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- 1. 3rd Grade Math Curriculum Map Isaac School District No. 5 Quarter 1 Unit Name and Description: Number Sense, Addition & Subtraction Cluster 1 Big Ideas/Enduring Understandings Essential Question(s) Numbers can be represented in many ways and are used to solve Why is it important to learn place everyday problems using a variety of methods. value? How can numbers be There are relationships between numbers. represented? The location of a digit determines its place value. What is the difference between comparing and ordering whole AZ Essential Learning Key Summative Standard Knowledge Skills Vocabulary Assessment S3C3PO1 Equivalent Forms of Whole Record equivalent forms of whole number Ones Numbers; Models through six digits by constructing models and Tens using numbers. Hundreds S1C1PO1 Whole Numbers; Multiple [Model] whole numbers through six digits using and One Thousand Representations connecting multiple representations. Ten Thousands Hundred [Analyze] whole numbers through six digits using Thousands and connecting multiple representations. Standard Form S1C1PO2 Place value; Whole numbers Compare whole numbers through six digits by applying Expanded Form the Word Form concept of place value. Ordinal Numbers Equal Order whole numbers through six digits by To S1C1PO3 Money; Coins; Bills Count money using coins and bills to Less Than Greater $100.00. Represent money using coins Than Not Equal To* = POs previously introduced Bold = Priority PO 1Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 2. 3rd Grade Math Curriculum Map Isaac School District No. 5 S1C2PO1 Whole Numbers Add whole number to four digits. Order Value Subtract whole numbers to four digits. Place Sum Addend S1C2PO2* Word Problems; Create word problems based on addition, subtraction, Addition Addition; Subtraction; multiplication, Difference Multiplication; Division and division. Subtractio S3C3PO2 Symbol; Unknown Quantities Use a symbol to represent an unknown quantity in a given n context. Commutativ e property S3C3PO3 One-Step Equations; Addition Solve simple one-step equations that can be solved using Zero property and addition multiplication facts. Associativ multiplication facts e property S5C2PO2 Relevant, Missing and Identify relevant information related to the solution to a Regroup Extraneous problem. Estimate Information Round Identify missing information related to the solution Front end to a problem. estimatio n Identify extraneous information related to the solution Friendly/ to a problem. Compatibl e numbers S5C2PO6 Mathematical Information; Summarize mathematical information. Clustering Reasoning; Conclusions Relevant Explain reasoning of mathematical informatio n Missing information. Draw conclusions of informatio n mathematical information. Extraneou s informatio n Draw conclusion* = POs previously introduced Bold = Priority PO 2Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 3. 3rd Grade Math Curriculum Map Isaac School District No. 5 Quarter 1 Unit Name and Description: Data Analysis Cluster 2 Big Ideas/Enduring Understandings Essential Question(s) Data can be collected, organized and analyzed to help us How can we collect, organize, and display data? make valid inferences, decisions, and arguments in real world situations. What types of data would you collect, organize and display? What conclusions can you make from data? AZ Standard Essential Learning Key Summative Knowledge Skills Vocabulary Assessment S2C1PO2 Frequency tables; Formulate and answer questions by interpreting Frequency Single bar graphs; and analyzing displays of data, including tables Single Single line graphs frequency tables, single bar graphs, or single bar graphs line graphs. Single line S5C2PO7* Solutions; Reasonable; Analyze and evaluate whether a solution is graphs Data Question; reasonable. Record Mathematically Correct Arrays Charts Analyze and evaluate whether a solution is Systematic mathematically correct. lists Counting Analyze and evaluate whether a solution answers the question. S2C1PO1 Frequency tables; Single Collect, record, organize, and display data using bar graphs; Single line frequency tables graphs single bar graphs single line graphs.* = POs previously introduced Bold = Priority PO 3Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 4. 3rd Grade Math Curriculum Map Isaac School District No. 5 S2C3PO1* Counting Problems; Represent all possibilities for a variety of counting Possibilities; Arrays; problems Charts; Systematic lists; using arrays, charts, and systematic lists. Conclusions; Representations Draw conclusions from these representations. S2C3PO2 Multiplication principle Solve a variety of problems based on the of counting multiplication principle of counting. S5C2PO6* Mathematical information; Summarize mathematical information Reasoning; Conclusions Draw conclusions of mathematical information. Defend conclusion of* = POs previously introduced Bold = Priority PO 4Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 5. 3rd Grade Math Curriculum Map Isaac School District No. 5 Quarter 2 Unit Name and Description: Multiplication & Division Cluster 3 Big Ideas/Enduring Understandings Essential Question(s) Multiplication and division is the grouping and ungrouping of objects How are multiplication and division alike? using patterns to solve everyday real world problems. What happens to the value of a number when you multiply it? There is an inverse relationship between multiplication and division. How might you use multiplication or division to solve problems in the real world? AZ Essential Learning Key Summative Standard Knowledge Skills Vocabulary Assessment S1C2PO3 Multiplication and Demonstrate the concept of multiplication and Multiplication Division; Concept; division using multiple models. Division Models Equal groups S1C1PO4* Sets of Whole Numbers Sort whole numbers into sets and justify the sort. Multiplication Array S1C2PO2 Word Problems; Addition; Create word problems based on addition, subtraction, Factors Subtraction; multiplication and division. Product Multiplication; Division Multiply Solve word problems based on addition, Multiples subtraction, multiplication and division. Divisibility S1C2PO4 Multiplication and Division Demonstrate fluency of multiplication and division facts Inverse Fluency through 10. operations Operation s* = POs previously introduced Bold = Priority PO 5Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 6. 3rd Grade Math Curriculum Map Isaac School District No. 5 S1C2PO5 Multiplication and Division; Apply the concept of multiplication and division as inverse Identity property Inverse operations operations to solve problems. Zero property Interpret the concept of multiplication and division as Commutative inverse operations to solve problems. property Arrays S1C2PO6* Whole Numbers; Operations; [Compare] the effect of operations (multiplication and Charts Effect; Multiplication; Division division) Systematic Whole Numbers Operations; on the size of whole numbers. lists S1C2PO7 Commutative, Zero and Identity Apply commutative, identity and zero properties to Numerical Properties; Division multiplication. sequence Apply the identity property to division. S2C3PO1 Counting Problems; Possibilities; Represent all possibilities for a variety of counting Arrays; Charts; Systematic problems lists; Conclusions; using arrays, charts, and systematic lists. Representations Draw conclusions from these representations. S3C1PO2 Numerical Sequence Rule Explain the rule for a given numerical sequence. Verify that the rule for a given numerical sequence works. S5C2PO3* Strategies; Problems Select and use one or more strategies to efficiently solve the problem. Justify the strategy (ies) used to efficiently solve the S5C2PO6* Mathematical Information; Summarize mathematical information. Reasoning; Conclusions Explain reasoning of mathematical information. [Defend] conclusions of* = POs previously introduced Bold = Priority PO 6Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 7. 3rd Grade Math Curriculum Map Isaac School District No. 5 S5C2PO7* Solutions; Reasonable; Analyze and evaluate whether a solution is reasonable. Question; Mathematically Correct Analyze and evaluate whether a solution is mathematically correct. Analyze and evaluate whether a solution answers the question.* = POs previously introduced Bold = Priority PO 7Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 8. 3rd Grade Math Curriculum Map Isaac School District No. 5 Quarter 2 Unit Name and Description: Geometry Cluster 3 Big Ideas/Enduring Understandings Essential Question(s) Our environment is made up of 2 dimensional & 3 dimensional figures. Why is it important to understand 2 and 3-dimensional figures? The attributes of 2 dimensional & 3 dimensional figures can help us How do you describe a 2- or 3-dimensional figure using its attributes? describe the environment and solve real-life problems. AZ Essential Learning Key Summative Standard Knowledge Skills Vocabulary Assessment S4C1PO4 Two and three-dimensional Describe and compare attributes of two- and Attributes Figures three- dimensional figures. 2-dimensional 3- S1C2PO6 Whole Numbers; Operations; [Compare] the effect of operations (multiplication and dimensional Effect; Multiplication; Division division) on the size of whole numbers. Similar Figures S4C1PO1 Sequences of 2-Dimensional [Create] sequences of 2-dimensional figures created by Sequence Figures; Number of sides; increasing the number of sides, changing size or Sphere Size; Orientation changing orientation. Cube Cone S4C2PO2 Symmetry; 2-dimensional figure Identify all lines of symmetry in a 2-dimensional figure. Cylinder Pyramid Justify all lines of symmetry in a 2-dimensional figure. Rectangular prism Translations Reflections Rotation* = POs previously introduced Bold = Priority PO 8Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 9. 3rd Grade Math Curriculum Map Isaac School District No. 5 S4C4PO4 Area of Arrays; Rectangular Determine the area of a rectangular figure using an array Line of symmetry figure; Model model. Symmetrical Area Perimete r Array Square unit(s) S4C4PO5 Perimeter; 2-dimensional figures Measure perimeter of 2-dimensional figures. Calculate perimeter of 2-dimensional figures. S5C2PO3 Strategies; Problem Select and use one or more strategies to efficiently solve the problem. S5C2PO6* Mathematical Information; Summarize mathematical information. Reasoning; Conclusions Explain reasoning of mathematical information. [Defend] conclusions of S5C2PO7 Solutions; Reasonable; Analyze and evaluate whether a solution is reasonable. Question; Mathematically Correct Analyze and evaluate whether a solution is mathematically correct. Analyze and evaluate whether a solution answers the question.* = POs previously introduced Bold = Priority PO 9Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 10. 3rd Grade Math Curriculum Map Isaac School District No. 5 Quarter 2 Unit Name and Description: Measurement Cluster 4 Big Ideas/Enduring Understandings Essential Question(s) Measurement is assigning a numerical unit to an attribute of a real What are some examples of when you might need to determine the world object. correct unit of measurement? There are appropriate units of measurement to use in different What are some different ways of measuring an object? situations. Why would we measure the area or perimeter of 2-dimensional objects? When would you need to find the area or perimeter of 2-dimensional objects? What might be some tools you can use to measure objects? AZ Essential Learning Key Summative Standard Knowledge Skills Vocabulary Assessment S4C4PO2 Length, Weight and Apply measurement skills to measure length, weight Measure Capacity; Measurement and Length Skills; US Customary units capacity using US Customary units. Weight S1C3PO1* Estimation; Situation; Make estimates appropriate to a given situation or Capacity Computation; Whole numbers computation with whole numbers. US Customary S4C4PO3 Conversions; Length; Weight; Convert units of length, weight, and capacity units Capacity inches or feet to yards, Equal groups ounces to pounds, and Multiplication cups to pints, pints to quarts, quarts to gallons. Array Factors Product Commutativ e* = POs previously introduced Bold = Priority PO 10Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 11. 3rd Grade Math Curriculum Map Isaac School District No. 5 S4C4PO4* Area of Arrays; Rectangular Determine the area of a rectangular figure using an array Property figure; Model model. Multiply Elapsed time Hours Minutes S4C4PO5* Perimeter; 2-dimensional figures Measure perimeter of 2-dimensional figures. Half hours Quarter Hour Calculate perimeter of 2-dimensional figures. Cup S2C1PO2 Frequency tables; Single bar Formulate and answer questions by interpreting and Foot graphs; Single line graphs analyzing displays of data, including frequency tables, Pint single bar graphs, or single line graphs. Miles Poun d S2C1PO1 Frequency tables; Single bar Collect, record, organize, and display data using Ruler graphs; Single line graphs • Frequency tables Weight scale • Single bar graphs Measuring cup • Single line graphs Inch Half inch S5C2PO3* Strategies; Problem Select and use one or more strategies to efficiently solve Yard the Quart problem. Gallon Ounce Justify the strategy (ies) used to efficiently solve the Area S5C2PO6* Mathematical Information; Summarize mathematical information. Perimete Reasoning; Conclusions r Array Explain reasoning of mathematical Square unit(s) 2-Dimensional information. [Defend] conclusions of* = POs previously introduced Bold = Priority PO 11Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 12. 3rd Grade Math Curriculum Map Isaac School District No. 5 S5C2PO7* Solutions; Reasonable; Analyze and evaluate whether a solution is reasonable. Question; Mathematically Correct Analyze and evaluate whether a solution is mathematically correct. Analyze and evaluate whether a solution answers the question.* = POs previously introduced Bold = Priority PO 12Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 13. 3rd Grade Math Curriculum Map Isaac School District No. 5 Quarter 2 Unit Name and Description: Patterns, Algebra, & Functions Cluster 5 Big Ideas/Enduring Understandings Essential Question(s) Patterns occur everywhere in nature. Why are finding patterns Patterns can be recognized, generalized, and extended with important? Where might you find words and symbols. patterns? Variables are symbols that take the place of numbers or ranges of How can two or more numbers be related? numbers. Functions can show the relationship between two sets of How do patterns help you think mathematically? numbers. AZ Essential Learning Summative Key Vocabulary Standard Knowledge Skills Assessment S3C2PO1 Relationship between two Recognize a relationship between two quantities, Quantities quantities; Chart; Table; given by a chart, table or graph, in which the Chart Graph; quantities change Table Words; Pictures; Expressions proportionally, using words, pictures or expressions. Graph Pattern Describe a relationship between two quantities, Function given by a chart, table or graph, in which the Add quantities change proportionally, using words, Addition S1C2PO2* Word Problems; pictures, or expressions. Create word problems based on addition, subtraction, Subtract Addition; Subtraction; multiplication, Subtractio Multiplication; Division and division. n Equivalent Unknown quantity* = POs previously introduced Bold = Priority PO 13Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 14. 3rd Grade Math Curriculum Map Isaac School District No. 5 S1C1PO4 Sets of Whole Numbers Sort whole numbers into sets and justify the sort. Solve Combinations S3C1PO2 Numerical Sequence Rule Explain the rule for a given numerical sequence. Verify that the rule for a given numerical sequence works. S3C2PO2 Whole Number Relationships; Translate Representations S5C2PO1 Problem Situations; Analyze a problem situation to determine the question(s) Questions to be answered. S5C2PO3* Strategies; Problem Select and use one or more strategies to efficiently solve the problem. Justify the strategy (ies) used to efficiently solve the problem. S5C2PO5 Problem Situations; Numbers; Represent a problem situation using any combinations of Pictures; Physical objects; words, numbers, pictures, physical objects or symbols. Symbols* = POs previously introduced Bold = Priority PO 14Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 15. 3rd Grade Math Curriculum Map Isaac School District No. 5 S5C2PO6* Mathematical Summarize mathematical information. Information; Reasoning; Conclusions Explain reasoning of mathematical information. [Defend] conclusions of* = POs previously introduced Bold = Priority PO 15Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 16. 3rd Grade Math Curriculum Map Isaac School District No. 5 Quarter 3 Unit Name and Description: Fractions Cluster 6 Big Ideas/Enduring Understandings Essential Question(s) Fractions represent equal parts or equal-sized portions of a whole or When might you use fractions? set. How are parts of a whole represented? How are parts of a set represented? What does it mean to be close to a whole? AZ Essential Learning Key Summative Standard Knowledge Skills Vocabulary Assessment S1C1PO5 Benchmark Fractions; Fair Express benchmark fractions as fair sharing, Fractions sharing; Parts of a whole; parts of a whole, or parts of a set. Numerator Parts of a set Denominator S1C1PO6 Benchmark Fractions Compare benchmark fractions. Order benchmark fractions. S5C2PO4 Problem Solving; Strategies Determine whether a problem to be solved is similar to previously solved problems. Identify possible strategies for solving the problem.* = POs previously introduced Bold = Priority PO 16Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 17. 3rd Grade Math Curriculum Map Isaac School District No. 5 S5C2PO5* Problem Situations; Numbers; Represent a problem situation using any combinations of Pictures; Physical objects; words, numbers, pictures, physical objects or symbols. Symbols S5C2PO6* Mathematical Information; Summarize mathematical information. Reasoning; Conclusions Explain reasoning of mathematical information. [Defend] conclusions of* = POs previously introduced Bold = Priority PO 17Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 18. 3rd Grade Math Curriculum Map Isaac School District No. 5 Quarter 3 Unit Name and Description: Number Sense, Addition & Subtraction Cluster 7 Big Ideas/Enduring Understandings Essential Question(s) Numbers can be represented in many ways and are used to solve Why is it important to learn place everyday problems using a variety of methods. value? How can numbers be There are relationships between numbers. represented? The location of a digit determines its place value. What is the difference between comparing and ordering whole AZ Essential Learning Key Summative Standard Knowledge Skills Vocabulary Assessment S3C3PO1 Equivalent Forms of Whole Record equivalent forms of whole number Ones Numbers; Models through six digits by constructing models and Tens using numbers. Hundreds S1C1PO1 Whole Numbers; Multiple [Model] whole numbers through six digits using and One Thousand Representations connecting multiple representations. Ten Thousands Hundred [Analyze] whole numbers through six digits using Thousands and connecting multiple representations. Standard Form S1C1PO2 Place value; Whole numbers Compare whole numbers through six digits by applying Expanded Form the Word Form concept of place value. Ordinal Numbers Equal Order whole numbers through six digits by To S1C1PO3 Money; Coins; Bills Count money using coins and bills to Less Than Greater $100.00. Represent money using coins Than Not Equal To* = POs previously introduced Bold = Priority PO 18Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 19. 3rd Grade Math Curriculum Map Isaac School District No. 5 S1C2PO1 Whole Numbers Add whole number to four digits. Order Value Subtract whole numbers to four digits. Place Sum Addend S1C2PO2* Word Problems; Create word problems based on addition, subtraction, Addition Addition; Subtraction; multiplication, Difference Multiplication; Division and division. Subtractio S3C3PO3 One-Step Equations; Addition Solve simple one-step equations that can be solved using n and addition multiplication facts. Commutativ multiplication facts e property S1C3PO1 Estimation; Situation; Make estimates appropriate to a given situation or Zero property Computation; computation with whole numbers. Associativ Whole numbers e property Regroup Estimate Round S5C2PO2 Relevant, Missing and Identify relevant information related to the solution to a Front end Extraneous problem. estimatio Information n Identify missing information related to the solution Friendly/ to a problem. Compatibl e numbers Identify extraneous information related to the solution Clustering to a problem. Relevant informatio S5C2PO6 Mathematical Information; Summarize mathematical information. n Missing Reasoning; Conclusions informatio Explain reasoning of mathematical n Extraneou information. Draw conclusions of s informatio mathematical information. n* = POs previously introduced Bold = Priority PO 19Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 20. 3rd Grade Math Curriculum Map Isaac School District No. 5 S2C3PO1* Counting Problems; Represent all possibilities for a variety of counting Possibilities; Arrays; problems Charts; Systematic lists; using arrays, charts, and systematic lists. Conclusions; Representations Draw conclusions from these representations. S2C3PO2 Multiplication principle Solve a variety of problems based on the of counting multiplication principle of counting. S1C2PO3 Multiplication and Demonstrate the concept of multiplication and Division; Concept; division using multiple models. Models S1C2PO4 Multiplication and Division Demonstrate fluency of multiplication and division facts Fluency through 10. S2C3PO1 Counting Problems; Represent all possibilities for a variety of counting Possibilities; problems Arrays; Charts; using arrays, charts, and systematic lists. Systematic lists; Conclusions; Draw conclusions from these representations. S4C4PO1 Elapsed Time; Months; [Assess] elapsed time Calendar; across months using a calendar Hours; Half hours; Clock by hours and half hours using a clock. S5C2PO6* Mathematical information; Summarize mathematical information Reasoning; Conclusions Draw conclusions of mathematical information. Defend conclusion of* = POs previously introduced Bold = Priority PO 20Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 21. 3rd Grade Math Curriculum Map Isaac School District No. 5 Quarter 3 Unit Name and Description: Geometry Cluster 8 Big Ideas/Enduring Understandings Essential Question(s) Our environment is made up of 2 dimensional & 3 dimensional figures. Why is it important to understand 2 and 3-dimensional figures? The attributes of 2 dimensional & 3 dimensional figures can help us How do you describe a 2- or 3-dimensional figure using its attributes? describe the environment and solve real-life problems. AZ Essential Learning Key Summative Standard Knowledge Skills Vocabulary Assessment S4C1PO4 Two and three-dimensional Describe and compare attributes of two- and Attributes Figures three- dimensional figures. 2-dimensional 3- S4C1PO2 Similar Figures [Compare] similar figures. dimensional Similar Figures S4C1PO3 3-Dimensional Figures; Identify and describe 3-dimensional figures including their Sequence Relationship; Real world relationship to real world objects: sphere, cube, cone, Sphere objects; Sphere; Cube; Cone; cylinder, pyramids, and rectangular prisms. Cube Cylinder; Cone S4C2PO1 Translation; Reflection; Rotation; Identify a translation and model its effect on a 2- Cylinder Model dimensional Pyramid figure. Rectangular prism Identify a reflection and model its effect on a 2- Translations S5C2PO3 Strategies; Problem Select and use one or more strategies to efficiently solve Reflections the Rotation problem. Justify the strategy (ies) used to efficiently solve the* = POs previously introduced Bold = Priority PO 21Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 22. 3rd Grade Math Curriculum Map Isaac School District No. 5 S5C2PO6* Mathematical Information; Summarize mathematical information. Line of symmetry Reasoning; Conclusions Explain reasoning of mathematical information. Symmetrical [Defend] conclusions of mathematical information. Area Perimete r Array Square unit(s) S5C2PO7 Solutions; Reasonable; Analyze and evaluate whether a solution is reasonable. Question; Mathematically Correct Analyze and evaluate whether a solution is mathematically correct. Analyze and evaluate whether a solution answers the question.* = POs previously introduced Bold = Priority PO 22Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 23. 3rd Grade Math Curriculum Map Isaac School District No. 5 Quarter 3 Unit Name and Description: Patterns, Algebra, & Functions Cluster 9 Big Ideas/Enduring Understandings Essential Question(s) Patterns occur everywhere in nature. Why are finding patterns Patterns can be recognized, generalized, and extended with important? Where might you find words and symbols. patterns? Variables are symbols that take the place of numbers or ranges of How can two or more numbers be related? numbers. Functions can show the relationship between two sets of How do patterns help you think mathematically? numbers. AZ Essential Learning Summative Key Vocabulary Standard Knowledge Skills Assessment S3C2PO1 Relationship between two Recognize a relationship between two quantities, Quantities quantities; Chart; Table; given by a chart, table or graph, in which the Chart Graph; quantities change Table Words; Pictures; Expressions proportionally, using words, pictures or expressions. Graph Pattern Describe a relationship between two quantities, Function given by a chart, table or graph, in which the Add quantities change proportionally, using words, Addition *S1C2PO1 Whole Numbers pictures, or expressions. digits. Add whole number to four Subtract Subtractio Subtract whole numbers to four digits. n Equivalent Unknown quantity* = POs previously introduced Bold = Priority PO 23Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 24. 3rd Grade Math Curriculum Map Isaac School District No. 5 S3C1PO1 Numerical Sequence; Missing Recognize missing terms in a numerical sequence. Equation terms Equals Describe missing terms in a numerical Rule sequence. Extend missing terms in a numerical sequence. Create missing terms in a numerical sequence. Find missing S3C3PO2 Symbol; Unknown Quantities Use a symbol to represent an unknown quantity in a given context. S3C3PO3 One-Step Equations; Addition Solve simple one-step equations that can be solved using and addition multiplication facts. multiplication facts Create one-step equations that can be solved using addition multiplication facts. *S5C2PO1 Problem situations; Questions Analyze a problem situation to determine the question(s) to be answered.* = POs previously introduced Bold = Priority PO 24Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 25. 3rd Grade Math Curriculum Map Isaac School District No. 5 *S5C2PO3 Strategies; Problem Select and use one or more strategies to efficiently solve the problem. Justify the strategy (ies) used to efficiently solve the *S5C2PO5 Problem Situations; Numbers; Represent a problem situation using any Pictures; Physical objects; combinations of Symbols words, numbers, pictures, physical objects or symbols. *S5C2PO6 Mathematical Information; Summarize mathematical information. Reasoning; Conclusions Explain reasoning of mathematical information. [Defend] reasoning of *S5C2PO7 Solutions; Reasonable; Question; Analyze and evaluate whether a solution is reasonable. Mathematically Correct Analyze and evaluate whether a solution is mathematically correct. Analyze and evaluate whether a solution answers the question.* = POs previously introduced Bold = Priority PO 25Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 26. 3rd Grade Math Curriculum Map Isaac School District No. 5 Quarter 3 Unit Name and Description: Discrete Mathematics Cluster 10 Big Ideas/Enduring Understandings Essential Question(s) Vertex-edge graphs are used to model and solve problems What conclusions can you make from vertex-edge involving paths, networks, and relationships. graphs? Why do we use vertex-edge graphs? Vertex-edge graphs can represent a real-world maps that helps us find routes and paths. Why is it important to find all the possible combinations of a given set of items? Systematic lists, charts, and arrays help us keep track of finding all possible combinations of a given set of items. AZ Essential Learning Summative Key Vocabulary Standard Knowledge Skills Assessment S2C4PO2 Vertex-Edge Graphs; Investigate properties of vertex-edge graphs Vertex-edge Circuits; Weights; Vertices circuits in a graph graphs weights on edges Circuits shortest path between two vertices. Weight s Paths S2C3PO1* Counting Problems; Possibilities; Represent all possibilities for a variety of counting Vertice Arrays; Charts; Systematic problems s lists; Conclusions; using arrays, charts, and systematic lists. Arrays Representations Charts Draw conclusions from these representations. Systematic S2C4PO1 Color Mapping Color complex maps using the least number of lists Relevant colors and justify the coloring. Extraneous Conjectures Data* = POs previously introduced Bold = Priority PO 26Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 27. 3rd Grade Math Curriculum Map Isaac School District No. 5 S2C4PO3 Vertex-Edge Graphs; Problems Solve problems using vertex-edge graphs. Experiment Coloring maps [Create] problems using vertex-edge graphs. Edge S5C2PO1* Problem situations; Questions Analyze a problem situation to determine the Vertex question(s) to be answered. S5C2PO2* Relevant, Missing and Extraneous Identify relevant information related to the solution to a Information problem. Identify missing information related to the solution to a problem. Identify extraneous information related to the solution to a problem. S5C2PO3* Strategies; Problem Select and use one or more strategies to efficiently solve the problem. Justify the strategy (ies) used to efficiently solve the problem. S5C2PO4* Problem Solving; Strategies Determine whether a problem to be solved is similar to previously solved problems. Identify possible strategies for solving the problem. S5C2PO6* Mathematical Information; Summarize mathematical information. Reasoning; Conclusions Explain reasoning of mathematical information. [Defend] reasoning of* = POs previously introduced Bold = Priority PO 27Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 28. 3rd Grade Math Curriculum Map Isaac School District No. 5 S5C2PO8 Conjectures; Data; Explorations; Make conjectures based on data (or information) Experiments collected from explorations and experiments. Test conjectures based on data (or information) collected from explorations and experiments. [Evaluate] conjectures based on data (or information) collected from exploration and experiments.* = POs previously introduced Bold = Priority PO 28Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 29. 3rd Grade Math Curriculum Map Isaac School District No. 5 Quarter 4 Unit Name and Description: Multiplication and Division Cluster 11 Big Ideas/Enduring Understandings Essential Question(s) There are multiple strategies to multiply and divide whole How are multiplication and division numbers. There is a relationship between multiplication and related? When might you use division. multiplication? When might you use division? What is the value of learning multiplication and division? AZ Essential Learning Key Summative Standard Knowledge Skills Vocabulary Assessment M4S1C2PO3 Multiplication and Division Demonstrate fluency of multiplication facts through Multiplication Fluency facts through 12 12. Division Factor Demonstrate fluency of division facts through 12. Multiple Product M4S1C2PO2 Multiple Strategies of [Develop] multiple strategies to multiply whole numbers Quotient Multiplication two-digit by two-digit and Divisor multi-digit by one-digit. Dividend Array M4S1C2PO4 Multiple Strategies of Division [Develop] multiple strategies to divide whole numbers. Digit Whole number Estimate Fraction* = POs previously introduced Bold = Priority PO 29Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011
- 30. 3rd Grade Math Curriculum Map Isaac School District No. 5 M4S1C3PO2 Estimates; Given situation; [Develop] estimates appropriate to a given situation or Numerator Computation with whole computation with whole numbers and fractions. Denominator numbers and fractions M4S5C2PO5 Problem situation; Combination Represent a problem situation using any combination of of words, numbers, pictures, physical objects, or symbols. words, numbers, pictures,* = POs previously introduced Bold = Priority PO 30Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 8-4-2011

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