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Core Standards & KS Math Indicators Alignment
Geometry - High School
Kansas Retired Indicators connected to Common Core Standards
Retired Kansas Indicators
Common Core Standards
3.1.K1 Recognizes and compares properties of two-and three-dimensional figures using concrete objects,
constructions, drawings, appropriate terminology, and appropriate technology
G.CO.12 Make formal geometric constructions with a variety of tools and methods (compass and
straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.) Copying a
segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines,
including the perpendicular bisector of a line segment; and constructing a line parallel to a given line
through a point not on the line.
G.SRT.2 Given two figures, use the definition of similarity in terms of similarity transformations to
decide if they are similar; explain using similarity transformations the meaning of similarity for triangles
as the equality of all corresponding pairs of angles & the proportionality of all corresponding pairs of
sides.
G.CO.8 Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition
of congruence in terms of rigid motions.
3.1.K4 Recognizes that similar figures have congruent angles, and their corresponding sides are proportional
3.1.K6 Recognizes and describes: a. congruence of triangles using: Side-Side-Side, Angle- Side-Angle, SideAngle-Side, and Angle-Angle- Side; b. the ratios of the sides in special right triangles
3.1.K7 Recognizes, describes, and compares the relationships of the angles formed when parallel lines are cut
by a transversal
3.1.K8 Recognizes and identifies parts of a circle: arcs, chords, sectors of circles, secant and tangent lines,
central and inscribed angles
G.CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a
transversal crosses parallel lines, alternate interior angles are congruent and cor-responding angles are
congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the
segment’s endpoints.
G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment,
based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
3.1.K5 Uses the Pythagorean Theorem to: a. determine if a triangle is a right triangle, b. find a missing side of
a right triangle
▲3.1.A1 Solves real-world problems by: a. using the properties of corresponding parts of similar and
congruent figures; b. ▲ applying the Pythagorean Theorem c. using properties of parallel lines
3.1.A2 Uses deductive reasoning to justify the relationships between the sides of 30°-60°-90° and 45°-45°-90°
triangles using the ratios of sides of similar triangles
G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relation-ships
in geometric figures.
G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied
problems.
G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the
triangle, leading to definitions of trigonometric ratios for acute angles.
3.2.K5 Uses given measurement formulas to find perimeter, area, volume, and surface area of two- and threedimensional figures (regular and irregular)
G.GMD.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
3.2.K6 Recognizes and applies properties of corresponding parts of similar and congruent figures to find
measurements of missing sides
▲3.4.K4 Finds and explains the relationship between the slopes of parallel and perpendicular lines
G.SRT.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to
be similar.
G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric
problems
S.CP.2 Understand that two events A and B are independent if the probability of A and B occurring
together is the product of their probabilities, and use this characterization to determine if they are
independent.
S.CP.3 Understand the conditional probability of A given B as P(A and B)/P(B), and interpret
independence of A and B as saying that the conditional probability of A given B is the same as the
probability of A, and the conditional probability of B given A is the same as the probability of B.
S.CP.5 Recognize and explain the concepts of conditional probability and independence in every-day
language and everyday situations. For example, compare the chance of having lung cancer if you are a
smoker with the chance of being a smoker if you have lung cancer.
S.CP.6 Find the conditional probability of A given B as the fraction of B’s outcomes that also be-long to
A, and interpret the answer in terms of the model.
S.CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with
each object being classified. Use the two-way table as a sample space to decide if events are independent
and to approximate conditional probabilities. For example, collect data from a random sample of students
in your school on their favorite subject among math, science, and English. Estimate the probability that a
randomly selected student from your school will favor science given that the student is in tenth grade. Do
the same for other subjects and compare the results.
S.CP.9+ Use permutations and combinations to compute probabilities of compound events and solve
problems.
4.1.K1 Finds the probability of two independent events in an experiment, simulation, or situation
4.1.K2 Finds the conditional probability of two dependent events in an experiment, simulation, or situation
4.1.A4 Uses conditional probabilities of two dependent events in an experiment, simulation, or situation to
make predictions and analyze decisions.
4.1.A1 Conducts an experiment or simulation with two dependent events; records the results in charts, tables,
or graphs; and uses the results to generate convincing arguments, draw conclusions and make predictions
4.1.A2 Uses theoretical or empirical probability of a simple or compound event composed of two or more
simple, independent events to make predictions and analyze decisions about real-world situations including: a.
work in economics, quality control, genetics, meteorology, and other areas of science, b. games, c. situations
involving geometric models
Core Standards & KS Math Indicators Alignment
4.1.A3 Compares theoretical probability with empirical probability of two independent and/or
dependent events and understands that the larger the sample size, the greater the likelihood that experimental
results will match theoretical probability
Geometry - High School
S.CP.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or
categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” and “not”).
Green - NEW Standards for Geometry
G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe
transformations as functions that take points in the plane as inputs and give other points as outputs. Compare
transformations that preserve distance and angle to those that do not
G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections
that carry it onto itself.
G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular
lines, parallel lines, and line segments.
G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using,
e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a
given figure onto another.
G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given
rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to
decide if they are congruent.
G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if
and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
G.CO.10 Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to
180°; base angles of isosceles triangles are congruent; the segment joining mid-points of two sides of a
triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
G.CO.11 Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite
angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are
parallelograms with congruent diagonals.
G.CO.13 Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle.
G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor: a. A dilation
takes a line not passing through the center of the dilation to a parallel line, & leaves a line passing through the
center unchanged. b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
G.SRT.4 Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides
the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.
G.SRT.9+ Derive the formula A = ½ ab sin(C) for the area of a triangle by drawing an auxiliary line from a
vertex perpendicular to the opposite side.
G.SRT.10+ Prove the Laws of Sines and Cosines and use them to solve problems.
G.SRT.11+ Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in
right and non-right triangles
G.C.1 Prove that all circles are similar.
G.C.2 Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship
between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the
radius of a circle is perpendicular to the tangent where the radius intersects the circle.
G.C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a
quadrilateral inscribed in a circle.
G.C.4+ Construct a tangent line from a point outside a given circle to the circle.
G.C.5 Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to
the radius, and define the radian measure of the angle as the constant of proportionality; derive the
formula for the area of a sector.
G.GPE.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem;
complete the square to find the center and radius of a circle given by an equation.
G.GPE.2 Derive the equation of a parabola given a focus and directrix.
G.GPE.4 Use coordinates to prove simple geometric theorems algebraically. For example, prove or
disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or
disprove that the point (1, 3) lies on the circle centered at the origin and containing the point (0, 2).
G.GPE.6 Find the point on a directed line segment between two given points that partitions the segment
in a given ratio.
G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles,
G.GMD.1 Give an informal argument for the formulas for the circumference of a circle, area of a circle,
volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal
limit arguments.
G.GMD.4 Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and
identify three-dimensional objects generated by rotations of two-dimensional objects.
G.MG.1 Use geometric shapes, their measures, and their properties to describe objects. (e.g., modeling a
tree trunk or a human torso as a cylinder)
G.MG.2 Apply concepts of density based on area and volume in modeling situations. (e.g., persons per
square mile, BTUs per cubic foot)
G.MG.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to
satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
S.CP.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms
of the model.
S.CP.8+ Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A)
= P(B)P(A|B), and interpret the answer in terms of the model.
S.MD.6+ Use probabilities to make fair decisions (e.g., drawing by lots, using a random number
generator).
S.MD.7+ Analyze decisions and strategies using probability concepts (e.g., product testing, medical
testing, pulling a hockey goalie at the end of a game).
Core Standards & KS Math Indicators Alignment
Geometry - High School
PINK – eliminated Indicators for Geometry
1.1.K1 Knows, explains, and uses equivalent representations for real numbers and algebraic
expressions including integers, fractions, decimals, percents, ratios; rational number bases with
integer exponents; rational numbers written in scientific notation; absolute value; time; & money
1.1.K2 Compares and orders real numbers and/or algebraic expressions and explains the relative
magnitude between them
1.1.K3 Knows and explains what happens to the product or quotient when a real number is
multiplied or divided by: a. a rational number greater than zero and less than one, b. a rational
number greater than one, c. a rational number less than zero.
1.1.A1 Generates and/or solves real-world problems using equivalent representations of real
numbers and algebraic expressions
1.1.A2 Determines whether or not solutions to real-world problems using real numbers and
algebraic expressions are reasonable
1.2.K1 Explains and illustrates the relationship between the subsets of the real number system
[natural (counting) numbers, whole numbers, integers, rational numbers, irrational numbers]
using mathematical models
1.2.K2 Identifies all the subsets of the real number system [natural (counting) numbers, whole
numbers, integers, rational numbers, irrational numbers] to which a given number belongs
▲1.2.K3 Names, uses, and describes these properties with the real number system and
demonstrates their meaning including the use of concrete objects: a. commutative, associative
distributive and substitution properties ; b. identity properties for addition and multiplication and
inverse properties of addition and multiplication c. symmetric property of equality; d. addition
and multiplication properties of equality and inequalities; e. zero product property
1.2.K4 Uses and describes these properties with the real number system: a. transitive property b.
reflexive property
1.2.A1 Generates and/or solves real-world problems with real numbers using the concepts of
these properties to explain reasoning: a. commutative, associative, distributive, and substitution
properties b. identity and inverse properties of addition and multiplication c. symmetric property
of equality, d. addition and multiplication properties of equality, e. zero product property
1.2.A2 Analyzes and evaluates the advantages and disadvantages of using integers, whole
numbers, fractions (including mixed numbers), decimals or irrational numbers and their rational
approximations in solving a given real-world problem
1.3.K1 Estimates real number quantities using various computational methods
1.3.K2 Uses various estimation strategies and explains how they were used to estimate real
number quantities and algebraic expressions
1.3.K3 Knows and explains why a decimal representation of an irrational number is an
approximate value
▲1.3.A1 Adjusts original rational number estimate of a real-world problem based on additional
information
1.3.A2 Estimates to check whether or not the result of a real-world problem using real numbers
and/or algebraic expressions is reasonable and makes predictions based on the information
1.3.A3 Determines if a real-world problem calls for an exact or approximate answer and performs the
appropriate computation using various computational strategies
1.3.A4 Explains the impact of estimation on the result of a real-world problem 1.(underestimate,
overestimate, range of estimates)
1.3.K4 Knows and explains between which two consecutive integers an irrational number lies
1.4.K1 Computes with efficiency and accuracy using various computational methods
1.4.K2 Performs & explains these computational procedures: a. addition, subtraction, multiplication, and
division using the order of operations, b. multiplication or division to find - a percent of a number,
percent of increase & decrease, percent one number is of another, a number when a percent of the
number is given, c. manipulation of variable quantities within an equation or inequality, d. simplification
of radical expressions (w/o rationalizing denominators) including square roots of perfect square
monomials & cube roots of perfect cubic monomials, e. simplification or evaluation of real numbers &
algebraic monomial expressions raised to a whole number power & algebraic binomial expressions
squared or cubed; simplification of products & quotients of real number & algebraic monomial
expressions using the properties of exponents, g. matrix addition, h. scalar-matrix multiplication
1.4.K3 Finds prime factors, greatest common factor, multiples, and the least common multiple of
algebraic expressions
▲1.4.A1 Generates and/or solves multi-step real-world problems with real numbers and algebraic
expressions using computational procedures and mathematical concepts with a. ▲ applications from
business, chemistry, and physics that involve addition, subtraction, multiplication, division, squares, and
square roots when the formulae are given as part of the problem and variables are defined, b. ▲ volume
and surface area given the measurement formulas of rectangular solids and cylinders, c. probabilities, d.
▲application of percents, e. simple exponential growth and decay (excluding logarithms) & economics
2.1.K1Identifies, states, and continues the following patterns using various formats including numeric,
algebraic, visual, verbal, kinesthetic, and written a. arithmetic and geometric sequences using real
numbers and/or exponents, b. patterns using geometric figures, c. algebraic patterns including
consecutive number patterns or equations of functions, d. special patterns
2.1.K2 Generates and explains a pattern
2.1.K3 Classify sequences as arithmetic, geometric, or neither
2.1.K4 Defines (2.4.K1a): a. a recursive or explicit formula for arithmetic sequences and finds any
particular term, b. a recursive or explicit formula for geometric sequences and finds any particular term.
2.1.A1 Recognizes the same general pattern presented in different representations
2.1.A2 Solves real-world problems with arithmetic or geometric sequences by using the explicit
equation of the sequence
2.2.K1 Knows and explains the use of variables as parameters for a specific variable situation
2.2.K2 Manipulates variable quantities within an equation or inequality
▲2.2.K3defg Solves: : a. linear equations and inequalities both analytically and graphically; b. quadratic
equations with integer solutions; c. ▲ systems of linear equations with two unknowns using integer
coefficients and constants; d. radical equations with no more than one inverse operation around the
radical expression; e. equations where the solution to a rational equation can be simplified as a linear
equation with a nonzero denominator, f. equations and inequalities with absolute value quantities
Core Standards & KS Math Indicators Alignment
2.2.A1 Represents real-world problems using variables, symbols, expressions, equations,
inequalities, and simple systems of linear equations
▲ 2.2.A2 Represents and/or solves real-world problems with: a. ▲ linear equations and
inequalities both analytically and graphically, b. quadratic equations with integer solutions, c.
systems of linear equations with two unknowns, d. radical equations with no more than one
inverse operation around the radical expression, e. a rational equation where the solution can be
simplified as a linear equation with a nonzero denominator
2.2.A3 Explains the mathematical reasoning that was used to solve a real world problem using
equations and inequalities and analyzes the advantages and disadvantages of various strategies
that may have been used to solve the problem
2.3.K1 Evaluates and analyzes functions using various methods
2.3.K2 matches equations and graphs quadratic functions limited to y = ax2 + c
2.3.K3 Determines whether a graph, list of ordered pairs, table of values, or rule represents a
function
2.3.K4 determines x- and y-intercepts and maximum and minimum values of the portion of the
graph that is shown on a coordinate plane
2.3.K5 identifies domain and range of: a. relationships given the graph or table, b. linear,
constant, and quadratic functions given the equation(s)
▲2.3.K6 recognizes how changes in the constant and/or slope within a linear function changes
the appearance of a graph
2.3.K7 uses function notation
2.3.K8 Evaluates function(s) given a specific domain
2.3.K9 Describes the difference between independent and dependent variables and identifies
independent and dependent variables
2.3.A1 Translates between the numerical, graphical, and symbolic representations of functions
▲2.3.A2 interprets the meaning of the x- and y- intercepts, slope, and/or points on and off the
line on a graph in the context of a real-world situation
2.3.A3 Analyzes: a. the effects of parameter changes (scale changes or restricted domains) on the
appearance of a function’s graph, b. how changes in the constants and/or slope within a linear
function affects the appearance of a graph, c. how changes in the constants and/or coefficients
within a quadratic function in the form of y = ax2 + c affects the appearance of a graph.
2.4.K1 knows, explains, and uses mathematical models to represent and explain mathematical
concepts, procedures, and relationships
2.4.A1 Recognizes that various mathematical models can be used to represent the same problem
situation
2.4.A2 Uses the mathematical modeling process to analyze and make inferences about real-world
situations
3.1.K2 Discusses properties of regular polygons related to: a. angle measures, b. diagonals.
3.1.K3 Recognizes and describes the symmetries (point, line, plane) that exist in three-D figures
3.1.A2 Uses deductive reasoning to justify the relationships between the sides of 30°-60°-90° and
45°-45°-90° triangles using the ratios of sides of similar triangles
3.1.A3 Understands the concepts of and develops a formal or informal proof through
understanding of the difference between a statement verified by proof (theorem) and a statement
supported by examples
3.2.K1 Determines and uses real number approximations (estimations) for length, width, weight,
Geometry - High School
containing one variable with a special emphasis on using a number line and the concept of absolute
value. g. exponential equations with the same base without the aid of a calculator or computer
3.2.K2 Selects and uses measurement tools, units of measure, and level of precision appropriate for a
given situation to find accurate real number representations for length, weight, volume, temperature,
time, distance, area, surface area, mass, midpoint, and angle measurements
3.2.K3 Approximates conversions between customary and metric systems given the conversion unit or
formula
3.2.K4 States, recognizes, and applies formulas for: a. perimeter and area of squares, rectangle, and
triangles; b. circumference and area of circles; volume of rectangular solids.
3.2.K7 Knows, explains, and uses ratios and proportions to describe rates of change
3.2.A1abcd Solves real-world problems by: a. converting within the customary and the metric systems,
b. finding the perimeter and the area of circles, squares, rectangles, triangles, parallelograms, and
trapezoids, c. finding the volume and the surface area of rectangular solids and cylinders, d. using the
Pythagorean theorem
3.2.A2 Estimates to check whether or not measurements or calculations for length, weight, volume,
temperature, time, distance, perimeter, area, surface area, and angle measurement in real-world
problems are reasonable and adjusts original measurement or estimation based on additional information
3.2.A3 Uses indirect measurements to measure inaccessible objects
3.3.K1 Describes and performs single and multiple transformations on two- and three-dimensional
figures
3.3.K2 Recognizes a three-dimensional figure created by rotating a simple two-dimensional figure
around a fixed line
3.3.K3 Generates a two-dimensional representation of a three-dimensional figure
3.3.K4Determines where and how an object or a shape can be tessellated using single or multiple
transformations and creates a tessellation
▲3.3.A1 Analyzes the impact of transformations on the perimeter and area of circles, rectangles, and
triangles and volume of rectangular prisms and cylinders
3.3.A2 Describes and draws a simple three-dimensional shape after undergoing one specified
transformation without using concrete objects to perform the transformation
3.3.A3 Uses a variety of scales to view and analyze two- and three dimensional figures
3.3.A4 Analyzes and explains transformations using such things as sketches and coordinate systems
3.4.K1 Recognizes and examines two- and three-dimensional figures and their attributes including the
graphs of functions on a coordinate plane using various methods
3.4.K2 Determines if a given point lies on the graph of a given line or parabola without graphing and
justifies the answer
3.4.K3 Calculates the slope of a line from a list of ordered pairs on the line and explains how the graph
of the line is related to its slope
3.4.K5 Uses the Pythagorean Theorem to find distance
▲3.4.K6 Recognizes the equation of a line and transforms the equation into slope-intercept form in
order to identify the slope and y-intercept and uses this information to graph the line
3.4.K7 Recognizes the equation y = ax2 + c as a parabola; represents and identifies characteristics of the
parabola including opens upward or opens downward, steepness (wide/narrow), the vertex, maximum
and minimum values, and line of symmetry; and sketches the graph of the parabola
3.4.K8 Explains the relationship between the solution(s) to systems of equations and systems of
inequalities in two unknowns and their corresponding graphs
3.4.A1 Represents, generates, and/or solves real-world problems that involve distance and two-
Core Standards & KS Math Indicators Alignment
volume, temperature, time, distance, perimeter, area, surface area, and angle measurement using
standard and nonstandard units of measure
3.4.A2 Translates between the written, numeric, algebraic, and geometric representations of a
real-world problem
3.4.A3 Recognizes and explains the effects of scale changes on the appearance of the graph of an
equation involving a line or parabola
3.4.A4 Analyzes how changes in the constants and/or leading coefficients within the equation of
a line or parabola affects the appearance of the graph of the equation
▲4.1.K3 Explains the relationship between probability and odds and computes one given the
other
4.2.K1 Organizes, displays, and reads quantitative and qualitative data in a clear, organized, and
accurate manner including a title, labels, categories, and rational number intervals using data
displays
4.2.K2 Explains how the reader’s bias, measurement errors, and display distortions can affect the
interpretation of data
4.2.K3 Calculates and explains the meaning of range, quartiles and interquartile range for a real
number data set
▲4.2.K4 Explains the effects of outliers on the measures of central tendency (mean, median,
mode) and range and interquartile range of a real number data set
Geometry - High School
dimensional geometric figures including parabolas in the form ax2 + c
▲4.2.K5 Approximates a line of best fit given a scatter plot and makes predictions using the graph or
the equation of that line
4.2.K6 Compares and contrasts the dispersion of two given sets of data in terms of range and the shape
of the distribution including: a. symmetrical (including normal), b. skew (left or right), c. bimodal, d.
uniform (rectangular)
▲4.2.A1 Uses data analysis (mean, median, mode, range, quartile, interquartile range) in real-world
problems with rational number data sets to compare and contrast two sets of data, to make accurate
inferences and predictions, to analyze decisions, and to develop convincing arguments from these data
displays
4.2.A2 Determines and describes appropriate data collection techniques and sampling techniques in a
given situation
4.2.A3Uses changes in scales, intervals, and categories to help support a particular interpretation of the
data
4.2.A4 Determines and explains the advantages and disadvantages of using each measure of central
tendency and the range to describe a data set
4.2.A5 Analyzes the effects of: a. outliers on the mean, median, and range of a real number data set; b.
changes within a real number data set on mean, median, mode, range, quartiles, and interquartile range.
4.2.A6 Approximates a line of best fit given a scatter plot, makes predictions, and analyzes decisions
using the equation of that line