# Investigations. Investigations and the Common Core State Standards GRADE. in Number, Data, and Space. Infinity Prime Donna Casey

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1 Infinity Prime Donna Casey GRADE K 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 Investigations in Number, Data, and Space Investigations and the Common Core State Standards

3 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

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. 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

7 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

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 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

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 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

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 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

15 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

16 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

17 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 = 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

18 Domain K.NBT Number and Operations in Base Ten Work with numbers 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 = ); 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

19 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

20 Unit 1 Who Is in School Today? Common Core Mathematical Practices (MP) Domains Counting and Cardinality (CC) Measurement and Data (MD) Geometry (G) INVESTIG ATION 1 The Attendance and Calendar Routines Day Session Common Core Adaptation Common Core Standards The Attendance Routine: How Many Are We? MATH WORKSHOP Exploring Materials Attendance: Counting Around the Circle Teaching Note Describing Relative Position Circulate and talk with students about what they are making. Ask them to describe their creations. Use mathematical language to describe what you see. For example: I see that you put the orange square on top of, or above, the green triangle. Are you going to put a shape under, or beneath, the triangle? In this way you can introduce, illustrate, and assess students understanding of phrases and words that describe relative position (e.g., above, below, next to). MP1, MP2, MP5 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.G.1 MP1, MP2, MP5 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC The Calendar Routine MP2, MP5 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC Calendar: Adding Special Days MP2, MP5 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC Comparing Materials MP4, MP5 K.CC.1, K.CC.4.b Making an Attendance Stick Math workshop Exploring More Materials Teaching Note Describing Relative Position Circulate to introduce, illustrate, and assess students understanding of phrases and words that describe relative position (e.g., above, below, next to). For example: I see that you put the red tile next to the blue tile. Will you put another tile next to the red tile? MP2, MP4, MP5, MP7 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.G.1 Instructional Plan CC1

21 INVESTIG ATION 2 The Counting Jar Teach this Investigation as is. Day Session Common Core Adaptation Common Core Standards The Counting Jar MP1, MP3, MP4 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC Describing Buttons MP2, MP4, MP7 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.G Button Match-Up MP2, MP3, MP7 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.G Attribute Block Match-Up MP2, MP3, MP7 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.G.1, K.G Counting Jar: How Many Did You Find? MP2, MP3, MP4, MP7 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5 CC2 Unit 1 Who Is in School Today?

22 INVESTIG ATION 3 The Today s Question Routine Teach this Investigation as is. Day Session Common Core Adaptation Common Core Standards Today s Question MP2, MP3, MP7 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.MD Counting Jar: Recording MP1, MP4, MP7 K.CC.1, K.CC.3, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC Sorting People MP1, MP2, MP7 K.CC.1, K.CC.3, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.MD Sorting Attribute Blocks MP2, MP4 K.CC.1, K.CC.3, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.MD.3, K.G.1, K.G Today s Question: What Did We Find Out? Counting Jar: How Did You Record? MP2, MP3, MP7 K.CC.1, K.CC.3, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.MD.3 MP4, MP7 K.CC.1, K.CC.3, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.MD What Did You Make? MP2, MP7 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.MD.3 Instructional Plan CC3

23 Unit 2 Counting and Comparing Common Core Mathematical Practices (MP) Domains Counting and Cardinality (CC) Measurement and Data (MD) Geometry (G) INVESTIG ATION 1 Counting Day Session Common Core Adaptation Common Core Standards A Counting Book MP4, MP6, MP8 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC Grab and Count MP2, MP4, MP6 CLASSROOM ROUTINEs Attendance: How Many Have Counted? In addition, spend a few minutes asking questions that focus on relative position after taking attendance. For example: Who is sitting next to [Carmen]? [Hugo], can you get up and move so that you are sitting in between [Lionel] and [Mia]? Who is sitting beside [Lisa]? Occasionally do this while students are at their desks or in line, so that you can focus on other phrases and words that describe relative position (e.g., in front of, behind). K.CC.1, K.CC.3, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.G Counting Jar MP6, MP7 K.CC.1, K.CC.3, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.MD Roll and Record MP2, MP4, MP8 K.CC.1, K.CC.3, K.CC.4.b, K.CC.4.c, K.CC How Did I Count? MP1, MP2, MP3 K.CC.1, K.CC.3, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC Does Order Matter When You Count? MP2, MP3, MP7 K.CC.1, K.CC.3, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.MD.3 CC4 Unit 2 Counting and Comparing

24 INVESTIG ATION 1 Counting, continued Day Session Common Core Adaptation Common Core Standards Build It MP2, MP4, MP5 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC Counting Jar MP2, MP3, MP7 K.CC.1, K.CC.3, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC Inventories MP1, MP3, MP6, MP7 K.CC.1, K.CC.3, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.MD Strategies for Accurate Counting MP1, MP4, MP6 K.CC.1, K.CC.3, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5 Instructional Plan CC5

25 INVESTIG ATION 2 Comparing Teach this Investigation as is. Day Session Common Core Adaptation Common Core Standards Measurement Towers MP2, MP3, MP6 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.MD.1, K.MD.2, K.MD How Did You Measure? MP2, MP6, MP7 K.MD.1, K.MD.2, K.MD Counting Backwards MP2, MP4, MP6 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.MD.1, K.MD.2, K.MD Grab and Count: Compare MP2, MP5, MP6 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.CC.6, K.MD The Game of Compare MP2, MP6, MP7 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.CC.6, K.CC.7, K.MD Comparing Two Inventory Bags MP2, MP4, MP5 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.CC.6, K.CC.7, K.MD.2 CC6 Unit 2 Counting and Comparing

26 INVESTIG ATION 2 Comparing, continued Day Session Common Core Adaptation Common Core Standards Letters in Our Names MP2, MP4 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.CC.6, K.CC.7, K.MD Counting Jar MP4, MP6, MP7 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.CC.6, K.CC.7, K.MD.2, K.MD Comparing Names MP2, MP3, MP4 K.CC.6, K.CC.7, K.MD Grab and Count: Ordering MP1, MP2 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.6, K.CC.7, K.MD Ordering Names MP1, MP3, MP6, MP7 K.CC.6, K.CC.7, K.MD.2, K.MD Ordering Cards MP1, MP3, MP4 K.CC.6, K.CC End-of-Unit Assessment and Ordering End-of-Unit Assessment and Ordering Our Names MP2, MP6 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.CC.6, K.CC.7, K.MD.2 MP1, MP6, MP7 K.CC.6, K.CC.7, K.MD.2, K.MD.3 Instructional Plan CC7

27 Unit 3 What Comes Next? Common Core Mathematical Practices (MP) Domains Counting and Cardinality (CC) Measurement and Data (MD) Geometry (G) INVESTIG ATION 1 What Do You Notice? Day Session Common Core Adaptation Common Core Standards Observation Walk MP2, K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c What s Missing? MP1, MP2, MP4, MP6, 3A MP7 Math Workshop Teaching Note What s Missing? K.MD.3, K.G.1, K.G.2 Describing Relative Position What s Missing? offers another chance to observe and talk with students about position and proximity. Ask them to describe the arrangement of objects and how they are remembering what s been taken away. Also, model the use of such language yourself. For example: I know the yellow crayon was next to the yellow bear, so I think there s a crayon in the bag. Do you remember what was below the yellow tile? Use this game as an opportunity to continue introducing, illustrating, and assessing students understanding of phrases and words that describe relative position (e.g., above, below, next to) Can You Do What I Do? MP2, MP4, MP7 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC Two Kinds of Cube Trains MP2, MP3, MP7 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c Cube Train Patterns MP1, MP2, MP3, MP6, MP7 K.MD.3 CC8 Unit 3 What Comes Next?

28 INVESTIG ATION 2 Constructing Patterns Teach this Investigation as is. Day Session Common Core Adaptation Common Core Standards Making Patterns MP2, MP4, MP5, MP7 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC Patterns on the Pocket Chart Recording Cube Train Patterns MP2, MP4, MP5, MP7 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.CC.6 MP2, MP3, MP5, MP7 K.CC.4.a, K.CC.4.b, K.MD Pattern Block Snakes MP3, MP4, MP5, MP7 K.CC.4.a One-Two Patterns MP2, MP3, MP4, MP5, MP7 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC What Comes Next? MP2, MP3, MP5, MP7 K.CC.4.a, K.CC.4.b, K.MD Is It a Pattern? MP3, MP4, MP5, MP Arrow Patterns MP1, MP4, MP5, MP Add On MP1, MP4, MP5, MP7 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC Sharing Patterns MP2, MP3, MP4, MP5, MP7 K.CC.1, K.CC.2, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5 Instructional Plan CC9

29 INVESTIG ATION 3 What s the Unit? Teach this Investigation as is. Day Session Common Core Adaptation Common Core Standards Break the Train MP2, MP3, MP5, MP7 K.MD Recording Break the Train MP1, MP4, MP5, MP7 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC How Many Cars? MP2, MP4, MP5, MP7 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC Break the Train with Other Materials MP2, MP4, MP5, MP7 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC Chips MP2, MP3, MP5, MP7 K.MD End-of-Unit Assessment and Comparing Patterns End-of-Unit Assessment and the Pattern Display MP1, MP2, MP3, MP5, MP7 MP1, MP2, MP3, MP4, MP5, MP7 CC10 Unit 3 What Comes Next?

30 Unit 4 Measuring and Counting INVESTIG ATION 1 Measuring and Counting Common Core Mathematical Practices (MP) Domains Counting and Cardinality (CC) Operations and Algebraic Thinking (OA) Measurement and Data (MD) Geometry (G) Day Session Common Core Adaptation Common Core Standards Measuring Our Shoes MP2, MP5, MP6 K.CC.1, K.CC.4.a, SESSION FOLLOW-UP Family Letter: Make copies of C2 C3, Family Letter, as a Homework K.CC.4.b, K.CC.4.c, replacement for M1 M2, Family Letter. K.MD Measuring Different Shoe Lengths MP4, MP5, MP6 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.MD Measuring with Sticks MP5, MP6, MP7 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.MD.1, K.MD Comparing Lengths of Shoes MP2, MP5, MP6, MP7 K.CC.3, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.CC.6, K.MD.1, K.MD Measuring with Cubes MP2, MP3, MP4, MP5, MP6 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.MD A Weight: Heavier or Lighter? 7 1.6B Measuring and Comparing Weights 8 1.6C More Measuring and Comparing Weights See p. CC15. See p. CC20. See p. CC24. MP5, MP6, MP7 K.CC.4.a, K.CC.4.b, K.CC.5, K.MD.1, K.MD.2 MP5, MP6, MP7 K.CC.4.a, K.CC.4.b, K.CC.5, K.MD.1, K.MD.2, K.MD.3 MP2, MP5, MP6 K.CC.1, K.CC.4.a, K.CC.4.b, K.CC.4.c, K.CC.5, K.CC.6, K.MD.1, K.MD.2 Instructional Plan CC11

31 INVESTIG ATION 2 Counting Some, Counting More Teach this Investigation as is. Day Session Common Core Adaptation Common Core Standards Revisiting Counting MP4, MP5, MP6 K.CC.1, K.CC.3, K.CC.4.a c, K.CC Collect 10 Together MP3, MP7 K.CC.1, K.CC.4.a c, K.CC.5, K.OA.1 2, K.MD Build On MP3, MP7 K.CC.1, K.CC.3, K.CC.4.a c, K.CC.5, K.OA Roll and Record 2 MP1, MP2, MP3 K.CC.1, K.CC.3, K.CC.4.a c, K.OA Quick Images: Ten-Frames MP2, MP4, MP5 K.CC.1, K.CC.3, K.CC.4.a c, K.CC.5, K.OA.1 2 INVESTIG ATION 3 Changing Quantities: How Many Now? Teach this Investigation as is. Day Session Common Core Adaptation Common Core Standards Racing Bears MP1, MP2, MP7 K.CC.1, K.CC.4.a c, K.CC.5, K.MD Story Problems MP1, MP2, MP3, MP7 K.CC.1, K.CC.3, K.CC.4.a c, K.CC.5 6, K.OA One More, One Fewer MP1, MP2, MP5 K.CC.1, K.CC.3, K.CC.4.a c, K.CC.5 6, K.OA Double Compare MP2, MP3, MP4, MP5 K.CC.1, K.CC.3, K.CC.4.a c, K.CC.5 7, K.OA.1 CC12 Unit 4 Measuring and Counting

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