This document outlines the 7th grade math curriculum for the first quarter at the Isaac School District. It includes two units, one on rational number operations and one on equations. The rational number operations unit covers ordering and representing rational numbers, operations with integers, prime factorization, absolute value, and estimating square roots. The equations unit focuses on two-step equations, proportions, ratios, and using equations to represent real-life situations. Each priority standard is listed along with the essential learning knowledge and skills, key vocabulary, and technology resources to support instruction.

1. 7 Grade Math Curriculum Map
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Isaac School District No. 5
Quarter 1
Unit Name and Description: Rational Number Operations
Cluster 1
Big Ideas/Enduring Understandings Essential Question(s)
Rational number skills are essential in solving real world problems What makes a number irrational or rational?
Estimation helps to verify the reasonableness of a solution. How do you apply the four operations to integers?
Rational numbers can be represented in various forms How many ways can you represent a single rational number?
AZ Essential Learning Technology
EIN Key Vocabulary
Standard Knowledge Skills Resources
E S1C2PO5 Order of operations; Simplify numerical expressions using the order of Irrational
mathematical properties operations and appropriate mathematical properties. Integers
Prime Factorization
I S1C1PO2 Prime Factorization; Find factors and multiples within a set of numbers Absolute Value
Factors; Standard Form
Multiples [Apply] prime factorization to a number Scientific
Notation
E S1C1PO4 Absolute Value Model simple problems involving absolute value Exponents
Consecutive
Solve simple problems involving absolute value Square Roots
Rational Numbers
E S1C2PO1 Integers Add, subtract, multiply, and divide integers Compare
Order
* = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 1
E= Essential P.O.
Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11
Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5
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2. I S1C2PO4 Scientific Notation; Represent numbers in [standard form] and scientific notation Order of
Positive (positive exponents only) Operations
Exponents Factors
Interpret numbers using [standard form] and Multiples
scientific notation (positive exponents only) Estimate
I S1C3PO1 Rational Numbers; Estimate rational numbers and common irrational numbers
Common irrational
numbers Apply benchmarks for rational numbers and
common irrational numbers
I S1C1PO3 Rational Numbers; Compare rational numbers using models and
Models; representations
Representations
Order rational numbers using models and representations
I S1C3PO2 Estimates [Justify] estimates appropriate to a give situation.
E S1C3PO3 Square Roots Estimate square roots of numbers less than a thousand by
locating them between two consecutive whole numbers
* = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 2
E= Essential P.O.
Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11
Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5
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3. 7 Grade Math Curriculum Map
th
Isaac School District No. 5
Quarter 1
Unit Name and Description: Equations
Cluster 2
Big Ideas/Enduring Understandings Essential Question(s)
Proportional reasoning helps to solve day to day problems involving fractions, What is equivalency?
percents, and ratios
What types of daily situations involve proportional logic?
Estimation simplifies daily mathematical computations.
What are variables used for?
Algebraic equations are
representative of real life situations How can we use equations to solve real life problems?
AZ Essential Learning Key Technology
EIN
Standard Knowledge Skills Vocabulary Resources
E S3C3PO5 Two-Step Equations; Inverse [Formulate] and solve two-step equations that Proportions
Operations; Rational Numbers can be solved using inverse operations with Ratios
rational numbers Discounts
Tax
I S1C1PO1 Positive and negative rational Recognize between expressions for positive and negative Convert
Numbers rational numbers, including fractions, decimals, Tips
percents, and ratios. Equivalent
Extraneous
Convert between expressions for positive and Relevant
negative rational numbers, including fractions, Variables
decimals, percents, and ratios Equations
Inequalities
* = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 3
E= Essential P.O.
Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11
Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5
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4. I S1C2PO2 Rational numbers; appropriate Solve problems with rational numbers and appropriate Fraction
operations; exact answers or operations using exact answers or estimates. Decimal
estimate Percent
Inverse
Operations
E S1C2PO3 Percentages; ratios; proportions; Solve problems involving percentages, ratios and
tax; discounts; tips; part-whole proportions, including tax, discounts, tips, and part-whole
relationships relationships
I S5C2PO10 Deductive Proof; Process of Demonstrate and explain that the process of solving
Solving equations equations is a deductive proof.
E S3C3PO3 Multi-Step Equations; Inverse Solve multi-step equations using inverse properties with
Properties; Rational Numbers rational numbers
E S3C3PO6 One-Step Inequalities; Whole Create and solve one-step inequalities with whole numbers
Numbers
* = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 4
E= Essential P.O.
Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11
Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5
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5. 7 Grade Math Curriculum Map
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Isaac School District No. 5
Quarter 2
Unit Name and Description: Algebraic Expressions
Cluster 3
Big Ideas/Enduring Understandings Essential Question(s)
Algebraic expressions are representative of real life situations.
How can we use expressions to solve real life problems?
An algebraic expression is different from an equation.
AZ Essential Learning Key
EIN Technology
Standard Knowledge Skills Vocabulary Resources
E S3C3PO2 Expression; Variables; Evaluate an expression containing one or two variables by Inverse Operations
Substitution substituting numbers for the variables Variables
Substitute
E S3C3PO1 Single variable algebraic [Generate] a single variable algebraic expression or one-step Evaluate
expressions; one-step equation given a contextual situation Expressions
equations Equation
I S5C2PO1 Problem Situations Analyze a problem situation to determine the question(s) to Inequalities
be answered Variable
I S5C2PO2 Problem Solving Analyze mathematical strategies for efficient problem
Strategies solving.
Select and use one or more strategies to solve a problem
N S5C2PO3 Information; Solution; [Discriminate] between relevant, missing, and extraneous
Problem information related to the solution to a problem.
* = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 5
E= Essential P.O.
Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11
Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5
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6. 7 Grade Math Curriculum Map
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Isaac School District No. 5
Quarter 2
Unit Name and Description: Functions
Cluster 4
Big Ideas/Enduring Understandings Essential Question(s)
Graphs, tables, and charts can be used to display and to analyze change How can we represent a function in various ways?
Structures in the universe contain patterns and can be translated into functions. What processes are used to identify patterns?
Functions can be efficiently displayed using visual representations. What constitutes a function?
AZ Essential Learning Key Technology
EIN
Standard Vocabulary Resources
Knowledge Skills
E S3C3PO4 Graphs; Tables; Translate between graphs and tables that represent linear equations Inverse Operations
Linear Equations Variables
[Construct a function and table given a graph] Simplify
Substitution
E S3C4PO1 Analysis of Use graphs and tables to model and analyze change.
Change Pattern
Sequence
[Formulate the rate of change in graphs, tables, and functions]
Equation
E S3C2PO1 Proportional Use a table of values to graph an equation or proportional relationship Evaluate
Relationships; Substitute
Table of values Describe the graph’s characteristics Graph
Table
E S3C1PO1 Numeric and Recognize, describe, create and analyze numerical and geometric
Geometric sequences using tables or graphs
Sequences;
Tables; Graphs [Develop and defend] conjectures about these sequences.
* = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 6
E= Essential P.O.
Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11
Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5
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7. 7 Grade Math Curriculum Map
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Isaac School District No. 5
Quarter 2
Unit Name and Description: Data Analysis
Cluster 5
Big Ideas/Enduring Understandings Essential Question(s)
Data can be communicated using different representations and displays What are the different forms used to display data?
Data can be efficiently interpreted and analyzed using specific representations Which representations most effectively and accurately
communicate data? How do you develop solutions to problems
Effective data analysis yields constructive information based on data analysis?
* = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 7
E= Essential P.O.
Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11
Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5
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8. AZ Essential Learning Key Technology
EIN
Standard Knowledge Skills Vocabulary Resources
* = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 8
E= Essential P.O.
Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11
Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5
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9. E S2C1PO1 Displays of data; Multi-line Solve problems by selecting, constructing, Outlier
graphs; Scatterplots and interpreting displays of data including Mode
multi-line graphs and scatterplots. Mean
Median
Range
I S2C1PO2 Trends; Data Set; Predicted or Interpret trends in a data set.
Positive
Estimated Value; Range
Negative
Estimate values for missing data
Venn
Diagram
Predict and [defend] values for points beyond the range of
Graph
the data set
E S2C1PO3 Outliers; Mean; Median; Identify outliers
Mode:
Range Determine the effect of outliers on the mean, median,
mode, and range.
I S2C3PO2 Counting Problems; Algebraic Solve counting problems using Venn diagrams
Venn Diagrams
Represent the answer algebraically
I S2C4PO1 Vertex-Edged Graphs; Euler Use vertex-edge graphs and algorithmic thinking to
Circuits represent
and find solutions to practical problems related to
Euler/Hamilton paths and circuits.
[Detect the most effective path to achieve the specified goal]
I S5C2PO4 Problem Situations; Multiple Represent a problem situation using multiple representations
Representations;
Reasonableness; Process Describe the process used to solve the problem
Verify the reasonableness of the solution.
I S5C2PO7 Mathematical Information; Isolate and organize mathematical information taken from
Symbols; Diagrams; Graphs; symbols, diagrams, and graphs to make inferences,
Inferences; Conclusions; draw conclusions, and justify reasoning.
* Reasoning
= 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 Revised 06-16-11
Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5
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10. 7 Grade Math Curriculum Map
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Isaac School District No. 5
Quarter 2
Unit Name and Description: Probability
Cluster 6
Big Ideas/Enduring Understandings Essential Question(s)
What is the difference between theoretical and experimental
Probability can be used to predict the outcome of an event.
probability?
The total number of outcomes affects the probability.
What is the difference between dependent and independent
Probability has a range from impossible (0) to certainty (1).
events?
AZ Essential Learning Key Technology
EIN
Standard Knowledge Skills Vocabulary Resources
E S2C2PO2 Independent Events; Experiment with two different events to determine Counting
Dependent Events whether the two events are dependent or independent of principal
each other Tree diagram
Probability
E S2C2PO1 Conditional Probabilities; Determine conditional probabilities (experimental) in Dependent
Compound Probabilities compound probability Independent
Compound
E S2C3PO1 Tree Diagrams; Relationships; Analyze relationships among the tree diagrams where Theoretical
Numerical Connections; items repeat and do not repeat Experimental
Multiplication Principal of Random
Counting Make numerical connections to the multiplication principle Non Random
of counting
* = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 10
E= Essential P.O.
Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11
Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5
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11. I S2C2PO4 Fairness; Probability; Compare probabilities to determine fairness in experimental
Experimental situations
Situations
E S2C2PO3 Probability Experiments; Compare the results of multiple repetitions of the same
Results; Repetitions; probability experiment to the theoretical probability
Theoretical
Probability
N S5C2PO5 Problem-solving strategy Apply a previous used problem-solving strategy in a new
context
I S2C1PO4 Simple Random and Non Distinguish between a simple random and non-random
Random sample
Samples
* = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 11
E= Essential P.O.
Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11
Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5
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12. 7 Grade Math Curriculum Map
th
Isaac School District No. 5
Quarter 3
Unit Name and Description: Geometry and Measurement
Cluster 7
Big Ideas/Enduring Understandings Essential Question(s)
Geometric properties and principles exist and provide solutions in everyday life How do geometric properties and principals solve and apply to
real world scenarios?
Geometry is based on rules and relationships that exist on a micro to macro
continuum What is the relationship between angles and intercepted arcs?
* = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 12
E= Essential P.O.
Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11
Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5
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13. AZ Essential Learning Key
EIN Technology
Standard Knowledge Skills Vocabulary Resources
* = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 13
E= Essential P.O.
Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11
Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5
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14. E S4C4PO1 Circumference; Area; Circle Solve problems involving the circumference and area Circumference
of a circle by calculating and estimating Area
Parallel
Perpendicular
I S4C1PO3 3-Dimensional Figures; Labels; Draw and classify 3-dimensional figures with the Arc
Attributes; Parallelism; appropriate labels showing specified attributes of Central angle
Congruence; Perpendicularity; parallelism, congruence, perpendicularity, and Interior
Symmetry symmetry Exterior
Angles
I S4C1PO1 Central Angles; Intercepted Arcs; Explain the relationship between central angles and Corresponding
Chords; Circle intercepted arc Pi
Chord
Identify arcs and chords of a circle Diameter
I S4C1PO4 Regular Polygons; Describe the relationship between the number of sides in
Interior Angles; a regular polygon and the sum of its interior angles
Sum; Relationship; Sides
E S4C1PO5 Congruent Figures; Identify corresponding parts of congruent figures
Corresponding Parts
N S5C2PO6 Answers; Questions; Problem; Communicate the answer(s) to the question(s) in a
Symbols; Representations; problem using appropriate representations,
Informal and Formal including symbols and informal and formal
Mathematical mathematical language
Language;
I S5C2PO11 Pi; Circumference; Diameter; Use manipulatives and other modeling techniques to
Manipulatives; Modeling defend (Pi) π as a ratio of circumference to diameter
Techniques
* = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 14
E= Essential P.O.
Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11
Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5
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15. * = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 15
E= Essential P.O.
Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11
Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5
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16. 7 Grade Math Curriculum Map
th
Isaac School District No. 5
Quarter 3
Unit Name and Description: Geometry and Measurement
Cluster 8
Big Ideas/Enduring Understandings Essential Question(s)
It is necessary to use appropriate units of measure depending on the situation How do you measure the appropriate dimension of a shape or solid?
Algebraic formulas represent relationships between geometric figures and How do you construct an algebraic formula to find the measure of a
their dimensions
figure?
Measurement can be applied to solve practical problems
AZ Essential Learning Key Technology
EIN
Standard Knowledge Skills Vocabulary Resources
E S5C1PO1 Composite Figures; [Develop] an algorithm to determine the area of a given Area
Algorithm; Area composite figure Perimeter
Algorithm
I S1C3PO4 System of Units; Conversion Estimate the measure of an object in one system of units given Composite Figures
Factor; Measure of an Object; the measure of that object in another system and the Conversion Factors
approximate conversion factor Semi-circle
Conversion
[Generate a process to estimate a measure of an object in one Polygon
system of units] Scale
Estimation
[Translate the measurement of an object from one system of
units to another using estimation]
* = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 16
E= Essential P.O.
Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11
Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5
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17. I S4C4PO2 Polygons; Perimeter; Area [Compare] polygons having the same perimeter or area
E S4C4PO3 Area; Perimeter; Composite Calculate the area and perimeter of composite 2 dimensional
2-Dimensional Figures figures
E S4C4PO4 Lengths; Scale Drawings; Maps Determine actual lengths based on scale drawings or maps
* = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 17
E= Essential P.O.
Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11
Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5
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18. 7 Grade Math Curriculum Map
th
Isaac School District No. 5
Quarter 3
Unit Name and Description: Geometry and Measurement
Cluster 9
Big Ideas/Enduring Understandings Essential Question(s)
Geometric properties and principles exist and provide solutions in everyday How do geometric properties and principals solve and apply to real
life world scenarios?
Geometry is based on rules and relationships that exist on a micro to macro How are we able to create new images based on transformations
continuum
AZ Essential Learning Key Technology
EIN
Standard Knowledge Skills Vocabulary Resources
E S4C4PO5 Net; Surface Area; Solid Create a net to calculate the surface area of a given solid Net
Volume
I S4C4PO6 Volume; Unit of Measure; Identify the appropriate unit of measure to compute the Transversal
Reasoning volume of an object and justify reasoning Coordinate
Plane
N S4C4PO7 Degree of Accuracy Measure to the appropriate degree of accuracy and justify Transformation
reasoning Reflection
E S4C2PO1 Double Transformation; Model the result of a double transformation (translations or Corresponding
Reflections; 2- Dimensional reflections) of a 2-dimensional figure on a coordinate Supplementary
Figure; Coordinate Plane; plane using all four quadrants Accurate
E S4C1PO2 Angles; Parallel Lines; Analyze and determine relationships between angles created Surface Area
Transversals by parallel lines cut by a transversal Parallel
Relationships Coordinate Plan
[Defend] the stated relationships between angles created Angle
by parallel lines cut by a transversal
* = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 18
E= Essential P.O.
Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11
Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5
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19. 7 Grade Math Curriculum Map
th
Isaac School District No. 5
Quarter 4
Unit Name and Description: Expressions, Inequalities, and Absolute Value
Cluster 10
Big Ideas/Enduring Understandings Essential Question(s)
Expressions and equations can be represented graphically and numerically Why do certain operations have to be performed in a specific order?
Algebra is a language of numbers, letters, and symbols used to solve problems What is the purpose of a variable in an expression, inequality, or equation?
AZ Essential Learning Key Technology
EIN
Standard Knowledge Skills Vocabulary Resources
E M08-S3C3PO3 Linear equations; Analyze, simplify, and solve situations problems involving Linear equations
Inequalities; Real linear equation and inequalities using the properties of Inequalities
number system; the real number system Exponents
Coefficients
Variables
I M08-S3C3PO5 Inequalities; Number line Graph an inequality on a number line Expressions
Equations
Inverse property
E M08-S1C1PO4 Absolute value; Problems Model and solve problems involving absolute value. Number line
Square roots
E M08-S1C2PO5 Square roots; Cube roots; Simplify numerical expressions using the order of operations Cube roots
Grouping symbols; that include grouping symbols, square roots, cube roots, Grouping Symbols
Positive exponents; absolute values, and positive exponents
Absolute value;
E M08-S4C4PO2 Geometric problems; Solve geometric problems using ratios and proportions
Ratios; Proportions
* = POs previously introduced EIN= Level of Priority for P.O. Bold = Priority PO 19
E= Essential P.O.
Italics = POs taught at earlier grade level I= Important P.O. [] = Increased skill rigor Revised 06-16-11
Underlining = Cognitive rigor N= Nice to Know P.O. Isaac School District No. 5
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