommodate more complex problems and/or students expanding repertoire of numbers. Analysis of the solution to a problem includes consideration of the effectiveness and choice of the tools. During Math Workshops, students continue to use tools to foster mathematical understanding and to practice skills. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions. Every session requires students to communicate with precision. The Student Math Handbook provides support in this endeavor. Strategies that students use are often named by the mathematics used in order to foster precise communication. Many of the sessions focal points stress the use of clear and concise notation. Students are expected to solve problems efficiently and accurately. Throughout the program, see the following examples in Grade 2: U1 Sessions 4.1, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8 U3 Sessions 2.1, 2.2, 2.3, 2.4 U6 Sessions 1.3, 1.4 U7 Sessions 2.3, 2.4 U8 Sessions 4.1, 4.2, 4.3, 4.4 Throughout the program, see the following examples in Grade 2: U1 Sessions 1.1, 1.2, 1.3, 1.4 U2 Sessions 1.1, 1.2, 1.3, 1.4, 2.4, 2.5, 2.6 U3 Session 1.3 U8 Sessions 3.1, 3.2, 3.3, 3.4, 3.5 U9 Sessions 2.1, 2.2, 2.3, 3.1, 3.2, 3.3, 3.4, 3.5 xii Correlation: Standards for Mathematical Practice

13 MP7 Look for and make use of structure. MP8 Look for and express regularity in repeated reasoning. 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. In each unit, students work between the concrete to the abstract, from numerical and geometrical patterns to general representations. Students are given opportunities and support to investigate, discover, conjecture, and make use of commonalities among related problems. Students use the structure of carefully chosen contexts and representations that embody important characteristics of mathematical relationships. Classroom Routines (Grades K-2) and Ten-Minute Math (Grades 3 5) afford more situations in which students discover and use the various structures of mathematics. Throughout the program, see the following examples in Grade 2: U3 Sessions 3.1, 3.2, 3.3, 3.4, 3.6, 3.7 U4 Session 2.7 U5 Sessions 2.1, 2.2, 2.3, 2.4 U6 Sessions 4.1, 4.2, 4.3 U8 Sessions 1.3, 1.4 U1 U9 Classroom Routines: Quick Images 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. A hallmark of the Investigations program is its emphasis on helping students become mathematical thinkers as they explore and practice strategies for solving problems. Through repeated application and comparison of various strategies and algorithms, students develop an understanding of which method is efficient for a particular type of problem. Each Investigations unit on numbers and operations includes a focus on reasoning and generalizing about number and operations and highlights what students already notice in regularities about numbers and operations. Throughout the program, see the following examples in Grade 2: U1 Sessions 4.6, 4.7, 4.8 U3 Sessions 1.1, 1.2, 1.5 U8 Sessions 1.3, 1.4, 2.1, 2.2, 4.1, 4.2, 4.4 Correlation: Standards for Mathematical Practice xiii

14 Correlation S T A N D A R D S F O R M A T H E M A T I C A L C O N T E N T This correlation includes Classroom Routines but does not include ongoing review in Daily Practice and Homework. Domain 2.OA Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction. 2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. Add and subtract within 20. U1 Sessions 1.1, 2.1, 2.2, 2.3, 2.4, 2.6, 2.7, 2.8, 4.1, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9 U2 Sessions 1.1, 1.2, 2.1, 2.4, 2.7 U3 Sessions 1.1, 1.3, 2.1, 2.2, 2.3, 2.4, 2.5A, 2.5, 2.6, 2.7, 4.4 U5 Session 1.5 U8 Sessions 1.1, 1.2, 3.1, 3.2, 3.3, 3.4, 3.5, 4.1, 4.2, 4.3, OA.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers. (See standard 1.OA.6 for a list of mental strategies.) Work with equal groups of objects to gain foundations for multiplication. U1 Sessions 1.1, 1.4, 1.5, 2.2, 2.4, 2.6, 2.7, 2.8, 3.1, 3.2, 3.3, 3.4, 3.5, 4.1, 4.2, 4.3, 4.4, 4.6, 4.7 U2 Sessions 1.1A, 1.1, 1.2, 1.4, 2.1, 2.4, 2.5, 2.6, 2.7, 2.10A U3 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 2.1, 2.2, 2.4, 2.5A, 4.3, 4.4 U4 Sessions 1.1, 1.4A, 2.1, 2.2 U5 Sessions 1.1 U6 Sessions 1.1, 1.2, 1.3, 1.4, 2.2, 2.4, 2.5 U8 Sessions 1.4, 2.1, 2.2 U9 Session 1.1A 2.OA.3 Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends. 2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. U3 Sessions 3.1, 3.2, 3.3 U5 Sessions 2.2 U6 Session 3.1 U8 Sessions 1.1, 1.2, 1.3, 1.4 U1 Sessions 3.2, 3.3, 3.4, 4.5, 4.7, 4.8, 4.9 U2 Sessions 1.2, 1.3, 2.4, 2.5, 2.6, 2.10A U3 Sessions 1.2, 1.6, 2.2, 2.4, 3.3, 4.1 U5 Sessions 1.1, 1.2, 1.3, 1.4 xiv Correlation: Standards for Mathematical Content

15 Grade 2 Curriculum Units U1 Counting, Coins, and Combinations U2 Shapes, Blocks, and Symmetry U3 Stickers, Number Strings, and Story Problems U4 Pockets, Teeth, and Favorite Things U5 How Many Floors? How Many Rooms? U6 How Many Tens? How Many Ones? U7 Parts of a Whole, Parts of a Group U8 Partners, Teams and Paper Clips U9 Measuring Length and Time Domain 2.NBT Number and Operations in Base Ten 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: U6 Session 5A.3 2.NBT.1.a 100 can be thought of as a bundle of ten tens called a hundred. 2.NBT.1.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). U6 Session 2.4 U8 Sessions 5A.3, 5A.4 U6 Sessions 5A.2, 5A.3, 5A.4, 5A.5 2.NBT.2 Count within 1000; skip-count by 5s, 10s, and 100s. U1 Sessions 1.2, 1.3, 1.4, 1.5, 2.1, 2.2, 2.3, 2.5, 2.6, 2.7, 2.8 U2 Sessions 1.3, 2.8 U3 Sessions 1.4, 3.1, 3.3, 3.4, 3.5, 3.6, 3.7, 4.1, 4.2, 4.3, 4.5 U4 Sessions 1.2, 2.1, 2.4 U5 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 2.1, 2.2, 2.3, 2.4, 2.5 U6 Sessions 1.3, 3.5, 4.1, 4.2, 4.3, 5A.1, 5A.4 U7 Sessions 1.1, 2.1 U8 Session 5A.1 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. U1 Session 2.3 U5 Sessions 1.2, 1.5 U6 Sessions 5A.2, 5A.3, 5A.4, 5A.5 U6 Sessions 5A.1, 5A.2, 5A.3, 5A.4 Correlation: Standards for Mathematical Content xv

16 Use place value understanding and properties of operations to add and subtract. 2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 2.NBT.6 Add up to four two-digit numbers using strategies based on place value and properties of operations. 2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds. 2.NBT.8 Mentally add 10 or 100 to a given number , and mentally subtract 10 or 100 from a given number NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.) U1 Sessions 3.5, 4.3, 4.4, 4.5 U3 Sessions 1.1, 2.1, 2.2, 2.3, 2.4, 2.5A, 2.5, 2.6, 2.7, 4.3, 4.4, 4.5, 4.6 U4 Sessions 1.1, 1.2, 1.7, 2.3, 2.6, 2.7 U5 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 2.2, 2.3 U6 Sessions 1.1, 1.2, 1.3, 1.4, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 4.1, 4.4 U7 Sessions 1.2, 1.4, 2.2, 2.4, 2.5 U8 Sessions 1.1, 1.2, 1.3, 1.4, 2.1, 3.1, 3.2, 3.3, 3.4, 3.5, 4.1, 4.2, 4.3, 4.4 U9 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 2.1, 2.2, 3.1, 3.2, 3.3, 3.5 U3 Session 2.1 U5 Session 1.4 U6 Sessions 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 5A.3 U8 Sessions 4.1, 4.2, 4.3, 4.4 U1 Sessions 4.1, 4.3, 4.4, 4.5 U8 Sessions 5A.1, 5A.2, 5A.3, 5A.4, 5A.5 U6 Sessions 5A.1, 5A.2, 5A.3, 5A.4, 5A.5 U1 Session 2.6 U3 Session 2.6 U6 Sessions 1.1, 1.2, 1.3, 1.4, 2.5, 2.6 U8 Sessions 3.1, 3.2, 3.3, 3.4, 4.1, 4.2, 4.3, 4.4 Domain 2.MD Measurement and Data Measure and estimate lengths in standard units. 2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes. U9 Sessions 1.1, 2.1, 2.2, 2.3, 3.1, 3.2, 3.3, 3.4, 3.5 xvi Correlation: Standards for Mathematical Content

17 2.MD.2 Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen. 2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters. 2.MD.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit. Relate addition and subtraction to length. 2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem. 2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2,, and represent whole-number sums and differences within 100 on a number line diagram. U9 Sessions 1.2, 1.4, 1.5, 1.6, 3.1, 3.3, 3.5, 3.6A U9 Sessions 3.2, 3.3, 3.4 U9 Sessions 1.4, 1.5, 1.6, 2.2, 3.2, 3.4 U9 Sessions 1.5, 1.6, 2.2, 2.3, 3.2, 3.5 U1 Sessions 1.3, 1.4, 1.5, 2.1, 2.4, 3.2, 3.3 U3 Sessions 1.4, 2.4, 4.3 U6 Sessions 1.3, 1.4, 2.4, 2.6, 3.2, 4.3 U8 Sessions 2.1, 3.1, 3.2, 3.3, 3.4, 4.1, 4.2, 4.4 Work with time and money. 2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m. 2.MD.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have? U1 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 2.1, 2.3, 2.4, 2.5, 2.7, 3.1, 3.5, 4.2, 4.3 U2 Sessions 1.4, 2.2, 2.5, 2.9 U3 Sessions 1.5, 2.3, 2.5, 2.7, 3.2, 3.6, 4.2 U4 Sessions 1.3A, 2.2, 2.5, 2.8 U5 Sessions 1.3, 2.1, 2.4 U6 Sessions 2.2, 2.5, 3.2, 3.6, 4.3, 5A.5 U7 Sessions 1.3, 2.3, 2.6 U8 Sessions 1.3, 3.2, 3.4, 4.4 U9 Sessions 1.6, 2.3, 3.4, 3.6A U1 Sessions 2.3, 2.4 U3 Sessions 3.5, 3.6, 3.7, 4.6 U4 Sessions 2.4, 2.6, 2.7 U5 Sessions 1.1, 2.2, 2.3 U6 Sessions 1.3, 2.3, 2.4, 3.2, 3.3, 3.4, 3.5, 3.6, 4.1, 4.2, 4.3, 4.4 U9 Session 3.1 Correlation: Standards for Mathematical Content xvii

18 Represent and interpret data. 2.MD.9 Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units. 2.MD.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. U9 Session 1.5 U4 Sessions 1.4A, 1.7, 2.3, 2.5, 2.6 U5 Session 2.3 Domain 2.G Geometry Reason with shapes and their attributes. 2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes. (Sizes are compared directly or visually, not compared by measuring.) 2.G.2 Partition a rectangle into rows and columns of same-size squares and count to find the total number of them. 2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape. U1 Session 1.2 U2 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 2.1, 2.2, 2.3, 2.5, 2.7, 2.8, 2.9 U4 Sessions 1.2, 1.3A U5 Sessions 1.5, 1.6 U6 Sessions 1.4, 2.6 U2 Sessions 2.3, 2.4, 2.6, 2.8, 2.10A U7 Sessions 1.1, 1.2, 1.3, 1.4, 2.1, 2.2, 2.3A, 2.3, 2.4, 2.5, 2.6 xviii Correlation: Standards for Mathematical Content