NCTM Principles and Standards for School Mathematics
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- Abigayle Townsend
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1 A Correlation of to the NCTM Principles and Standards for School Mathematics Grades K-5 N/M-507
2 Introduction This document demonstrates how well Investigations in Number, Data, and Space aligns with the. Each mathematics standard is presented with the location of direct instruction that corresponds in the Investigations program. Investigations in Number, Data, and Space is a Kindergarten through Grade 5 curriculum consisting of a series of Teacher s Editions that focus on major mathematical ideas, content, and pedagogy. Each book emphasizes depth of mathematical thinking over fragmented topics. Students invent strategies and approaches to solving problems and rely less on rote learning stressed in traditional textbooks. The program blends concrete materials with appropriate technology, including calculators in everyday mathematical lessons. Developed by TERC under a grant from the National Science Foundation, Investigations in Number, Data, and Space is comprehensive in its approach to students of diverse cultural, ethnic and language groups. In an effort to give mathematical lessons a broader spectrum, students are encouraged to explore working in groups, individually and as a whole class. By incorporating these methods into everyday learning, students learn to express mathematical thinking through talking, drawing, and writing. Investigations in Number, Data and Space was developed after three years of nationwide field-testing and includes teacher s practical suggestions, student dialogues, and teacher notes.
3 TABLE OF CONTENTS Grades Kindergarten-2 Number and Operations Standard....1 Algebra Standard Geometry Standard...24 Measurement Standard...34 Data Analysis and Probability Standard Problem Solving Standard...47 Reasoning and Proof Standard Communication Standard Connections Standard Representation Standard Grades 3-5 Number and Operations Standard Algebra Standard Geometry Standard. 116 Measurement Standard. 133 Data Analysis and Probability Standard Problem Solving Standard. 159 Reasoning and Proof Standard Communication Standard Connections Standard Representation Standard
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5 Investigations in Number, Data, and Space to the Grades K-2 Number and Operations Standard In kindergarten through grade 2 all students should Understand numbers, ways of representing numbers, relationships among numbers, and number systems count with understanding and recognize "how many" in sets of objects; References: Kindergarten: Mathematical Thinking in Kindergarten Investigations 1, 2, 3 About Classroom Routines: Pattern Trains and Hopscotch Paths About Classroom Routines: Collecting, Counting, and Measuring Investigations 1, 2, 3, 4, 5 About Classroom Routines: Counting Ourselves and Others Investigations 1, 3, 4 About Classroom Routines: Making Shapes and Building Blocks About Classroom Routines: How Many in All? Investigations 1, 2, 3, 4 About Classroom Routines: Grade 1: Mathematical Thinking at Grade 1 Investigation 2: Sessions 4-6 Investigation 4: Sessions 4-6 Building Number Sense Investigation 1: Sessions 1-8 Investigation 2: Sessions 1-9 Investigation 3: Sessions 1-9 1
6 Investigation 4: Sessions 1-10 Quilt Squares and Block Towns Investigation 1: Sessions 2-10 Investigation 3: Sessions 6-7 Number Games and Story Problems Investigation 2: Sessions 1-8, Bigger, Taller, Heavier, Smaller Investigation 2: Sessions 1-7 Grade 2: Mathematical Thinking at Grade 2 Investigation 2: Sessions 6, 7 Investigation 4: Sessions 1-5 Investigation 5: Sessions 1-5 Coins, Coupons, and Combinations Investigation 1: Sessions 1-3 Investigation 2: Sessions 1-10 Investigation 4: Sessions 1-4 Putting Together and Taking Apart Investigation 2: Sessions 1-7 Investigation 4: Sessions 2-4 Investigation 5: Sessions 2-3, 6 use multiple models to develop initial understandings of place value and the base-ten number system; References: Kindergarten: Mathematical Thinking in Kindergarten Investigations 1, 2, 3 About Classroom Routines: Pattern Trains and Hopscotch Paths About Classroom Routines: Collecting, Counting, and Measuring Investigations 1, 2, 3, 4, 5 About Classroom Routines: Counting Ourselves and Others Investigations 1, 3, 4 About Classroom Routines:
7 Making Shapes and Building Blocks About Classroom Routines: How Many in All? Investigations 1, 2, 3, 4 About Classroom Routines: Grade 1: Mathematical Thinking at Grade 1 Investigation 2: Sessions 4-6 Investigation 4: Sessions 4-6 Building Number Sense Investigation 1: Sessions 1-8 Investigation 2: Sessions 1-9 Investigation 3: Sessions 1-9 Investigation 4: Sessions 1-10 Quilt Squares and Block Towns Investigation 1: Sessions 2-10 Investigation 3: Sessions 6-7 Number Games and Story Problems Investigation 2: Sessions 1-8, Bigger, Taller, Heavier, Smaller Investigation 2: Sessions 1-7 Grade 2: Mathematical Thinking at Grade 2 Investigation 2: Sessions 6, 7 Investigation 4: Sessions 1-5 Investigation 5: Sessions 1-5 Coins, Coupons, and Combinations Investigation 1: Sessions 1-3 Investigation 2: Sessions 1-10 Investigation 4: Sessions 1-4 Putting Together and Taking Apart Investigation 2: Sessions 1-7 Investigation 4: Sessions 2-4 Investigation 5: Sessions 2-3, 6 develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections; References: 3
8 Kindergarten: Collecting, Counting, and Measuring Investigations 5-6 Grade 1: Mathematical Thinking at Grade 1 Investigation 2: Sessions 2-3 Building Number Sense Investigation 3: Sessions 1-7, 9 Number Games and Story Problems Investigation 2: Sessions 6-9 Grade 2: Putting Together and Taking Apart Investigation 2: Sessions 1-4 Investigation 5: Sessions 2-3, 6, 8 Timelines and Rhythm Patterns Investigation 1: Sessions 1-5 develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers; References: Kindergarten: Collecting, Counting, and Measuring Investigations 4-6 How Many in All? Investigations 2-4 Grade 1: Mathematical Thinking in Grade 1 Investigation 2: Sessions 1-6 Investigation 4: Sessions 2-6 Investigation 5: Sessions 2-4 Building Number Sense Investigation 1: Sessions 1-6, 9 Investigation 2: Sessions 1-9 Investigation 3: Sessions 1-7, 9 Investigation 4: Sessions 1-10 Number Games and Story Problems Investigation 1: Sessions 1-10 Investigation 2: Sessions 1-13 Investigation 3: Sessions
9 Grade 2: Mathematical Thinking at Grade 2 Investigation 1: Session 1 Investigation 2: Sessions 1-6, 8 Investigation 4: Sessions 1, 5 Investigation 5: Sessions 1-3 Coins, Coupons, and Combinations Investigation 1: Sessions 1-11 Investigation 2: Session 10 Investigation 3: Sessions 1-5 Investigation 4: Sessions 2-4 Putting Together and Taking Apart Investigation 1: Sessions 1-6 Investigation 2: Sessions 1-7 Investigation 3: Sessions 1-5 Investigation 4: Sessions 1-4 Investigation 5: Sessions 1-8 Timelines and Rhythm Patterns Investigation 1: Sessions 1-5 connect number words and numerals to the quantities they represent, using various physical models and representations; References: Kindergarten: Mathematical Thinking in Kindergarten Investigations 1, 2, 3 About Classroom Routines: Pattern Trains and Hopscotch Paths About Classroom Routines: Collecting, Counting, and Measuring Investigations 1, 2, 3, 4, 5 About Classroom Routines: Counting Ourselves and Others Investigations 1, 3, 4 About Classroom Routines: Making Shapes and Building Blocks About Classroom Routines: How Many in All? Investigations 1, 2, 3, 4 5
10 About Classroom Routines: Grade 1: Mathematical Thinking at Grade 1 Investigation 2: Sessions 4-6 Investigation 4: Sessions 4-6 Building Number Sense Investigation 1: Sessions 1-8 Investigation 2: Sessions 1-9 Investigation 3: Sessions 1-9 Investigation 4: Sessions 1-10 Quilt Squares and Block Towns Investigation 1: Sessions 2-10 Investigation 3: Sessions 6-7 Number Games and Story Problems Investigation 2: Sessions 1-8, Bigger, Taller, Heavier, Smaller Investigation 2: Sessions 1-7 Grade 2: Mathematical Thinking at Grade 2 Investigation 2: Sessions 6, 7 Investigation 4: Sessions 1-5 Investigation 5: Sessions 1-5 Coins, Coupons, and Combinations Investigation 1: Sessions 1-3 Investigation 2: Sessions 1-10 Investigation 4: Sessions 1-4 Putting Together and Taking Apart Investigation 2: Sessions 1-7 Investigation 4: Sessions 2-4 Investigation 5: Sessions 2-3, 6 understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2. Students using Investigations in Number, Data, and Space are introduced to fraction concepts in Grade 1. Kindergarten students gain experience with preliminary concepts, which will lead to the introduction of fractions, including the subdivision of shapes into equal parts. Grade 1 students divide shapes and groups into equal parts or equal groups. They explore halves in units on measuring capacity and length. A sample reference for Kindergarten is given below. 6
11 References: Kindergarten: Grade 1: Making Shapes and Building Blocks Investigation 4: Choice Time: Fill the Hexagons Building Number Sense Investigation 1: Session 2 Bigger, Taller, Heavier, Smaller Investigation 2: Sessions 2-4 Investigation 3: Session 2 Grade 2: Shapes, Halves, and Symmetry Investigation 3: Sessions 1-8 Understand meanings of operations and how they relate to one another understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations; References: Kindergarten: Collecting, Counting, and Measuring Investigation 4 How Many in All? Investigations 2-4 Grade 1: Mathematical Thinking in Grade 1 Investigation 2: Sessions 1-6 Investigation 4: Sessions 2-6 Investigation 5: Sessions 2-4 Building Number Sense Investigation 1: Sessions 1-6, 9 Investigation 2: Sessions 1-9 Investigation 4: Sessions 1-10 Number Games and Story Problems Investigation 1: Sessions 1-10 Investigation 2: Sessions 1-8, Investigation 3: Sessions 1-13 Grade 2: Mathematical Thinking at Grade 2 Investigation 1: Session 1 Investigation 2: Sessions 1-6, 8 7
12 Investigation 4: Sessions 1, 5 Investigation 5: Sessions 1-3 Coins, Coupons, and Combinations Investigation 1: Sessions 1-11 Investigation 2: Session 10 Investigation 3: Sessions 1-5 Investigation 4: Sessions 2-4 Putting Together and Taking Apart Investigation 1: Sessions 1-6 Investigation 2: Sessions 1-7 Investigation 3: Sessions 1-5 Investigation 4: Sessions 1-4 Investigation 5: Sessions 1-8 understand the effects of adding and subtracting whole numbers; References: Kindergarten: Collecting, Counting, and Measuring Investigation 4 How Many in All? Investigations 2-4 Grade 1: Mathematical Thinking in Grade 1 Investigation 2: Sessions 1-6 Investigation 4: Sessions 2-6 Investigation 5: Sessions 2-4 Building Number Sense Investigation 1: Sessions 1-6, 9 Investigation 2: Sessions 1-9 Investigation 4: Sessions 1-10 Number Games and Story Problems Investigation 1: Sessions 1-10 Investigation 2: Sessions 1-8, Investigation 3: Sessions 1-13 Grade 2: Mathematical Thinking at Grade 2 Investigation 1: Session 1 Investigation 2: Sessions 1-6, 8 Investigation 4: Sessions 1, 5 Investigation 5: Sessions 1-3 8
13 Coins, Coupons, and Combinations Investigation 1: Sessions 1-11 Investigation 2: Session 10 Investigation 3: Sessions 1-5 Investigation 4: Sessions 2-4 Putting Together and Taking Apart Investigation 1: Sessions 1-6 Investigation 2: Sessions 1-7 Investigation 3: Sessions 1-5 Investigation 4: Sessions 1-4 Investigation 5: Sessions 1-8 understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally. Students using Investigations in Number, Data, and Space are gradually and progressively introduced to multiplication and division concepts in Kindergarten through Grade 2. Kindergarten students gain experience with preliminary concepts, which will lead to understanding situations that entail multiplication and division, including the subdivision of shapes into equal parts. Grade 1 students divide shapes and groups into equal parts and equal groups. They also gain experience with repeated addition and skip counting. Grade 2 students practice skip counting by 2 s, 5 s, and 10 s. They explore the relationship between skip counting and grouping and apply these concepts to problem situations. References: Kindergarten: Making Shapes and Building Blocks Investigation 4: Choice Time: Fill the Hexagons Grade 1: Building Number Sense Investigation 1: Session 2 Number Games and Story Problems Investigation 1: Sessions 1-3 Investigation 2: Sessions 1-2, 4-8, Grade 2: Mathematical Thinking at Grade 2 Investigation 2: Session 6 Investigation 4: Sessions 1-4 Investigation 5: Sessions 4-5 Coins, Coupons, and Combinations Investigation 2: Sessions
14 Compute fluently and make reasonable estimates develop and use strategies for whole-number computations, with a focus on addition and subtraction; References: Kindergarten: Collecting, Counting, and Measuring Investigation 4 How Many in All? Investigations 2-4 Grade 1: Mathematical Thinking in Grade 1 Investigation 2: Sessions 1-6 Investigation 4: Sessions 2-6 Investigation 5: Sessions 2-4 Building Number Sense Investigation 1: Sessions 1-6, 9 Investigation 2: Sessions 1-9 Investigation 4: Sessions 1-10 Number Games and Story Problems Investigation 1: Sessions 1-10 Investigation 2: Sessions 1-8, Investigation 3: Sessions 1-13 Grade 2: Mathematical Thinking at Grade 2 Investigation 1: Session 1 Investigation 2: Sessions 1-6, 8 Investigation 4: Sessions 1, 5 Investigation 5: Sessions 1-3 Coins, Coupons, and Combinations Investigation 1: Sessions 1-11 Investigation 2: Session 10 Investigation 3: Sessions 1-5 Investigation 4: Sessions 2-4 Putting Together and Taking Apart Investigation 1: Sessions 1-6 Investigation 2: Sessions 1-7 Investigation 3: Sessions 1-5 Investigation 4: Sessions 1-4 Investigation 5: Sessions
15 develop fluency with basic number combinations for addition and subtraction; References: Kindergarten: Collecting, Counting, and Measuring Investigation 4 How Many in All? Investigations 2-4 Grade 1: Mathematical Thinking at Grade 1 Investigation 2: Sessions 1-6 Investigation 4: Sessions 2-4, 6 Investigation 5: Sessions 2-4 Building Number Sense Investigation 1: Sessions 1-9 Investigation 2: Sessions 1-9 Investigation 3: Sessions 5-7 Investigation 4: Sessions 1-10 Survey Questions and Secret Rules Investigation 4: Sessions 4-5 Quilt Squares and Block Towns Investigation 1: Sessions 3-6 Investigation 3: Sessions 6-7 Number Games and Story Problems Investigation 1: Sessions 1-10 Investigation 2: Sessions 1-13 Investigation 3: Sessions 1-13 Grade 2: Mathematical Thinking at Grade 2 Investigation 1: Session 1 Investigation 2: Sessions 1-3, 6, 8 Investigation 4: Sessions 1-5 Investigation 5: Sessions 1-3 Coins, Coupons, and Combinations Investigation 1: Sessions 1-11 Investigation 2: Session 10 Investigation 3: Sessions 1-5 Investigation 4: Sessions 2-4 Putting Together and Taking Apart Investigation 1: Sessions 1-6 Investigation 2: Sessions
16 Investigation 3: Sessions 1-5 Investigation 4: Sessions 1-4 Investigation 5: Sessions 1-8 use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators. References: Kindergarten: Collecting, Counting, and Measuring Investigation 4 How Many in All? Investigations 2-4 Grade 1: Mathematical Thinking at Grade 1 Investigation 2: Sessions 1-6 Investigation 4: Sessions 2-4, 6 Investigation 5: Sessions 2-4 Building Number Sense Investigation 1: Sessions 1-9 Investigation 2: Sessions 1-9 Investigation 3: Sessions 5-7 Investigation 4: Sessions 1-10 Survey Questions and Secret Rules Investigation 4: Sessions 4-5 Quilt Squares and Block Towns Investigation 1: Sessions 3-6 Investigation 3: Sessions 6-7 Number Games and Story Problems Investigation 1: Sessions 1-10 Investigation 2: Sessions 1-13 Investigation 3: Sessions 1-13 Grade 2: Mathematical Thinking at Grade 2 Investigation 1: Session 1 Investigation 2: Sessions 1-3, 6, 8 Investigation 4: Sessions 1-5 Investigation 5: Sessions 1-3 Coins, Coupons, and Combinations Investigation 1: Sessions
17 Investigation 2: Session 10 Investigation 3: Sessions 1-5 Investigation 4: Sessions 2-4 Putting Together and Taking Apart Investigation 1: Sessions 1-6 Investigation 2: Sessions 1-7 Investigation 3: Sessions 1-5 Investigation 4: Sessions 1-4 Investigation 5: Sessions
18 Algebra Standard In kindergarten through grade 2 all students should Understand patterns, relations, and functions sort, classify, and order objects by size, number, and other properties; Kindergarten: Kindergarten students using Investigations in Number, Data, and Space sort, classify, and order objects in a variety of settings. Students explore and compare the attributes of various geometric manipulatives, including pattern blocks and geoblocks. Students classify and sort data. They classify shapes in the environment. Sample References: Mathematical Thinking in Kindergarten Investigation 1: Choice Time Investigation 4: Choice Time: Staircase Patterns Collecting, Counting, and Measuring Investigation 4 Investigation 5 Investigation 6 Counting Ourselves and Others Investigation 1 Investigation 2 Investigation 3 Investigation 4 Making Shapes and Building Blocks Investigation 1 Investigation 3 Investigation 4 Investigation 5 Grade 1: In addition to the following references, every text in the Grade 1 Investigations in Number, Data, and Space series includes a description of sorting games in the appendix of the text, entitled About Classroom Routines. The first game, entitled, Guess My Rule, requires students to determine the common attribute of a set of objects. After students have become familiar with this game, they can play Guess My Object, in which students ask yes-or-no questions, based on attributes, and use the process of elimination to determine which particular object was secretly chosen from a set of objects. Sample References: Survey Questions and Secret Rules Investigation 1: Sessions
19 Investigation 2: Sessions 3-6 Investigation 4: Sessions 2-3 Quilt Shapes and Block Towns Investigation 1: Sessions Grade 2: Second graders sort, classify, and order objects using a number of techniques in a variety of situations. For example, students sort manipulative materials based on their attributes. They sort and classify information. The children sort two-dimensional geometric shapes and three-dimensional geometric solids. They use Venn diagrams to show relationships within a group of related objects. Sample References: Mathematical Thinking at Grade 2 Investigation 1: Sessions 2-4 Investigation 3: Sessions 1-5 Investigation 5: Sessions 1-2, 4-6 Does It Walk, Crawl, or Swim? Investigation 1: Sessions 1-6 Investigation 2: Sessions 1-4 Investigation 3: Sessions 1-3 Investigation 4: Sessions 1-3 recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another; References: Kindergarten: Mathematical Thinking in Kindergarten Investigation 3 About Classroom Routines, pp. 71, Pattern Trains and Hopscotch Paths Investigations 1, 2, 3, 4 About Classroom Routines, pp. 95, Collecting, Counting, and Measuring About Classroom Routines, pp. 105, Counting Ourselves and Others About Classroom Routines, pp. 99, Making Shapes and Building Blocks About Classroom Routines, pp. 109, Appendix: Shapes Teacher Tutorial, pp How Many in All? About Classroom Routines, pp. 103,
20 Grade 1: Mathematical Thinking at Grade 1 Investigation 3: Sessions 1-6 Investigation 4: Sessions 2-3, 5 Building Number Sense Investigation 3: Sessions 1-8 Investigation 4: Session 10 Survey Questions and Secret Rules Investigation 3: Sessions 2-3 Quilt Squares and Block Towns Investigation 1: Sessions Number Games and Story Problems Investigation 2: Sessions 2, 6-9 Grade 2: Mathematical Thinking at Grade 2 Investigation 3: Sessions 1-4, 6 Coins, Coupons, and Combinations Investigation 2: Sessions 1-2, 4-5, 10 Investigation 3: Session 1 Investigation 4: Sessions 1-4 Shapes, Halves, and Symmetry Investigation 1: Sessions 2-8 Investigation 2: Sessions 1, 3 Investigation 4: Sessions 1-7 Putting Together and Taking Apart Investigation 2: Sessions 1-2 Timelines and Rhythm Patterns Investigation 2: Sessions 1-5 analyze how both repeating and growing patterns are generated. References: Kindergarten: Mathematical Thinking in Kindergarten 16
21 Investigation 3 About Classroom Routines, pp. 71, Pattern Trains and Hopscotch Paths Investigations 1, 2, 3, 4 About Classroom Routines, pp. 95, Collecting, Counting, and Measuring About Classroom Routines, pp. 105, Counting Ourselves and Others About Classroom Routines, pp. 99, Making Shapes and Building Blocks About Classroom Routines, pp. 109, Appendix: Shapes Teacher Tutorial, pp How Many in All? About Classroom Routines, pp. 103, Grade 1: Mathematical Thinking at Grade 1 Investigation 3: Sessions 1-6 Investigation 4: Sessions 2-3, 5 Building Number Sense Investigation 3: Sessions 1-8 Investigation 4: Session 10 Survey Questions and Secret Rules Investigation 3: Sessions 2-3 Quilt Squares and Block Towns Investigation 1: Sessions Number Games and Story Problems Investigation 2: Sessions 2, 6-9 Grade 2: Mathematical Thinking at Grade 2 Investigation 3: Sessions 1-4, 6 Coins, Coupons, and Combinations 17
22 Investigation 2: Sessions 1-2, 4-5, 10 Investigation 3: Session 1 Investigation 4: Sessions 1-4 Shapes, Halves, and Symmetry Investigation 1: Sessions 2-8 Investigation 2: Sessions 1, 3 Investigation 4: Sessions 1-7 Putting Together and Taking Apart Investigation 2: Sessions 1-2 Timelines and Rhythm Patterns Investigation 2: Sessions
23 Represent and analyze mathematical situations and structures using algebraic symbols illustrate general principles and properties of operations, such as commutativity, using specific numbers; References: Kindergarten: How Many in All? Investigations 2, 4 Grade 1: Mathematical Thinking at Grade 1 Investigation 2: Session 4:Teacher Note Building Number Sense Investigation 2: Sessions 1-2, 4-9 Number Games and Story Problems Investigation 1: Sessions 1-10 Investigation 4: Sessions 1, 6-9 Grade 2: Coins, Coupons, and Combinations Investigation 1: Session 1 Putting Together and Taking Apart Investigation 2: Session 1 Investigation 4: Sessions 1-4 Investigation 5: Session 6 use concrete, pictorial, and verbal representations to develop an understanding of invented and conventional symbolic notations. References: Kindergarten: How Many in All? Investigations 1, 2, 3, 4 Teacher Note, p. 45 Grade 1: Building Number Sense Investigation 1: Sessions 2, 7-9 Investigation 2: Sessions 1-2, 6-8 Investigation 4: Sessions 1-2, 6-10 Number Games and Story Problems Investigation 1: Sessions 1-10 Investigation 2: Sessions 1-2, Investigation 3: Sessions 1-13 Teacher Notes: Introducing Notation, p. 162 Grade 2: Mathematical Thinking at Grade 2 Investigation 1: Session 1 19
24 Investigation 2: Sessions 1, 4-6 Investigation 3: Session 5 Investigation 5: Session 3 Coins, Coupons, and Combinations Investigation 2: Session 3 Investigation 3: Sessions 1-5 Investigation 4: Sessions 2-4 Putting Together and Taking Apart Investigation 1: Sessions 5-6 Investigation 3: Sessions 3-5: Teacher Note, p. 85 Investigation 5: Session 7 Timelines and Rhythm Patterns Investigation 2: Sessions 1-5 Use mathematical models to represent and understand quantitative relationships model situations that involve the addition and subtraction of whole numbers, using objects, pictures, and symbols. References: Kindergarten: Collecting, Counting, and Measuring Investigation 4 How Many in All? Investigations 2-4 Grade 1: Mathematical Thinking in Grade 1 Investigation 2: Sessions 1-6 Investigation 4: Sessions 2-6 Investigation 5: Sessions 2-4 Building Number Sense Investigation 1: Sessions 1-6, 9 Investigation 2: Sessions 1-9 Investigation 4: Sessions 1-10 Number Games and Story Problems Investigation 1: Sessions 1-10 Investigation 2: Sessions 1-8, Investigation 3: Sessions 1-13 Grade 2: Mathematical Thinking at Grade 2 Investigation 1: Session 1 Investigation 2: Sessions 1-6, 8 Investigation 4: Sessions 1, 5 20
25 Investigation 5: Sessions 1-3 Coins, Coupons, and Combinations Investigation 1: Sessions 1-11 Investigation 2: Session 10 Investigation 3: Sessions 1-5 Investigation 4: Sessions 2-4 Putting Together and Taking Apart Investigation 1: Sessions 1-6 Investigation 2: Sessions 1-7 Investigation 3: Sessions 1-5 Investigation 4: Sessions 1-4 Investigation 5: Sessions 1-8 Analyze change in various concepts describe qualitative change, such as a student's growing taller; Students in Kindergarten through Grade 2 using Investigations in Number, Data, and Space apply concepts of qualitative change to extend patterns related to geometric size and shape. Kindergarten students explore changing combinations of shapes, which can cover a given area, and they explore changing arrangements of a given number of objects. Grade 1 students explore changes in weather data the cyclical nature of time. While reading a story about weight and capacity, first graders discuss gradual changes in the level at which a boat rests on a surface of water as animals climb into the boat, one at a time. Second graders describe qualitative changes in rhythm patterns. References: Kindergarten: Pattern Trains and Hopscotch Paths Investigations 1, 2, 3, 4 Making Shapes and Building Blocks Investigations 2, 3, 4 How Many in All? Investigation 2 Grade 1: Building Number Sense About Classroom Routines: Understanding Time and Changes Survey Questions and Secret Rules Investigation 3: Session 3 21
26 Quilt Squares and Block Towns Investigation 1: Sessions About Classroom Routines: Understanding Time and Changes Bigger, Taller, Heavier, Smaller Investigation 1: Sessions 1-2, 5-6 About Classroom Routines: Understanding Time and Changes Grade 2: Mathematical Thinking at Grade 2 Investigation 1: Session 1 Shapes, Halves, and Symmetry Investigation 2: Session 3 Timelines and Rhythm Patterns Investigation 2: Sessions 1-5 describe quantitative change, such as a student's growing two inches in one year. Kindergarten students describe quantitative change as they graph classroom attendance data using an attendance stick and name cards or name pins to see how many children are present and absent for each day of school. They estimate quantitative change as they compare how many objects are in the Counting Jar (in About Classroom Routines ) over several days. They illustrate quantitative change as they explore changing combinations of numbers with a given sum. First grade students progress from qualitative to quantitative weight comparisons as they gradually add weight units (e.g., washers, blocks) to achieve equilibrium on a balance scale. They solve combining problems involving unknown change, where students are given initial and final amounts and are asked to come up with a quantitative representation of how the initial value changed. Second graders find quantitative change as they calculate differences between numbers on a hundred chart, and as they calculate the change necessary to begin at a given number and end at one hundred. They explore and chart quantitative changes in time on timelines. 22
27 In addition to the following references, each unit of study in Investigations in Number, Data, and Space includes a feature entitled, About Classroom Routines, which includes a section related to changes over time. In Kindergarten this section is entitled, Calendar, and contains activities related to the passage of time. In Grade 1 this section is entitled, Understanding Time and Changes, and contains ideas for helping students develop an understanding of time-related ideas such as sequencing events and understanding relationships among time periods. In Grade 2 this section is entitled, Time and Time Again, and contains suggestions for activities to help students develop an understanding of time-related ideas such as sequencing events, the passage of time, duration of time periods, and identifying important times in their day. References: Kindergarten: Mathematical Thinking in Kindergarten Investigations 1, 3 Counting Ourselves and Others About Classroom Routines, p. 97 How Many in All? Investigation 4 Grade 1: Survey Questions and Secret Rules Investigation 4: Sessions 2-3 Number Games and Story Problems Investigation 3: Sessions 9-13 Bigger, Taller, Heavier, Smaller Investigation 1: Sessions 5-6 Grade 2: Coins, Coupons, and Combinations Investigation 4: Sessions 2-4: Dialogue Box, p. 120 Putting Together and Taking Apart Investigation 2: Sessions 3-7 Investigation 3: Sessions 2-5 Timelines and Rhythm Patterns Investigation 1: Sessions
28 Geometry Standard In kindergarten through grade 2 all students should Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships recognize, name, build, draw, compare, and sort two- and three-dimensional shapes; References: Kindergarten: Mathematical Thinking in Kindergarten Investigation 1: Choice Time, pp , 22, 23 Making Shapes and Building Blocks Investigations 1, 2, 3, 4, 5 Shapes Teacher Tutorial, pp Grade 1: Mathematical Thinking at Grade 1 Investigation 1: Sessions 1-4 Building Number Sense Investigation 1: Sessions 1-9 Investigation 2: Sessions 6-8 Investigation 3: Sessions 3-7 Investigation 4: Sessions 6-9 Survey Questions and Secret Rules Investigation 1: Sessions 1-2 Investigation 2: Sessions 3-4 Quilt Squares and Block Towns Investigation 1: Sessions 1-15 Investigation 2: Sessions 1-10 Investigation 3: Sessions 1-7 Number Games and Story Problems Investigation 1: Sessions 1-6 Investigation 3: Sessions 6-8 Grade 2: Mathematical Thinking at Grade 2 24
29 Investigation 3: Sessions 1-6 Shapes, Halves, and Symmetry Investigation 1: Sessions 1-8 Investigation 2: Sessions 1-6 Investigation 3: Sessions 1-8 Investigation 4: Sessions 1-7 describe attributes and parts of two- and three-dimensional shapes; References: Kindergarten: Mathematical Thinking in Kindergarten Investigation 1: Choice Time, pp , 22, 23 Making Shapes and Building Blocks Investigations 1, 2, 3, 4, 5 Shapes Teacher Tutorial, pp Grade 1: Mathematical Thinking at Grade 1 Investigation 1: Sessions 1-4 Building Number Sense Investigation 1: Sessions 1-9 Investigation 2: Sessions 6-8 Investigation 3: Sessions 3-7 Investigation 4: Sessions 6-9 Survey Questions and Secret Rules Investigation 1: Sessions 1-2 Investigation 2: Sessions 3-4 Quilt Squares and Block Towns Investigation 1: Sessions 1-15 Investigation 2: Sessions 1-10 Investigation 3: Sessions 1-7 Number Games and Story Problems Investigation 1: Sessions 1-6 Investigation 3: Sessions 6-8 Grade 2: Mathematical Thinking at Grade 2 25
30 Investigation 3: Sessions 1-6 Shapes, Halves, and Symmetry Investigation 1: Sessions 1-8 Investigation 2: Sessions 1-6 Investigation 3: Sessions 1-8 Investigation 4: Sessions 1-7 investigate and predict the results of putting together and taking apart two- and threedimensional shapes. References: Kindergarten: Making Shapes and Building Blocks Investigations 1, 2, 3, 4, 5 Grade 1: Quilt Squares and Block Towns Investigation 1: Sessions 2-10, Investigation 2: Sessions 4-10 Investigation 3: Sessions 1-5 Appendix: Shapes Tutorial Bigger, Taller, Heavier, Smaller Investigation 2: Sessions 2-4 Grade 2: Mathematical Thinking at Grade 2 Investigation 3: Sessions 3-4, 6 Appendix: Shapes Tutorial Shapes, Halves, and Symmetry Investigation 1: Sessions 2-8 Investigation 2: Sessions
31 Specify locations and describe spatial relationships using coordinate geometry and other representational systems describe, name, and interpret relative positions in space and apply ideas about relative position; In addition to physical manipulation of shapes and objects, students in Kindergarten through Grade 2 using Investigations in Number, Data, and Space apply concepts of relative positions in space through the use of Shapes. Shapes is a software program that allows students to construct and manipulate geometric shapes, see objects move according to rules they specify, and explore rotation and reflection. Students in Grade 2 also use Geo-Logo software, which enables students to extend their investigations to coordinate geometry and angles. References: Kindergarten: Making Shapes and Building Blocks Investigations 2, 3, 4 Grade 1: Building Number Sense Investigation 1: Sessions 1-9 Investigation 2: Sessions 6-8 Quilt Squares and Block Towns Investigation 1: Sessions 8-10 Investigation 3: Sessions 6-7 Appendix: Shapes Tutorial Number Games and Story Problems Investigation 1: Sessions 1-3, 6 Grade 2: Mathematical Thinking at Grade 2 Appendix: Shapes Tutorial How Long? How Far? Investigation 2: Sessions 2-8 Ongoing Excursion: Geo-Logo: Shapes and Pictures 27
32 describe, name, and interpret direction and distance in navigating space and apply ideas about direction and distance; In addition to physical movement and measurement of shapes and objects, students in Kindergarten through Grade 2 using Investigations in Number, Data, and Space apply concepts of direction and distance through the use of a software program entitled Shapes. This program allows students to construct and manipulate geometric shapes, see objects move according to rules they specify, and explore rotation and reflection. Students in Grade 2 also use Geo-Logo software, which enables students to extend their investigations to coordinate geometry and angles. References: Kindergarten: Making Shapes and Building Blocks Investigation 2, 3, 4 Grade 1: Quilt Squares and Block Towns Investigation 3: Sessions 6-7 Appendix: Shapes Tutorial Grade 2: Mathematical Thinking at Grade 2 Appendix: Shapes Tutorial Putting Together and Taking Apart Investigation 5: Session 8 How Long? How Far? Investigation 1: Sessions 2-4 Investigation 2: Sessions 1-8 Ongoing Excursion: Geo-Logo: Shapes and Pictures find and name locations with simple relationships such as "near to" and in coordinate systems such as maps. Kindergarten students using Investigations in Number, Data, and Space use Hopscotch Paths as a means of exploring paths and relating them to patterns. Grade 2 students use Geo-Logo software to explore coordinate geometry. References: Kindergarten: Pattern Trains and Hopscotch Paths Investigation 3 Grade 1: Grade 2: Quilt Squares and Block Towns Investigation 3: Sessions 5-7 Putting Together and Taking Apart Investigation 5: Session 8 How Long? How Far? 28
33 Investigation 1: Sessions 2-4 Investigation 2: Sessions 1-8 Ongoing Excursion: Geo-Logo: Shapes and Pictures Apply transformations and use symmetry to analyze mathematical situations recognize and apply slides, flips, and turns; Kindergarten students using Investigations in Number, Data, and Space apply slides and turns as they visualize how a shape needs to be moved or turned in order to fit into a particular space or design. In addition to physical manipulation of shapes and objects, students in Kindergarten through Grade 2 recognize and apply slides, flips, and turns through the use of a software program, Shapes. This program allows students to construct and manipulate geometric shapes, see objects move according to rules they specify, and explore rotation and reflection. References: Kindergarten: Making Shapes and Building Blocks Investigations 2, 3 Grade 1: Quilt Squares and Block Towns Investigation 1: Sessions 3-6, 8-10, Investigation 3: Sessions 6-7 Appendix: Shapes Tutorial Grade 2: Mathematical Thinking at Grade 2 Appendix: Shapes Tutorial How Long? How Far? Investigation 2: Sessions 2-8 Ongoing Excursion: Geo-Logo: Shapes and Pictures recognize and create shapes that have symmetry. Students using Investigations in Number, Data, and Space are not formally introduced to the concept of symmetry until Grade 2. Kindergarten and Grade 1 students explore preliminary skills, including the manipulation of shapes through physical manipulation, drawing, and computer technology, as they construct murals and create designs and drawings using basic shapes. They are exposed to symmetry as they examine and manipulate geometric shapes and solids. References: Kindergarten: Making Shapes and Building Blocks Investigations 1, 2, 3, 4, 5 Grade 1: Quilt Squares and Block Towns Investigation 1: Sessions
34 Investigation 2: Sessions 1-10 Investigation 3: Sessions 1-7 Appendix: Shapes Tutorial Grade 2: Mathematical Thinking at Grade 2 Appendix: Shapes Tutorial Shapes, Halves, and Symmetry Investigation 4: Sessions 1-7 Use visualization, spatial reasoning, and geometric modeling to solve problems create mental images of geometric shapes using spatial memory and spatial visualization; Students in Kindergarten through Grade 2 using Investigations in Number, Data, and Space create mental images of geometric shapes using spatial memory and spatial visualization throughout the course as they study geometric shapes and solids and their properties through physical manipulation, paper-and-pencil drawing, and the use of computer technology. For example, Kindergarten students use Shapes software to manipulate shapes as they visualize how a shape needs to be moved or turned in order to fit into a particular space or design. Grade 1 students wrap boxes at home and bring them to school, then classmates use spatial memory and visualization as they attempt to identify the Mystery Boxes. Second graders create mental images of geometric shapes using spatial memory and visualization as they follow descriptions written by other students to build rectangles, and as they draw rectangles from memory and describe them in writing. References: Kindergarten: Mathematical Thinking in Kindergarten Investigation 1: Choice Time, pp , 22, 23 Making Shapes and Building Blocks Investigations 1, 2, 3, 4, 5 Shapes Teacher Tutorial, pp Grade 1: Mathematical Thinking at Grade 1 Investigation 1: Sessions 1-4 Building Number Sense Investigation 1: Sessions 1-9 Investigation 2: Sessions 6-8 Investigation 3: Sessions 3-7 Investigation 4: Sessions 6-9 Survey Questions and Secret Rules Investigation 1: Sessions 1-2 Investigation 2: Sessions
35 Quilt Squares and Block Towns Investigation 1: Sessions 1-15 Investigation 2: Sessions 1-10 Investigation 3: Sessions 1-7 Number Games and Story Problems Investigation 1: Sessions 1-6 Investigation 3: Sessions 6-8 Grade 2: Mathematical Thinking at Grade 2 Investigation 3: Sessions 1-6 Appendix: Shapes Tutorial Shapes, Halves, and Symmetry Investigation 1: Sessions 1-8 Investigation 2: Sessions 1-6 Investigation 3: Sessions 1-8 Investigation 4: Sessions 1-7 recognize and represent shapes from different perspectives; Students in Kindergarten through Grade 2 using Investigations in Number, Data, and Space recognize and represent shapes from different perspectives throughout the course as they study geometric shapes and solids and their properties through physical manipulation, paper-andpencil drawing, and the use of computer technology. For example, Kindergarten students match a three-dimensional block to a two-dimensional outline of one of the block s faces. Grade 1 students draw two-dimensional representations of three-dimensional objects, and construct three-dimensional objects from two-dimensional representations. Second graders create two- and three-dimensional symmetrical structures with mirrors, paper folding, and geoblocks. References: Kindergarten: Mathematical Thinking in Kindergarten Investigation 1: Choice Time, pp , 22, 23 Making Shapes and Building Blocks Investigations 1, 2, 3, 4, 5 Shapes Teacher Tutorial, pp Grade 1: Mathematical Thinking at Grade 1 Investigation 1: Sessions 1-4 Building Number Sense Investigation 1: Sessions 1-9 Investigation 2: Sessions 6-8 Investigation 3: Sessions 3-7 Investigation 4: Sessions
36 Survey Questions and Secret Rules Investigation 1: Sessions 1-2 Investigation 2: Sessions 3-4 Quilt Squares and Block Towns Investigation 1: Sessions 1-15 Investigation 2: Sessions 1-10 Investigation 3: Sessions 1-7 Number Games and Story Problems Investigation 1: Sessions 1-6 Investigation 3: Sessions 6-8 Grade 2: Mathematical Thinking at Grade 2 Investigation 3: Sessions 1-6 Appendix: Shapes Tutorial Shapes, Halves, and Symmetry Investigation 1: Sessions 1-8 Investigation 2: Sessions 1-6 Investigation 3: Sessions 1-8 Investigation 4: Sessions 1-7 relate ideas in geometry to ideas in number and measurement; References: Kindergarten: Collecting, Counting, and Measuring Investigations 1, 3, 4, 5, 6 Making Shapes and Building Blocks Investigations 1, 4, 5 Grade 1: Building Number Sense Investigation 3: Sessions 3-4 Quilt Squares and Block Towns Investigation 1: Sessions 1-10 Investigation 2: Sessions 7-10 Investigation 3: Sessions 6-7 Bigger, Taller, Heavier, Smaller Investigation 1: Sessions 5-6 Investigation 2: Sessions 2-4 Investigation 3: Sessions 4-5 Grade 2: Mathematical Thinking at Grade 2 Investigation 3: Sessions 3-4, 6 32
37 Shapes, Halves, and Symmetry Investigation 1: Sessions 2-8 Investigation 2: Sessions 3-6 Investigation 3: Sessions 1-8 Putting Together and Taking Apart Investigation 5: Session 8 How Long? How Far? Investigation 1: Sessions 1-8 Investigation 2: Sessions 1-8 Ongoing Excursion: Geo-Logo: Shapes and Pictures recognize geometric shapes and structures in the environment and specify their location. References: Kindergarten: Making Shapes and Building Blocks Investigations 1, 2, 3 Grade 1: Grade 2: Quilt Squares and Block Towns Investigation 1: Session 1 Investigation 3: Sessions 3-4 Shapes, Halves, and Symmetry Investigation 1: Session 1 33
38 Measurement Standard In kindergarten through grade 2 all students should Understand measurable attributes of objects and the units, systems, and processes of measurement recognize the attributes of length, volume, weight, area, and time; In addition to the following references, each unit of study in Investigations in Number, Data, and Space includes a feature entitled, About Classroom Routines, which includes a section related to changes over time. In Kindergarten this section is entitled Calendar and contains activities related to the passage of time. In Grade 1 this section is entitled Understanding Time and Changes and contains ideas for helping students develop an understanding of time-related ideas such as sequencing events and understanding relationships among time periods. In Grade 2 this section is entitled Time and Time Again and contains suggestions for activities to help students develop an understanding of time-related ideas such as sequencing events, the passage of time, duration of time periods, and identifying important times in their day. References: Kindergarten: Mathematical Thinking in Kindergarten Investigation 3 Collecting, Counting, and Measuring Investigation 3 Making Shapes and Building Blocks Investigations 2, 3, 4 How Many in All? Investigation 1 Grade 1: Building Number Sense Investigation 3: Sessions 3-7 Survey Questions and Secret Rules Investigation 3: Sessions 1-3 Quilt Squares and Block Towns Investigation 3: Sessions 6-7 Bigger, Taller, Heavier, Smaller Investigation 1: Sessions 1-6 Investigation 2: Sessions 1-7 Investigation 3: Sessions 1-5 Grade 2: Shapes, Halves, and Symmetry 34
39 Investigation 1: Sessions 2-6 Investigation 2: Sessions 2-5 How Long? How Far? Investigation 1: Sessions 1-8 Investigation 2: Sessions 1-8 Timelines and Rhythm Patterns Investigation 1: Sessions 1-6 Investigation 2: Sessions 4-5 compare and order objects according to these attributes; References: Kindergarten: Collecting, Counting, and Measuring Investigation 3 How Many in All? Investigation 1 Grade 1: Building Number Sense Investigation 3: Sessions 3-4 Quilt Squares and Block Towns Investigation 3: Sessions 6-7 Bigger, Taller, Heavier, Smaller Investigation 1: Sessions 1-6 Investigation 2: Sessions 1-7 Investigation 3: Sessions 1-5 Grade 2: Shapes, Halves, and Symmetry Investigation 2: Session 2 How Long? How Far? Investigation 1: Sessions 1-8 Investigation 2: Sessions 4-8 Timelines and Rhythm Patterns Investigation 1: Sessions 1-6 understand how to measure using nonstandard and standard units; References: 35
40 Kindergarten: Mathematical Thinking in Kindergarten Investigation 3 Collecting, Counting, and Measuring Investigation 3 How Many in All? Investigation 1 Grade 1: Building Number Sense Investigation 3: Sessions 3-7 Quilt Squares and Block Towns Investigation 3: Sessions 6-7 Bigger, Taller, Heavier, Smaller Investigation 1: Sessions 1-6 Investigation 2: Sessions 1-7 Investigation 3: Sessions 1-5 Grade 2: Shapes, Halves, and Symmetry Investigation 1: Sessions 2-6 Investigation 2: Sessions 4-5 How Long? How Far? Investigation 1: Sessions 1-8 Investigation 2: Sessions 1-8 select an appropriate unit and tool for the attribute being measured. References: Kindergarten: Mathematical Thinking in Kindergarten Investigation 3 Collecting, Counting, and Measuring Investigation 3 How Many in All? Investigation 1 Grade 1: Building Number Sense Investigation 3: Sessions 3-7 Quilt Squares and Block Towns Investigation 3: Sessions
41 Bigger, Taller, Heavier, Smaller Investigation 1: Sessions 1-6 Investigation 2: Sessions 1-7 Investigation 3: Sessions 1-5 Grade 2: Shapes, Halves, and Symmetry Investigation 1: Sessions 2-6 Investigation 2: Sessions 4-5 How Long? How Far? Investigation 1: Sessions 1-8 Investigation 2: Sessions 1-8 Apply appropriate techniques, tools, and formulas to determine measurements measure with multiple copies of units of the same size, such as paper clips laid end to end; References: Kindergarten: Collecting, Counting, and Measuring Investigation 3 How Many in All? Investigation 1 Grade 1: Building Number Sense Investigation 3: Sessions 3-4 Bigger, Taller, Heavier, Smaller Investigation 1: Sessions 5-6 Investigation 2: Sessions 2-7 Investigation 3: Sessions 3-5 Grade 2: How Long? How Far? Investigation 1: Sessions
42 use repetition of a single unit to measure something larger than the unit, for instance, measuring the length of a room with a single meterstick; Kindergarten students using Investigations in Number, Data, and Space quantify length measurements using a repeating nonstandard unit. The following reference for Kindergarten is to the estimation of a measurement of something much larger than the measuring unit, before actually measuring with multiple copies of units of the same size to confirm the estimate. Grade 1 students measure the capacity of a cup by repeatedly filling a spoon with sand and emptying it into the cup. They also measure distances using their hands and feet. Second graders measure the length of their classroom with movable sets of linked cubes. References: Kindergarten: How Many in All? Investigation 1 Grade 1: Grade 2: Bigger, Taller, Heavier, Smaller Investigation 2: Session 1 Investigation 3: Session 2 How Long? How Far? Investigation 1: Session 8 use tools to measure; References: Kindergarten: Mathematical Thinking in Kindergarten Investigation 3 Collecting, Counting, and Measuring Investigation 3 How Many in All? Investigation 1 Grade 1: Building Number Sense Investigation 3: Sessions 3-7 Quilt Squares and Block Towns Investigation 3: Sessions 6-7 Bigger, Taller, Heavier, Smaller Investigation 1: Sessions 1-6 Investigation 2: Sessions 1-7 Investigation 3: Sessions 1-5 Grade 2: Shapes, Halves, and Symmetry 38
43 Investigation 1: Sessions 2-6 Investigation 2: Sessions 4-5 How Long? How Far? Investigation 1: Sessions 1-8 Investigation 2: Sessions 1-8 develop common referents for measures to make comparisons and estimates. In addition to the following references, Kindergarten students using Investigations in Number, Data, and Space develop common referents for units of time in throughout the course through the recurring feature, About Classroom Routines: Calendar: A Sense of Time. References: Kindergarten: Collecting, Counting, and Measuring Investigation 3 How Many in All? Investigation 1 Grade 1: Building Number Sense Investigation 3: Sessions 3-4 Quilt Squares and Block Towns Investigation 3: Sessions 6-7 Bigger, Taller, Heavier, Smaller Investigation 1: Sessions 1-6 Investigation 2: Sessions 1-7 Investigation 3: Sessions 1-5 Grade 2: How Long? How Far? Investigation 1: Sessions 1-8 Timelines and Rhythm Patterns Investigation 1: Sessions
44 Data Analysis and Probability Standard In kindergarten through grade 2 all students should Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them pose questions and gather data about themselves and their surroundings; In addition to the following references, the end of each unit of Investigations in Number, Data, and Space contains a feature entitled About Classroom Routines. In Kindergarten this includes a section entitled, Today s Question, which consists of an activity involving students collecting, displaying, and interpreting data. Students may represent data using charts or graphs. The Grade 1 series includes a section in the appendix entitled, Exploring Data, which includes ideas for class surveys which involve students collecting, organizing, and displaying data. Another section, Understanding Time and Changes, includes ideas for exploring the monthly calendar and collecting and displaying weather data. The Grade 2 series includes a section entitled, How Many Pockets?, which describes a long-term activity in which students collect, organize, and represent data on how many pockets everyone in class is wearing on a particular day. Students may use a Hundred Number Wall Chart and a Pocket Data Chart to interpret and record their data. References: Kindergarten: Mathematical Thinking in Kindergarten Investigation 1 Counting Ourselves and Others Investigations 1-3 Grade 1: Mathematical Thinking at Grade 1 Investigation 5: Sessions 1-6 Survey Questions and Secret Rules Investigation 2: Sessions 1-6 Investigation 3: Sessions 1-3 Investigation 4: Sessions 1-5 Grade 2: Mathematical Thinking at Grade 2 Investigation 2: Session 6 Investigation 5: Sessions 1-6 Coins, Coupons, and Combinations Investigation 1: Session 11 Investigation 2: Sessions 2, 6, 10 Investigation 5: Session 1 Does It Walk, Crawl, or Swim? 40
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