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6th Grade Math Curriculum Map
                                                          Isaac School District No. 5
Quarter 1
Unit Name and Description: Number Sense and Operations
Cluster 1
Big 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                            1
Italics         = POs taught at earlier grade level       I = Important P.O.                   []    = Increased skill rigor                  Update 06-16-11
Underlining     = Cognitive rigor                        N = Nice to Know P.O.                                                                Isaac School District No. 5
                                                                                     E
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                          2
Italics       = POs taught at earlier grade level             I = Important P.O.              []     = Increased skill rigor                Update 06-16-11
Underlining   = Cognitive rigor                              N = Nice to Know P.O.                                                          Isaac School District No. 5
                                                                                         E
6th Grade Math Curriculum Map
                                                            Isaac School District No. 5
Quarter 1
Unit Name and Description: Fractions, Decimals, Percents, and Ratios
Cluster 2
Big 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                             3
Italics       = POs taught at earlier grade level           I = Important P.O.                  []     = Increased skill rigor                   Update 06-16-11
Underlining   = Cognitive rigor                            N = Nice to Know P.O.                                                                 Isaac School District No. 5
                                                                                       E
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              4
Italics       = POs taught at earlier grade level            I = Important P.O.              []     = Increased skill rigor    Update 06-16-11
Underlining   = Cognitive rigor                             N = Nice to Know P.O.                                              Isaac School District No. 5
                                                                                        E
6th Grade Math Curriculum Map
                                                              Isaac School District No. 5
Quarter 2
Unit Name and Description: Integers
Cluster 3
Big 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                          5
Italics       = POs taught at earlier grade level            I = Important P.O.                 []     = Increased skill rigor                Update 06-16-11
Underlining   = Cognitive rigor                             N = Nice to Know P.O.                                                             Isaac School District No. 5
                                                                                        E
6th Grade Math Curriculum Map
                                                                 Isaac School District No. 5
Quarter 2
Unit Name and Description: Algebra
Cluster 4
Big 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                          6
Italics       = POs taught at earlier grade level            I = Important P.O.                 []      = Increased skill rigor                Update 06-16-11
Underlining   = Cognitive rigor                             N = Nice to Know P.O.                                                              Isaac School District No. 5
                                                                                        E
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                          7
Italics       = POs taught at earlier grade level              I = Important P.O.              []     = Increased skill rigor                Update 06-16-11
Underlining   = Cognitive rigor                               N = Nice to Know P.O.                                                          Isaac School District No. 5
                                                                                          E
6th Grade Math Curriculum Map
                                                                 Isaac School District No. 5
Quarter 2
Unit Name and Description: Area, Perimeter, Circumference and Volume

Cluster 5
Big 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, and
can 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                             8
Italics       = POs taught at earlier grade level              I = Important P.O.                 []     = Increased skill rigor                   Update 06-16-11
Underlining   = Cognitive rigor                               N = Nice to Know P.O.                                                                Isaac School District No. 5
                                                                                          E
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                          9
Italics       = POs taught at earlier grade level               I = Important P.O.              []     = Increased skill rigor                Update 06-16-11
Underlining   = Cognitive rigor                                N = Nice to Know P.O.                                                          Isaac School District No. 5
                                                                                           E
6th Grade Math Curriculum Map
                                                           Isaac School District No. 5
Quarter 3
Unit Name and Description: Measurement
Cluster 6
Big 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                             10
Italics       = POs taught at earlier grade level              I = Important P.O.                 []     = Increased skill rigor                   Update 06-16-11
Underlining   = Cognitive rigor                               N = Nice to Know P.O.                                                                Isaac School District No. 5
                                                                                          E
6th Grade Math Curriculum Map
                                                               Isaac School District No. 5
Quarter 3
Unit Name and Description: Graphing
Cluster 7
Big 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 of
Appropriate 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                          11
Italics       = POs taught at earlier grade level              I = Important P.O.                 []     = Increased skill rigor                Update 06-16-11
Underlining   = Cognitive rigor                               N = Nice to Know P.O.                                                             Isaac School District No. 5
                                                                                          E
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                            12
Italics       = POs taught at earlier grade level               I = Important P.O.              []     = Increased skill rigor                  Update 06-16-11
Underlining   = Cognitive rigor                                N = Nice to Know P.O.                                                            Isaac School District No. 5
                                                                                           E
6th Grade Math Curriculum Map
                                                               Isaac School District No. 5
V




Quarter 3
Unit Name and Description: Transformations
Cluster 8
Big 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                         13
Italics       = POs taught at earlier grade level              I = Important P.O.                 []     = Increased skill rigor               Update 06-16-11
Underlining   = Cognitive rigor                               N = Nice to Know P.O.                                                            Isaac School District No. 5
                                                                                          E
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                          14
Italics       = POs taught at earlier grade level               I = Important P.O.              []     = Increased skill rigor                Update 06-16-11
Underlining   = Cognitive rigor                                N = Nice to Know P.O.                                                          Isaac School District No. 5
                                                                                           E
6th Grade Math Curriculum Map
                                                             Isaac School District No. 5
Quarter 3
Unit Name and Description: Probability

Cluster 9
Big 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                             15
Italics       = POs taught at earlier grade level            I = Important P.O.                 []     = Increased skill rigor                   Update 06-16-11
Underlining   = Cognitive rigor                             N = Nice to Know P.O.                                                                Isaac School District No. 5
                                                                                        E
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                            16
Italics       = POs taught at earlier grade level               I = Important P.O.              []     = Increased skill rigor                  Update 06-16-11
Underlining   = Cognitive rigor                                N = Nice to Know P.O.                                                            Isaac School District No. 5
                                                                                           E
6th Grade Math Curriculum Map
                                                            Isaac School District No. 5
Quarter 3
Unit Name and Description: Vertex-Edge Graphs

Cluster 10
Big 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                          17
Italics       = POs taught at earlier grade level           I = Important P.O.                  []     = Increased skill rigor                Update 06-16-11
Underlining   = Cognitive rigor                            N = Nice to Know P.O.                                                              Isaac School District No. 5
                                                                                       E
6th Grade Math Curriculum Map
                                                             Isaac School District No. 5
Quarter 4
Unit Name and Description: Integers II
Cluster 11
Big 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                             18
Italics       = POs taught at earlier grade level            I = Important P.O.                 []     = Increased skill rigor                   Update 06-16-11
Underlining   = Cognitive rigor                             N = Nice to Know P.O.                                                                Isaac School District No. 5
                                                                                        E

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6th Grade Math Curriculum Map

  • 1. 6th Grade Math Curriculum Map Isaac School District No. 5 Quarter 1 Unit Name and Description: Number Sense and Operations Cluster 1 Big 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 1 Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11 Underlining = 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 2 Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11 Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
  • 3. 6th Grade Math Curriculum Map Isaac School District No. 5 Quarter 1 Unit Name and Description: Fractions, Decimals, Percents, and Ratios Cluster 2 Big 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 3 Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11 Underlining = 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 4 Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11 Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
  • 5. 6th Grade Math Curriculum Map Isaac School District No. 5 Quarter 2 Unit Name and Description: Integers Cluster 3 Big 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 5 Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11 Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
  • 6. 6th Grade Math Curriculum Map Isaac School District No. 5 Quarter 2 Unit Name and Description: Algebra Cluster 4 Big 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 6 Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11 Underlining = 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 7 Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11 Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
  • 8. 6th Grade Math Curriculum Map Isaac School District No. 5 Quarter 2 Unit Name and Description: Area, Perimeter, Circumference and Volume Cluster 5 Big 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, and can 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 8 Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11 Underlining = 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 9 Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11 Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
  • 10. 6th Grade Math Curriculum Map Isaac School District No. 5 Quarter 3 Unit Name and Description: Measurement Cluster 6 Big 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 10 Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11 Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
  • 11. 6th Grade Math Curriculum Map Isaac School District No. 5 Quarter 3 Unit Name and Description: Graphing Cluster 7 Big 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 of Appropriate 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 11 Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11 Underlining = 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 12 Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11 Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
  • 13. 6th Grade Math Curriculum Map Isaac School District No. 5 V Quarter 3 Unit Name and Description: Transformations Cluster 8 Big 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 13 Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11 Underlining = 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 14 Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11 Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
  • 15. 6th Grade Math Curriculum Map Isaac School District No. 5 Quarter 3 Unit Name and Description: Probability Cluster 9 Big 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 15 Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11 Underlining = 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 16 Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11 Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
  • 17. 6th Grade Math Curriculum Map Isaac School District No. 5 Quarter 3 Unit Name and Description: Vertex-Edge Graphs Cluster 10 Big 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 17 Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11 Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E
  • 18. 6th Grade Math Curriculum Map Isaac School District No. 5 Quarter 4 Unit Name and Description: Integers II Cluster 11 Big 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 18 Italics = POs taught at earlier grade level I = Important P.O. [] = Increased skill rigor Update 06-16-11 Underlining = Cognitive rigor N = Nice to Know P.O. Isaac School District No. 5 E