Ohio Academic Content Standards for Mathematics Grade Level Indicators Grades K-5

A Correlation of 2009 to the Ohio Academic Content Standards for Mathematics Grade Level Indicators Grades K-5 G/M-235DRAFT 6.6.06

INTRODUCTION This document demonstrates how Investigations in Number, Data, and Space integrates with the for Mathematics, Grade Level Indicators. The citations within this correlation provide Investigations in Number, Data, and Space Curriculum Unit number, title, and sub-title followed by the unit Benchmarks that correlate to the for Math. Classroom Routines may be cited as well.

TABLE OF CONTENTS Kindergarten....1 Grade 1.....10 Grade 2.......26 Grade 3.........41 Grade 4........ 61 Grade 5.....79

to the for Mathematics Grade Level Indicators Kindergarten Number, Number Sense and Operations Standard Students demonstrate number sense including an understanding of number systems and operations, and how they relate to one another. Students compute fluently and make reasonable estimates using paper and pencil, technology-supported and mental methods. Number and Number Systems 1. Compare and order whole numbers up to 10. Unit 2 Counting and Comparing: Measurement and the Number System: Benchmark 3: Compare two quantities up to 10 to see which is greater Unit 4 Measuring and Counting: Measurement and the Number System: Benchmark 6: Figure out what is one more or one fewer than a number 2. Explain rules of counting, such as each object should be counted once and that order does not change the number. Unit 2 Counting and Comparing: Measurement and the Number System: Benchmark 1: Count a set of up to 10 objects Unit 4 Measuring and Counting: Measurement and the Number System: Benchmark 5: Count a set of up to 15 objects Unit 6 How Many Do You Have?: Addition, Subtraction, and the Number System: Benchmark 2: Count a set of up to 20 objects 3. Count to twenty; e.g., in play situations or while reading number books. Unit 2 Counting and Comparing: Measurement and the Number System: Benchmark 1: Count a set of up to 10 objects Unit 4 Measuring and Counting: Measurement and the Number System: Benchmark 5: Count a set of up to 15 objects Grade One 1

Unit 6 How Many Do You Have?: Addition, Subtraction, and the Number System: Benchmark 2: Count a set of up to 20 objects 4. Determine how many in sets (groups) of 10 or fewer objects. Unit 2 Counting and Comparing: Measurement and the Number System: Benchmark 1: Count a set of up to 10 objects Unit 4 Measuring and Counting: Measurement and the Number System: Benchmark 5: Count a set of up to 15 objects Unit 6 How Many Do You Have?: Addition, Subtraction, and the Number System: Benchmark 2: Count a set of up to 20 objects 5. Relate, read and write numerals for single-digit numbers (0 to 9). Unit 4 Measuring and Counting: Measurement and the Number System: Benchmark 6: Figure out what is one more or one fewer than a number Unit 6 How Many Do You Have?: Addition, Subtraction, and the Number System: Benchmark 1: Write the numbers up to 10 6. Construct multiple sets of objects each containing the same number of objects. Could be included in Unit 6 How Many Do You Have?: Addition, Subtraction, and the Number System: Benchmark 3: Combine two small quantities 7. Compare the number of objects in two or more sets when one set has one or two more, or one or two fewer objects. Unit 4 Measuring and Counting: Measurement and the Number System: Benchmark 6: Figure out what is one more or one fewer than a number 8. Represent and use whole numbers in flexible ways, including relating, composing and decomposing numbers; e.g., 5 marbles can be 2 red and 3 green or 1 red and 4 green. Unit 4 Measuring and Counting: Measurement and the Number System: Benchmark 6: Figure out what is one more or one fewer than a number Kindergarten 2

9. Identify and state the value of a penny, nickel and dime. Could be included in Unit 2 Counting and Comparing: Measurement and the Number System Unit 4 Measuring and Counting: Measurement and the Number System Meaning of Operations 10. Model and represent addition as combining sets and counting on, and subtraction as take-away and comparison. For example: a. Combine and separate small sets of objects in contextual situations; e.g., add or subtract one, two, or another small amount. Unit 6 How Many Do You Have?: Addition, Subtraction, and the Number System: Benchmark 3: Combine two small quantities b. Count on (forward) and count back (backward) on a number line between 0 and 10. Unit 4 Measuring and Counting: Measurement and the Number System: Benchmark 6: Figure out what is one more or one fewer than a number 11. Demonstrate joining multiple groups of objects, each containing the same number of objects; e.g., combining 3 bags of candy, each containing 2 pieces. Could be included in Unit 6 Many Do You Have?: Addition, Subtraction, and the Number System Benchmark 3: Combine two small quantities 12. Partition or share a small set of objects into groups of equal size; e.g., sharing 6 stickers equally among 3 children. Could be included in Grade 1 Unit 8 Twos, Fives, and Tens: Addition, Subtraction, and the Number System: Benchmark 2: Begin to use groups in meaningful ways Kindergarten 3

Computation and Estimation 13. Recognize the number or quantity of sets up to 5 without counting; e.g., recognize without counting the dot arrangement on a domino as 5. Could be developed from Unit 2 Counting and Comparing: Measurement and the Number System: Benchmark 1: Count a set of up to 10 objects Measurement Standard Students estimate and measure to a required degree of accuracy and precision by selecting and using appropriate units, tools and technologies. Measurement Units 1. Identify units of time (day, week, month, year) and compare calendar elements; e.g., weeks are longer than days. Could be included in units on Measurement and the Number System: Unit 2 Counting and Comparing: Measurement and the Number System Unit 4 Measuring and Counting: Measurement and the Number System (note: time measurement not referenced until Grade 2 Unit 9) Use Measurement Techniques and Tools 2. Compare and order objects of different lengths, areas, weights and capacities; and use relative terms, such as longer, shorter, bigger, smaller, heavier, lighter, more and less. Unit 2 Counting and Comparing: Measurement and the Number System: Benchmark 2: Decide which of two objects is longer 3. Measure length and volume (capacity) using uniform objects in the environment. For example, find: a. how many paper clips long is a pencil; b. how many small containers it takes to fill one big container using sand, rice, beans. Unit 4 Measuring and Counting: Measurement and the Number System: Benchmark 4: Measure the length of an object by lining up multiple units Kindergarten 4

4. Order events based on time. For example: a. activities that take a long or short time; b. review what we do first, next, last; c. recall what we did or plan to do yesterday, today, tomorrow. These concepts could be incorporated as part of everyday classroom routines. (note: time measurement not referenced until Grade 2 Unit 9) Geometry and Spatial Sense Standard Students identify, classify, compare and analyze characteristics, properties and relationships of one-, two-, and three-dimensional geometric figures and objects. Students use spatial reasoning, properties of geometric objects and transformations to analyze mathematical situations and solve problems. Characteristics and Properties 1. Identify and sort two-dimensional shapes and three-dimensional objects. For example: a. Identify and describe two-dimensional figures and three-dimensional objects from the environment using the child s own vocabulary. Unit 5 Make a Shape, Build a Block: 2D and 3D Geometry: Benchmark 1: Describe the overall size (e.g., it s big), shape (e.g., it looks like a ball), function (e.g., it rolls), and/or features (e.g., it has a triangle on one side, this part is pointy) of familiar 2- and 3-D shapes b. Sort shapes and objects into groups based on student-defined categories. Could be included in Unit 5 Make a Shape, Build a Block: 2D and 3D Geometry: Benchmark 1: Describe the overall size (e.g., it s big), shape (e.g., it looks like a ball), function (e.g., it rolls), and/or features (e.g., it has a triangle on one side, this part is pointy) of familiar 2- and 3-D shapes Unit 7 Sorting and Surveys: Data Analysis: Benchmark 3: Sort a set of objects according to their attributes Kindergarten 5

c. Select all shapes or objects of one type from a group. References: Could be included in Unit 5 Make a Shape, Build a Block: 2D and 3D Geometry: Benchmark 1: Describe the overall size (e.g., it s big), shape (e.g., it looks like a ball), function (e.g., it rolls), and/or features (e.g., it has a triangle on one side, this part is pointy) of familiar 2- and 3-D shapes Unit 7 Sorting and Surveys: Data Analysis: Benchmark 3: Sort a set of objects according to their attributes d. Build two-dimensional figures using paper shapes or tangrams; build simple three-dimensional objects using blocks. Unit 5 Make a Shape, Build a Block: 2D and 3D Geometry: Benchmark 2: Construct 2-D and 3-D shapes Benchmark 3: Make 2-D and 3-D shapes by combining shapes Spatial Relationships 2. Name and demonstrate the relative position of objects as follows: a. place objects over, under, inside, outside, on, beside, between, above, below, on top of, upside-down, behind, in back of, in front of; b. describe placement of objects with terms, such as on, inside, outside, above, below, over, under, beside, between, in front of, behind. Could be included in Unit 5 Make a Shape, Build a Block: 2D and 3D Geometry: Benchmark 1: Describe the overall size (e.g., it s big), shape (e.g., it looks like a ball), function (e.g., it rolls), and/or features (e.g., it has a triangle on one side, this part is pointy) of familiar 2- and 3-D shapes Kindergarten 6

Patterns, Functions and Algebra Standard Students use patterns, relations and functions to model, represent and analyze problem situations that involve variable quantities. Students analyze, model and solve problems using various representations such as tables, graphs and equations. Use Patterns, Relations and Functions 1. Sort, classify and order objects by size, number and other properties. For example: a. Identify how objects are alike and different. b. Order three events or objects according to a given attribute, such as time or size. c. Recognize and explain how objects can be classified in more than one way. d. Identify what attribute was used to sort groups of objects that have already been sorted. Unit 7 Sorting and Surveys: Data Analysis: Benchmark 3: Sort a set of objects according to their attributes 2. Identify, create, extend and copy sequences of sounds (such as musical notes), shapes (such as buttons, leaves or blocks), motions (such as hops or skips), and numbers from 1 to 10. Unit 3 What Comes Next?: Patterns and Functions: Benchmark 1: Copy, construct, and extend simple patterns, such as AB, ABC Benchmark 2: Begin to identify the unit of a repeating pattern 3. Describe orally the pattern of a given sequence. Unit 3 What Comes Next?: Patterns and Functions: Benchmark 1: Copy, construct, and extend simple patterns, such as AB, ABC Benchmark 2: Begin to identify the unit of a repeating pattern Kindergarten 7

Use Algebraic Representations 4. Model a problem situation using physical materials. This content standard is central to the philosophy guiding the curriculum in the Investigations series. Students use physical materials to model a problem situation in every lesson, every day. Unit 1 Who Is in School Today?: Classroom Routines and Materials Unit 2 Counting and Comparing: Measurement and the Number System Unit 3 What Comes Next?: Patterns and Functions Unit 4 Measuring and Counting: Measurement and the Number System Unit 5 Make a Shape, Build a Block: 2D and 3D Geometry Unit 6 How Many Do You Have?: Addition, Subtraction, and the Number System Unit 7 Sorting and Surveys: Data Analysis Data Analysis and Probability Standard Students pose questions and collect, organize, represent, interpret and analyze data to answer those questions. Students develop and evaluate inferences, predictions and arguments that are based on data. Data Collection 1. Gather and sort data in response to questions posed by teacher and students; e.g., how many sisters and brothers, what color shoes. Unit 7 Sorting and Surveys: Data Analysis: Benchmark 1: Represent a set of data Benchmark 2: Use data to solve a problem 2. Arrange objects in a floor or table graph according to attributes, such as use, size, color or shape. Unit 7 Sorting and Surveys: Data Analysis: Benchmark 1: Represent a set of data Benchmark 3: Sort a set of objects according to their attributes Kindergarten 8

Statistical Methods 3. Select the category or categories that have the most or fewest objects in a floor or table graph. Could be included in Unit 7 Sorting and Surveys: Data Analysis: Benchmark 1: Represent a set of data Benchmark 2: Use data to solve a problem Kindergarten 9

to the for Mathematics Grade Level Indicators Grade One Number, Number Sense and Operations Standard Students demonstrate number sense including an understanding of number systems and operations, and how they relate to one another. Students compute fluently and make reasonable estimates using paper and pencil, technology-supported and mental methods. Number and Number Systems 1. Use ordinal numbers to order objects; e.g., first, second, third. Unit 1 How Many of Each?: Addition, Subtraction, and the Number System 1: Benchmark 2: Compare and order quantities up to 12 2. Recognize and generate equivalent forms for the same number using physical models, words and number expressions; e.g., concept of ten is described by 10 blocks, full tens frame, numeral 10, 5 + 5, 15-5, one less than 11, my brother s age. Unit 1 How Many of Each?: Addition, Subtraction, and the Number System 1: Benchmark 5: Find more than one combination of two addends for a number up to 10 (e.g.: 7 is 4 and 3 and it's also 5 and 2) Unit 3 Solving Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 5: Represent numbers using equivalent expressions Unit 8 Twos, Fives, and Tens: Addition, Subtraction, and the Number System 4: Benchmark 3: Demonstrate fluency with the two-addend combinations of 10 3. Read and write the numerals for numbers to 100. Unit 3 Solving Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 7: Rote count, read, and write numbers up to 65 Grade One 10

4. Count forward to 100, count backwards from 100, and count forward or backward starting at any number between 1 and 100. Unit 3 Solving Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 7: Rote count, read, and write numbers up to 65 5. Use place value concepts to represent whole numbers using numerals, words, expanded notation and physical models with ones and tens. For example: a. Develop a system to group and count by twos, fives and tens. Unit 7 Color, Shape, and Number Patterns: Patterns and Functions: Benchmark 5: Construct, extend, and describe a pattern that has a constant increase for the sequences 1, 3, 5, ; 2, 4, 6, ; 1, 4, 7, ; 2, 5, 8, ; and 3, 6, 9, through counting and building Unit 8 Twos, Fives, and Tens: Addition, Subtraction, and the Number System 4: Benchmark 2: Begin to use groups in meaningful ways b. Identify patterns and groupings in a 100's chart and relate to place value concepts. Unit 3 Solving Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 7 : Rote count, read, and write numbers up to 65 Unit 8 Twos, Fives, and Tens: Addition, Subtraction, and the Number System 4: Benchmark 1: Identify, read, write, and sequence numbers up to 105 Benchmark 2: Begin to use groups in meaningful ways c. Recognize the first digit of a two digit number as the most important to indicate size of a number and the nearness to 10 or 100. Unit 3 Solving Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 7 : Rote count, read, and write numbers up to 65 Unit 8 Twos, Fives, and Tens: Addition, Subtraction, and the Number System 4: Benchmark 1: Identify, read, write, and sequence numbers up to 105 Grade One 11

6. Identify and state the value of a penny, nickel, dime, quarter and dollar. Could be developed from Unit 5 Fish Lengths and Animal Jumps: Measurement Unit 7 Color, Shape, and Number Patterns: Patterns and Functions: Benchmark 5: Construct, extend, and describe a pattern that has a constant increase for the sequences 1, 3, 5, ; 2, 4, 6, ; 1, 4, 7, ; 2, 5, 8, ; and 3, 6, 9, through counting and building Unit 8 Twos, Fives, and Tens: Addition, Subtraction, and the Number System 4: Benchmark 2: Begin to use groups in meaningful ways 7. Determine the value of a small collection of coins (with a total value up to one dollar) using 1 or 2 different type coins, including pennies, nickels, dimes and quarters. Could be developed from Unit 7 Color, Shape, and Number Patterns: Patterns and Functions: Benchmark 5: Construct, extend, and describe a pattern that has a constant increase for the sequences 1, 3, 5, ; 2, 4, 6, ; 1, 4, 7, ; 2, 5, 8, ; and 3, 6, 9, through counting and building Unit 8 Twos, Fives, and Tens: Addition, Subtraction, and the Number System 4: Benchmark 2: Begin to use groups in meaningful ways 8. Show different combinations of coins that have the same value. Could be developed from Unit 3 Solving Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 5: Represent numbers using equivalent expressions 9. Represent commonly used fractions using words and physical models for halves, thirds and fourths, recognizing fractions are represented by equal size parts of a whole and of a set of objects. Unit 5 Fish Lengths and Animal Jumps: Measurement: Benchmark 2: Know at least one way of describing a measurement that falls between two whole numbers Grade One 12

Meaning of Operations 10. Model, represent and explain addition as combining sets (part + part = whole) and counting on. For example: a. Model and explain addition using physical materials in contextual situations. b. Draw pictures to model addition. c. Write number sentences to represent addition. d. Explain that adding two whole numbers yields a larger whole number. Unit 1 How Many of Each?: Addition, Subtraction, and the Number System 1: Benchmark 3: Combine two small quantities Benchmark 4: Interpret (retell the action and sequence) and solve addition story problems Benchmark 5: Find more than one combination of two addends for a number up to 10 (e.g.: 7 is 4 and 3 and it's also 5 and 2) Unit 3 Solving Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 1: Find at least five combinations of two addends for a number up to 15 Benchmark 2: Combine two small quantities Benchmark 3: Make sense of (retell the action and sequence) and solve addition and subtraction story problems Unit 6 Number Games and Crayon Puzzles: Addition, Subtraction, and the Number System 3: Benchmark 1: Find at least 5 two-addend combinations of 10 Benchmark 2: Combine two small quantities by at least counting on Benchmark 3: Interpret (retell the action and sequence) and solve addition and subtraction story problems Unit 8 Twos, Fives, and Tens: Addition, Subtraction, and the Number System 4: Benchmark 3: Demonstrate fluency with the two-addend combinations of 10 Grade One 13

11. Model, represent and explain subtraction as take-away and comparison. For example: a. Model and explain subtraction using physical materials in contextual situations. b. Draw pictures to model subtraction. c. Write number sentences to represent subtraction. d. Explain that subtraction of whole numbers yields an answer smaller than the original number. Unit 3 Solving Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 3: Make sense of (retell the action and sequence) and solve addition and subtraction story problems Benchmark 4: Subtract one small quantity from another Unit 6 Number Games and Crayon Puzzles: Addition, Subtraction, and the Number System 3: Benchmark 3: Interpret (retell the action and sequence) and solve addition and subtraction story problems Benchmark 4: Subtract one small quantity from another 12. Use conventional symbols to represent the operations of addition and subtraction. Unit 1 How Many of Each?: Addition, Subtraction, and the Number System 1: Benchmark 3: Combine two small quantities Benchmark 4: Interpret (retell the action and sequence) and solve addition story problems Benchmark 5: Find more than one combination of two addends for a number up to 10 (e.g.: 7 is 4 and 3 and it's also 5 and 2) Unit 3 Solving Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 1: Find at least five combinations of two addends for a number up to 15 Benchmark 2: Combine two small quantities Benchmark 3: Make sense of (retell the action and sequence) and solve addition and subtraction story problems Benchmark 4: Subtract one small quantity from another Grade One 14

Unit 6 Number Games and Crayon Puzzles: Addition, Subtraction, and the Number System 3: Benchmark 1: Find at least 5 two-addend combinations of 10 Benchmark 2: Combine two small quantities by at least counting on Benchmark 3: Interpret (retell the action and sequence) and solve addition and subtraction story problems Benchmark 4: Subtract one small quantity from another Unit 8 Twos, Fives, and Tens: Addition, Subtraction, and the Number System 4: Benchmark 3: Demonstrate fluency with the two-addend combinations of 10 13. Model and represent multiplication as repeated addition and rectangular arrays in contextual situations; e.g., four people will be at my party and if I want to give 3 balloons to each person, how many balloons will I need to buy? Unit 7 Color, Shape, and Number Patterns: Patterns and Functions: Benchmark 5: Construct, extend, and describe a pattern that has a constant increase for the sequences 1, 3, 5, ; 2, 4, 6, ; 1, 4, 7, ; 2, 5, 8, ; and 3, 6, 9, through counting and building Unit 8 Twos, Fives, and Tens: Addition, Subtraction, and the Number System 4: Benchmark 2: Begin to use groups in meaningful ways 14. Model and represent division as sharing equally in contextual situations; e.g., sharing cookies. Could be developed from Unit 8 Twos, Fives, and Tens: Addition, Subtraction, and the Number System 4: Benchmark 2: Begin to use groups in meaningful ways 15. Demonstrate that equal means the same as using visual representations. Unit 1 How Many of Each?: Addition, Subtraction, and the Number System 1: Benchmark 5: Find more than one combination of two addends for a number up to 10 (e.g.: 7 is 4 and 3 and it's also 5 and 2) Unit 3 Solving Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 5: Represent numbers using equivalent expressions Unit 8 Twos, Fives, and Tens: Addition, Subtraction, and the Number System 4: Benchmark 3: Demonstrate fluency with the two-addend combinations of 10 Grade One 15

Computation and Estimation 16. Develop strategies for basic addition facts, such as: a. counting all; b. counting on; c. one more, two more; d. doubles; e. doubles plus or minus one; f. make ten; g. using tens frames; h. identity property (adding zero). Unit 1 How Many of Each?: Addition, Subtraction, and the Number System 1: Benchmark 3: Combine two small quantities Benchmark 4: Interpret (retell the action and sequence) and solve addition story problems Benchmark 5: Find more than one combination of two addends for a number up to 10 (e.g.: 7 is 4 and 3 and it's also 5 and 2) Unit 3 Solving Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 1: Find at least five combinations of two addends for a number up to 15 Benchmark 2: Combine two small quantities Benchmark 3: Make sense of (retell the action and sequence) and solve addition and subtraction story problems Unit 6 Number Games and Crayon Puzzles: Addition, Subtraction, and the Number System 3: Benchmark 1: Find at least 5 two-addend combinations of 10 Benchmark 2: Combine two small quantities by at least counting on Benchmark 3: Interpret (retell the action and sequence) and solve addition and subtraction story problems Unit 8 Twos, Fives, and Tens: Addition, Subtraction, and the Number System 4: Benchmark 3: Demonstrate fluency with the two-addend combinations of 10 Grade One 16

17. Develop strategies for basic subtraction facts, such as: a. relating to addition (for example, think of 7-3 =? as 3 plus? equals 7 ); b. one less, two less; c. all but one (for example, 8-7, 5-4); d. using tens frames; e. missing addends. Unit 3 Solving Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 3: Make sense of (retell the action and sequence) and solve addition and subtraction story problems Benchmark 4: Subtract one small quantity from another Unit 6 Number Games and Crayon Puzzles: Addition, Subtraction, and the Number System 3: Benchmark 3: Interpret (retell the action and sequence) and solve addition and subtraction story problems Benchmark 4: Subtract one small quantity from another Measurement Standard Students estimate and measure to a required degree of accuracy and precision by selecting and using appropriate units, tools and technologies. Measurement Units 1. Recognize and explain the need for fixed units and tools for measuring length and weight; e.g., rulers and balance scales. Unit 5 Fish Lengths and Animal Jumps: Measurement: Benchmark 1: Demonstrate measuring techniques when measuring a distance with nonstandard or standard units. These techniques include starting at the beginning, ending at the end, leaving no gaps or overlaps, measuring in a straight line, and keeping track of the number of units Benchmark 2: Know at least one way of describing a measurement that falls between two whole numbers Benchmark 3: Understand that the same results should be obtained when the same object is measured twice, or when two different people measure the same object (assuming a consistent unit) Benchmark 4: Understand that using different-sized units to measure will result in different numbers Grade One 17

2. Tell time to the hour and half hour on digital and analog (dial) timepieces. Classroom Routines focus on Developing vocabulary to talk about time and sequence (first, next, last, before, after, during, etc.) Using the calendar as a tool for keeping track of time 3. Order a sequence of events with respect to time; e.g., summer, fall, winter and spring; morning, afternoon and night. Classroom Routines focus on Developing vocabulary to talk about time and sequence (first, next, last, before, after, during, etc.) Using the calendar as a tool for keeping track of time Use Measurement Techniques and Tools 4. Estimate and measure weight using non-standard units; e.g., blocks of uniform size. Could be developed from investigations involving measurement: Unit 5 Fish Lengths and Animal Jumps: Measurement: Benchmark 2: Know at least one way of describing a measurement that falls between two whole numbers Benchmark 3: Understand that the same results should be obtained when the same object is measured twice, or when two different people measure the same object (assuming a consistent unit) Benchmark 4: Understand that using different-sized units to measure will result in different numbers 5. Estimate and measure lengths using non-standard and standard units; i.e., centimeters, inches and feet. Unit 5 Fish Lengths and Animal Jumps: Measurement: Benchmark 1: Demonstrate measuring techniques when measuring a distance with nonstandard or standard units. These techniques include starting at the beginning, ending at the end, leaving no gaps or overlaps, measuring in a straight line, and keeping track of the number of units Grade One 18

Benchmark 2: Know at least one way of describing a measurement that falls between two whole numbers Benchmark 3: Understand that the same results should be obtained when the same object is measured twice, or when two different people measure the same object (assuming a consistent unit) Benchmark 4: Understand that using different-sized units to measure will result in different numbers Geometry and Spatial Sense Standard Students identify, classify, compare and analyze characteristics, properties and relationships of one-, two-, and three-dimensional geometric figures and objects. Students use spatial reasoning, properties of geometric objects and transformations to analyze mathematical situations and solve problems. Characteristics and Properties 1. Identify, compare and sort two-dimensional shapes; i.e., square, circle, ellipse, triangle, rectangle, rhombus, trapezoid, parallelogram, pentagon and hexagon. For example: a. Recognize and identify triangles and rhombuses independent of position, shape or size; Unit 2 Making Shapes and Designing Quilts: 2D Geometry: Benchmark 2: Use geometric language to describe and identify important features of familiar 2-D shapes Benchmark 3: Identify and describe triangles Benchmark 4: Describe and sort 2-D shapes b. Describe two-dimensional shapes using attributes such as number of sides and number of vertices (corners or angles). Unit 2 Making Shapes and Designing Quilts: 2D Geometry: Benchmark 2: Use geometric language to describe and identify important features of familiar 2-D shapes Benchmark 3: Identify and describe triangles Benchmark 4: Describe and sort 2-D shapes Grade One 19

2. Create new shapes by combining or cutting apart existing shapes. Unit 2 Making Shapes and Designing Quilts: 2D Geometry: Benchmark 1: Fill a given region in different ways with a variety of shapes Benchmark 5: Compose and decompose shapes 3. Identify the shapes of the faces of three-dimensional objects. Unit 9 Blocks and Boxes: 3D Geometry: Benchmark 1: Attend to features of 3-D shapes, such as overall size and shape, the number and shape of faces, and the number of corners Benchmark 2: Match a 2-D representation to a 3-D shape or structure Spatial Relationships 4. Extend the use of location words to include distance (near, far, close to) and directional words (left, right). Could be included in units on linear measurement and 3D geometry: Unit 5 Fish Lengths and Animal Jumps: Measurement Unit 9 Blocks and Boxes: 3D Geometry 5. Copy figures and draw simple two-dimensional shapes from memory. Classroom Routines focus on Identifying, drawing, and comparing shapes Could be included in unit on 2D geometry: Unit 2 Making Shapes and Designing Quilts: 2D Geometry Grade One 20

Patterns, Functions and Algebra Standard Students use patterns, relations and functions to model, represent and analyze problem situations that involve variable quantities. Students analyze, model and solve problems using various representations such as tables, graphs and equations. Use Patterns, Relations and Functions 1. Sort, classify and order objects by two or more attributes, such as color and shape, and explain how objects were sorted. Unit 2 Making Shapes and Designing Quilts: 2D Geometry: Benchmark 4: Describe and sort 2-D shapes Unit 4 What Would You Rather Be? : Data Analysis: Benchmark 1: Sort a group of objects according to a given attribute 2. Extend sequences of sounds, shapes or simple number patterns, and create and record similar patterns. For example: a. Analyze and describe patterns with multiple attributes using numbers and shapes; e.g., AA, B, aa, b, AA, B, aa, b, Unit 7 Color, Shape, and Number Patterns: Patterns and Functions: Benchmark 1: Construct, describe, and extend a repeating pattern with the structure AB, ABC, AAB, or ABB Benchmark 2: Identify the unit of a repeating pattern for patterns with the structure AB or ABC Benchmark 3: Describe how various AB or ABC patterns are alike (e.g., how is a red-blue pattern like a yellow-green pattern?) Benchmark 4: Determine what comes several steps beyond the visible part of an AB, ABC, AAB, or ABB repeating pattern Benchmark 5 : Construct, extend, and describe a pattern that has a constant increase for the sequences 1, 3, 5, ; 2, 4, 6, ; 1, 4, 7, ; 2, 5, 8, ; and 3, 6, 9, through counting and building b. Continue repeating and growing patterns with materials, pictures and geometric items; e.g., XO, XOO, XOOO, XOOOO. Unit 7 Color, Shape, and Number Patterns: Patterns and Functions: Benchmark 1: Construct, describe, and extend a repeating pattern with the structure AB, ABC, AAB, or ABB Benchmark 2: Identify the unit of a repeating pattern for patterns with the structure AB or ABC Grade One 21

Benchmark 3: Describe how various AB or ABC patterns are alike (e.g., how is a red-blue pattern like a yellow-green pattern?) Benchmark 4: Determine what comes several steps beyond the visible part of an AB, ABC, AAB, or ABB repeating pattern Benchmark 5 : Construct, extend, and describe a pattern that has a constant increase for the sequences 1, 3, 5, ; 2, 4, 6, ; 1, 4, 7, ; 2, 5, 8, ; and 3, 6, 9, through counting and building 3. Describe orally the basic unit or general plan of a repeating or growing pattern. Unit 7 Color, Shape, and Number Patterns: Patterns and Functions: Benchmark 1: Construct, describe, and extend a repeating pattern with the structure AB, ABC, AAB, or ABB Benchmark 2: Identify the unit of a repeating pattern for patterns with the structure AB or ABC Benchmark 3: Describe how various AB or ABC patterns are alike (e.g., how is a red-blue pattern like a yellow-green pattern?) Benchmark 4: Determine what comes several steps beyond the visible part of an AB, ABC, AAB, or ABB repeating pattern Benchmark 5 : Construct, extend, and describe a pattern that has a constant increase for the sequences 1, 3, 5, ; 2, 4, 6, ; 1, 4, 7, ; 2, 5, 8, ; and 3, 6, 9, through counting and building Use Algebraic Representations 4. Solve open sentences by representing an expression in more than one way using the commutative property; e.g., 4 + 5 = 5 + 4 or the number of blue balls plus red balls is the same as the number of red balls plus blue balls (R + B = B + R). Could be included in Unit 1 How Many of Each?: Addition, Subtraction, and the Number System 1: Benchmark 5: Find more than one combination of two addends for a number up to 10 (e.g.: 7 is 4 and 3 and it's also 5 and 2) Unit 3 Solving Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 5: Represent numbers using equivalent expressions Unit 8 Twos, Fives, and Tens: Addition, Subtraction, and the Number System 4: Benchmark 3: Demonstrate fluency with the two-addend combinations of 10 Grade One 22

5. Describe orally and model a problem situation using words, objects or number phrase or sentence. Unit 1 How Many of Each?: Addition, Subtraction, and the Number System 1: Benchmark 4: Interpret (retell the action and sequence) and solve addition story problems Unit 3 Solving Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 3: Make sense of (retell the action and sequence) and solve addition and subtraction story problems Unit 6 Number Games and Crayon Puzzles: Addition, Subtraction, and the Number System 3: Benchmark 3: Interpret (retell the action and sequence) and solve addition and subtraction story problems Unit 8 Twos, Fives, and Tens: Addition, Subtraction, and the Number System 4: Invesigation 2: Begin to use groups in meaningful ways Data Analysis and Probability Standard Students pose questions and collect, organize, represent, interpret and analyze data to answer those questions. Students develop and evaluate inferences, predictions and arguments that are based on data. Data Collection 1. Identify multiple categories for sorting data. Unit 4 What Would You Rather Be?: Data Analysis: Benchmark 1: Sort a group of objects according to a given attribute Benchmark 2: Represent a set of data with two categories Benchmark 3: Interpret a variety of data representations with two categories 2. Collect and organize data into charts using tally marks. Unit 4 What Would You Rather Be?: Data Analysis: Benchmark 1: Sort a group of objects according to a given attribute Benchmark 2: Represent a set of data with two categories Grade One 23

3. Display data in picture graphs with units of 1 and bar graphs with intervals of 1. Unit 4 What Would You Rather Be?: Data Analysis: Benchmark 2: Represent a set of data with two categories 4. Read and interpret charts, picture graphs and bar graphs as sources of information to identify main ideas, draw conclusions, and make predictions. Unit 4 What Would You Rather Be?: Data Analysis: Benchmark 3: Interpret a variety of data representations with two categories Benchmark 4: Describe a set of data including how many are in each group, which group is greater and how many people responded to the survey 5. Construct a question that can be answered by using information from a graph. Unit 4 What Would You Rather Be?: Data Analysis: Benchmark 3: Interpret a variety of data representations with two categories Benchmark 4: Describe a set of data including how many are in each group, which group is greater and how many people responded to the survey Statistical Methods 6. Arrange five objects by an attribute, such as size or weight, and identify the ordinal position of each object. Unit 4 What Would You Rather Be?: Data Analysis: Benchmark 1: Sort a group of objects according to a given attribute 7. Answer questions about the number of objects represented in a picture graph, bar graph or table graph; e.g., category with most, how many more in a category compared to another, how many altogether in two categories. Unit 4 What Would You Rather Be?: Data Analysis: Benchmark 3: Interpret a variety of data representations with two categories Benchmark 4: Describe a set of data including how many are in each group, which group is greater and how many people responded to the survey Grade One 24

Probability 8. Describe the likelihood of simple events as possible/impossible and more likely/less likely; e.g., when using spinners or number cubes in classroom activities. Concepts of probability are taught in Grades 4 and 5 in the Investigations series (Grade 4, Unit 2, Benchmark 6 and Grade 5, Unit 9, Benchmark 4). Grade One 25

to the for Mathematics Grade Level Indicators Grade Two Number, Number Sense and Operations Standard Students demonstrate number sense including an understanding of number systems and operations, and how they relate to one another. Students compute fluently and make reasonable estimates using paper and pencil, technology-supported and mental methods. Number and Number Systems 1. Use place value concepts to represent, compare and order whole numbers using physical models, numerals and words, with ones, tens and hundreds. For example: a. Recognize 10 can mean 10 ones or a single entity (1 ten) through physical models and trading games. Unit 3 Stickers, Number Strings, and Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 6: Interpret and solve problems about the number of tens and ones in a quantity Unit 6 How Many Tens? How Many Ones?: Addition, Subtraction, and the Number System 3 b. Read and write 3-digit numerals (e.g., 243 as two hundred forty three, 24 tens and 3 ones, or 2 hundreds and 43 ones, etc.) and construct models to represent each. Unit 3 Stickers, Number Strings, and Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 6: Interpret and solve problems about the number of tens and ones in a quantity Unit 6 How Many Tens? How Many Ones?: Addition, Subtraction, and the Number System 3 Grade Two 26

2. Recognize and classify numbers as even or odd. Unit 3 Stickers, Number Strings, and Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 3: Define even and odd numbers in terms of groups of two or two equal groups Unit 8 Partners, Teams, and Paper Clips: Addition, Subtraction, and the Number System 4: Benchmark 2: Reason about partners, teams, and leftovers to make and justify generalizations about what happens when even and odd numbers are added 3. Count money and make change using coins and a dollar bill. Unit 1 Counting, Coins, and Combinations: Addition, Subtraction, and the Number System 1 Unit 3 Stickers, Number Strings, and Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 4: Know coin values and coin equivalencies 4. Represent and write the value of money using the sign and in decimal form when using the $ sign. Unit 1 Counting, Coins, and Combinations: Addition, Subtraction, and the Number System 1 Unit 3 Stickers, Number Strings, and Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 4: Know coin values and coin equivalencies 5. Represent fractions (halves, thirds, fourths, sixths and eighths), using words, numerals and physical models. For example: a. Recognize that a fractional part can mean different amounts depending on the original quantity. Unit 7 Parts of a Whole, Parts of a Group: Fractions: Benchmark 1: Identify 1/2, 1/3, and 1/4 of a region Benchmark 2: Find 1/2 of a set of objects Benchmark 3: Recognize that a fraction divides the whole into equal parts Grade Two 27

b. Recognize that a fractional part of a rectangle does not have to be shaded with contiguous parts. Unit 7 Parts of a Whole, Parts of a Group: Fractions: Benchmark 1: Identify 1/2, 1/3, and 1/4 of a region Benchmark 3: Recognize that a fraction divides the whole into equal parts c. Identify and illustrate parts of a whole and parts of sets of objects. Unit 7 Parts of a Whole, Parts of a Group: Fractions: Benchmark 1: Identify 1/2, 1/3, and 1/4 of a region Benchmark 2: Find 1/2 of a set of objects Benchmark 3: Recognize that a fraction divides the whole into equal parts d. Compare and order physical models of halves, thirds and fourths in relations to 0 and 1. Unit 7 Parts of a Whole, Parts of a Group: Fractions: Benchmark 1: Identify 1/2, 1/3, and 1/4 of a region Benchmark 3: Recognize that a fraction divides the whole into equal parts Meaning of Operations 6. Model, represent and explain subtraction as comparison, take-away and part-to-whole; e.g., solve missing addend problems by counting up or subtracting, such as I had six baseball cards, my sister gave me more, and I now have ten. How many did she give me? can be represented as 6 +? = 10 or 10-6 =?. Unit 1 Counting, Coins, and Combinations: Addition, Subtraction, and the Number System 1: Benchmark 2: Determine the difference between two numbers (up to 45) Benchmark 3: Interpret addition and subtraction story problems (read a story problem and determine what needs to be figured out) Benchmark 4: Have at least one strategy for solving addition and subtraction (as removal) story problems Unit 3 Stickers, Number Strings, and Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 2: Interpret and solve subtraction (removal) and unknown change story problems with totals up to 40 Grade Two 28

Unit 6 How Many Tens? How Many Ones?: Addition, Subtraction, and the Number System 3: Benchmark 1: Write an equation that represents an addition or subtraction situation Unit 8 Partners, Teams, and Paper Clips: Addition, Subtraction, and the Number System 4: Benchmark 1: Subtract 2-digit numbers 7. Model, represent and explain multiplication as repeated addition, rectangular arrays and skip counting. Unit 1 Counting, Coins, and Combinations: Addition, Subtraction, and the Number System 1: Benchmark 6: Understand what it means to double a quantity Unit 2 Shapes, Blocks, and Symmetry: 2D and 3D Geometry: Benchmark 2: Identify the number of rows and the number of squares in each row in an array Benchmark 6: Demonstrate fluency with addition combinations: doubles combinations to 10 + 10 Unit 6 How Many Tens? How Many Ones?: Addition, Subtraction, and the Number System 3: Benchmark 3: Count by 2s, 5s, and 10s, up to 110 8. Model, represent and explain division as sharing equally and repeated subtraction. Unit 7 Parts of a Whole, Parts of a Group: Fractions: Benchmark 2: Find 1/2 of a set of objects Benchmark 3: Recognize that a fraction divides the whole into equal parts 9. Model and use the commutative property for addition. Unit 3 Stickers, Number Strings, and Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 1: Use known combinations to add several numbers in any order Grade Two 29

Computation and Estimation 10. Demonstrate fluency in addition facts with addends through 9 and corresponding subtractions; e.g., 9 + 9 = 18, 18 9 = 9. Unit 1 Counting, Coins, and Combinations: Addition, Subtraction, and the Number System 1: Benchmark 5: Demonstrate fluency with addition combinations: plus 1, plus 2, and make 10 addition combinations Unit 2 Shapes, Blocks, and Symmetry: 2D and 3D Geometry: Benchmark 6: Demonstrate fluency with addition combinations: doubles combinations to 10 + 10 Unit 3 Stickers, Number Strings, and Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 1: Use known combinations to add several numbers in any order Benchmark 7: Demonstrate fluency with addition combinations: near double combinations Unit 4 Pockets, Teeth, and Favorite Things: Data Analysis: Benchmark 7: Demonstrate fluency with addition combinations: plus ten combinations Unit 8 Partners, Teams, and Paper Clips: Addition, Subtraction, and the Number System 4: Benchmark 4: Demonstrate fluency with addition combinations: plus 9 and the remaining combinations 11. Add and subtract multiples of 10. Unit 4 Pockets, Teeth, and Favorite Things: Data Analysis: Benchmark 7: Demonstrate fluency with addition combinations: plus ten combinations Unit 6 How Many Tens? How Many Ones?: Addition, Subtraction, and the Number System 3: Benchmark 4: Add multiples of 5, up to 100 Grade Two 30

12. Demonstrate multiple strategies for adding and subtracting 2- or 3-digit whole numbers, such as: a. compatible numbers; b. compensatory numbers; c. informal use of commutative and associative properties of addition. Unit 1 Counting, Coins, and Combinations: Addition, Subtraction, and the Number System 1: Benchmark 2: Determine the difference between two numbers (up to 45) Unit 3 Stickers, Number Strings, and Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 1: Use known combinations to add several numbers in any order Benchmark 2: Interpret and solve subtraction (removal) and unknown change story problems with totals up to 40 Benchmark 5: Count on or break numbers apart to add two or more numbers up to a total of 40 Benchmark 7: Demonstrate fluency with addition combinations: near double combinations Unit 4 Pockets, Teeth, and Favorite Things: Data Analysis: Benchmark 7: Demonstrate fluency with addition combinations: plus ten combinations Unit 6 How Many Tens? How Many Ones?: Addition, Subtraction, and the Number System 3: Benchmark 4: Add multiples of 5, up to 100 Unit 8 Partners, Teams, and Paper Clips: Addition, Subtraction, and the Number System 4: Benchmark 1: Subtract 2-digit numbers Benchmark 3: Add two 2-digit numbers accurately and efficiently Benchmark 4: Demonstrate fluency with addition combinations: plus 9 and the remaining combinations 13. Estimate the results of whole number addition and subtraction problems using front-end estimation, and judge the reasonableness of the answers. Unit 1 Counting, Coins, and Combinations: Addition, Subtraction, and the Number System 1: Benchmark 3: Interpret addition and subtraction story problems (read a story problem and determine what needs to be figured out) Grade Two 31

Benchmark 4: Have at least one strategy for solving addition and subtraction (as removal) story problems Unit 3 Stickers, Number Strings, and Story Problems: Addition, Subtraction, and the Number System 2: Benchmark 2: Interpret and solve subtraction (removal) and unknown change story problems with totals up to 40 Unit 6 How Many Tens? How Many Ones?: Addition, Subtraction, and the Number System 3: Benchmark 1: Write an equation that represents an addition or subtraction situation Benchmark 2: Determine the distance to any multiple of 10, up to 100 Unit 8 Partners, Teams, and Paper Clips: Addition, Subtraction, and the Number System 4: Benchmark 2: Reason about partners, teams, and leftovers to make and justify generalizations about what happens when even and odd numbers are added Measurement Standard Students estimate and measure to a required degree of accuracy and precision by selecting and using appropriate units, tools and technologies. Measurement Units 1. Identify and select appropriate units of measure for: a. length centimeters, meters, inches, feet or yards; b. volume (capacity) liters, cups, pints or quarts; c. weight grams, ounces or pounds; d. time hours, half-hours, quarter-hours or minutes and time designations, a.m. or p.m. Unit 9 Measuring Length and Time: Measurement: Benchmark 2: Recognize that the same count of different-sized units yields different lengths Benchmark 3: Recognize that, when measuring the same length, larger units yield smaller counts Benchmark 4: Measure objects using inches and centimeters Benchmark 5: Use a ruler to measure lengths longer than one foot Grade Two 32

Benchmark 6: Solve problems involving the beginning time of an event, ending time of an event, and duration of the event; given two of these, find the third for events beginning and ending on the hour or half-hour Benchmark 7: Use a timeline to record and determine duration to the hour or half-hour 2. Establish personal or common referents for units of measure to make estimates and comparisons; e.g., the width of a finger is a centimeter, a large bottle of soda pop is 2 liters, a small paper clip weighs about one gram. Could be included in Unit 9 Measuring Length and Time: Measurement: Benchmark 1: Identify sources of measurement error Benchmark 2: Recognize that the same count of different-sized units yields different lengths 3. Describe and compare the relationships among units of measure, such as centimeters and meters; inches, feet and yards; cups, pints and quarts; ounces and pounds; and hours, half-hours, and quarter-hours; e.g., how many inches in a foot? Unit 9 Measuring Length and Time: Measurement: Benchmark 2: Recognize that the same count of different-sized units yields different lengths Benchmark 3: Recognize that, when measuring the same length, larger units yield smaller counts 4. Tell time to the nearest minute interval on digital and to the nearest 5- minute interval on analog (dial) timepieces. Unit 9 Measuring Length and Time: Measurement: Benchmark 6: Solve problems involving the beginning time of an event, ending time of an event, and duration of the event; given two of these, find the third for events beginning and ending on the hour or half-hour Benchmark 7: Use a timeline to record and determine duration to the hour or half-hour Grade Two 33