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
I S1C2PO5 Mathematical argument; Provide a mathematical argument to explain operations with Operations
Operations; Fractions; two or more fractions or decimals. Divisor
Decimals Dividend
Quotient
I S1C3PO2 Estimates; Make estimates appropriate to a given situation and verify the
Place value
Given situation; reasonableness of the results.
Product
Factors
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E= Essential P.O.
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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
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E= Essential P.O.
Bold = Priority PO 2
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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
Key Technology
EIN AZ 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 solving; Prime
Strategies; select and use one or more strategies to solve a problem. factorization
Problem Prime numbers
solving; Compare mathematical strategies for efficient problem solving; Greatest common
Strategies; Factor
select and use one or more strategies to solve a problem.
Problem Least common
multiple
* = POs previously introduced EIN= Level of Priority for P.O.
E= Essential P.O.
Bold = Priority PO 3
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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
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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
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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?
Essential Learning Key Technology
EIN AZ
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.
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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
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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
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E= Essential P.O.
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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 (pi); Ratio; Define (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
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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?
Essential Learning Key Technology
EIN AZ
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
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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 Vocabulary Resources
Knowledge Skills
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. Modes of Central
and-Leaf Tendency
plots Answer questions by interpreting, analyzing, and drawing Extreme values
inferences from displays of data, including histograms and (outliers)
stem-and-leaf plots. Mean
N S2C3PO2 Counting problems; Explore counting problems with Venn diagrams using three Median
Venn Diagrams attributes. Mode
Range
I S5C2PO2 Information Analysis; Identify relevant, missing, and extraneous information related Scatterplot
Relevant, missing, and to the solution to a problem. Venn Diagram
extraneous information; Origin
Solution; Problem X-axis and Y-axis
* = 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
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12. 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,
information; diagrams, and graphs to make inferences, draw conclusions,
Symbols; Diagrams; and justify reasoning.
Graphs; Inferences;
I S3C4PO1 Pattern; Missing values; Determine a pattern to predict missing values on a line
Line graph; Scatterplot graph 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
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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 n a 2-dimensional figure Translation
plane; Quadrants on a coordinate plane using all four quadrants. Coordinate plane
Quadrant
Draw a reflection of a polygon in the coordinate plane using a Ordered pair
I S4C2PO2 Reflections; Polygon;
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
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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
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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
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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
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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
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18. I S5C2PO2 Relevant, missing, and Identify relevant, missing, and extraneous information related
extraneous information; to the solution to a problem.
Solution;
N S5C2PO9 Logic Problems; Solve simple logic problems, including conditional
Conditional statements; statements, and justify solution methods and reasoning.
Solution; Methods;
* = 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
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19. 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 19
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
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