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# 3rd grade math curriculum map 2011 2012-1

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### Transcript of "3rd grade math curriculum map 2011 2012-1"

1. 1. 3rd Grade Math Curriculum Map Isaac School District No. 5 Quarter 1 Unit Name and Description: Number Sense, Addition & Subtraction/ Trading Stickers, Combining Coins Unit 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 value? everyday problems using a variety of methods. How can numbers be represented? There are relationships between numbers. What is the difference between comparing and ordering whole The location of a digit determines its place value. numbers? AZ Essential Learning Key Summative Standard Knowledge Skills Vocabulary Assessment S3C3PO1 Equivalent Forms of Whole Record equivalent forms of whole number through six Ones Numbers; Models digits by constructing models and using numbers. Tens Hundreds S1C1PO1 Whole Numbers; [Model] whole numbers through six digits using and One Thousand Multiple Representations connecting multiple representations. Ten Thousands Hundred [Analyze] whole numbers through six digits using and Thousands connecting multiple representations. Standard Form Expanded Form S1C1PO2 Place value; Whole numbers Compare whole numbers through six digits by applying the Word Form concept of place value. Ordinal Numbers Equal To Order whole numbers through six digits by applying the Less Than concept of place value. Greater than* = POs previously introduced Bold = Priority PO 1Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 1/6/2012
3. 3. 3rd Grade Math Curriculum Map Isaac School District No. 5 Quarter 1 Unit Name and Description: Data Analysis/ Surveys and Line Plots Unit 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 Essential Learning Key Summative Standard Knowledge Skills Vocabulary Assessment S2C1PO2 Frequency tables; Formulate and answer questions by interpreting and Frequency tables Single bar graphs; analyzing displays of data, including frequency tables, Single bar graphs Single line graphs single bar graphs, or single line graphs. Single line graphs Data S2C1PO1 Frequency tables; Collect, record, organize, and display data using Record Single bar graphs;  frequency tables Arrays Single line graphs  single bar graphs Charts  single line graphs. Systematic Lists Counting* = POs previously introduced Bold = Priority PO 3Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 1/6/2012
4. 4. 3rd Grade Math Curriculum Map Isaac School District No. 5 S2C3PO1 Counting Problems; Represent all possibilities for a variety of counting problems Possibilities; Arrays; using arrays, charts, and systematic lists. Charts; Systematic lists; Conclusions; Draw conclusions from these representations. Representations S2C3PO2 Multiplication Solve a variety of problems based on the multiplication principle of counting principle of counting. S2C4PO1 Color Color complex maps using the least number of Mapping colors and justify the coloring.* = POs previously introduced Bold = Priority PO 4Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 1/6/2012
5. 5. 3rd Grade Math Curriculum Map Isaac School District No. 5 Quarter 1 (Thru the beginning of Quarter 2) Unit Name and Description: Multiplication & Division/ Collection and Travel Stories Unit 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 Key Summative Standard Learning Vocabulary Assessment Knowledge Skills S1C2PO3 Multiplication; 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 Factors S1C2PO2 Word Problems; Addition; Create word problems based on addition, subtraction, Product Subtraction; multiplication and division. Multiply Multiplication; Multiples Division Solve word problems based on addition, Divisibility subtraction, multiplication and division. Inverse operations S1C2PO4 Multiplication and Division Demonstrate fluency of multiplication and division facts Operations Fluency through 10. Identity property Zero property S1C2PO5 Multiplication and Division; Apply the concept of multiplication and division as inverse Commutative Inverse operations operations to solve problems. property Arrays Interpret the concept of multiplication and division as Charts inverse operations to solve problems.* = POs previously introduced Bold = Priority PO 5Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 1/6/2012
6. 6. 3rd Grade Math Curriculum Map Isaac School District No. 5 S1C2PO6 Whole Numbers; [Compare] the effect of operations (multiplication and division) Systematic lists Multiplication; Division on the size of whole numbers. Numerical Whole Numbers Operations sequence S1C2PO7 Commutative, Zero and Apply commutative, identity and zero properties to Identity Properties; Division multiplication. Apply the identity property to division. S2C3PO1* Counting Problems; Represent all possibilities for a variety of counting problems Possibilities; Arrays; Charts; using arrays, charts, and systematic lists. Systematic lists; Conclusions 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.* = POs previously introduced Bold = Priority PO 6Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 1/6/2012
7. 7. 3rd Grade Math Curriculum Map Isaac School District No. 5 Quarter 2 Unit Name and Description: Measurement Unit Cluster 4a 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 capacity using US Customary units. Length Skills; US Customary Weight units Capacity US Customary S1C3PO1 Estimation; Situation; Make estimates appropriate to a given situation or units Computation; Whole numbers computation with whole numbers. Equal groups Multiplication Array Factors Product Commutative* = POs previously introduced Bold = Priority PO 7Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 1/6/2012
8. 8. 3rd Grade Math Curriculum Map Isaac School District No. 5 S4C4PO3 Conversions; Length; Weight; Convert units of length, weight, and capacity Property Capacity  inches or feet to yards, Multiply  ounces to pounds, and Elapsed time  cups to pints, pints to quarts, quarts to gallons. Hours Minutes Half hours S4C4PO4 Area of Arrays; Rectangular Determine the area of a rectangular figure using an array Quarter Hour figure; Model model. Cup Foot Pint Miles Pound S4C4PO5 Perimeter; 2-dimensional Measure perimeter of 2-dimensional figures. Ruler figures Weight scale Calculate perimeter of 2-dimensional figures. Measuring cup S2C1PO2* Frequency tables; Single bar Formulate and answer questions by interpreting and Inch graphs; Single line graphs analyzing displays of data, including frequency tables, Half inch single bar graphs, or single line graphs. Yard Quart Gallon Ounce S2C1PO1* Frequency tables; Single bar Collect, record, organize, and display data using Area Perimeter graphs; Single line graphs • Frequency tables • Single bar graphs • Single line graphs* = POs previously introduced Bold = Priority PO 8Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 1/6/2012
9. 9. 3rd Grade Math Curriculum Map Isaac School District No. 5 Quarter 2 Unit Name and Description: Geometry/ Perimeter, Angles, and Area Unit Cluster 4b 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 three- 2-dimensional Figures dimensional figures. 3-dimensional Similar Figures S1C2PO6* Whole Numbers; Operations; [Compare] the effect of operations (multiplication and Sequence Effect; Multiplication; Division division) on the size of whole numbers. Sphere Cube Cone S4C1PO1 Sequences of 2-Dimensional [Create] sequences of 2-dimensional figures created by Cylinder Figures; Number of sides; increasing the number of sides, changing size or Pyramid Size; Orientation changing orientation. Rectangular prism S4C4PO5* Perimeter; 2-dimensional figures Measure perimeter of 2-dimensional figures. Translations Reflections Calculate perimeter of 2-dimensional figures. Rotation Line of symmetry Symmetrical S4C1PO2 Similar Figures [Compare] similar figures (This is a Supplemental PO to be taught with Area Perimeter this unit..) Array Square unit(s)* = POs previously introduced Bold = Priority PO 9Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 1/6/2012
10. 10. 3rd Grade Math Curriculum Map Isaac School District No. 5 S4C2PO2 Symmetry; 2-dimensional figure Identify all lines of symmetry in a 2-dimensional figure. Justify all lines of symmetry in a 2-dimensional figure. (This is a Supplemental PO to be taught with this unit..) S2C4PO2 Vertex-Edge Graphs; Investigate properties of vertex-edge graphs Circuits; Weights;  circuits in a graph Vertices  weights on edges  shortest path between two vertices. (This is a Supplemental PO to be taught with this unit..) S2C4PO3 Vertex-Edge Graphs; Problems Solve problems using vertex-edge graphs. [Create] problems using vertex-edge graphs. (This is a Supplemental PO to be taught with this unit..)* = POs previously introduced Bold = Priority PO 10Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 1/6/2012
11. 11. 3rd Grade Math Curriculum Map Isaac School District No. 5 Quarter 2 Unit Name and Description: Multiplication and Division/ Equal Groups Unit Cluster 5 Big Ideas/Enduring Understandings Essential Question(s) Multiplication and division is the grouping and ungrouping of How are multiplication and division alike? objects 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 Division; Demonstrate the concept of multiplication and division Quantities Concept; Models using multiple models. Chart Table Graph S1C2PO2* Word Problems; Create word problems based on addition, subtraction, Pattern Function Addition; Subtraction; multiplication, and division. Add Addition Multiplication; Division Subtract S1C1PO4* Sets of Whole Numbers Solve wordnumbers into setson addition,the sort. Sort whole problems based and justify subtraction, Subtraction Equivalent Unknown quantity S3C1PO2* Numerical Sequence Rule Explain the rule for a given numerical sequence. Solve Combinations Verify that the rule for a given numerical sequence works.* = POs previously introduced Bold = Priority PO 11Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 1/6/2012
12. 12. 3rd Grade Math Curriculum Map Isaac School District No. 5* = POs previously introduced Bold = Priority PO 12Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 1/6/2012
13. 13. 3rd Grade Math Curriculum Map Isaac School District No. 5 S3C2PO2 2 Whole Number Quarter Translate between the different representations of whole Relationships; number relationships, including symbolic, numerical, verbal or Unit Name Representations and Description: Patterns, pictorial. and Change/ Stories, Tables and Graphs Functions S4C4PO4* Area of Arrays; Rectangular Determine the area of a rectangular figure using an array figure; Model Unit Cluster 6 model. Big Ideas/Enduring Understandings Essential Question(s) S2C3PO1* Counting Problems; Represent all possibilities for a variety of counting problems Possibilities; using arrays, charts, and systematic lists. Patterns occur everywhere in nature. Arrays; Charts; Systematic Why are finding patterns important? Where might you find patterns? S1C2PO5* lists; Conclusions;Division; and aw conclusions from these representations. as inverse Patterns canMultiplication and Dr be recognized, generalized, Apply the concept of multiplication and division extended with How can two or more numbers be related? Inverse operations operations to solve problems. words and symbols. How do patterns help you think mathematically? S1C2PO6*are symbols that take the place ofntompare] or concept of operations (multiplication and Variables Whole Numbers; Operations; [C I erpret the effect of multiplication and division as numbers the ranges of Effect; Multiplication; Division division) on the size of whole numbers. numbers. Functions can show the relationship between two sets of S3C3PO1* Equivalent Forms of Whole Record equivalent forms of whole number through six digits numbers. Numbers; Models by constructing models and using numbers. AZ Essential Learning Summative Key Vocabulary Standard One-Step Equations; S3C3PO3* Knowledge Solve simple one-step equations that can be solved using Skills Assessment S3C2PO1 Addition and between Relationship addition multiplication facts.between two quantities, given Recognize a relationship Quantities multiplication facts two quantities; Chart; by a chart, table or graph, in which the quantities change Chart S4C4PO2* Table; Graph; Applyte one-step using words,measure length, weight and Crea measurement skills that pictures or expressions. proportionally, equations to can be solved using Table Graph Length, Pictures; Words; Weight and capacity using US Customary units. (This is a Supplemental PO to Pattern Function Capacity; be taught with this unit..) Expressions Describe a relationship between two quantities, given by Add Addition Measurement Skills; a chart, table or graph, in which the quantities change Subtract US Customary units proportionally, using words, pictures, or expressions. Subtraction S4C4PO3* Conversions; Length; Convert units of length, weight, and capacity Equivalent S1C2PO1” Weight; Capacity Whole Numbers Add wholefeet to yards, digits. inches or number to four Unknown quantity  ounces to pounds, and Equations Subtract pints, pints to quarts, quarts to gallons cups to whole numbers to four digits. Equals (This is a Supplemental PO to be taught with this unit..) Rule* = POs previously introduced Bold = Priority PO 13Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 1/6/2012
14. 14. 3rd Grade Math Curriculum Map Isaac School District No. 5 S3C1PO1 Numerical Sequence; Recognize missing terms in a numerical sequence. Missing terms Describe missing terms in a numerical sequence. Extend missing terms in a numerical sequence. Create missing terms in a numerical sequence. Find missing terms in a numerical sequence. S3C3PO2 Symbol; Unknown Use a symbol to represent an unknown quantity in a given Quantities context. S3C3PO3 One-Step Equations; Solve simple one-step equations that can be solved using Addition and addition multiplication facts. multiplication facts Create one-step equations that can be solved using* = POs previously introduced Bold = Priority PO 14Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 1/6/2012
15. 15. 3rd Grade Math Curriculum Map Isaac School District No. 5 Quarter 3 Unit Name and Description: Fractions and Decimals/ Finding Fair Shares Unit Cluster 7 Big Ideas/Enduring Understandings Essential Question(s) Fractions represent equal parts or equal-sized portions of a whole 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, parts of a sharing; Parts of a whole, or parts of a set. whole; Parts of a set S1C1PO6 Benchmark Fractions Compare and order benchmark fractions. S1C1PO1* Whole Numbers; Multiple [Model] whole numbers through six digits using and Representations connecting multiple representations. [Analyze] whole numbers through six digits using and connecting multiple representations. S1C1PO2* Place value; Whole numbers Compare whole numbers through six digits by applying the concept of place value. Order whole numbers through six digits by applying the concept of place value.* = POs previously introduced Bold = Priority PO 15Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 1/6/2012
16. 16. 3rd Grade Math Curriculum Map Isaac School District No. 5 S1C1PO3* Money; Coins; Bills Count money using coins and bills to 100.00. Represent money using coins and bills to 100.00. S1C2PO1* Whole Numbers Add whole number to four digits. Subtract whole numbers to four digits. S1C2PO2* Word Problems; Create word problems based on addition, subtraction, Addition; Subtraction; multiplication, and division. Multiplication; Division Solve word problems based on addition, subtraction, multiplication, and division. S1C3PO1* Estimation; Situation; Make estimates appropriate to a given situation or Computation; computation with whole numbers. Whole numbers 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.* = POs previously introduced Bold = Priority PO 16Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 1/6/2012
17. 17. 3rd Grade Math Curriculum Map Isaac School District No. 5 Quarter 3 Unit Name and Description: Addition and Subtraction and the Number System 3/ How Many Hundreds? How Many Miles? Unit Cluster 8 Big Ideas/Enduring Understandings Essential Question(s) Numbers can be represented in many ways and are used to solve How can two or more numbers be related? everyday problems using a variety of methods. How do patterns help you think mathematically? There are relationships between numbers. Why is it important to learn place value? How can numbers be The location of a digit determines its place value. represented? What is the difference between comparing and ordering whole numbers? AZ Essential Learning Key Summative Standard Knowledge Skills Vocabulary Assessment S3C3PO1* Equivalent Forms of Whole Record equivalent forms of whole number Ones, tens, Numbers; Models through six digits by construction models and hundreds, one using numbers. thousand, ten S1C1PO1” Whole Numbers; [Model] whole numbers through six digits using and thousands, Multiple Representations connecting multiple representations. hundred thousands, S1C1PO2” Place value; Whole numbers [Analpare whole numbers through six digits using and the Com yze] by applying standard form, concept of place value. expanded form, word form, Order whole numbers through six digits by applying ordinal the concept of place value.* = POs previously introduced Bold = Priority PO 17Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 1/6/2012
18. 18. 3rd Grade Math Curriculum Map Isaac School District No. 5 S3C3PO3* One-Step Equations; Addition Solve simple one-step equations that can be solved using numbers, equal and addition multiplication facts. to, less than , multiplication facts positive, Create one-step equations that can be solved using negative, addition multiplication facts. expressions, estimate, S1C3PO1 Estimation; Situation; Make estimates appropriate to a given situation or Computation; Whole numbers computation with whole numbers. S1C2PO2* Word Problems; Addition; Create word problems based on addition, subtraction, Subtraction; multiplication and division. Multiplication; Division Solve word problems based on addition, subtraction, multiplication and division.* = POs previously introduced Bold = Priority PO 18Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 1/6/2012
19. 19. 3rd Grade Math Curriculum Map Isaac School District No. 5 Quarter 3 Unit Name and Description: 3-D Geometry and Measurement/ Solids and Boxes Unit Cluster 9 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-dimensional S4C1PO2* Similar Figures [Compare] similar figures. Similar Figures Sequence Sphere S4C1PO3 3-Dimensional Figures; Identify and describe 3-dimensional figures including their Cube Cone Real world objects; Sphere; relationship to real world objects: sphere, cube, cone, Cylinder Pyramid Cube; Cone; Cylinder; cylinder, pyramids, and rectangular prisms. Rectangular Pyramids; Rectangular prism Prisms Translations Reflections S4C2PO1 Translation; Reflection; Identify a translation and model its effect on a 2-dimensional Rotation Rotation; Model figure. Line of symmetry Symmetrical Identify a reflection and model its effect on a 2-dimensional Area figure.* = POs previously introduced Bold = Priority PO 19Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 1/6/2012
20. 20. 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;  circuits in a graph graphs Vertices  weights on edges Circuits  shortest path between two vertices. Weights Paths Vertices Arrays S2C3PO1* Counting Problems; Represent all possibilities for a variety of counting problems Charts Possibilities; Arrays; Charts; using arrays, charts, and systematic lists. Systematic lists Systematic lists; Relevant Conclusions; Draw conclusions from these representations. Extraneous S2C4PO1* Color Mapping Color complex maps using the least number of colors and Conjectures Data justify the coloring. Exploration Experiment Coloring maps S2C4PO3* Vertex-Edge Graphs; Solve problems using vertex-edge graphs. Problems [Create] problems using vertex-edge graphs.* = POs previously introduced Bold = Priority PO 20Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 1/6/2012
21. 21. 3rd Grade Math Curriculum Map Isaac School District No. 5 Process Objectives: MUST BE Integrated throughout Clusters Big Ideas/Enduring Understandings Essential Question(s) Essential Learning Summative AZ Standard Key Vocabulary Assessment Knowledge Skills S5C2PO1 Analytical skills Analyze a problem situation to determine the question(s) to be answered Questions S5C2PO2 Information; Identify relevant, missing and extraneous Relevant; information related to the solution of a problem. Extraneous S5C2PO3 Mathematical Select and apply one or more strategies to Strategies efficiently solve the problem and justify the selection of the strategy. S5C2PO4 Problem-Solving Determine whether a problem to be solved is Strategies similar to previously solved problems, and identify possible strategies for solving the problem.* = POs previously introduced Bold = Priority PO 21Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 1/6/2012
22. 22. 3rd Grade Math Curriculum Map Isaac School District No. 5 S5C2PO5 Representations; Represent a problem situation using any Words; Numbers; combination of words, numbers, pictures, Pictures; Physical physical objects, or symbols. Objects; Symbols S5C2PO6 Conclusions; Summarize mathematical information, explain, Reasoning reasoning, and draw conclusions. S5C2PO7 Problems Analyze and evaluate whether a solution is reasonable, is mathematically correct, and answers the questions being asked. S5C2PO8 Data; Explorations; Make and test conjectures based on data Experiments collected from explorations and experiments.* = POs previously introduced Bold = Priority PO 22Italics = POs taught at earlier grade level [] = Increased Skill Rigor Isaac School DistrictUnderlining = Cognitive rigor 1/6/2012