1. 8th Grade Math Curriculum Map
Isaac School District No. 5
Quarter 1
Unit Name and Description: Compare and Order Real Numbers
Cluster 1
Big Ideas/Enduring Understandings Essential Question(s)
Real numbers are classified as either rational or irrational numbers. Describe how multiplying or dividing a number by less than one affects the
number?
The value of all numbers is dependent on its place value.
Why is checking the reasonableness of answer important?
How do we use scientific notation to express equivalent forms of rational
number?
How do we compare and order real numbers?
AZ Essential Learning Key Technology
EIN
Standard Knowledge Skills Vocabulary Resources
E S1C1PO1 Real numbers; Large and Compare real numbers including very large and small Natural number
small integers; Decimals; integers, and decimals, and fractions close to zero Counting number
Fractions Whole Numbers
I S1C1PO2 Rational numbers; Irrational Classify realnumbers including very large and small, and
Order real numbers as rational or irrational Integers
numbers; Real numbers Rational numbers
Irrational number
I S1C1PO3 Real number system; Model the relationship between the subsets of the real number Real number
Relationship; Subsets system Standard notation
Scientific notation
Estimation
* = 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. E S1C2PO1 Prime number; Composite Solve problems with factors, multiples, divisibility or
numbers; Multiples and remainders, prime numbers, and composite numbers
Factors; Divisibility and
Remainders
I S1C3PO2 Rational numbers; Estimate the location of rational and common irrational
irrational numbers; numbers on a number line
number line
I S1C2PO4 Standard notation; Convert standard notation to scientific notation and vice versa
Scientific notation; (include positive and negative exponents)
Positive and negative
exponents
I S1C2PO2 Multiplying and dividing Describe the effect of multiplying and dividing a rational
rational number by
numbers • a number less than zero
• a number between zero and one
• a number greater than one
I S1C3PO1 Estimation; Situation Make estimates appropriate to a given situation
* = 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. 8th Grade Math Curriculum Map
Isaac School District No. 5
Quarter 1
Unit Name and Description: Solving Algebraic Equations and Inequalities
Cluster 2
Big Ideas/Enduring Understandings Essential Question(s)
Algebraic equations, inequalities, and graphs are representative of real life What is absolute value? Why do we have absolute value?
situations.
How do we use simple interest to track the growth of our money?
How can we use equations to solve real life problems?
AZ Essential Learning Key Technology
EIN
Standard Knowledge Skills Vocabulary Resources
E S3C3PO3 Linear equations; Analyze situations involving linear equations and Linear equations
Inequalities; Real inequalities using the properties of the real number system Inequalities
number system Equations
Simplify problems involving linear equations and Expression
inequalities using the properties of the real number system Percent increase
Percent decrease
Solve problems involving linear equations and inequalities Absolute value
using the properties of the real number system Solution
E S3C3PO1 Algebraic expressions; Write algebraic expressions, equations, or inequalities that Principle
Equations; represent a situation Interest rates
Inequalities
Identify algebraic expressions, equations, or inequalities that
represent a situation
* = 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. E S3C3PO5 Inequalities; Number line Graph an inequality on a number line
E S1C1PO4 Absolute value Model problems involving absolute value
Solve problems involving absolute value
I S1C2PO3 Simple interest rates; Solve problems involving percent increase, percent decrease,
Percent and simple interest rates
increase/decrease;
Ending balance
E S3C3PO2 Expressions; Rational Evaluate an expression containing variables by substituting
numbers; rational numbers for the variables
Variables
E S1C2PO5 Square roots; Cube roots; Simplify numerical expressions using the order of operations
Grouping that include grouping symbols, square roots, cube roots,
symbols; Positive absolute values, and positive exponents
exponents; Absolute
I S3C4PO2 Simple rates Solve problems involving simple rates
I S5C2PO6 Informal mathematical Communicate the answer(s) to the question(s) in a problem
language; using appropriate representations, including symbols and
Formal mathematical informal and formal mathematical language
language; Symbols;
Representations
* = 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. 8th Grade Math Curriculum Map
Isaac School District No. 5
Quarter 2
Unit Name and Description: Ratios and Proportions
Cluster 3
Big Ideas/Enduring Understandings Essential Question(s)
Ratios and proportions are used to determine the relationship between ideas. How do unit multipliers help me convert?
How can we translate real-life situations into algorithms?
How do we convert between customary and metric systems?
AZ Essential Learning Key Technology
EIN
Standard Knowledge Skills Vocabulary Resources
E S4C4PO2 Geometric problems; Solve geometric problems using ratios and proportions Ratios
Ratios; Proportions Proportions
Corresponding
I S4C4PO1 Problems; Measurement Solve problems involving conversions within the same
sides/angles
system; Conversions measurement system
Congruency
I S4C1PO3 Proportional reasoning; Use proportional reasoning to determine congruence and Similarity
Similar Triangles; similarity of triangles Geometric
Congruence; Problems
E S5C1PO1 Algorithm; Proportional Create an algorithm to solve problems involving indirect Algorithm
reasoning; Density; measurements, using proportional reasoning, dimensional Density
Dimensional analysis analysis, and the concepts of density and rate. Scale Factor
I S5C2PO8 Problem solving; Describe when to use proportional reasoning to solve a Unit Rate
Proportional problem. Density
reasoning Dimensional
* = 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. 8th Grade Math Curriculum Map
Isaac School District No. 5
Quarter 2
Unit Name and Description: Pythagorean Theorem
Cluster 4
Big Ideas/Enduring Understandings Essential Question(s)
The Pythagorean Theorem can be used to calculate the distance between two How the Pythagorean Theorem applies to right triangles?
points.
How do we apply the Pythagorean Theorem to calculate the distance of a line
segment?
AZ Essential Learning Key Technology
EIN
Standard Knowledge Skills Vocabulary Resources
E S4C3PO2 Pythagorean Theorem; Use the Pythagorean Theorem to [calculate] the distance Pythagorean
Coordinate between two points in the coordinate plane Theorem
plane; Distance; Points Leg(s)
Hypotenuse
E S4C1PO4 Pythagorean Theorem Use the Pythagorean Theorem to solve problems
Midpoint
I S4C3PO1 Midpoint; Conjecture; Make a conjecture about how to [calculate] the midpoint
Points; between any two points in the coordinate plane
Coordinate plane
Test a conjecture about how to [calculate] the midpoint
between any two points in the coordinate plane
I S5C2PO13 Pythagorean Theorem; Verify the Pythagorean Theorem using a valid argument
Valid argument
* = 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. 8th Grade Math Curriculum Map
Isaac School District No. 5
Quarter 2
Unit Name and Description: Functions and Linear Relationships
Cluster 5
Big Ideas/Enduring Understandings Essential Question(s)
Functions represent given situations from real life. How do we determine if a graph is a function?
Two variables are related. How do we determine if a graph is proportional?
Explain how to determine if an equation is linear.
How many output values are assigned to a function?
How does changing the slope of a line affect its steepness?
AZ Essential Learning Key Technology
EIN Standard Vocabulary Resources
Knowledge Skill
E S3C4PO1 Linear equations; s
Interpret, the relationship between a linear equation Slope-intercept
Linear relationships; and its graph. form
Slope; Intercept Standard form
Identifying slope and intercepts Slope
Y-intercept
Computing slope and intercepts Proportionality
Linear equations
I S3C2PO5 Proportional relationships; Demonstrate that proportional relationships are linear using
Linear functions
Linear; Equations; equations, graphs, or tables
Functions
Graphs; Tables
Function table
* = 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. E S3C3PO4 Representations; Translate between different representations of linear
Linear equations; equations
Graphs, Tables, Written using symbols, graphs, tables, or written descriptions
descriptions
I S3C2PO3 Rule; Algebraic notation; Write the rule for a simple function using algebraic notation
Simple functions
I S3C2PO2 Relationship; Graph; Determine if a relationship represented by a graph or table is
Table; a function
Function
I S3C2PO4 Linear and nonlinear Identify functions as linear or nonlinear and contrast
functions; graphs, distinguishing properties of functions using equations,
or tables graphs, or tables
I S3C1PO1 Numerical and geometric Recognize and describe numerical and geometric sequences
sequences; Tables, using tables, graphs, words, or symbols.
Graphs, Words, Symbols;
Conjectures Create and analyze numerical and geometric sequences
using tables, graphs, words, or symbols.
I S5C2PO12 Conclusions; Make conclusions and generalizations about linear
Generalizations; relationships
Linear relationships
Validate conclusions and generalizations about
linear relationships
* = 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. 8th Grade Math Curriculum Map
Isaac School District No. 5
Quarter 2
Unit Name and Description: Geometric Shapes
Cluster 6
Big Ideas/Enduring Understandings Essential Question(s)
Geometric shapes are evident in everyday life. How does the area of the base affect an objects volume?
Geometric formulas can be manipulated to solve for the unknown attribute of How do you use a rectangle to calculate the surface area of a cylinder?
a shape.
Will a given transformations affect an objects size or shape?
How does doubling the diameter of a circle affect its area?
AZ Essential Learning Key Technology
EIN
Standard Knowledge Skills Vocabulary Resources
E S4C1PO2 Geometric planes and Predict results of combining, subdividing, and changing Rectangular prism
solids shapes of plane figures and solids Triangular prism
Cylinder
Surface area
E S4C4PO3 Rectangular prisms; Calculate the surface area and volume of rectangular prisms, Volume
Cylinders; right triangular prisms, and cylinders Radius
Right triangular prisms Diameter
Chords
* = POs previously introduced EIN = Level of Priority for P.O. Bold = Priority PO 9
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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10. E S4C1PO1 Radius; Diameter; Chords; Identify for the attributes of circles: radius, diameter, chords, Tangent
Tangents; Secants; tangents, secants, inscribed angles, central angles, intercepted Secants
Inscribed angles; Central; arcs, circumference, and area Inscribed angles
angles; Intercepted arcs; Central
[Solve for the circumference and the area of a circle] anglesIntercepted
arcs
Circumference
N S4C2PO2 Transformations; Describe the transformations that create a given tessellation
Rotations (turn)
Tessellations
Origin
Rotational
symmetry
Reflective
N S4C2PO1 Rotations; Origin; 45 Model the result of rotations in multiples of 45 degrees of a 2- symmetry
degrees, 2- dimensional figure about the origin Tessellations
Dimensional figure Midpoint
Pi (π)
Parallelogram
Trapezoid
N S4C2PO3 Lines of symmetry; Identify lines of symmetry in plane figures Rhombus
Plane figures; Quadrilateral
2-Dimensional figures [Determine] lines of symmetry in plane figures Prism
Complex polygon
Classify types of symmetries of 2-dimensional figures Composite figure
Polyhedron
* = 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. 8th Grade Math Curriculum Map
Isaac School District No. 5
Quarter 2
Unit Name and Description: Data Display
Cluster 7
Big Ideas / Enduring Understandings Essential Question(s)
Data allows us to analyze the past and make predictions about the future. How do we determine which graph is the most appropriate representation of a
given data set?
There are multiple ways to represent data.
How do we determine which measure of central tendency is most
representative of a given data set?
How do outliers affect the mean of a data set?
Will each measure of central tendency be representative of your data set?
AZ Essential Learning Key Technology
EIN
Standard Knowledge Skills Vocabulary Resources
E S2C1PO3 Summary statistics; Describe how summary statistics relate to the shape of the Box and whisker
Shape of distribution distribution plot
First quartile
Median
Third quartile
I S2C1PO2 Summary statistics; Data Make inferences by comparing the same summary statistic for Lower extreme
sets; Inferences two or more data sets Upper extreme
Inter-quartile range
Random sampling
* = 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. I S2C1PO1 Displays of data; Box and Solve problems by selecting and constructing, displays of Sample
whisker plots; Scatterplots data, including box and whisker plots and scatterplots Biased surveys
Circle graphs
Solve problems by interpreting and calculating displays of Time-distance
data, including box and whisker plots and scatterplots graph
Directed graph
N S2C1PO4 Information; Sources of Determine whether information is represented effectively and Experiment
bias; Representations of appropriately given a graph or a set of data by identifying Experimental
data; Graphs; (Histograms; sources of bias and compare and contrast the effectiveness of design
Circle graphs; Stem- different representations of data Scatterplots
and-leaf plot; Scatterplots;
Line) graph; Double line
graph; Venn diagram
N S3C2PO1 Graph; Context; Sketch a graph that models a given context
Interpret a graph that models a given context
Describe a context that is modeled by a given graph
I S5C2PO7 Information; Symbols; Isolate mathematical information taken from symbols,
Diagrams; diagrams, and graphs to make inferences, draw conclusions,
Graphs; Inferences; and justify reasoning
Conclusions; Reasoning
(Frequency tables; Venn Organize mathematical information taken from symbols,
diagrams; Bar graphs; diagrams, and graphs to make inferences, draw conclusions,
Circle and justify reasoning
I S2C4PO1 Directed graphs; Problems Use directed graphs to solve problems
N S5C2PO1 Problem situation; Analyze a problem situation to determine the question(s) to be
Questions answered
N S2C1PO5 Experimental design Evaluate the design of an experiment
* = 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. 8th Grade Math Curriculum Map
Isaac School District No. 5
Quarter 3
Unit Name and Description: Probability
Cluster 8
Big Ideas/Enduring Understandings Essential Question(s)
Probability can be used to predict the outcome of an event. How does changing the total outcome of an event affect the probability?
The total number of outcomes affects the probability of an event. How do dependent events affect the probability of a compound event?
What is the difference between theoretical and experimental probability?
What is the difference between combinations and permutations?
AZ Essential Learning Key Technology
EIN Standard Vocabulary Resources
Knowledge Skills
E S2C2PO1 Theoretical probability; Determine theoretical and experimental conditional Theoretical
Experimental probabilities in compound probability experiments probability
probability; Compound Experimental
probability; probability
Compound events
Independent events
Dependent events
I S2C2PO2 Probability; Outcome; Interpret probabilities within a given context
Mutually exclusive
Experiment; Predictions;
Fundamental
Context Experiments Compare the outcome of an experiment to predictions made
counting principle
prior to performing the experiment
* = 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. I S2C2PO3 Possible outcomes; Sample Use all possible outcomes (sample space) to determine the Possible outcomes
space; Probability; probability of dependent and independent events Tree diagram.
Dependent events; Permutations
Independents events Combinations
Factorial notation
E S2C3PO2 Problems; Factorial Solve counting problems algebraically including factorial Sample space
notation; notation
Counting principal
Represent counting principles algebraically including factorial
notation
I S2C3PO1 Counting problems Represent, analyze, and solve counting problems with or
without ordering repetitions
N S5C2PO9 Conjectures; Information; Make conjectures based on information collected from
Explorations; Experiments explorations and experiments
Test conjectures based on information collected from
explorations and experiments
N S5C2PO10 Logical conclusions; Solve logic problems involving multiple variables, conditional
Conditional statements; statements, conjectures, and negation using words,
Conjectures; Negation; charts, and pictures
Charts; Pictures
I S5C2PO11 Simple valid arguments; Identify simple valid arguments using If… then statements.
If… then statements
* = 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. 8th Grade Math Curriculum Map
Isaac School District No. 5
Quarter 3
Unit Name and Description: Logical Evaluations
Cluster 9
Big Ideas/Enduring Understandings Essential Question(s)
There are various strategies for problem solving. Why do we use different mathematical strategies to solve a problem?
Logical processes help them to eliminate unreasonable solutions. How do we identify pertinent and extraneous information from a question?
AZ Essential Learning Key Technology
EIN Standard Resources
Knowledge Skill Vocabulary
E S5C2PO2 s
Mathematical strategies; Analyze and compare mathematical strategies for efficient Expressions
Problem problem solving Guess and check
solving Substitute
Select and use one or more strategies to solve a problem Extraneous
information
I S5C2PO3 Relevant, missing, and Identify relevant, missing, and extraneous information related Pertinent
extraneous information; to the solution to a problem information
Relevant
I S5C2PO4 Problem situation; Represent a problem situation using multiple representations information
Representations; Conditional
Process; Reasonableness; Describe the process used to solve the problem statement
Verify the reasonableness of the solution
I S5C2PO5 Problem solving strategy; Apply a previously used problem-solving strategy in a new
context
* = 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. 8th Grade Math Curriculum Map
Isaac School District No. 5
Quarter 4
Unit Name and Description: Algebra and Equations
Cluster 10
Big Ideas/Enduring Understandings Essential Question(s)
Functions model real life situations. How are inequalities represented on the coordinate plane?
Algebra is essential in using functional notation. Why do problems involving absolute value have two answers?
Absolute value represents the distance from zero. What is the relationship between rate of change and slope?
What is the relationship between tables, functions, and graphs?
AZ Essential Learning Key Technology
EIN
Standard Knowledge Skills Vocabulary Resources
E MHS-S4C3PO5 Linear equation; Graph a linear equation or linear inequality in two Slope-intercept
Linear inequalities; variables form
Two variables Linear inequalities
Standard form
I MHS-S3C3PO5 Linear equations; absolute Solve linear equations and equations involving absolute value System of
value; Variable with one variable equations
Absolute value
Constant rate of
change
Functional notation
Domain
* = 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. E MHS-S3C4PO1 Slope; Intercepts; Graph; Determine the slope and intercepts of the graph of a linear
Slope; Constant rate function, interpreting slope as a constant rate of change
of change; Linear
functions
I MHS-S3C2PO3 Functions notation; Use function notation; evaluate a function at a specified value
Functions; Value; Domain in its domain
I MHS-S3C3PO3 Equations; Table of values; Write an equation given a table of values, two points on the
Points; Line; Slope; Graph line, the slope and a point on the line, or the graph of the line
I MHS-S3C3PO6 Linear inequalities; Solve linear inequalities in one variable
Variable
* = 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
E