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- 1. 6th Grade Math Curriculum Map Isaac School District No. 5Quarter 1Unit Name and Description: Number Sense and OperationsCluster 1Big Ideas/Enduring Understandings Essential Question(s)The order of operations will affect solutions. Decimal placement affects the What are the math properties and why do we use them?value of the solution. Algorithms are useful strategies for computing. What argument can you provide to explain your solution? What are the strategies we use to multiply and divide fractions? What is an algorithm? What are the strategies we use to multiply and divide decimals? Essential Learning AZ Key Technology EIN Standard Knowledge Skills Vocabulary Resources E S5C1PO1 Algorithms; Analyze algorithms for multiplying and dividing fractions Associative Fractions; Decimals; and decimals using the associative, commutative, and Commutative Associative; distributive properties Distributive Commutative; Fraction Distributive Decimal Operations I S1C2PO5 Mathematical argument; Provide a mathematical argument to explain operations with Divisor Operations; Fractions; two or more fractions or decimals. Dividend Decimals Quotient I S1C3PO2 Estimates; Make estimates appropriate to a given situation and verify the Place value Given situation; reasonableness of the results. Product Factors* = POs previously introduced EIN = Level of Priority for P.O. E = Essential P.O. Bold = Priority PO 1Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
- 2. I S5C2PO6 Informal and formal Communicate the answer(s) to the question(s) in a problem Exponents mathematical using appropriate representations, including symbols and Parentheses language; Symbols informal and formal mathematical language. Algorithm Inverse operations Estimates E S1C2PO4 Fractions Multiply and divide fractions. Argument Simplify S1C1PO2 Prime factorization; Use prime factorization to: Reduce Cross E Whole number; express a whole number as a product of its prime factors cancel Prime factors; Greatest Greatest common common factor; Least determine the greatest common factor and least common factor common multiple; multiple of two whole numbers Identity Property of Product one Identity Property of zero E S1C2PO3 Multi-digit whole Divide multi-digit whole numbers and decimals by decimal numbers; divisors with and without remainders. Decimals; Decimal divisors; Remainders; Division E S1C2PO2 Multi-digit decimals; Multiply multi-digit decimals through thousandths. Thousandths; Multiplication* = POs previously introduced EIN = Level of Priority for P.O. E = Essential P.O. Bold = Priority PO 2Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
- 3. 6th Grade Math Curriculum Map Isaac School District No. 5Quarter 1Unit Name and Description: Fractions, Decimals, Percents, and RatiosCluster 2Big Ideas/Enduring Understandings Essential Question(s)The same number can be written as a fraction, decimal, percent, and ratio. How are parts of a number represented?How a number is represented depends on the given situation and/or need. How are fractions, decimals, percents, and ratios related? Why is it important to know the equivalent forms of numbers? Why is it important to know the percent of a number? How can using benchmarks help us to determine the value of a number or to compare values? Essential Learning AZ Key Technology EIN Standard Knowledge Skills Vocabulary Resources E S1C1PO1 Fractions; Decimals; Convert between expressions for positive rational numbers, Fraction Percents; Ratios; including fractions, decimals, percents, and ratios. Decimal Positive rational Percent numbers Ratio I S5C2PO3 Mathematical Analyze mathematical strategies for efficient problem Prime factorization Strategies; solving; select and use one or more strategies to solve a Prime numbers Problem solving; problem. Greatest common Strategies; Factor Problem Least common Compare mathematical strategies for efficient problem multiple solving; select and use one or more strategies to solve a Benchmarks problem. Rates Proportion* = POs previously introduced EIN = Level of Priority for P.O. E = Essential P.O. Bold = Priority PO 3Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
- 4. E S1C1PO3 Fractions; Rates; [Interpret ]fractions as rates, division of whole numbers, parts Division; Whole of a whole, parts of a set, and locations on a real number line. numbers; Parts of a whole; Parts of a set; Number line E S1C1PO4 Integers; Positive Compare integers; and positive fractions, decimals, and fractions; percents Decimals; Percents Order integers; and positive fractions, decimals, and percents I S1C3PO1 Benchmarks; Rational Use benchmarks as meaningful points of comparison for numbers rational numbers. E S1C1PO2 Prime factorization; Use prime factorization to: Whole number; express a whole number as a product of its prime factors Prime factors; Greatest common determine the greatest common factor and least common factor; Least multiple of two whole numbers common multiple; Product* = POs previously introduced EIN = Level of Priority for P.O. E = Essential P.O. Bold = Priority PO 4Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
- 5. 6th Grade Math Curriculum Map Isaac School District No. 5Quarter 2Unit Name and Description: IntegersCluster 3Big Ideas/Enduring Understandings Essential Question(s)Integers are used in a wide array of contexts. What is absolute value? How do you order integers? How do you model integers? How do you determine the question to be answered in a word problem? AZ Essential Learning Key Technology EIN Standard Knowledge Skills Vocabulary Resources E S1C2PO1 Addition; Apply and interpret the concepts of addition and subtraction with Absolute value Subtraction; integers using models Positive Integers; Models Negative Integers E S5C2PO1 Problem situation; Analyze a problem situation to determine the question(s) to be answered. Number line Questions Model E S5C2PO4 Problem-solving Apply a previously used problem-solving strategy in a new context Sum strategy Difference Addends E S1C1PO4* Integers; Positive Compare integers; and positive fractions, decimals, and percents Subtrahend fractions; Decimals; Percents Order integers; and positive fractions, decimals, and percents Minuend I S1C1PO5 Absolute Value; Express that a number’s distance from zero on the number line is its Number line absolute value* = POs previously introduced EIN = Level of Priority for P.O. E = Essential P.O. Bold = Priority PO 5Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
- 6. 6th Grade Math Curriculum Map Isaac School District No. 5Quarter 2Unit Name and Description: AlgebraCluster 4Big Ideas/Enduring Understandings Essential Question(s)Variables represent numbers. What does a variable represent?Estimates can be used to verify the reasonableness of a result. How do you solve/interpret equations and expressions?Algebra is used to solve real world situations. How do you know if your answer is reasonable? How do you discover the relationship between two or more quantities? What are the multiple ways you can represent the process and solution? AZ Essential Learning Key Technology EIN Standard Knowledge Skills Vocabulary Resources E S3C3PO2 Two-step equations; Create two-step equations that can be solved using inverse Equation Inverse properties; properties with fractions and decimals. Expression Fractions; Decimals Order of Solve two-step equations that can be solved using inverse operations Two- properties with fractions and decimals. step equations I S3C2PO1 Relationship; Quantities; Recognize a relationship between two quantities, given by a Function Tables Chart; chart, table, or graph, using words and expressions. Commutative Table; Graph; Words; Property Expressions Describe a relationship between two quantities, given by a Associative chart, table, or graph, using words and expressions. Property* = POs previously introduced EIN = Level of Priority for P.O. E = Essential P.O. Bold = Priority PO 6Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
- 7. I S5C2PO5 Problem situation; Represent a problem situation using multiple representations, Identity property Representations; describe the process used to solve the problem, and verify the of one reasonableness of the solution. Estimation I S1C3PO2* Estimates; Given Make estimates appropriate to a given situation and verify the Reasonableness Situation; Results reasonableness of the results. Simplify Translate I S5C2PO6* Informal and formal Communicate the answer(s) to the question(s) in a problem Inverse mathematical using appropriate representations, including symbols and Addition language; Symbols informal and formal mathematical language. property of I S3C1PO1 Operations; Numerical Recognize a numerical sequence involving fractions and equality sequence; decimals using all four basic operations. Subtraction Fractions; Decimals property of Describe a numerical sequence involving fractions and equality decimals using all four basic operations. Multiplication I S3C3PO4 Algebraic Expression; Evaluate an expression involving the four basic operations by property of Operations; Fractions; substituting given fractions and decimals for the variable equality Decimals; Variable Division S3C3PO1 Algebraic expressions; Use an algebraic expression to represent a quantity in a given property of I Quantity; Given context context. equality Distributive I S3C3PO3 Verbal description; Translate both ways between a verbal description and an property Algebraic algebraic expression or equation Identity property of Expression; Equation zero E S1C2PO6 Commutative; Apply the commutative, associative, distributive, and identity Associative; properties to evaluate numerical expressions involving whole Distributive; Identity numbers Properties; Whole numbers E S1C2PO7 Numerical expressions; Simplify numerical expressions (involving fractions, decimals, Fractions; Decimals; and exponents) using the order of operations with or without Exponents; Grouping grouping symbols. symbols I S1C1P06 Inverse relationships; Express the inverse relationships between exponents and roots Exponents; Cubes for perfect squares and cubes. Square roots; Squares* = POs previously introduced EIN = Level of Priority for P.O. E = Essential P.O. Bold = Priority PO 7Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
- 8. 6th Grade Math Curriculum Map Isaac School District No. 5Quarter 2Unit Name and Description: Area, Perimeter, Circumference and VolumeCluster 5Big Ideas/Enduring Understandings Essential Question(s)There are multiple attributes of 2 dimensional and 3 dimensional figures that What real world use is there for knowing area, perimeter, andcan be measured and labeled. volume? How do you solve for the area of a compound figure? What is the relationship between area, perimeter, and volume? What are properties of complementary, supplementary, and vertical angles? Essential Learning AZ Key Technology EIN Standard Vocabulary Resources Knowledge Skills E S5C1PO2 Algorithm; Area; Create an algorithm to determine the area of a given Area Compound compound figure using parallelograms and triangles. Perimeter Figures; Volume Parallelograms; Justify an algorithm to determine the area of a Algorithm Triangles given compound figure using parallelograms and Parallelogram triangles. Triangle E S4C4PO4 Problems; Area; Solve problems involving the area of simple polygons using Polygon Simple Polygons; formulas for rectangles and triangles. Rectangle Formulas; Rectangles; Cube Triangles Rectangular prisms Compound figure* = POs previously introduced EIN = Level of Priority for P.O. E = Essential P.O. Bold = Priority PO 8Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
- 9. I S4C4PO6 Relationship; Volume; Describe the relationship between the volume of a figure and Length Figure; the area of its base. Width Area; Base Height Circumference Pi Circle I S4C1PO1 π (pi); Ratio; Define π (pi) as the ratio between the circumference and Radius Circumference; diameter of a circle and explain the relationship among the Diameter Diameter; Circle; diameter, radius, and circumference. Ratio Relationship; Supplementary Radius; Circle Complementary Vertical angles I S4C4PO5 Problems; Area; Solve problems involving area and perimeter of regular and Simple polygon Perimeter; Regular irregular polygons. Regular and and irregular polygons Irregular polygon I S4C1PO2 Properties of Angles; Solve problems using properties of supplementary, Supplementary; complementary, and vertical angles Complementary; Vertical* = POs previously introduced EIN = Level of Priority for P.O. E = Essential P.O. Bold = Priority PO 9Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
- 10. 6th Grade Math Curriculum Map Isaac School District No. 5Quarter 3Unit Name and Description: MeasurementCluster 6Big Ideas/Enduring Understandings Essential Question(s)There are appropriate units of measure for different situations. What are the units in the U.S. customary system? What are the units in the metric system? How do you convert between units? AZ Essential Learning Key Technology EIN Standard Vocabulary Resources Knowledge Skills E S4C4PO2 Conversion; US Solve problems involving conversion within the Capacity; Length Customary; Metric U.S. Customary and within the metric system. Mass; Pound; Ton; System Ounce; Inches; Feet; Yards; Miles; Fluid; ounce I S4C4PO1 Unit of Measure; Mass Determine the appropriate unit of measure for a given Cup; Pint; Quart; Measurement tool; context and the appropriate tool to measure to the needed Gallon; Kilo; Centi; Precision; Length; precision (including length, capacity, angles, time, and Milli; Meter; Gram; Capacity; Angles; Time; mass). Liter; Metric; U.S. Customary Scale; Seconds; Minutes; Hours N S4C4PO3 Measure of objects; Estimate the measure of objects using a scale drawing or Days; Proportion Estimation; map. Ratio Scale drawing; Map* = POs previously introduced EIN = Level of Priority for P.O. E = Essential P.O. Bold = Priority PO 10Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
- 11. 6th Grade Math Curriculum Map Isaac School District No. 5Quarter 3Unit Name and Description: GraphingCluster 7Big Ideas/Enduring Understandings Essential Question(s)Charts, tables, and graphs help us make valid inferences, decisions, and How can you collect, organize, and display data?arguments. How does the type of data influence the choice ofAppropriate graphs need to be used in specific situations. graph? How do you use modes of central tendency? How do we determine which information is relevant or missing? Essential Learning Key Technology EIN AZ Standard Knowledge Skills Vocabulary Resources E S2C1PO2 Question; Inferences; Formulate questions by interpreting, analyzing, and Histogram Displays of data; drawing inferences from displays of data, including Stem-and-leaf plots Histograms; Stem- histograms and stem-and-leaf plots. Data and-Leaf Interpret plots Answer questions by interpreting, analyzing, and drawing Modes of Central inferences from displays of data, including histograms and Tendency stem-and-leaf plots. Extreme values I S5C2PO2 Relevant, missing, and Identify relevant, missing, and extraneous information related (outliers) extraneous information; to the solution to a problem. Mean Solution; Median Mode N S5C2PO9 Logic Problems; Solve simple logic problems, including conditional statements, Conditional statements; and justify solution methods and reasoning. Range Solution; Methods; Scatterplot Venn Diagram* = POs previously introduced EIN = Level of Priority for P.O. E = Essential P.O. Bold = Priority PO 11Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
- 12. N S2C3PO2 Counting problems; Explore counting problems with Venn diagrams using three Range Venn Diagrams attributes. Interpret Data set I S5C2PO2 Information Analysis; Identify relevant, missing, and extraneous information related to Origin Relevant, missing, and the solution to a problem. X-axis extraneous information; Solution; Problem Y-axis N S5C2PO9 Logic Problems; Solve simple logic problems, including conditional statements, Conditional statements; and justify solution methods and reasoning. N S2C3PO2 Counting problems; Explore counting problems with Venn diagrams using three Venn Diagrams attributes. Attributes I S1C3PO2* Estimates; Given Make estimates appropriate to a given situation and verify the Situation; reasonableness of the results. I S2C1PO3 Extreme values; Mean; Use extreme values, mean, median, mode, and range to analyze Median; Mode; Range; and describe the distribution of a given data set. Modes of Central Tendency; Data set I S5C2PO7 Mathematical Isolate mathematical information taken from symbols, diagrams, information; and graphs to make inferences, draw conclusions, and justify Symbols; Diagrams; reasoning. Graphs; Inferences; Conclusions; Reasoning Organize mathematical information taken from symbols, diagrams, and graphs to make inferences, draw conclusions, and justify reasoning. I S3C4PO1 Pattern; Missing values; Determine a pattern to predict missing values on a line graph Line graph; Scatterplot or scatterplot I S2C1PO1 Problems; Displays of Solve problems by selecting, constructing, and interpreting data; Histograms; Stem- displays of data, including histograms and stem-and-leaf plots and-Leaf Plots* = POs previously introduced EIN = Level of Priority for P.O. E = Essential P.O. Bold = Priority PO 12Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
- 13. 6th Grade Math Curriculum Map Isaac School District No. 5VQuarter 3Unit Name and Description: TransformationsCluster 8Big Ideas/Enduring Understandings Essential Question(s)Drawing polygons on a coordinate plane involves translations and What is a transformation?reflections. How do you use a coordinate plane? How do you find a missing coordinate? What are the features of a coordinate plane? How do values on a coordinate plane relate to integers? Essential Learning Key Technology EIN AZ Standard Vocabulary Resources Knowledg Skills E S4C2PO1 e Simple translations; [Draw] a simple translation or reflection. Transformation 2-Dimensional Reflection figure; Coordinate Model the transformation’s effect on a 2-dimensional figure Translation plane; Quadrants on a coordinate plane using all four quadrants. Coordinate plane Quadrant I S4C2PO2 Reflections; Polygon; Draw a reflection of a polygon in the coordinate plane using a Ordered pair Coordinate plane; horizontal or vertical line of reflection. Coordinates Horizontal /vertical Positive integers line Vertical Horizontal* = POs previously introduced EIN = Level of Priority for P.O. E = Essential P.O. Bold = Priority PO 13Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
- 14. I S4C3PO2 Given figure; Ordered State the missing coordinate of a given figure on the coordinate Origin Pairs; Geometric plane using geometric properties to justify the solution. 2-dimensional properties; Solution; x-axis Coordinate Plane y-axis I S4C3PO1 Ordered Pairs; Quadrant; Graph ordered pairs in any quadrant of the coordinate plane. Coordinate Plane I S5C2PO6* Informal and formal Communicate the answer(s) to the question(s) in a problem mathematical language; using appropriate representations, including symbols and Answers; Questions; informal and formal mathematical language. Problem; Representations; Symbols* = POs previously introduced EIN = Level of Priority for P.O. E = Essential P.O. Bold = Priority PO 14Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
- 15. 6th Grade Math Curriculum Map Isaac School District No. 5Quarter 3Unit Name and Description: ProbabilityCluster 9Big Ideas/Enduring Understandings Essential Question(s)Probability is a form of estimation. How are theoretical probability and experimental probability different?Using a systematic approach can confirm solutions. What is a sample space and its use? What is a conjecture? Why do we replicate an experiment? What are the multiple ways you can represent a sample space? Essential Learning AZ Key Technology EIN Standard Vocabulary Resources Knowledge Skills E S2C2PO2 Theoretical Use theoretical probability to: Theoretic probability; predict experimental outcomes, Probability Experimental Organized list outcomes; compare the outcome of the experiment to the Venn diagram Experiment; prediction Possible outcomes Prediction; Results Conjecture replicate the experiment and compare results. Attribute* = POs previously introduced EIN = Level of Priority for P.O. E = Essential P.O. Bold = Priority PO 15Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
- 16. N S2C3PO2* Counting problems; Explore counting problems with Venn diagrams using three Experimental Venn Diagrams; attributes probability Attributes Sample space Tree diagram Trial I S2C2PO1 Data; Multiple trials; Use data collected from multiple trials of a single event to form Single event; a conjecture about the theoretical probability. Conjecture; Theoretical probability I S5C2PO8 Conjectures; Make conjectures based on information collected from Information; explorations and experiments Explorations; Experiments Test conjectures based on information collected from explorations and experiments I S2C3PO1 Tree Diagrams; Items Build tree diagrams where items repeat Explore tree diagrams where items repeat. I S2C2PO3 Possible outcomes; Determine all possible outcomes (sample space) of a given Sample space; situation using a systematic approach Given situation* = POs previously introduced EIN = Level of Priority for P.O. E = Essential P.O. Bold = Priority PO 16Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
- 17. 6th Grade Math Curriculum Map Isaac School District No. 5Quarter 3Unit Name and Description: Vertex-Edge GraphsCluster 10Big Ideas/Enduring Understandings Essential Question(s)Students will understand that vertex-edge graphs are an example of map What is a Hamilton path?skills. What is a Hamilton circuit? Essential Learning AZ Key Technology EIN Standard Vocabulary Resources Knowledge Skill I S2C4PO2 Hamilton Paths and s Solve problems related to Hamilton paths and circuits. Vertex-edge graph Circuits Hamilton path Hamilton N S2C4PO1 Hamilton Paths and Investigate properties of vertex-edge graphs circuit Circuits • Hamilton paths, Shortest route • Hamilton circuits, and shortest route. Vertex Edge* = POs previously introduced EIN = Level of Priority for P.O. E = Essential P.O. Bold = Priority PO 17Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
- 18. 6th Grade Math Curriculum Map Isaac School District No. 5Quarter 4Unit Name and Description: Integers IICluster 11Big Ideas/Enduring Understandings Essential Question(s)Rational and irrational number skills are essential in solving real world What makes a number irrational or rational?problems. How do you apply the four operations to integers?Rational and irrational numbers can be represented in various forms. How many ways can you represent a single rational number? Essential Learning Key Technology EIN AZ Standard Vocabulary Resources Knowledge Skills E M07-S1C2PO1 Integers Add, subtract, multiply, and divide integers Integers Absolute value E M07-S1C1PO4 Simple problems; Model simple problems involving absolute value. Rational Absolute value Irrational Solve simple problems involving absolute value. E M07-S1C1PO3 Rational Numbers; Compare rational numbers using various models Models; and representations Representations Order rational numbers using various models and representations E M07-S1C3PO1 Rational Numbers; Estimate benchmarks for rational numbers and common Benchmarks; irrational numbers Common irrational numbers Apply benchmarks for rational numbers and common irrational numbers.* = POs previously introduced EIN = Level of Priority for P.O. E = Essential P.O. Bold = Priority PO 18Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E

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