GRADE Infinity Prime Donna Casey K Investigations in Number, Data, and Space INV12_TEK_FM_TitleCR.indd 1 Investigations and the Common Core State Standards This fractal is a classic spiral, which is my favorite, and I m always amazed at the variations and the endlessly repeating patterns that can be created out of such a primary shape. Donna Casey 4/27/11 7:55 AM
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-0095450. 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: 978-0-328-70803-1 ISBN-10: 0-328-70803-8 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 C24, 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 07458. 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 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. 1 2 3 4 5 6 7 8 9 10 V011 15 14 13 12 11
Contents A B O U T T H I S G U I D E Overview New Program Components Understanding This Guide Grade K 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 Who Is in School Today? CC1 Sessions Resource Masters U N I T 2 Counting and Comparing CC4 U N I T 3 What Comes Next? CC8 U N I T 4 Measuring and Counting CC11 CC15 C2 U N I T 5 Make a Shape, Build a Block CC27 U N I T 6 How Many Do You Have? CC31 CC35 C8 U N I T 7 Sorting and Surveys CC59 CC62 C24 Contents
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 K units in order and as written. Investigations and the Common Core State Standards in Grade K 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 K Investigations Common Core Edition 780328 697519 in number, Data, and Space SPACE Investigations and the Common Core State Standards in Grade K iv 9 K Student Activity Book IN NUMBER, DATA, AND Investigations and the Common Core State Standards Investigations ISBN-13: 978-0-328-69751-9 ISBN-10: 0-328-69751-6 Snap-In Tabs for Instructional Plans 69751_GK_SE_SAB_FSD.indd 1 Student Activity Book Common Core Edition 6/9/11 11:51 AM About This Guide INV12_TEK_FM_ATG.indd 4 6/22/11 2:02 PM
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 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 K Pacing Unit Original Sessions New Sessions Total Sessions 1 18 0 18 2 24 0 24 3 22 0 22 4 26 3 29 5 20 0 20 6 26 6 32 7 17 1 18 Total 153 10 163 About This Guide v
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. 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. Grade K, Unit 1 Instructional Plan vi About This Guide
Common Core Standards Every session is correlated to Common Core State Standards and Mathematical Practices. Family Letters When necessary, family letters have been revised to match the content adjustments. Sessions These new sessions build on existing content to introduce new ideas. Classroom Routines These adaptations should be read prior to doing the Classroom Routine activity. Grade K, Unit 6 Instructional Plan About This Guide vii
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. 1 2 3 4 5 6 7 8 9 10 11 12 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 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Red Number Sequence 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Blue Number Sequence 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 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
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, 16 2 4 6 8 10 12 14 16 1 2 3 4 5 6 7 8 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. 2 4 6 8 9, 10 11, 12 13, 14 15, 16 D. 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 4 4 4 4 8 8 16 E. 4 people have 8 hands 8 people have 8 + 8 hands 2 + 8 = 10 6 + 10 = 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. 16 + 16 + 16 = 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
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 K: U2 Sessions 1.9, 1.10 U4 Sessions 3.2, 3.3 U5 Sessions 1.1, 1.2 U6 Session 2.3 U7 Sessions 3.1, 3.2, 3.3 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 K: U2 Sessions 2.1, 2.2, 2.3, 2.4, 2.5, 2.6 U3 Sessions 3.3, 3.4 U4 Sessions 3.1, 4.4 U5 Sessions 3.5, 3.6 U1 U7 Classroom Routines: Attendance x Correlation: Standards for Mathematical Practice
Grade K Curriculum Units U1 Who Is in School Today? U2 Counting and Comparing U3 What Comes Next? U4 Measuring and Counting U5 Make a Shape, Build a Block U6 How Many Do You Have? U7 Sorting and Surveys 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 K: U1 Sessions 2.5, 3.1, 3.5 U2 Sessions 1.6, 2.1, 2.12 U4 Sessions 1.5, 2.2, 3.4, 3.7, 4.5 U6 Sessions 4.2, 4.3, 4.4, 4.5 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 K: U1 Session 2.5 U2 Sessions 1.1, 1.2, 2.7, 2.8, 2.9 U4 Session 4.7 U6 Sessions 1.1, 1.2, 1.3, 1.4, 3.3 Correlation: Standards for Mathematical Practice xi
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 K: U2 Sessions 1.1, 1.2, 1.3 U4 Sessions 1.1, 1.2, 1.3, 1.4, 1.5 U5 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 1.6 U6 Sessions 2.6, 3.3 Throughout the program, see the following examples in Grade K: U1 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 1.6 U2 Session 1.7 U4 Sessions 1.1, 1.2, 1.3, 1.4, 1.5 U5 Sessions 1.2, 1.3, 1.5, 3.1 xii Correlation: Standards for Mathematical Practice
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 7 5 + 7 3, 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 2 + 7. 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 K: U1 Sessions 2.2, 2.3, 2.4 U3 Sessions 1.3, 1.4, 1.5 U4 Sessions 2.2, 2.3, 4.2, 4.5 U5 Sessions 1.1, 2.2, 3.2 U7 Sessions 1.3, 1.4, 1.5, 1.6 U3 U7 Classroom Routines: Patterns on the Pocket Chart 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 K: U2 Session 1.1 U4 Sessions 3.5, 3.7 U6 Sessions 2.4, 2.5, 3.5, 3.6, 3.7 U7 Sessions 1.2, 1.3, 1.4, 1.5, 1.6 Correlation: Standards for Mathematical Practice xiii
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 K.CC Counting and Cardinality Know number names and the count sequence. K.CC.1 Count to 100 by ones and by tens. U1 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 2.1, 2.2, 2.3, 2.4, 2.5, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7 U2 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 2.1, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.10, 2.13 U3 Sessions 1.1, 1.3, 1.4, 2.1, 2.2, 2.5, 2.9, 2.10, 3.2, 3.3, 3.4 U4 Sessions 1.1, 1.2, 1.3, 1.5, 1.6C, 2.1, 2.2, 2.3, 2.4, 2.5, 3.1, 3.2, 3.3, 3.4, 3.7, 4.2, 4.6, 4.8, 4.9 U5 Sessions 1.1, 1.5, 2.3, 2.4, 2.5, 2.6, 3.1, 3.2, 3.3, 3.4, 3.5 U6 Sessions 1.1, 1.3A, 1.4, 1.5, 1.6, 1.7, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 3.2, 3.3, 3.4, 3.5, 4.1, 4.5, 5A.1, 5A.2, 5A.3, 5A.4, 5A.5 U7 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7A, 2.1, 2.3, 2.5, 3.1, 3.3, 3.5 K.CC.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1). K.CC.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0 20 (with 0 representing a count of no objects). U3 Session 2.10 U5 Session 1.3 U6 Sessions 1.3A, 1.4, 2.2, 2.6, 3.4, 4.1, 4.5, 5A.1, 5A.2, 5A.3, 5A.4, 5A.5 U7 Sessions 1.3, 1.7A, 2.1, 2.3, 2.5, 3.3, 3.5 U1 Sessions 3.2, 3.3, 3.4, 3.5, 3.6 U2 Sessions 1.2, 1.3, 1.4, 1.5, 1.6, 1.8, 1.9, 1.10 U4 Sessions 1.4, 2.1, 2.3, 2.4, 2.5, 3.2, 3.3, 3.4, 4.4 U6 Sessions 1.2, 2.6, 3.1, 3.2, 3.3, 3.5, 3.7, 5A.2, 5A.3, 5A.4, 5A.5 xiv Correlation: Standards for Mathematical Content
Grade K Curriculum Units U1 Who Is in School Today? U2 Counting and Comparing U3 What Comes Next? U4 Measuring and Counting U5 Make a Shape, Build a Block U6 How Many Do You Have? U7 Sorting and Surveys Count to tell the number of objects. K.CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality. K.CC.4.a When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object. K.CC.4.b Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. U1 Sessions 1.1, 1.2, 1.3, 1.4, 1.6, 2.1, 2.2, 2.3, 2.4, 2.5, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7 U2 Sessions 1.1, 1.2, 1.3, 1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 2.1, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.10, 2.13 U3 Sessions 1.1, 1.3, 1.4, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.9, 2.10, 3.2, 3.3, 3.4 U4 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 1.6A, 1.6B, 1.6C, 2.1, 2.2, 2.3, 2.4, 2.5, 3.1, 3.2, 3.3, 3.4, 3.7, 4.8, 4.9 U5 Sessions 1.1, 1.2, 1.5, 1.6, 2.3, 2.4, 2.5, 2.6, 3.1, 3.2, 3.3, 3.4, 3.5 U6 Sessions 1.1, 1.4, 1.5, 1.6, 1.7, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 3.2, 3.3, 3.4, 3.5, 4.1, 4.5, 5A.2, 5A.3, 5A.4, 5A.5 U7 Sessions 1.1, 1.2, 1.4, 1.5, 1.6, 1.7A, 2.3, 3.1, 3.5 U1 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 2.1, 2.2, 2.3, 2.4, 2.5, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7 U2 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 2.1, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.10, 2.13 U3 Sessions 1.1, 1.3, 1.4, 2.1, 2.2, 2.3, 2.5, 2.6, 2.9, 2.10, 3.2, 3.3, 3.4 U4 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 1.6A, 1.6B, 1.6C, 2.1, 2.2, 2.3, 2.4, 2.5, 3.1, 3.2, 3.3, 3.4, 3.7, 4.8, 4.9 U5 Sessions 1.1, 1.2, 1.5, 1.6, 2.4, 2.5, 2.6, 3.1, 3.2, 3.3, 3.4, 3.5 U6 Sessions 1.1, 1.4, 1.5, 1.6, 1.7, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 3.2, 3.3, 3.4, 3.5, 4.1, 4.5, 5A.2, 5A.3, 5A.4, 5A.5 U7 Sessions 1.1, 1.2, 1.4, 1.5, 1.6, 1.7A, 2.3, 3.1, 3.5 Correlation: Standards for Mathematical Content xv
K.CC.4.c Understand that each successive number name refers to a quantity that is one larger. K.CC.5 Count to answer how many? questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1 20, count out that many objects. U1 Sessions 1.1, 1.2, 1.3, 1.4, 1.6, 2.1, 2.2, 2.3, 2.4, 2.5, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7 U2 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 2.1, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.10, 2.13 U3 Sessions 1.1, 1.3, 1.4, 2.1, 2.2, 2.5, 2.9, 2.10, 3.2, 3.3, 3.4 U4 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 1.6C, 2.1, 2.2, 2.3, 2.4, 2.5, 3.1, 3.2, 3.3, 3.4, 3.7, 4.8, 4.9 U5 Sessions 1.1, 1.2, 1.5, 1.6, 2.1, 2.3, 2.4, 2.5, 2.6, 3.1, 3.2, 3.3, 3.4, 3.5 U6 Sessions 1.1, 1.4, 1.5, 1.6, 1.7, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 3.2, 3.3, 3.4, 3.5, 4.1, 4.5, 5A.2, 5A.3, 5A.4, 5A.5 U7 Sessions 1.1, 1.2, 1.4, 1.5, 1.6, 1.7A, 2.3, 3.1, 3.5 U1 Sessions 1.1, 1.2, 1.3, 1.4, 1.6, 2.1, 2.2, 2.5, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6 U2 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.13 U3 Sessions 1.3, 2.1, 2.2, 2.5, 2.9, 2.10, 3.2, 3.3, 3.4 U4 Sessions 1.2, 1.3, 1.4, 1.5, 1.6A, 1.6B, 1.6C, 2.1, 2.2, 2.3, 2.5, 3.1, 3.2, 3.3, 3.4, 4.8 U5 Sessions 2.4, 2.5, 2.6, 3.2, 3.3, 3.4, 3.5 U6 Sessions 1.4, 1.5, 1.6, 1.7, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 3.2, 3.3, 3.4, 3.5 U7 Sessions 1.1, 1.2, 1.4, 1.6, 2.6 xvi Correlation: Standards for Mathematical Content
Compare numbers. K.CC.6 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, e.g., by using matching and counting strategies. K.CC.7 Compare two numbers between 1 and 10 presented as written numerals. U2 Sessions 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 2.10, 2.11, 2.12, 2.13, 2.14 U3 Session 2.2 U4 Sessions 1.4, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7 U5 Sessions 2.3 U6 Sessions 3.2, 3.3, 3.4 U7 Sessions 2.6 U2 Sessions 2.5, 2.6, 2.7, 2.8, 2.9, 2.10, 2.11, 2.12, 2.13, 2.14 U4 Sessions 3.4, 3.5, 3.6, 3.7 U6 Sessions 3.2, 3.3, 3.4, 3.5, 3.6, 3.7 Domain K.OA Operations and Algebraic Thinking Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations. U4 Sessions 2.2, 2.3, 2.4, 2.5, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 4.2, 4.4, 4.5 U6 Sessions 1.1, 1.2, 1.3, 1.4, 2.1, 2.2, 2.4, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 5A.2 K.OA.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem. K.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). K.OA.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using objects or drawings, and record the answer with a drawing or equation. U4 Sessions 2.2, 2.3, 2.4, 2.5, 3.2, 3.3, 3.5, 3.7, 4.2, 4.5 U6 Sessions 3.1, 3.3, 3.4, 3.5, 3.6, 3.7, 4.1, 4.4, 4.5 U4 Sessions 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9 U6 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 5A.2, 5A.4, 5A.5 U4 Sessions 4.3, 4.4, 4.5, 4.6, 4.7, 4.9 U6 Sessions 1.3, 1.4, 1.5, 1.6, 1.7, 4.2, 4.3, 4.4, 4.5, 4.6, 5A.2, 5A.4, 5A.5 K.OA.5 Fluently add and subtract within 5. U6 Sessions 1.1, 1.2, 1.3, 1.4, 1.6, 1.7, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 5A.1, 5A.5 Correlation: Standards for Mathematical Content xvii
Domain K.NBT Number and Operations in Base Ten Work with numbers 11 19 to gain foundations for place value. K.NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones. U6 Sessions 5A.3, 5A.4, 5A.5 Domain K.MD Measurement and Data Describe and compare measurable attributes. K.MD.1 Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object. U2 Sessions 2.1, 2.2, 2.3 U4 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 1.6A, 1.6B, 1.6C U6 Sessions 2.3, 2.4, 2.5, 2.6 K.MD.2 Directly compare two objects with a measurable attribute in common, to see which object has more of / less of the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter. Classify objects and count the number of objects in each category. K.MD.3 Classify objects into given categories; count the numbers of objects in each category and sort the categories by count. U2 Sessions 2.1, 2.2, 2.3, 2.4, 2.6, 2.7, 2.8, 2.9, 2.10, 2.11, 2.13, 2.14 U4 Sessions 1.4, 1.6A, 1.6B, 1.6C U1 Sessions 3.1, 3.3, 3.4, 3.5, 3.6, 3.7 U2 Sessions 1.3, 1.6, 1.9, 2.1, 2.2, 2.3, 2.5, 2.8, 2.11, 2.14 U3 Sessions 1.2, 1.5, 2.3, 2.6, 3.1, 3.5 U4 Sessions 1.3, 1.6B, 2.2, 3.1, 3.5, 4.2, 4.4, 4.6 U5 Sessions 1.2, 1.6, 2.4, 3.2, 3.6 U6 Sessions 1.2, 1.6, 2.3, 3.1, 3.5, 4.2, 4.6 U7 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 2.1, 2.2, 2.3, 2.4, 2.6, 3.1, 3.2, 3.3, 3.4, 3.5 xviii Correlation: Standards for Mathematical Content
Domain K.G Geometry Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). K.G.1 Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to. U1 Sessions 1.1, 1.6, 2.2, 2.3, 2.4, 3.4 U2 Session 1.2 U3 Session 1.2 U4 Session 4.1 U5 Sessions 1.1, 1.2, 1.3, 1.5, 1.6, 2.1, 3.1, 3.3 K.G.2 Correctly name shapes regardless of their orientations or overall size. U1 Sessions 2.4, 3.4 U3 Session 1.2 U5 Sessions 1.2, 1.3, 1.4, 1.5 K.G.3 Identify shapes as two-dimensional (lying in a plane, flat ) or threedimensional ( solid ). Analyze, compare, create, and compose shapes. K.G.4 Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/ corners ) and other attributes (e.g., having sides of equal length). K.G.5 Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes. K.G.6 Compose simple shapes to form larger shapes. For example, Can you join these two triangles with full sides touching to make a rectangle? U5 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8 U5 Sessions 1.1, 1.2, 1.3, 1.4, 1.5, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8 U5 Sessions 1.2, 1.3, 1.4, 1.5, 1.6, 2.1, 2.5, 3.4, 3.7 U5 Sessions 2.2, 2.3, 2.4, 2.5, 2.6, 3.6, 3.7 Correlation: Standards for Mathematical Content xix