Mathematics Curriculum Guide
Diocese of Sioux City
Grades 9-12
Standards and Benchmarks with Critical Objectives aligned with ITED
Standard 1: Understands and applies concepts of numbers and operations.
Benchmark 1: Describes the properties of numbers and number systems
Vocabulary
Critical Objectives:
1.1.1. Understands properties of real numbers and its subsystems
Relative magnitude
9
10
11
12
Absolute value
(ITED ** ** ** **)
Natural numbers
1.1.2. Knows the relationships among the subsystems of the real
Integers
numbers system
Rational numbers
1.1.3. Understands the type of equations that can and cannot be solved
Irrational numbers
within each subsystem
Real numbers
Subsystem
1.1.4. Represents numbers within each subsystem (ITED 9 10 11 12)
Matrix
1.1.5. Uses the appropriate number system representation for given
Vector
problem situations (ITED 9 10 11 12)
Scalar
1.1.6. Interprets numerical answers on a calculator or computer display
Multiplication
1.1.7. Explores new number systems, such as vectors and matrices
Magnitude
Direction
1.1.8. Knows what operation properties hold for operations with
Fraction
matrices and vectors
Decimal
1.1.9. Determines what operation properties hold for matrix addition
Percent
and multiplication
Equivalent formats
1.1.10. Calculates sums, differences, and products of matrices
Squaring
Square root
1.1.11. Determines what operation properties hold for vector addition
Exponent
and subtraction
Base
1.1.12. Calculates vector addition and multiplication
Expanded notation
1.1.13. Uses the appropriate form of a rational number (fraction,
decimal, percent) in computations (ITED 9*** 10 *** 11*** 12***)
1.1.14. Understands fractions, decimals, and percents can be expressed in various ways
1.1.15. Knows which rational number is most appropriate based on the context of the
problem
1.1.16. Converts fractions, decimals, and percents to equivalent forms (ITED 9 10 11 12)
1.1.17. Identifies the appropriate rational number to use in a problem situation (ITED 9 10 11
12
)
1.1.18. Uses the properties of roots, exponents in computations (ITED 9** 10** 11** 12**)
1.1.19. Knows squaring is the product of a whole number multiplied by itself
1.1.20. Knows squaring and square root are inverse operations
1.1.21. Knows an exponent tells how many times a base is used as a factor
1.1.22. Knows the rules for multiplying an dividing numbers with exponents
1.1.23. Knows the rules for raising a number with an exponent to a power
1.1.24. Finds the square root of any number
1.1.25. Writes exponents in expanded notation
1.1.26. Simplifies expressions containing exponents (ITED 9 10 11 12)
1.1.27. Writes expressions using scientific notation (ITED 9 10 11 12)
Diocese of Sioux City
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2006
Mathematics Curriculum Guide
Diocese of Sioux City
Grades 9-12
Standards and Benchmarks with Critical Objectives aligned with ITED
Benchmark 2: Understands the properties of operations
Vocabulary
Critical Objectives:
1.2.1. Uses the properties of operations to simplify computations
Identity property
Inverse property
1.2.2. Knows the inverse operations undo each other
Distributive property
1.2.3. Knows the identity properties of addition and multiplication
Associative property
1.2.4. Knows the distributive, associative, and commutative properties of
Commutative property
addition and multiplication
Squaring
1.2.5. Knows squaring and square root are inverse operations
Square root
Like terms
1.2.6. Simplifies equations using properties of operations
Order of operations
1.2.7. Explains the meaning of adding, subtracting, multiplying, and
Grouping
dividing integers
Inverse operations
1.2.8. Uses inverse properties and relationships to solve problems
1.2.9. Finds the square root of any number
1.2.10. Uses the properties of operations to solve problems (ITED 9*** 10*** 11*** 12***)
1.2.11. Recognizes like terms
1.2.12. Understands rules for combining variables
1.2.13. Knows the order of operations
1.2.14. Knows the inverse relationship between properties of operations
1.2.15. Uses order of operation, including grouping symbols, to solve problems (ITED 9 10 11
12
)
Benchmark 3: Computes fluently and makes reasonable estimates
Critical Objectives:
1.3.1. Uses a variety of operations on expressions containing complex
numbers (ITED 9*** 10*** 11*** 12***)
1.3.2. Knows the algorithms of operations for complex numbers
1.3.3. Adds, subtracts, multiplies, divides, and simplifies expressions of
complex numbers (ITED 9 10 11 12)
1.3.4. Uses estimation strategies for computing complex numbers (ITED
9
*** 10*** 11*** 12***)
1.3.5. Knows when an estimate or an exact answer is more appropriate
1.3.6. Knows how to judge the reasonableness of an answer
1.3.7. Understands that rounding and estimation inherently add discrepancy
1.3.8. Understands appropriate places to round when estimating
1.3.9. Checks answers using estimation strategies (ITED 11 12)
1.3.10. Uses the appropriate places when estimating answers (ITED 9 10 11 12)
1.3.11. Makes reasonable estimates (ITED 9 10 11 12)
Diocese of Sioux City
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Vocabulary
Simplify
Complex numbers
Estimation
Exact answer
Mental computation
Rounding
2006
Mathematics Curriculum Guide
Diocese of Sioux City
Grades 9-12
Standards and Benchmarks with Critical Objectives aligned with ITED
Standard 2: Understands and applies concepts of algebra and functions.
Benchmark 1: Represents patterns and relationships in a variety of ways
Critical Objectives:
2.1.1. Uses patterns and relationships to analyze mathematical situations
(ITED 10 * 11* 12*)
2.1.2. Knows sequences and series can be used to model problems
2.1.3. Uses words, tables, and graphs and symbolic rules to describe
patterns (ITED 10 11 12)
2.1.4. Describes the relationship of sequences symbolically
2.1.5. Generates formulas to describe a pattern
Vocabulary
Sequences
Series
Recursive patterns
Iterative patterns
Benchmark 2: Describes the properties and characteristics of functions
Vocabulary
Critical Objectives:
Function
2.2.1. Describes functions and their properties using function notation
Domain
9 10 11 12
(ITED * * * *)
Range
2.2.2. Knows for every value in the domain of a function, there is one
One-to-one
and only one corresponding value in the range
Correspondence
Function notation
2.2.3. Understands the concept of a function as the correspondence
Polynomial
between the elements of two sets
Exponential
2.2.4. Understands the definition of a function: domain, range, function,
Rational
non-function
Logarithmic
2.2.5. Identifies the domain, range, and rule of a function
Periodic
Parameter
2.2.6. Describes functions and their properties using function notation
2.2.7. Recognizes the graphs of non-linear functions (ITED 10 11 12)
2.2.8. Describes from a graph the relationship between two variables (ITED 9 10 11 12)
2.2.9. Explores the properties of different classes of functions (ITED 9* 10** 11** 12**)
2.2.10. Knows the same function can be represented in a variety of forms
2.2.11. Knows the limitations of non-linear functions
2.2.12. Understands the concept of a class of functions
2.2.13. Identifies functions expressed numerically or algebraically as linear or non-linear
(ITED 10 11 12)
2.2.14. Recognizes properties of families of functions and how the values of parameters
shape the graphs (ITED 9 10 11 12)
2.2.15. Compares properties of various functions to find common characteristics
Diocese of Sioux City
-3-
2006
Mathematics Curriculum Guide
Diocese of Sioux City
Grades 9-12
Standards and Benchmarks with Critical Objectives aligned with ITED
Benchmark 3: Uses expressions and symbols to represent mathematical
Vocabulary
relationships
Critical Objectives:
Equivalent forms
Dimensional analysis
2.3.1. Rewrites algebraic expression in equivalent forms (ITED 9***
10
11
12
Monomials
*** ** **)
Binomials
2.3.2. Recognizes like terms
Polynomials
2.3.3. Knows rules to simplify expressions
Common monomial factor
2.3.4. Knows the order of operations
Factoring
Perfect square
2.3.5. Understands the meaning of equivalent forms of expressions
2.3.6. Simplifies algebraic expressions by combining like terms and
applying appropriate properties (ITED 9 10)
2.3.7. Uses dimensional analysis to organize conversions and computations (ITED 9 10 11 12)
2.3.8. Operates fluently on algebraic expressions by combining them and re-expressing
them in alternate forms (ITED 9 10 11 12)
2.3.9. Manipulates polynomial expressions
2.3.10. Knows the various methods to factor polynomial expressions
2.3.11. Knows the properties of combining polynomials: addition, subtraction, multiplication,
and division
2.3.12. Knows some polynomials cannot be solved precisely
2.3.13. Adds, subtracts, multiplies, and divides monomials and polynomials
2.3.14. Applies basic factoring techniques to second and simple third-degree polynomials
2.3.15. Simplifies fractions with polynomials in the numerator and denominator
2.3.16. Finds the number and type of roots of a polynomial equation
Benchmark 4: Uses models to represent mathematical situations
Critical Objectives:
2.4.1 Uses a variety of methods to solve equations (ITED 9*** 10***
11
*** 12***)
2.4.2 Recognizes like terms
2.4.3 Understands rules for combining variables
2.4.4 Knows the order of operations
2.4.5 Knows the inverse relationship between addition and subtraction
and multiplication and division
2.4.6 Understands such operations as taking the opposite, finding the
reciprocal, taking the square root
2.4.7 Solves equations for a specified variable (ITED 9 10 11 12)
2.4.8 Solves multi-step problems (ITED 9 10 11 12)
2.4.9 Writes an equation for a specific problem (ITED 9 10 11 12)
2.4.10 Uses a variety of methods to solve quadratic equations
2.4.11 Knows the strengths and limitations of each method
2.4.12 Understands the roots of a quadratic equation are given by the
quadratic formula
2.4.13 Knows the quadratic formula gives exact values
Diocese of Sioux City
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Vocabulary
Multi-step problems
Quadratic equation
Factoring
Completing the square
Quadratic formula
Roots
Discriminant
Linear equation
Inequality
Slope
x-intercept
y-intercept
General line equation
Dependent variable
Independent variable
System of equations
Substitution
Elimination
2006
Mathematics Curriculum Guide
Diocese of Sioux City
Grades 9-12
Standards and Benchmarks with Critical Objectives aligned with ITED
2.4.14 Knows the discriminant can provide information about the roots of a quadratic
equation
2.4.15 Solves quadratic equations by graphing, factoring, completing the square, and the
quadratic formula
2.4.16 Analyzes problem situations to decide which method of solving quadratic equations is
appropriate
2.4.17 Uses a variety of methods to graph linear equations and inequalities (ITED 11* 12*)
2.4.18 Knows how the slope and y-intercept of a graph are related to the equation
2.4.19 Knows the algebraic significance of the parts of a graph
2.4.20 Understands properties of graphs and relationships between a graph and its
corresponding expression
2.4.21 Knows the numerical value of the slope
2.4.22 Knows the numerical value of y-intercept
2.4.23 Graphs a linear equation and inequality
2.4.24 Recognizes a linear equation and inequality from its graph (ITED 11 12)
2.4.25 Finds the slope, x-intercept, and y-intercept of a line given its graph, its equation, or
two points on the line (ITED 11 12)
2.4.26 Writes equations in the General Line Equation format
2.4.27 Identifies the dependent and independent variables
2.4.28 Graphs a linear equation and computes the x- and y-intercepts
2.4.29 Verifies a point lies on a line given an equation of the line
2.4.30 Uses a variety of methods to solve systems of equations
2.4.31 Knows the strengths and limitations of each method
2.4.32 Knows whether a system of equations has one solution, no solutions, or infinitely
many solutions
2.4.33 Uses a graph to find the solution of a system of equations
2.4.34 Uses substitution to solve a system of equations
2.4.35 Uses elimination to solve a system of equations
Benchmark 5: Analyzes change in a variety of situations
Vocabulary
Critical Objectives:
9 10
2.5.1 Uses a variety of representations to analyze change (ITED * *
Rates of change
11
** 12**)
Attribute
2.5.2 Understands change can be described mathematically
Slope
2.5.3 Understands how rates of change can be described numerically and
graphically
2.5.4 Represents constant rates as the slope of a straight line graph (ITED 11 12)
2.5.5 Interprets slope as the amount of one quantity (y) per unit amount of another (x)
(ITED 11 12)
2.5.6 Expresses rate of change graphically (ITED 11 12)
2.5.7 Predicts rate of change from numerical and graphical data (ITED 9 10 11 12)
Diocese of Sioux City
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2006
Mathematics Curriculum Guide
Diocese of Sioux City
Grades 9-12
Standards and Benchmarks with Critical Objectives aligned with ITED
Standard 3: Understands and applies properties of geometry.
Vocabulary
Benchmark 1: Uses properties of figures to verify relationships
Critical Objectives:
3.1.1. Describes figures by their characteristics
3.1.2. Knows the characteristics of figures
3.1.3. Describes geometric figures using their characteristics
3.1.4. Classifies figures by their discrete characteristics
3.1.5. Uses properties of lines to describe relationships between figures
3.1.6. Knows the properties of line segments
3.1.7. Knows the midpoint of a line segment divides the line into two
equal parts
3.1.8. Knows how to find the length of line segments
3.1.9. Describes relationships of figures using line properties
3.1.10. Uses properties of angles to describe relationships between figures
3.1.11. Knows the properties of angles
3.1.12. Understands the relationship of angles when two parallel lines are
cut by a transversal
3.1.13. Knows the relationship between the number of sides of a polygon
and the measure of its interior angles
3.1.14. Describes relationships of figures using angle properties
3.1.15. Uses properties of circles to describe relationships between figures
3.1.16. Knows the properties of circles
3.1.17. Describes relationships of figures using properties of circles
3.1.18. Uses congruence and similarity to describe relationships among
figures
3.1.19. Knows the properties of congruent and similar figures
3.1.20. Knows the difference between similarity and congruence
3.1.21. Knows the ratio for corresponding sides of similar triangles are the
same
3.1.22. Recognizes figures as congruent or similar
3.1.23. Uses proportionality to show similarity
Diocese of Sioux City
-6-
Polygon
Triangle
Circle
Quadrilateral
Rhombus
Kite
Rectangle
Square
Trapezoid
Cone
Cylinder
Prism
Pyramid
Sphere
Venn Diagram
Line
segment
Ray
Parallel lines
Perpendicular lines
Skew lines
Intersection
Bisecting
Midpoint
Collinear
Coplanar
Vertical angle
Adjacent angle
Complementary angle
Supplementary angle
Right angle
Interior angle
Exterior angle
Corresponding angle
Transversal
Circle
Diameter
Radius
Arc
Chord
Secant
Inscribed angle
Semicircle
Congruent
Similar
Corresponding parts
Proportionality
Similar figures
Congruent figures
2006
Mathematics Curriculum Guide
Diocese of Sioux City
Grades 9-12
Standards and Benchmarks with Critical Objectives aligned with ITED
Benchmark 2: Uses coordinate geometry to verify relationships
Vocabulary
Critical Objectives:
3.2.1. Uses the coordinate plane to show how geometric relationships
Coordinate plane
Distance formula
correspond directly to algebraic concepts
Midpoint formula
3.2.2. Knows selecting the origins of a figure makes the calculations
Slope formula
easier
Vertex-edge graph
3.2.3. Knows the formulas for distance, midpoint, and slope
3.2.4. Finds the distance and midpoints of segments in the coordinate plane
3.2.5. Compares the slopes and distances of line segments to verify a figure classification
3.2.6. Uses vertex-edge graphs to model and solve problems involving paths, networks, or
relationships among a finite number of objects
Benchmark 3: Applies the concepts of transformation and symmetry
Critical Objectives:
3.3.1. Uses various representations to describe transformations
3.3.2. Knows that a transformation is a one-to-one correspondence
3.3.3. Knows the difference between the types of transformations
3.3.4. Knows how to describe position using matrices
3.3.5. Represents transformations using sketches, coordinates, vectors,
function notation, and matrices
3.3.6. Identifies the types of transformations that make up a composition
3.3.7. Uses matrices to represent transformations
3.3.8. Describes figures in terms of their symmetry
3.3.9. Knows the difference among the types of symmetry
3.3.10. Identifies the type of symmetry in figures
Diocese of Sioux City
-7-
Vocabulary
Transformation
Image
Pre-image
Isometry
Orientation
Translation
Composition
Rotation
Reflection
Dilation
Matrix
Symmetry
Reflectional symmetry
Rotational symmetry
Point symmetry
2006
Mathematics Curriculum Guide
Diocese of Sioux City
Grades 9-12
Standards and Benchmarks with Critical Objectives aligned with ITED
Benchmark 4: Uses geometric reasoning to solve problems
Vocabulary
Critical Objectives:
3.4.1. Uses proofs to build logical reasoning skills
Conjecture
Proof
3.4.2. Knows the difference between a definition, theorem, and a
Theorem
postulate
Postulate
3.4.3. Knows the steps for completing a proof
Axiom
3.4.4. Uses inductive and deductive reasoning to verify properties and
Inductive reasoning
relationships
Deductive reasoning
Formula
3.4.5. Uses proofs to write convincing arguments
Perimeter
3.4.6. Establishes the validity of conjectures
Circumference
3.4.7. Uses formulas for perimeter, area, and volume of various figures
Area
(ITED 9*** 10*** 11*** 12***)
Surface area
3.4.8. Knows the formulas for perimeter, area, surface area, and volume
Lateral area
Volume
3.4.9. Knows how to solve a formula for any given variable
9 10 11 12
Composite figure
3.4.10. Computes the perimeter of various figures (ITED
)
Pythagorean Theorem
9 10 11 12
3.4.11. Computes the circumference of a circle (ITED
)
30-60-90 triangles
3.4.12. Finds the length of an arc (ITED 11)
45-45 triangles
3.4.13. Computes the area of various figures (ITED 9 10 11 12)
Right triangles
9 10 11 12
Trigonometry
3.4.14. Computes the volume of various figures (ITED
)
Sine
3.4.15. Uses properties of triangles to prove and verify relationships
Cosine
9 10
(ITED * *)
Tangent
3.4.16. Knows the Pythagorean Theorem
Inverse sine
3.4.17. Knows the properties of special triangles
Inverse cosine
Inverse tangent
3.4.18. Uses the Pythagorean Theorem and its converse to find segment
9 10
lengths (ITED )
3.4.19. Uses the properties of special right triangles to solve problems
3.4.20. Uses trigonometric relationships to determine lengths and angle measurements
3.4.21. Knows the trigonometric ratios
3.4.22. Determines the appropriate trigonometric ratio for a specific problem
3.4.23. Uses trigonometric ratios to find lengths and angle measurements
Diocese of Sioux City
-8-
2006
Mathematics Curriculum Guide
Diocese of Sioux City
Grades 9-12
Standards and Benchmarks with Critical Objectives aligned with ITED
Standard 4: Understands and applies concepts of measurement.
Benchmark 1: Understands measurable attributes and the process of
Vocabulary
measurement
Critical Objectives:
Attribute
Indirect measure
4.1.1. Uses indirect and derived measures to express measures of
9 10 11 12
Derived measure
attributes (ITED * * * *)
Rate
4.1.2. Knows some attributes can only be measured indirectly
Increasing
4.1.3. Knows some measures are derived measures
Approximation
4.1.4. Knows some measurements of attributes are determined by a
Process
Attribute
sequence of increasing approximations
Appropriate
4.1.5. Selects the appropriate indirect approach to solve a problem
Comparison
situation
4.1.6. Calculates attributes using indirect measures (ITED 9 10 11 12)
4.1.7. Uses rates as a measure of attributes
4.1.8. Uses increasing approximations to determine measures of attributes (ITED 9 10 11 12)
4.1.9. Applies the measurement process (ITED 9*)
4.1.10. Understands the process to be used when measuring attributes
4.1.11. Calculates error
4.1.12. Identifies the attribute to be measured
4.1.13. Chooses an appropriate unit (ITED 9)
4.1.14. Compares the unit with the object to be measured
Benchmark 2: Uses a variety of techniques for measurement
Vocabulary
Critical Objectives:
Measurement system
4.2.1. Converts measurements between systems (ITED 9** 10** 11* 12**)
Dimensional analysis
4.2.2. Knows units should be reported along with numerical values
Viewing window
4.2.3. Understands the meaning of equivalent forms of units
Scale
4.2.4. Knows units can be used to organize conversions
Logarithmic scale
4.2.5. Uses dimensional analysis to organize conversions and
Formula
Perimeter
computations (ITED 9 10 11 12)
Circumference
4.2.6. Converts measurements from one system to another (ITED 10 11 12)
Area
4.2.7. Understands the importance of scale selection
Surface area
4.2.8. Knows choices about scale and/or viewing windows help solve
Lateral area
problems more effectively
Volume
Composite figures
4.2.9. Knows choices about scale and/or viewing windows can distort
Degree of accuracy
solutions
Degree of precision
4.2.10. Uses the appropriate scale and/or viewing window to solve a
Approximation
problem
4.2.11. Uses formulas to find perimeter, area, and volume of various figures (ITED 9***
10
*** 11** 12**)
4.2.12. Knows the formulas for perimeter, circumference, area, surface area, and volume
4.2.13. Knows how to solve a formula for a given variable
4.2.14. Computes the perimeter of various figures (ITED 9 10 11 12)
4.2.15. Computes the circumference of a circle (ITED 11 12)
Diocese of Sioux City
-9-
2006
Mathematics Curriculum Guide
Diocese of Sioux City
Grades 9-12
Standards and Benchmarks with Critical Objectives aligned with ITED
4.2.16. Computes the area of various figures (ITED 9 10 11 12)
4.2.17. Computes the volume of various figures (ITED 9 10 11 12)
4.2.18. Makes reasonable estimates about the accuracy of solutions (ITED 11* 12*)
4.2.19. Knows measurements of continuous quantities are approximations
4.2.20. Knows the degree of precision for a solution is dependent upon the accuracy of the
measurement
4.2.21. Uses the appropriate degree of accuracy for reporting solutions (ITED 11 12)
4.2.22. Estimates answers to check accuracy of a solution
Diocese of Sioux City
-10-
2006
Mathematics Curriculum Guide
Diocese of Sioux City
Grades 9-12
Standards and Benchmarks with Critical Objectives aligned with ITED
Standard 5: Understands and applies concepts of data analysis and probability.
Benchmark 1: Collects, organizes, and displays data to answer a question
Critical Objectives:
Vocabulary
5.1.1. Gathers data to answer questions (ITED 9* 10*)
Convenience sampling
5.1.2. Knows different ways to collect a sample and the inherent bias in
Survey sampling
each
Random sampling
5.1.3. Knows how to formulate a questions that can be verified by data
Bias
Sampling error
collection
Bar graph
5.1.4. Knows factors which add or detract from certainty of a data set
Line graph
5.1.5. Formulates a question that can be answered by data collection
Circle graph
5.1.6. Collects data using a sampling technique
Stem-and-leaf plot
5.1.7. Compares data from two or more samples to determine how
Box-and-whisker plot
Frequency table
sampling can influence results
Histogram
5.1.8. Uses knowledge of sampling, certainty, and data gathering to
Scatter plot
9 10
ascertain the certainty of the data (ITED )
Errors
5.1.9. Identifies possible bias in sampling
Misrepresentation
5.1.10. Represents data to convey results (ITED 9*** 10*** 11*** 12***)
5.1.11. Knows the basic types of charts, graphs, and tables
5.1.12. Knows different types of graphs convey different messages
5.1.13. Knows the criteria for selecting a graphical representation for a set of data
5.1.14. Knows types of errors in data representation that can lead to misinterpretation
5.1.15. Creates graphical representations appropriate for data type (ITED 9 10 11 12)
5.1.16. Identifies misleading representations of data
5.1.17. Extracts data from one graph and redisplays the data with a more appropriate
representation (ITED 10 11 12)
5.1.18. Reads data from graphs (ITED 9 10 11 12)
5.1.19. Draws conclusions from data represented in a graph (ITED 9 10 11 12)
5.1.20. Makes predictions from data represented in a graph (ITED 9 10 11 12)
Diocese of Sioux City
-11-
2006
Mathematics Curriculum Guide
Diocese of Sioux City
Grades 9-12
Standards and Benchmarks with Critical Objectives aligned with ITED
Benchmark 2: Uses statistical methods to describe data
Vocabulary
Critical Objectives:
5.2.1. Describes data using central tendency and other statistical terms
Central tendency
Outlier
(ITED 11* 12*)
Variability
5.2.2. Knows when to remove outliers from a data set
Quartile range
5.2.3. Knows an outlier may represent an error in data collection or a
Interquartile range
significant variation in the data set
Correlation
5.2.4. Knows the variability of a data set describes the "spread" of the
Gap
Cluster
numbers
Distribution
5.2.5. Knows correlations can be causally related or incidental
Normal curve
5.2.6. Explains the mean's sensitivity to outliers
Central limit
5.2.7. Determines the best measure of central tendency to describe a data
Theorem
set
Curve fitting
Lines of best fit
5.2.8. Calculates and compares measures of central tendency in two data
Regression line
sets
Least squares
5.2.9. Interprets representations of central tendency and variability
Regression
(ITED 11 12)
5.2.10. Recognizes correlations as causal or incidental
5.2.11. Calculates correlations for a given data set
5.2.12. Describes factors that affect measures of central tendency (ITED 11* 12*)
5.2.13. Knows adding numbers to a data set can affect measures of central tendency
5.2.14. Knows an outlier is a data point that does not correspond with the trend in the data set
5.2.15. Knows outliers can affect measures of central tendency
5.2.16. Knows gaps are an area of the distribution where there are no data points
5.2.17. Knows a cluster is a group of localized points
5.2.18. Identifies situations in which the mean, mode, or median would contain the most
relevant information
5.2.19. Calculates measures of central tendency with and without outliers (ITED 11 12)
5.2.20. Describes how the inclusion/exclusion of outliers affects measures of central
tendency
5.2.21. Identifies gaps and clusters in a data set
5.2.22. Uses different curve fitting methods to "fit" data
5.2.23. Knows the significance of quartile divisions under the normal curve
5.2.24. Knows the properties of the normal curve and how it can be used to describe data
5.2.25. Knows the advantages and disadvantages of curve fitting methods
5.2.26. Identifies data sets in which the results would be expected to approximate the normal
curve
5.2.27. Chooses the best method of curve fitting for a given data set
Diocese of Sioux City
-12-
2006
Mathematics Curriculum Guide
Diocese of Sioux City
Grades 9-12
Standards and Benchmarks with Critical Objectives aligned with ITED
Benchmark 3: Reads and interprets data
Critical Objectives:
5.3.1. Uses sampling distribution to make informal inferences (ITED 9*
10
*** 11* 12*)
5.3.2. Knows how bias can affect the interpretation of data
5.3.3. Knows possible sources of sampling error
5.3.4. Knows what constitutes a representative sample
5.3.5. Finds confidence intervals
5.3.6. Estimates statistical uncertainty
5.3.7. Draws inferences about a population from a sample (ITED 9 10 11 12)
5.3.8. Describes population parameters based on sample statistics
Benchmark 4: Uses probability concepts
Critical Objectives:
5.4.1. Uses a variety of methods to determine probabilities (ITED 9* 10*
11 12
* *)
5.4.2. Knows the advantages and disadvantages of experimental,
simulation, and theoretical methods for determining probability
5.4.3. Knows experimental probabilities tend to mirror theoretical
probabilities
5.4.4. Knows the distinction between theoretical and experimental
probability
5.4.5. Knows how combinations are calculated to determine an outcome
Vocabulary
Sampling distribution
Confidence interval
Uncertainty
Bias
Parameter
Statistic
Margin of error
Vocabulary
Simulation
Theoretical model
Experimental model
Monte Carlo
Probability
Combinations
Independent event
Dependent event
Simple event
Compound event
Conditional event
5.4.6. Uses a variety of methods to determine probability of events
5.4.7. Determines the best method for determining probability for a given
situation
5.4.8. Compares theoretical probabilities with experimental probabilities for dependent
events, independent events, and mutually exclusive events
5.4.9. Uses combinations to represent a given situation (ITED 9 10 11 12)
5.4.10. Applies the concepts of conditional probability and independent events (ITED 11* 12*)
5.4.11. Knows how to find the probability of two disjoint events
5.4.12. Knows how to find the probability of one independent event followed by another
independent event
5.4.13. Knows the probability for some outcomes depends upon one or more other events
occurring
5.4.14. Identifies simple and compound events
5.4.15. Identifies dependent and independent events (ITED 11* 12*)
5.4.16. Computes the probability of conditional and independent events
Diocese of Sioux City
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2006
Mathematics Curriculum Guide
Diocese of Sioux City
Grades 9-12
Standards and Benchmarks with Critical Objectives aligned with ITED
Standard 6: Understands and applies problem solving strategies.
Benchmark 1: Uses a variety of strategies to solve problems
Critical Objectives:
6.1.1. Uses a variety of strategies to understand new mathematical
content (ITED 9*** 10*** 11*** 12***)
6.1.2. Knows the general problem solving strategies
6.1.3. Knows the same situation can often be represented in more than
one way
6.1.4. Knows different problems may be solved using the same method
6.1.5. Extracts the main idea of a problem (ITED 9 10 11 12)
6.1.6. Chooses appropriate strategies to solve problems in the context of
the problem situation (ITED 9 10 11 12)
6.1.7. Uses previously learned strategies, skills, knowledge, and concepts
to solve problems (ITED 9 10 11 12)
6.1.8. Identifies pertinent and irrelevant information (ITED 9 10 11 12)
6.1.9. Translates words to numbers to symbolic expressions (ITED 9 10 11 12)
6.1.10. Generalizes solutions to new problem situations (ITED 9 10 11 12)
Benchmark 2: Justifies the process used to solve a numerical problem
Critical Objectives:
6.2.1. Specifies the kind of information and resources used to solve a
problem
6.2.2. Understands how to make an argument for a solution
6.2.3. Knows that conjectures are subject to verification
6.2.4. Knows ways to verify a conjecture
6.2.5. Knows that one counter example disproves a conjecture
6.2.6. Formulates conjectures and argues why they must be true
6.2.7. Uses conjectures previously justified to solve a problem
6.2.8. Generalizes conjectures to new problem situations
Diocese of Sioux City
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Vocabulary
Pertinent information
Irrelevant information
Insufficient information
Act it out
Make or use a model
Find or use a pattern
Draw a picture
Guess and check
Make a chart, table, graph,
or organized list
Use logical reasoning
Vocabulary
Verification
Conjecture
Validation
Algorithm
Justification
Evidence
Valid argument
Invalid argument
Counter example
2006
Mathematics Curriculum Guide
Diocese of Sioux City
Grades 9-12
Standards and Benchmarks with Critical Objectives aligned with ITED
Standard 7: Communicates and reasons mathematically.
Benchmark 1: Comprehends mathematical language
Critical Objectives:
7.1.1. Comprehends mathematical texts
7.1.2. Knows strategies to help learn vocabulary
7.1.3. Knows the text is set up to help vocabulary understanding
7.1.4. Uses graphic organizers to understand mathematical terms
Vocabulary
Graphic organizers
Benchmark 2: Expresses ideas using mathematical terms and representations
Vocabulary
Critical Objectives:
7.2.1. Connects ideas to mathematical terms
Grade level mathematical
7.2.2. Knows expressions represent rules and generalizations
terms
7.2.3. Knows strategies to organize ideas
7.2.4. Knows the characteristics of a well-written solution
7.2.5. Organizes mathematical ideas for understanding by a third party
7.2.6. Writes coherent solutions
7.2.7. Uses correct mathematical terms, language, and drawings for grade level content
7.2.8. Presents solutions using mathematical terms and representations
Benchmark 3: Analyzes and evaluates mathematical thinking
Critical Objectives:
7.3.1. Reviews mathematical thinking
7.3.2. Knows strategies to organize ideas
7.3.3. Knows mathematicians defend solutions
7.3.4. Knows the characteristics of a well-written solution
7.3.5. Organizes work and labels drawings to make meaning clear
7.3.6. Checks for clarity in solutions and revises
7.3.7. Gives reasons for decisions made while solving a problem
7.3.8. Considers the solutions of others and learns from them
7.3.9. Supports solutions with evidence
7.3.10. Answers questions regarding solutions
Vocabulary
Clarity
Reasons
Evidence
Solutions
Characteristics
Benchmark 4: Uses technology to enhance mathematical learning
Vocabulary
Critical Objectives:
7.4.1. Uses tools and technology to solve problems
Tools and technology
7.4.2. Knows how to use the tools and technology
appropriate at grade level
7.4.3. Understands a type of tool or technology is more appropriate in
certain contexts
7.4.4. Identifies the appropriate tools or technology for the problem situation
7.4.5. Uses tools or technology to simplify the task
Diocese of Sioux City
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2006