Arizona Mathematics Standard Articulated by Grade Level Grades K 6

A Correlation of 2010 to the Arizona Mathematics Standard Articulated by Grade Level Grades K 6 M/M-159

Correlation Introduction This correlation is designed to show the close alignment between Pearson focusmath and the Arizona Mathematics Standards Articulated by Grade Level (2008). Correlation page references are to the Teacher s Edition. Lessons in the Teacher s Edition contain facsimile Student Edition pages. focusmath provides districts and schools with a flexible program to meet any framework. This curriculum can be used in a variety of settings, including before- or after-school programs, summer school, pull-out or resource-room instruction, or tutoring programs. focusmath features concise Steps which target the NCTM Focal Points. Focusing on a smaller number of key skills allows the teacher to spend an extended amount of time on one concept. This strategy provides the student with a deeper understanding of the concept, better mathematical fluency, and the ability to transfer meaningful mathematics to different situations. Teacher s Edition There is one Teacher s Edition per grade, which contains support for all three student books, Teaching Tool Masters, Assessment Masters, and Answer Keys Student Books There are three consumable student books per grade, one for each Focal Point. Students may be recommended for one or more of the books depending on the results of their Program Placement Test. Each student book can be completed in 4-6 weeks Manipulatives The manipulative kits provide students with hands-on learning materials that support in-depth conceptual development

Table of Contents Kindergarten 1 Grade One 4 Grade Two 9 Grade Three 15 Grade Four 20 Grade Five 27 Grade Six 33

to the Arizona Mathematics Standards Articulated by Grade Level Kindergarten Arizona Mathematics Standards Articulated by Grade Level - Kindergarten Kindergarten Strand 1: Number and Operations Concept 1: Number Sense Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems. PO 1: Express whole numbers 0 to 20 using and TE: 6-7, 8-9, 10-11, 12-13, 16-17, 18-19, 22-23, connecting multiple representations. 24-25, 26-27, 28-29, 30-31, 32-33, 34-35, 36-37 PO 2: Count forward to 20 and backward from 10 TE: 2-3, 22-23 with or without objects using different starting points. PO 3: Identify numbers which are one more or less TE: 26-27, 29, 31, 33, 34, 36 than a given number to 20. PO 4: Compare and order whole numbers through TE: 4-5, 12-13, 18-19, 20-21 20. PO 5: Recognize and compare the ordinal position of TE: 14-15 at least five objects. Concept 2: Numerical Operations Understand and apply numerical operations and their relationship to one another. PO 1: Solve contextual problems by developing, TE: 26-27, 28-29, 30-31, 32-33, 34-35, 36-37 applying, and recording strategies with sums and minuends to 10 using objects, pictures, and symbols. PO 2: Develop and use multiple strategies to determine a: sums to 10 and TE: 26-27, 28-29, 30-31 b: differences with minuends to 10. TE: 32-33, 34-35, 36-37 PO 3: Create word problems based on sums to 10 and differences with minuends to 10. TE (Concept Development): 26-27, 28-29, 32-33, 34-35, 36-37 Concept 3: Estimation Use estimation strategies reasonably and fluently while integrating content from each of the other strands. PO 1: Identify quantities to 20 as more or less than 5 or as more or less than 10. Students compare and order numbers and interpret displays of counters and other objects in ten-frames. TE: 4-5, 10-11, 12-13, 16-17, 18-19, 20-21, 24-25 Strand 2: Data Analysis, Probability, and Discrete Mathematics Concept 1: Data Analysis (Statistics) Understand and apply data collection, organization, and representation to analyze and sort data. PO 1: Construct simple displays of data using objects or pictures. PO 2: Ask and answer questions by counting, comparing quantities, and interpreting simple displays of data. Students organize counters into ten-frames to display numbers to 10. TE: 10, 16 Students compare and order numbers and interpret displays of counters and other objects in ten-frames. TE: 4-5, 10-11, 12-13, 16-17, 18-19, 20-21, 24-25 1

Articulated by Grade Level - Kindergarten Concept 2: Probability Understand and apply data collection, organization, and representation to analyze and sort data. In Grade K, there are no performance objectives in this concept. Performance objectives begin in Grade 3. Concept 3: Systematic Listing and Counting Understand and demonstrate the systematic listing and counting of possible outcomes. PO 1: Sort, classify, count, and represent up to 20 TE: 40-41, 46-47 objects and justify the sorting rule. Concept 4: Vertex Edge Graphs Understand and apply vertex-edge graphs. In Grade K, there are no performance objectives in this concept. Performance objectives begin in Grade 2. Strand 3: Patterns, Algebra, and Functions Concept 1: Patterns Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands. PO 1: Recognize, describe, extend, create, and record simple repeating patterns. PO 2: Recognize, describe, extend, and record simple growing patterns. Students use a number line to order numbers from 0 to 20. TE: 20-21 Concept 2: Functions and Relationships Describe and model functions and their relationships. In Grade K, there are no performance objectives in this concept. Performance objectives begin in Grade 2. Concept 3: Algebraic Representations Represent and analyze mathematical situations and structures using algebraic representations. PO 1: Record equivalent forms of whole numbers to TE: 10-11, 16-17, 18-19, 20-21, 22-23, 24-25, 10 by constructing models and using numbers. 26-27, 28-29, 30-31, 32-33, 34-35, 36-37 PO 2: Compare expressions using spoken words and TE: 4-5, 18-19, 26-27, 28-29, 30-31, 34-35 the symbol =. Concept 4: Analysis of Change Analyze how changing the values of one quantity corresponds to change in the values of another quantity. In Grade K, there are no performance objectives in this concept. Performance objectives begin in Grade 4. Strand 4: Geometry and Measurement Concept 1: Geometric Properties Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships. PO 1: Identify, analyze, and describe circles, TE: 42-43, 44-45 triangles, and rectangles (including squares) in different orientations and environments. PO 2: Build, draw, compare, describe, and sort 2- TE: 40-41, 42-43 dimensional figures (including irregular figures) using attributes. 2

Articulated by Grade Level - Kindergarten Concept 2: Transformation of Shapes Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations. In Grade K, there are no performance objectives in this concept. Performance objectives begin in Grade 1. Concept 3: Coordinate Geometry Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands. In Grade K, there are no performance objectives in this concept. Performance objectives begin in Grade 4. Concept 4: Measurement Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements. PO 1: Compare and order objects according to TE: 50-51, 52-53, 54-55, 56-57 observable and measureable attributes. PO 2: Use the attribute of length to describe and TE: 50-51, 52-53 compare objects using non-standard units. Strand 5: Structure and Logic Concept 1: Algorithms and Algorithmic Thinking Use reasoning to solve mathematical problems. In Grade K, there are no performance objectives in this concept. Performance objectives begin in Grade 4. Concept 2: Logic, Reasoning, Problem Solving and Proof Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions, and recognize their applications. PO 1: Identify the question(s) asked and any other questions that need to be answered in order to find a solution. PO 2: Identify the given information that can be used to find a solution. PO 3: Select from a variety of problem-solving strategies and use one or more strategies to arrive at a solution. PO 4: Represent a problem situation using any combination of words, numbers, pictures, physical TE (Concept Development section): 2-3, 4-5, 6-7, 8-9, 18-19, 26-27, 28-29, 30-31, 32-33, 34-35, 50-51, 52-53, 54-55, 56-57 TE (Concept Development section): 2-3, 4-5, 6-7, 8-9, 18-19, 26-27, 28-29, 30-31, 32-33, 34-35, 50-51, 52-53, 54-55, 56-57 TE (Concept Development section): 26, 28, 32, 34, 50-51, 52, 54, 56 TE (Concept Development section): 2-3, 4-5, 6-7, 8-9, 18-19, 26-27, 28-29, 30-31, 32-33, 34-35, 50-51, 52-53, 54-55, 56-57 objects, or symbols. PO 5: Explain and clarify mathematical thinking. TE (Concept Development section): 2-3, 4-5, 6-7, 8-9, 18-19, 26-27, 28-29, 30-31, 32-33, 34-35, 50-51, 52-53, 54-55, 56-57 PO 6: Determine whether a solution is reasonable. While discussing students ideas for solving problems and modeling a solution strategy, the teacher can demonstrate that the solution is reasonable. TE (Concept Development section): 3, 5, 7, 9, 19, 27, 29, 31, 33, 35, 51, 53, 55, 57 3

to the Arizona Mathematics Standards Articulated by Grade Level Grade One Arizona Mathematics Standards Articulated by Grade Level Grade 1 GRADE: Grade 1 Strand 1: Number and Operations Concept 1: Number and Operations Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems. PO 1: Express whole numbers 0 to 100, in groups of tens and ones using and connecting multiple representations. PO 2: Count forward to 100 and backward from 100 by 1s and 10s using different starting points, and count forward to 100 by 2s and 5s. PO 3: Identify numbers which are 10 more or less than a given number to 90. PO 4: Compare and order whole numbers through 100 by applying the concepts of place value. PO 5: Recognize and compare ordinal numbers, first through tenth. TE: A2-A3, A4-A5, A6-A7, A8-A9, A10-A11, A12- A13, A17, A18-A19, A20-A21, A22-A23, B2-B3, B4-B5, B6-B7, B18-B19, B20-B21, B24-B25, B26-B27, B28-B29, B30-B31, B32-B33 TE: A3, A5, A7, B3, B5, B26-B27, B28-B29, B30- B31, B34-B35 TE: A34-A35, A36-A37, A38, A40, B36-B37 TE: A26-A27, B8-B9, B10-B11, B12-B13, B14- B15, B16-B17, B23, B38-B39, B40-B41, B42- B43, B44-B45, B46-B47 Students order numbers to 10 using the terms least, between, and greatest, and on a number line. TE: B12-B13, B14-B15 Concept 2: Numerical Operations Understand and apply numerical operations and their relationship to one another. PO 1: Solve contextual problems using multiple representations for addition and subtraction facts. PO 2: Demonstrate addition and subtraction of numbers that total less than 100 by using various representations that connect to place value concepts. PO 3: Develop and use multiple strategies for addition facts to 10+10 and their related subtraction facts. PO 4: Create word problems based on addition and subtraction facts. TE: A8-A9, A10-A11, A12-A13, A14-A15, A16- A17, A18-A19, A20-A21, A22-A23, A24-A25, A26-A27, A28-A29, A30-A31, A32-A33, A34-A35, A36-A37, A38-A39, A40-A41, A42-A43, A44-A45, A46-A47, A48-A49, A50-A51, A52-A53, A54-A55, A56-A57, A58-A59, B20-B21, B22-B23 TE: A34-A35, A36-A37, A38, A40, B20-B21, B36-B37 TE: A8-A9, A10-A11, A12-A13, A14-A15, A16- A17, A18-A19, A20-A21, A22-A23, A24-A25, A26-A27, A28-A29, A30-A31, A32-A33, A34-A35, A36-A37, A38-A39, A40-A41, A42-A43, A44-A45, A46-A47, A48-A49, A50-A51, A52-A53, A54-A55, A56-A57, A58-A59 TE: A15, A25, A27, A29, A33, A41, A51, A55, A58-A59 (Concept Development: A14-A15, A16-A17, A18- A19, A20-A21, A22-A23, A24-A25, A26-A27, A28-A29, A30-A31, A34-A35, A36-A37, A46-A47, A48-A49, A50-A51, B22-B23) 4

Articulated by Grade Level Grade 1 PO 5: Apply properties to solve addition/subtraction problems a: identity property of addition/subtraction and TE: A30-A31, A46-A47 b: commutative property of addition. TE: A42-A43 Concept 3: Estimation Use estimation strategies reasonably and fluently while integrating content from each of the other strands. PO 1: Use estimation to determine if sums are more or less than 5, more or less than 10, or more or less Students compare numbers and interpret than 20. displays of counters in ten-frames. TE: A6-A7, A26-A27, A34-A35, A38, A41, B18- B19, B20-B21, B23, B38-B39, B40-B41 Strand 2: Data Analysis, Probability, and Discrete Mathematics Concept 1: Data Anaylsis (Statistics) Understand and apply data collection, organization, and representation to analyze and sort data. PO 1: Collect, record, organize, and display data using tally charts or pictographs. PO 2: Ask and answer questions by interpreting simple displays of data, including tally charts or pictographs. Students organize counters into ten-frames to display numbers to 10, and on part-part-whole mats. TE: A6, A12, A18, A20, A22, A34, A36, A48, A52, B6, B18, B20 Students interpret displays of counters and other objects in ten-frames, number lines, and hundred charts. TE: A6-A7, A12, A34-A35, A36, A38, A40, B6- B7, B14-B15, B18-B19, B20-B21, B28, B34-B35, B44-B45 Concept 2: Probability Understand and apply the basic concepts of probability. In Grade 1, there are no performance objectives in this concept. Performance objectives begin in Grade 3 Concept 3: Systematic Listing and Counting Understand and demonstrate the systematic listing and counting of possible outcomes. PO 1: Use Venn diagrams to sort, classify, and count objects and justify the sorting rule. Students sort plane shapes and solid figures. TE: C12-C13, C30-C31 Concept 4: Vertex Edge Graphs Understand and apply vertex-edge graphs. In Grade 1, there are no performance objectives in this concept. Performance objectives begin in Grade 2. Strand 3: Patterns, Algebra, and Functions Concept 1: Patterns Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands. PO 1: Recognize, describe, extend, create, and record repeating patterns. PO 2: Recognize, describe, extend, create, and record growing patterns. TE: B26-B27, B28-B29, B34-B35 5

Articulated by Grade Level Grade 1 Concept 2: Functions and Relationships Describe and model functions and their relationships. In Grade 1, there are no performance objectives in this concept. Performance objectives begin in Grade 2. Concept 3: Algebraic Representations Represent and analyze mathematical situations and structures using algebraic representations. PO 1: Record equivalent forms of whole numbers to 100 by constructing models and using numbers. PO 2: Compare expressions using spoken words and the symbols = and "is not equal to". TE: A2-A3, A4-A5, A6-A7, A8-A9, A10-A11, A12- A13, A17, A18-A19, A20-A21, A22-A23, B2-B3, B4-B5, B6-B7, B18-B19, B20-B21, B24-B25, B26-B27, B28-B29, B30-B31, B32-B33 TE: A26-A27, B8-B9, B10-B11, B23, B38-B39, B40-B41 PO 3: Represent a word problem requiring addition TE: A15, A25, A27, A29, A41, A51, A55, A58- or subtraction facts using an equation. A59 Concept 4: Analysis of Change Analyze how changing the values of one quantity corresponds to change in the values of another quantity. In Grade 1, there are no performance objectives in this concept. Performance objectives begin in Grade 4. Strand 4: Geometry and Measurement Concept 1: Geometric Properties Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships. PO 1: Identify and draw 2-dimensional geometric figures based on given attributes regardless of size or orientation. PO 2: Compare and sort basic 2-dimensional figures (including irregular figures) using attributes and explain the reasoning for the sorting. TE: C2-C3, C4-C5, C6-C7, C8-C9, C10-C11, C12-C13, C14-C15, C16-C17, C18-C19, C20- C21 TE: C10-C11, C12-C13, C14-C15 PO 3: Describe the results of composing and TE: C16-C17, C18-C19 decomposing 2-dimensional figures. Concept 2: Transformation of Shapes Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations. In Grade 1, there are no performance objectives in this concept. Performance objectives begin in Grade 2. Concept 3: Coordinate Geometry Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands. In Grade 1, there are no performance objectives in this concept. Performance objectives begin in Grade 4. Concept 4: Measurement Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements. PO 1: Compare and order objects according to length, capacity, and weight. Students compare and order lengths of cube trains representing numbers through 10. TE: B12-B13 6

Articulated by Grade Level Grade 1 PO 2: Measure and compare the length of objects using the benchmark of one inch. PO 3: Sequence the days of the week and the months of the year. Strand 5: Structure and Logic Concept 1: Algorithms and Algorithmic Thinking Use reasoning to solve mathematical problems. In Grade 1, there are no performance objectives in this concept. Performance objectives begin in Grade 4. Concept 2: Logic, Reasoning, Problem Solving and Proof Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions, and recognize their applications. PO 1: Identify the question(s) asked and any other questions that need to be answered in order to find a solution. PO 2: Identify the given information that can be used to find a solution. PO 3: Select from a variety of problem-solving strategies and use one or more strategies to arrive at a solution. PO 4: Represent a problem situation using any combination of words, numbers, pictures, physical objects, or symbols. PO 5: Explain and clarify mathematical thinking. TE: B16-B17 (Concept Development: A14-A15, A16-A17, A18- A19, A20-A21, A22-A23, A24-A25, A26-A27, A28-A29, A30-A31, A34-A35, A36-A37, A46-A47, A48-A49, A50-A51, B22-B23) TE: B16-B17 (Concept Development: A14-A15, A16-A17, A18- A19, A20-A21, A22-A23, A24-A25, A26-A27, A28-A29, A30-A31, A34-A35, A36-A37, A46-A47, A48-A49, A50-A51, B22-B23) TE: A38-A39, A40-A41, B16-B17 (Concept Development: A14-A15, A16-A17, A24- A25, A26-A27, A28-A29, A30-A31, A50-A51, B22-B23) TE: B16-B17 (Concept Development: A14-A15, A16-A17, A18- A19, A20-A21, A22-A23, A24-A25, A26-A27, A28-A29, A30-A31, A34-A35, A36-A37, A46-A47, A48-A49, A50-A51, B22-B23) TE: B16-B17 (Concept Development: A14-A15, A16-A17, A18- A19, A20-A21, A22-A23, A24-A25, A26-A27, A28-A29, A30-A31, A34-A35, A36-A37, A46-A47, A48-A49, A50-A51, B22-B23) 7

Articulated by Grade Level Grade 1 PO 6: Determine whether a solution is reasonable. While discussing students ideas for solving problems and modeling a solution strategy, the teacher can demonstrate that the solution is reasonable. TE: B16-B17 (Concept Development: A14-A15, A16-A17, A18- A19, A20-A21, A22-A23, A24-A25, A26-A27, A28-A29, A30-A31, A34-A35, A36-A37, A46-A47, A48-A49, A50-A51, B22-B23) 8

to the Arizona Mathematics Standards Articulated by Grade Level Grade Two Arizona Mathematics Standards Articulated by Grade Level Grade 2 Grade 2 Strand 1: Number and Operations Concept 1: Number Sense Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems. PO 1: Express whole numbers 0 to 1000, in groups of hundreds, tens and ones using and connecting multiple representations. PO 2: Count forward to 1000 and backward from 1000 by 1s, 10s, and 100s using different starting points. PO 3: Identify numbers which are 100 more or less than a given number to 900. PO 4: Compare and order whole numbers through 1000 by applying the concept of place value. PO 5: Count money to $1.00. PO 6: Sort whole numbers through 1000 into odd and even, and justify the sort. TE: A2-A3, A10-A11, A12-A13, A14-A15, A16- A17, A18-A19, A20-A21, A22-A23, A24-A25, A34-A35, A36-A37, A38-A39, A40-A41, A42-A43, A44-A45, A48-A49, A50 TE: A16-A17, A18-A19, A20-A21, A24-A25, A26- A27, A36-A37, A38-A39 TE: A28-A29, A38-A39, A44-A45, A46-A47, B36- B37, B38-B39 TE: A4-A5, A6-A7, A8-A9, A30-A31, A32-A33, A36-A37, A48-A49, A50-A51, A52-A53 Students can extend whole number place-value concepts to apply to decimals and money. TE: A22-A23, A28-A29, A40-A41 Students count by 2s to create patterns of even numbers. TE: A24-A25, A26-A27 Concept 2: Numerical Operations Understand and apply numerical operations and their relationship to one another. PO 1: Solve contextual problems using multiple representations involving a: addition and subtraction with one- and/or two-digit numbers, TE: B2-B3, B4-B5, B6-B7, B8-B9, B10-B11, B12- B13, B14-B15, B16-B17, B18-B19, B20-B21, B22-B23, B24-B25, B26-B27, B28-B29, B36-B37, B38-B39, B40-B41, B42-B43, B44-B45, B46-B47, B48-B49, B50-B51, B52-B53, B54-B55, B56-B57, B58-B59 b: multiplication for 1s, 2s, 5s, and 10s, and Students skip count to create patterns of multiples. They analyze patterns of numbers on number lines and hundred charts. TE: A16-A17, A18-A19, A24-A25, A26-A27, A36- A37, A46-A47 c: adding and subtracting money to $1.00. Students can extend whole number place-value concepts used to add multi-digit numbers to apply to decimals and money. TE: B36-B37, B38-B39, B40-B41, B42-B43, B44- B45, B46-B47, B48-B49, B50-B51, B52-B53, B54-B55, B56-B57, B58-B59 9

Articulated by Grade Level Grade 2 PO 2: Demonstrate the ability to add and subtract whole numbers (to at least two digits) and decimals (in the context of money) a: with up to three addends and TE: B2-B3, B4-B5, B6-B7, B8-B9, B10-B11, B12- B13, B14-B15, B16-B17, B18-B19, B20-B21, B22-B23, B24-B25, B26-B27, B28-B29, B36-B37, B38-B39, B40-B41, B42-B43, B44-B45, B46-B47, B48-B49, B50-B51, B52-B53, B54-B55, B56-B57, B58-B59 b: to $1.00. Students can extend whole number place-value concepts used to add multi-digit numbers to apply to decimals and money. TE: B36-B37, B38-B39, B40-B41, B42-B43, B44- B45, B46-B47, B48-B49, B50-B51, B52-B53, B54-B55, B56-B57, B58-B59 PO 3: Demonstrate fluency of addition and subtraction facts. PO 4: Apply and interpret the concept of addition and subtraction as inverse operations to solve problems. PO 5: Create and solve word problems based on addition and subtraction of two-digit numbers. PO 6: Demonstrate the concept of multiplication for 1s, 2s, 5s, and 10s. PO 7: Describe the effect of operations (addition and subtraction) on the size of whole numbers. TE: B2-B3, B4-B5, B6-B7, B8-B9, B10-B11, B12- B13, B14-B15, B16-B17, B18-B19, B20-B21, B22-B23, B24-B25, B26-B27, B28-B29 TE: B26-B27, B28-B29, B58-B59 TE: B47, B49 Students skip count to create patterns of multiples. They analyze patterns of numbers on number lines and hundred charts. TE: A16-A17, A18-A19, A24-A25, A26-A27, A36- A37, A46-A47 TE: B2-B3, B4-B5, B6-B7, B8-B9, B10-B11, B12- B13, B14-B15, B16-B17, B18-B19, B20-B21, B22-B23, B24-B25, B26-B27, B28-B29, B36-B37, B38-B39, B40-B41, B42-B43, B44-B45, B46-B47, B48-B49, B50-B51, B52-B53, B54-B55, B56-B57, B58-B59 PO 8: Apply properties to solve addition/subtraction problems a: identity property of addition/subtraction, TE: B6-B7 b: commutative property of addition, and TE: B4-B5 c: associative property of addition. TE: B18-B19 Concept 3: Estimation Use estimation strategies reasonably and fluently while integrating content from each of the other strands. PO 1: Use estimation to determine if sums of two 2- digit numbers are more or less than 20, more or less than 50, or more or less than 100. TE: B30-B31, B32-B33, B34-B35 Strand 2: Data Analysis, Probability, and Discrete Mathematics Concept 1: Data Analysis (Statistics) Understand and apply data collection, organization, and representation to analyze and sort data. PO 1: Collect, record, organize, and display data using pictographs, frequency tables, or single bar graphs. 10

Articulated by Grade Level Grade 2 PO 2: Formulate and answer questions by interpreting displays of data, including pictographs, frequency tables, or single bar graphs. Concept 2: Probability Understand and apply the basic concepts of probability. In Grade 2, there are no performance objectives in this concept. Performance objectives begin in Grade 3. Concept 3: Systematic Listing and Counting Understand and demonstrate the systematic listing and counting of possible outcomes. PO 1: List all possibilities in counting situations. PO 2: Solve a variety of problems based on the addition principle of counting. Understand and apply vertex-edge graphs. PO 1: Color simple pictures or maps using the least number of colors and justify the coloring. PO 2: Build vertex-edge graphs using concrete materials and explore simple properties of vertexedge graphs a: number of vertices and edges, b: neighboring vertices, and c: paths in a graph. Concept 4: Vertex Edge Graphs PO 3: Construct simple vertex-edge graphs from simple pictures or maps. Strand 3: Patterns, Algebra, and Functions Concept 1: Patterns Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands. PO 1: Recognize, describe, extend, create, and find missing terms in a numerical or symbolic pattern. PO 2: Explain the rule for a given numerical or symbolic pattern and verify that the rule works. TE: A16-A17, A18-A19, A24-A25, A26-A27, A36- A37, A46-A47 TE: A16-A17, A18-A19, A24-A25, A26-A27, A36- A37, A46-A47 11

Articulated by Grade Level Grade 2 Concept 2: Functions and Relationships PO 1: Describe a rule that represents a given relationship between two quantities using words or pictures. Students explore functional and inverse relationships between numbers and between operations. TE: A28-A29, A44-A45, A46-A47, B6-B7, B8-B9, B24-B25, B26-B27, B28-B29, B36-B37, B38-B39, B58-B59 Concept 3: Algebraic Representations Represent and analyze mathematical situations and structures using algebraic representations. PO 1: Record equivalent forms of whole numbers to TE: A2-A3, A10-A11, A12-A13, A14-A15, A16-1000 by constructing models and using numbers. A17, A18-A19, A20-A21, A22-A23, A24-A25, A34-A35, A36-A37, A38-A39, A40-A41, A42-A43, A44-A45, A46-A47, A48-A49, A50, A52-A53 PO 2: Compare expressions using spoken words and the symbols =, "is not equal to", and the symbols =,, <, and >. PO 3: Represent a word problem requiring addition or subtraction through 100 using an equation. PO 4: Identify the value of an unknown number in an equation involving an addition or subtraction fact. TE: A4-A5, A30-A31, A48-A49, B4-B5, B26-B27, B28-B29 TE: B3, B5, B9, B11, B21, B22-B23, B47, B49 TE: B2-B3, B4-B5, B6-B7, B8-B9, B10-B11, B12- B13, B14-B15, B16-B17, B18-B19, B20-B21, B22-B23, B24-B25, B26-B27, B28-B29 Concept 4: Analysis of Change Analyze how changing the values of one quantity corresponds to change in the values of another quantity. In Grade 2, there are no performance objectives in this concept. Performance objectives begin in Grade 4. Strand 4: Geometry and Measurement Concept 1: Geometric Properties Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships. PO 1: Describe and compare the attributes of polygons up to six sides using the terms side, vertex, point, and length. Students measure the lengths of objects whose outlines are in the shape of a polygon. TE: C14-C15, C19, C20-C21, C24, C26, C28- C29 Concept 2: Transformation of Shapes Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations. PO 1: Identify, with justification, whether a 2- dimensional figure has lines of symmetry. Concept 3: Coordinate Geometry Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands. In Grade 2, there are no performance objectives in this concept. Performance objectives begin in Grade 4. 12

Articulated by Grade Level Grade 2 Concept 4: Measurement Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements. PO 1: Tell time to the nearest minute using analog and digital clocks. PO 2: Apply measurement skills to measure the attributes of an object (length, capacity, weight). PO 3: Read temperatures on a thermometer using Fahrenheit and Celsius. PO 4: Demonstrate unit conversions a: 1 foot = 12 inches, TE: C20-C21 b: 1 quart = 4 cups, c: 1 pound = 16 ounces, d: 1 hour = 60 minutes, e: 1 day = 24 hours, f: 1 week = 7 days, and g: 1 year = 12 months. TE: C2-C3, C4-C5, C6-C7, C8-C9, C10-C11, C12-C13, C14-C15, C16-C17, C18-C19, C20- C21, C22-C23, C24-C25, C26-C27, C28-C29 Strand 5: Structure and Logic Concept 1: Algorithms and Algorithmic Thinking Use reasoning to solve mathematical problems. In Grade 2, there are no performance objectives in this concept. Performance objectives begin in Grade 4. Concept 2: Logic, Reasoning, Problem Solving and Proof Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions, and recognize their applications. PO 1: Identify the question(s) asked and any other questions that need to be answered in order to find a solution. PO 2: Identify the given information that can be used to find a solution. PO 3: Select from a variety of problem-solving strategies and use one or more strategies to arrive at a solution. PO 4: Represent a problem situation using any combination of words, numbers, pictures, physical objects, or symbols. TE: B3, B5, B9, B11, B21, B22-B23, B47, B49 TE: B3, B5, B9, B11, B21, B22-B23, B47, B49 TE (Concept Development): B2-B3, B6-B7, B10- B11, B20-B21, B22-B23, B46-B47, B48-B49 TE: B3, B5, B9, B11, B21, B22-B23, B47, B49 PO 5: Explain and clarify mathematical thinking. TE (Concept Development): B2-B3, B4-B5, B8- B9, B10-B11, B20-B21, B22-B23, B46-B47, B48- B49 13

Articulated by Grade Level Grade 2 PO 6: Determine whether a solution is reasonable. Students estimate sums and differences of numbers. Also, while discussing students ideas for solving problems and modeling a solution strategy, the teacher can demonstrate that the solution is reasonable. TE: B32-B33, B34-B35 (Concept Development): B2-B3, B4-B5, B8-B9, B10-B11, B20-B21, B22-B23, B46-B47, B48-B49 14

to the Arizona Mathematics Standards Articulated by Grade Level Grade Three Arizona Mathematics Standards Articulated by Grade Level Grade 3 Grade 3 Strand 1: Number and Operations Concept 1: Number Sense Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems. PO 1: Express whole numbers through six digits using and connecting multiple representations. PO 2: Compare and order whole numbers through six digits by applying the concept of place value. PO 3: Count and represent money using coins and bills to $100.00. PO 4: Sort whole numbers into sets and justify the sort. PO 5: Express benchmark fractions as fair sharing, parts of a whole, or parts of a set. TE: A2, A4, A8, A10-A11, A14-A15, A16, A22, A24, A26, A28, A34, A36, B2, B4, B6 TE: B2-B3, B4-B5, B6-B7, B8-B9, B10-B11 Students count by 2s to create patterns of even numbers. TE: A6-A7 TE: B14-B15, B16-B17, B18-B19, B20-B21, B22- B23, B24-B25, B26-B27, B28-B29, B30-B31, B32-B33, B34-B35, B36-B37, B38-B39, B40-B41, B42-B43, B44-B45, B46-B47, B48-B49, B50-B51, B52-B53 PO 6: Compare and order benchmark fractions. TE: B34-B35, B40-B41, B42-B43, B44-B45, B46- B47, B48-B49, B50-B51, B52-B53 Concept 2: Numerical Operations Understand and apply numerical operations and their relationship to one another. PO 1: Add and subtract whole numbers to four digits. PO 2: Create and solve word problems based on addition, subtraction, multiplication, and division. TE: A2-A3, A4-A5, A8-A9, A10-A11 TE: A9, A11, A17, A19, A23, A25, A27, A29, A31, A34-A35, A40-A41, A42-A43, A45, A46- A47, A48-A49, A50-A51 PO 3: Demonstrate the concept of multiplication and division using multiple models. PO 4: Demonstrate fluency of multiplication and division facts through 10. TE: A12-A13, A14-A15, A16-A17, A18-A19, A20- A21, A22-A23, A24-A25, A26-A27, A28-A29, A30-A31, A32-A33, A34-A35, A36-A37, A38-A39, A40-A41, A42-A43, A44-A45, A46-A47, A48-A49, A50-A51 TE: A16-A17, A18-A19, A20-A21, A22-A23, A24- A25, A26-A27, A28-A29, A30-A31, A32-A33, A38-A39, A40-A41, A42-A43, A44-A45 15

Articulated by Grade Level Grade 3 PO 5: Apply and interpret the concept of multiplication and division as inverse operations to solve problems. PO 6: Describe the effect of operations (multiplication and division) on the size of whole numbers. PO 7: Apply commutative, identity, and zero properties to multiplication and apply the identity property to division. TE: A38-A39, A40-A41, A42-A43, A44-A45 TE: A12-A13, A14-A15, A16-A17, A18-A19, A20- A21, A22-A23, A24-A25, A26-A27, A28-A29, A30-A31, A32-A33, A34-A35, A36-A37, A38-A39, A40- A41, A42-A43, A44-A45, A46-A47, A48-A49, A50-A51 TE: A18, A20-A21, A25, A26-A27, A29, A30-A31, A33, A46-A47 Concept 3: Estimation Use estimation strategies reasonably and fluently while integrating content from each of the other strands. PO 1: Make estimates appropriate to a given TE: B12-B13 situation or computation with whole numbers. Strand 2: Data Analysis, Probability, and Discrete Mathematics Concept 1: Data Analysis (Statistics) Understand and apply data collection, organization, and representation to analyze and sort data. PO 1: Collect, record, organize, and display data using frequency tables, single bar graphs, or single line graphs. PO 2: Formulate and answer questions by interpreting and analyzing displays of data, including frequency tables, single bar graphs, or single line graphs. Concept 2: Probability Understand and apply the basic concepts of probability. In Grade 3, there are no performance objectives in this concept. Performance objectives begin in Grade 4. Concept 3: Systematic Listing and Counting Understand and demonstrate the systematic listing and counting of possible outcomes. PO 1: Represent all possibilities for a variety of counting problems using arrays, charts, and systematic lists; draw conclusions from these representations. PO 2: Solve a variety of problems based on the multiplication principle of counting. Understand and apply vertex-edge graphs. PO 1: Color complex maps using the least number of colors and justify the coloring. TE: A2, A4, A8, A10-A11, A14-A15, A16, A22, A24, A26, A28, A34, A36, B2, B4, B6 Concept 4: Vertex Edge Graphs 16

Articulated by Grade Level Grade 3 PO 2: Investigate properties of vertex-edge graphs a: circuits in a graph, b: weights on edges, and c: shortest path between two vertices. PO 3: Solve problems using vertex-edge graphs. Strand 3: Patterns, Algebra, and Functions Concept 1: Patterns Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands. PO 1: Recognize, describe, extend, create, and find TE: A6-A7, A16-A17, A18, A20-A21, A27, A30- missing terms in a numerical sequence. A31, B10-B11 PO 2: Explain the rule for a given numerical TE: A16-A17, A18, A20-A21, A30-A31 sequence and verify that the rule works. Concept 2: Functions and Relationships Describe and model functions and their relationships. PO 1: Recognize and describe a relationship between two quantities, given by a chart, table or graph, in which the quantities change proportionally, using words, pictures, or expressions. PO 2: Translate between the different representations of whole number relationships, including symbolic, numerical, verbal, or pictorial. TE: C16-C17, C20 TE: A2, A4, A8, A10-A11, A14-A15, A16, A22, A24, A26, A28, A34, A36, B2, B4, B6 Concept 3: Algebraic Representations Represent and analyze mathematical situations and structures using algebraic representations. PO 1: Record equivalent forms of whole numbers to TE: A2, A4, A8, A10-A11, A14-A15, A16, A22, six digits by constructing models and using numbers. A24, A26, A28, A34, A36, B2, B4, B6 PO 2: Use a symbol to represent an unknown TE: A48-A49 quantity in a given context. PO 3: Create and solve simple one-step equations TE: A48-A49 that can be solved using addition and multiplication facts. Concept 4: Analysis of Change Analyze how changing the values of one quantity corresponds to change in the values of another quantity. In Grade 3, there are no performance objectives in this concept. Performance objectives begin in Grade 4. Strand 4: Geometry and Measurement Concept 1: Geometric Properties Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships. PO 1: Describe sequences of 2-dimensional figures created by increasing the number of sides, changing size, or changing orientation. Students identify congruent figures in different orientations. They identify shapes in a table with increasing numbers of sides and vertices. TE: C20, C30-C31, C32-C33 17

Articulated by Grade Level Grade 3 PO 2: Recognize similar figures. Students explore congruent figures. TE: C30-C31, C32-C33 PO 3: Identify and describe 3-dimensional figures including their relationship to real world objects: sphere, cube, cone, cylinder, pyramids, and rectangular prisms. PO 4: Describe and compare attributes of two- and TE: C8-C9, C10-C11, C12-C13, C14-C15, C16- three-dimensional figures. C17, C18-C19, C20-C21, C22-C23, C24-C25, C26-C27, C28-C29, C30-C31, C32-C33, C34- C35, C36-C37 Concept 2: Transformation of Shapes Apply spatial reasoning to create transformations and use symmetry to analyze mathematical situations. Students are expected to: PO 1: Identify a translation, reflection, or rotation and model its effect on a 2-dimensional figure. Students are expected to: PO 2: Identify, with justification, all lines of symmetry in a 2-dimensional figure. Students identify congruent figures in different orientations. TE: C30-C31, C32-C33 TE: C34-C35, C36-C37 Concept 3: Coordinate Geometry Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands. In Grade 3, there are no performance objectives in this concept. Performance objectives begin in Grade 4. Concept 4: Measurement Understand and apply appropriate units of measure, measurement techniques, and formulas to determine measurements. PO 1: Determine elapsed time a: across months using a calendar b: by hours and half hours using a clock. PO 2: Apply measurement skills to measure length, weight, and capacity using US Customary units. PO 3: Convert units of length, weight, and capacity a: inches or feet to yards, b: ounces to pounds, and c: cups to pints, pints to quarts, quarts to gallons. PO 4: Determine the area of a rectangular figure using an array model. 18

Articulated by Grade Level Grade 3 PO 5: Measure and calculate perimeter of 2- dimensional figures Strand 5: Structure and Logic Concept 1: Algorithms and Algorithmic Thinking Use reasoning to solve mathematical problems. In Grade 3, there are no performance objectives in this concept. Performance objectives begin in Grade 4. Concept 2: Logic, Reasoning, Problem Solving and proof Evaluate situations, select problem-solving strategies, draw logical conclusions, develop and describe solutions, and recognize their applications. Students are expected to: PO 1: Analyze a problem situation to determine the question(s) to be answered. PO 2: Identify relevant, missing, and extraneous information related to the solution to a problem. PO 3: Select and use one or more strategies to efficiently solve the problem and justify the selection. PO 4: Determine whether a problem to be solved is similar to previously solved problems, and identify possible strategies for solving the problem. PO 5: Represent a problem situation using any combination of words, numbers, pictures, physical objects, or symbols. PO 6: Summarize mathematical information, explain reasoning, and draw conclusions. PO 7: Analyze and evaluate whether a solution is reasonable, is mathematically correct, and answers the question. PO 8: Make and test conjectures based on data (or information) collected from explorations and experiments. TE: A9, A11, A17, A19, A23, A25, A27, A29, A31, A34-A35, A40-A41, A42-A43, A45, A46- A47, A48-A49, A50-A51, C28-C29 TE: A9, A11, A17, A19, A23, A25, A27, A29, A31, A34-A35, A40-A41, A42-A43, A45, A46- A47, A48-A49, A50-A51, C28-C29 TE: A9, A11, A17, A19, A23, A25, A27, A29, A31, A34-A35, A40-A41, A42-A43, A45, A46- A47, A48-A49, A50-A51, B15, C9, C28-C29 TE: A9, A11, A17, A19, A23, A25, A27, A29, A31, A34-A35, A40-A41, A42-A43, A45, A46- A47, A48-A49, A50-A51, C28-C29 TE: A9, A11, A17, A19, A23, A25, A27, A29, A31, A34-A35, A40-A41, A42-A43, A45, A46- A47, A48-A49, A50-A51, C28-C29 TE: A9, A11, A13, A16-A17, A18-A19, A20-A21, A23, A25, A27, A29, A31, A34-A35, A39, A40- A41, A42-A43, A44-A45, A46-A47, A48-A49, A50-A51, B29, B53, C21, C28-C29, C33 TE: A9, A11, A13, A17, A19, A23, A25, A27, A29, A31, A34-A35, A40-A41, A42-A43, A45, A46-A47, A48-A49, A50-A51, C28-C29 TE: C28-C29 19

to the Arizona Mathematics Standards Articulated by Grade Level Grade Four Arizona Mathematics Standards Articulated by Grade Level Grade 4 Grade 4 Strand 1: Number and Operations Concept 1: Number Sense Understand and apply numbers, ways of representing numbers, and the relationships among numbers and different number systems. PO 1: Express whole numbers, fractions, decimals, and percents using and connecting multiple representations. PO 2: Compose and decompose whole numbers using factors and multiples. PO 3: Express fractions as fair sharing, parts of a whole, parts of a set, and locations on a real number line. TE: B2-B3, B4-B5, B6-B7, B8-B9, B10-B11, B12- B13, B14-B15, B16-B17, B18-B19, B20-B21, B22-B23, B24-B25, B26-B27, B28-B29, B30-B31, B32-B33, B34-B35, B36-B37, B38-B39, B40-B41, B42-B43, B44-B45, B46-B47 TE: A2-A3, A4-A5, A6-A7, A8-A9, A10-A11, A12- A13, A14-A15, A16-A17, A18-A19, A20-A21, A22-A23, A24-A25, A26-A27, A28-A29, A30-A31, A32-A33, A34-A35, A36-A37, A38-A39, A40-A41, A42-A43, A44-A45, A46-A47, A48-A49, A50-A51, A52-A53, A54-A55, C2-C3, C4-C5, C6-C7, C8- C9, C10-C11, C12-C13, C14-C15, C16-C17, C18-C19, C20-C21 TE: B6-B7, B8-B9,M B10-B11, B12-B13, B14- B15, B16-B17, B18-B19, B20-B21, B22-B23, B44-B45, B46-B47 PO 4: Compare and order decimals to hundredths. TE: B36-B37, B38-B39, B40-B41, B42-B43, B44- B45, B46-B47 PO 5: Use simple ratios to describe problems in context. TE: B6-B7, B8-B9, B10-B11, B12-B13, B14-B15, B16-B17, B18-B19, B20-B21, B22-B23, B28-B29, B30-B31, B32-B33, B44-B45, B46-B47 Concept 2: Numerical Operations Understand and apply numerical operations and their relationship to one another. PO 1: Add and subtract decimals through hundredths including money to $1000.00 and fractions with like denominators. PO 2: Use multiple strategies to multiply whole numbers a: two-digit by two-digit and TE: A38-A39, A40-A41 b: multi-digit by one-digit. TE: A10-A11, A26-A27, A28-A29, A30-A31, A32- A33, A34-A35, C2-C3, C18-C19, C20-C21 PO 3: Demonstrate fluency of multiplication and division facts through 12. TE: A2-A3, A4-A5, A6-A7, A8-A9, A10-A11, A12- A13, A14-A15, A16-A17, A18-A19, A20-A21, A22-A23, A42-A43, A44-A45, A46-A47, A48-A49, A50-A51, A52-A53, C2-C3, C4-C5, C6-C7, C8- C9, C10-C11, C12-C13, C14-C15, C16-C17 20

Articulated by Grade Level Grade 4 PO 4: Use multiple strategies to divide whole numbers. PO 5: Apply associative and distributive properties to solve multiplication and division problems. TE: A42-A43, A44-A45, A46-A47, A48-A49, A50- A51, A52-A53, A54-A55 TE: A24-A25, A26-A27, A28-A29, A30-A31, A32- A33, A34-A35, A38-A39, A40-A41, A44-A45, A52-A53, C4-C5, C6-C7, C8-C9, C10-C11, C12- C13, C14-C15, C16-C17, C18-C19, C20-C21 PO 6: Apply order of operations with whole numbers. Students apply the order of operations with whole numbers as they break numbers apart to multiply. TE: A24-A25, A26-A27, A28-A29, A30-A31, A32- A33, A40-A41, C6-C7, C8-C9, C10-C11, C12- C13, C18-C19, C20-C21 Concept 3: Estimation Use estimation strategies reasonably and fluently while integrating content from each of the other strands. PO 1: Use benchmarks as meaningful points of TE: B4-B5, B12-B13, B14-B15, B16-B17, B20- comparison for whole numbers, decimals, and B21, B22-B23, B28-B29, B30-B31, B32-B33, fractions. B34-B35, B36-B37, B38-B39, B40-B41, B42-B43, PO 2: Make estimates appropriate to a given situation or computation with whole numbers and fractions. B44-B45, B46-B47 TE: B4-B5, B12-B13 Strand 2: Data Analysis, Probability, and Discrete Mathematics This Concept 1: Data Analysis (Statistics) Understand and apply data collection, organization, and representation to analyze and sort data. PO 1: Collect, record, organize, and display data using double bar graphs, single line graphs, or circle graphs. PO 2: Formulate and answer questions by interpreting and analyzing displays of data, including double bar graphs, single line graphs, or circle graphs. PO 3: Use median, mode, and range to describe the distribution of a given data set. PO 4: Compare two sets of related data. 21

Articulated by Grade Level Grade 4 Concept 2: Probability Understand and apply the basic concepts of probability. PO 1: Describe elements of theoretical probability by listing or drawing all possible outcomes of a given event and predicting the outcome using word and number benchmarks. Concept 3: Systematic Listing and Counting Understand and demonstrate the systematic listing and counting of possible outcomes. PO 1: Construct tree diagrams to solve problems in context by a: representing all possibilities for a variety of counting problems, b: explaining how its properties relate to the problem, c: representing the same counting problem in multiple ways, and d: drawing conclusions. PO 2: Justify that all possibilities have been enumerated without duplication. Understand and apply vertex-edge graphs. PO 1: Demonstrate the connection between map coloring and vertex coloring. PO 2: Construct vertex-edge graphs to represent concrete situations and identify paths and circuits. Concept 4: Vertex Edge Graphs PO 3: Solve conflict problems by constructing and coloring vertex-edge graphs. Strand 3: Patterns, Algebra, and Functions Concept 1: Patterns Identify patterns and apply pattern recognition to reason mathematically while integrating content from each of the other strands. PO 1: Recognize, describe, create, extend, and find TE: A8-A9, A10-A11, A12-A13, A35, C2-C3, C4- missing terms in a numerical sequence involving C5, C15 whole numbers using all four basic operations. 22

Articulated by Grade Level Grade 4 PO 2: Explain the rule for a given numerical TE: A8-A9, A10-A11, A12-A13, A35, C2-C3, C4- sequence, verify that the rule works, and use the rule C5, C15 to make predictions. Concept 2: Functions and Relationships Describe and model functions and their relationships. In Grade 4, there are no performance objectives in this concept. Concept 3: Algebraic Representations Represent and analyze mathematical situations and structures using algebraic representations. PO 1: Use a symbol to represent an unknown quantity in a simple algebraic expression involving all operations. PO 2: Create and solve one-step equations that can be solved using addition, subtraction, multiplication, and division of whole numbers. The underscore is used to represent a missing quantity in a numerical expression or equation. TE: A2-A3, A4-A5, A6, A8-A9, A10-A11, A12- A13, A14, A16-A17, A18-A19, A20-A21, A23, A25, A26-A27, A28, A30, A32, A34-A35, A42, A44-A45, A46-A47, A48-A49, A50-A51, A52-A53, B3 (#30), B25 (#20), C2-C3, C4-C5, C6-C7, C8- C9, C10-C11, C12-C13, C15, C16-C17 Students complete number sentences involving operations with whole numbers. TE: A2-A3, A4-A5, A6-A7, A8-A9, A10-A11, A12- A13, A14, A16-A17, A18-A19, A20-A21, A23, A24-A25, A26-A27, A28, A30, A32, A34-A35, A42, A44-A45, A46-A47, A48-A49, A50-A51, A52-A53, C2-C3, C4-C5, C6-C7, C8-C9, C10- C11, C12-C13, C15, C16-C17 Concept 4: Analysis of Change Analyze how changing the values of one quantity corresponds to change in the values of another quantity. PO 1: Identify the change in a quantity over time and make simple predictions. Strand 4: Geometry and Measurement Concept 1: Geometric Properties Analyze the attributes and properties of 2- and 3- dimensional figures and develop mathematical arguments about their relationships. PO 1: Draw and describe the relationships between points, lines, line segments, rays, and angles including parallelism and perpendicularity. PO 2: Justify which objects in a collection match a given geometric description. TE: C22-C23, C24-C25 23

Articulated by Grade Level Grade 4 PO 3: Describe and classify triangles by angles and sides. PO 4: Recognize which attributes (such as shape or area) change and which do not change when 2- dimensional figures are cut up or rearranged. PO 5: Recognize and draw congruent figures, and match them in a given collection. PO 6: Draw right, acute, obtuse, and straight angles and identify these angles in other geometric figures. PO 7: Recognize the relationship between a 3- dimensional figure and its corresponding net(s). TE: C36-C37, C38-C39 Concept 2: Transformation of Shapes In Grade 4, there are no performance objectives in this concept. Concept 3: Coordinate Geometry Specify and describe spatial relationships using rectangular and other coordinate systems while integrating content from each of the other strands. PO 1: Name, locate, and graph points in the first quadrant of the coordinate plane using ordered pairs. PO 2: Plot line segments in the first quadrant of the coordinate plane using a set of ordered pairs in a table. PO 3: Construct geometric figures with vertices at points on the coordinate plane. TE: C39 (#7, #8) 24