Download MATH - Geometry

MATH - Geometry
CUSD 303
Year 2012-2013
Content
Cluster Standard
Standard
Congruence
Experiment with
G.GCO1 Know precise definitions of angle, circle, perpendicular
transformations in the plane line, parallel line, and line segment, based on the undefined notions
of point, line, distance along a line, and distance around a circular
arc
G.GCO7 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.GCO1 Define a circle based on the undefined notions of point,
line, distance along a line, and distance around a circular arc
G.GCO2 Illustrate transformations in the plane using, e.g.,
transparencies and geometry software
G.GCO2 Describe transformations as functions that take points in
the plane as inputs and give other points as outputs
G.GCO2 Compare transformations that preserve distance and
angle to those that do not
G.GCO3 Given a rectangle, parallelogram, trapezoid, or regular
polygon, describe the rotations that carry it onto itself
G.GCO3 Given a rectangle, parallelogram, trapezoid, or regular
polygon, describe the reflections that carry it onto itself
G.GCO4 Develop definitions of rotations in terms of angles, circles,
perpendicular lines, parallel lines, and line segments
G.GCO4 Develop definitions of reflections in terms of angles,
circles, perpendicular lines, parallel lines, and line segments
G.GCO4 Develop definitions of translations in terms of angles,
circles, perpendicular lines, parallel lines, and line segments
G.GCO5 Rotate a geometric figure using, e.g., graph paper, tracing
paper, or geometry software
G.GCO5 Reflect a geometric figure using, e.g., graph paper, tracing
paper, or geometry software
G.GCO5 Translate a geometric figure using, e.g., graph paper,
tracing paper, or geometry software
G.GCO5 Create a sequence of transformations that will carry a
given figure onto another
G.GCO6 Transform figures using geometric descriptions of rigid
motions
G.GCO6 Predict the effect of a given rigid motion on a given figure
using geometric descriptions of rigid motions
G.GCO6 Determine if two figures are congruent using the definition
of congruence in terms of rigid motions
G.GCO7 Apply 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.GCO8 Explain how the criteria for triangle congruence (ASA,
SAS, and SSS) follow from the definition of congruence in terms of
rigid motions
G.GCO8 Explain how the criteria for triangle congruence (ASA,
SAS, and SSS) follow from the definition of congruence in terms of
rigid motions
G.GCO2 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 (e.g., translation versus horizontal stretch)
G.CO3 Given a rectangle, parallelogram, trapezoid, or regular
polygon, describe the rotations and reflections that carry it onto itself
G.GCO4 Develop definitions of rotations, reflections, and
translations in terms of angles, circles, perpendicular lines, parallel
lines, and line segments
G.GCO5 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
Understand congruence in
terms of rigid motions
Skill Statement
G.GCO1 Define perpendicular line, parallel line, and line segment
based on the undefined notions of point, line, and distance along a
line, and distance around a circular arc
G.GCO1 Define an angle based on the undefined notions of point,
line, and distance along a line, and distance around a circular arc
G.GCO6 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
1 of 7
Resources
Core
Connections
Geometry , 2012,
College
Preparatory
Mathematics
(CPM)
Content
Congruence
(cont'd)
Cluster Standard
Prove geometric theorems
Standard
Skill Statement
G.GCO9 Prove theorems about lines and angles. Theorems include: G.GCO9 Prove theorems about lines and angles
vertical angles are congruent; when a transversal crosses parallel
lines, alternate interior angles are congruent and corresponding
angles are congruent; points on a perpendicular bisector of a line
segment are exactly those equidistant from the segment’s endpoints
G.GCO10 Prove theorems about triangles. Theorems include:
G.GCO10 Prove theorems about triangles
measures of interior angles of a triangle sum to 180°; base angles of
isosceles triangles are congruent; the segment joining midpoints 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.GCO11 Prove theorems about parallelograms. Theorems include: G.GCO11 Prove theorems about parallelograms
opposite sides are congruent, opposite angles are congruent, the
diagonals of a parallelogram bisect each other, and conversely,
rectangles are parallelograms with congruent diagonals
Make geometric
constructions
Similarity, Right
Triangles, and
Trigonometry
Understand similarity in
terms of similarity
transformations
Prove theorems involving
similarity
G.GCO12 Make formal geometric constructions with a variety of
G.GCO12 Create formal geometric constructions with a variety of
tools and methods (compass and straightedge, string, reflective
tools and methods (compass and straightedge, string, reflective
devices, paper folding, dynamic geometric software, etc.). Copying a devices, paper folding, dynamic geometric software, etc.)
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.GCO13 Construct an equilateral triangle, a square, and a regular
hexagon inscribed in a circle
G.GSRT1 Verify experimentally the properties of dilations given by a
center and a scale factor
G.GSRT1a A dilation takes a line not passing through the center of
the dilation to a parallel line, and leaves a line passing through the
center unchanged
G.GSRT1b The dilation of a line segment is longer or shorter in the
ratio given by the scale factor
G.GSRT2 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 and the
proportionality of all corresponding pairs of sides
G.GCO13 Construct equilateral polygons
G.GSRT1 Verify experimentally the properties of dilations given by a
center and a scale factor
G.GSRT1a A dilation takes a line not passing through the center of
the dilation to a parallel line, and leaves a line passing through the
center unchanged
G.GSRT1b The dilation of a line segment is longer or shorter in the
ratio given by the scale factor
G.GSRT2 Determine if two figures are similar using the definition of
similarity in terms of similarity transformations
G.GSRT2 Explain using similarity transformations the meaning of
similarity for triangles as the equality of all corresponding pairs of
angles
G.GSRT2 Explain using similarity transformations the meaning of
similarity for triangles as the proportionality of all corresponding pairs
of sides
G.GSRT3 Use the properties of similarity transformations to
G.GSRT3 Establish the AA criterion for two triangles to be similar
establish the AA criterion for two triangles to be similar
using the properties of similarity transformations
G.GSRT4 Prove theorems about triangles. Theorems include: a line G.GSRT4 Prove theorems about triangles.
parallel to one side of a triangle divides the other two proportionally,
and conversely; the Pythagorean Theorem proved using triangle
similarity
G.GSRT5 Use congruence and similarity criteria for triangles to
G.GSRT5 Apply congruence and similarity criteria for triangles to
solve problems and to prove relationships in geometric figures**
solve problems
2 of 7
Resources
Core
Connections
Geometry, 2012,
College
Preparatory
Mathematics
(CPM)
Content
Similarity, Right
Triangles, and
Trigonometry
(cont'd)
Modeling with
Geometry
Geometric
Measurement
and Dimension
Expressing
Geometric
Properties with
Equations
Cluster Standard
Prove theorems involving
similarity (cont'd)
Define trigonometric ratios
and solve problems
involving right triangles
Standard
Skill Statement
G.GSRT5 Apply congruence and similarity criteria for triangles to
prove relationships in geometric figures
G.GSRT6 Understand that by similarity, side ratios in right triangles G.GSRT6 Recognize that, by similarity, side ratios in right triangles
are properties of the angles in the triangle, leading to definitions of
are properties of the angles in the triangle
trigonometric ratios for acute angles
G.GSRT6 Develop the trigonometric ratios for acute angles
G.GSRT7 Explain and use the relationship between the sine and
G.GSRT7 Explain the relationship between the sine and cosine of
cosine of complementary angles
complementary angles
G.GSRT7 Apply the relationship between the sine and cosine of
complementary angles
G.GSRT8 Use trigonometric ratios and the Pythagorean Theorem to G.GSRT8 Solve right triangles in applied problems using
solve right triangles in applied problems
trigonometric ratios
G.GSRT8 Solve right triangles in applied problems using the
Pythagorean Theorem
Apply trigonometry to
G.GSRT9 (+) Derive the formula A = 1/2 ab sin(C) for the area of a G.GSRT9 (+) Derive the formula A = 1/2 ab sin(C) for the area of a
general triangles
triangle by drawing an auxiliary line from a vertex perpendicular to
triangle by drawing an auxiliary line from a vertex perpendicular to
the opposite side
the opposite side
G.GSRT10 (+) Prove the Laws of Sines and Cosines and use them G.GSRT10 (+) Prove the Law of Sines
to solve problems
G.GSRT10 (+) Prove the Law of Cosines
G.GSRT10 (+) Solve problems using Law of Sines
G.GSRT10 (+) Solve problems using Laws of Cosines
G.GSRT11 (+) Understand and apply the Law of Sines and the Law G.GSRT11 (+) Apply the Law of Sines and the Law of Cosines to
of Cosines to find unknown measurements in right and non-right
find unknown measurements of triangles (e.g., surveying problems,
triangles (e.g., surveying problems, resultant forces)
resultant forces)
Apply geometric concepts in G.GMG1 Use geometric shapes, their measures, and their
G.GMG1 Describe objects using geometric shapes, their measures,
modeling situations
properties to describe objects (e.g., modeling a tree trunk or a
and their properties
human torso as a cylinder)
G.GMG2 Apply concepts of density based on area and volume in
G.GMG2 Apply concepts of density based on area in modeling
modeling situations (e.g., persons per square mile, BTUs per cubic situations
foot)
G.GMG2 Apply concepts of density based on volume in modeling
situations
G.GMG3 Apply geometric methods to solve design problems (e.g., G.GMG3 Apply geometric methods to solve design problems
designing an object or structure to satisfy physical constraints or
minimize cost; working with typographic grid systems based on
ratios)
Explain volume formulas
G.GGMD1 Give an informal argument for the formulas for the
G.GGMD1 Give an informal argument for the formulas for the
and use them to solve
circumference of a circle, area of a circle, volume of a cylinder,
perimeter, area, and volume of geometric figures
problems
pyramid, and cone. Use dissection arguments, Cavalieri’s principle,
and informal limit arguments
G.GGMD3 Use volume formulas for cylinders, pyramids, cones, and G.GGMD3 Solve problems using volume formulas for 3-dimensional
spheres to solve problems
figures
Visualize the relation
G.GGMD4 Identify the shapes of two-dimensional cross-sections of G.GGMD4 Identify the shapes of two-dimensional cross-sections of
between two-dimensional
three-dimensional objects, and identify three-dimensional objects
three-dimensional objects
and three-dimensional
generated by rotations of two-dimensional objects
G.GGMD4 Identify three-dimensional objects generated by rotations
objects
of two-dimensional objects
Translate between the
G.GGPE1 Derive the equation of a circle of given center and radius G.GGPE1 Derive the equation of a circle of given center and radius
geometric description and
using the Pythagorean Theorem; complete the square to find the
using the Pythagorean Theorem
the equation for a conic
center and radius of a circle given by an equation
G.GGPE1 Complete the square to find the center and radius of a
section
circle given by an equation
3 of 7
Resources
Core
Connections
Geometry, 2012,
College
Preparatory
Mathematics
(CPM)
Content
Expressing
Geometric
Properties with
Equations
(cont'd)
Cluster Standard
Standard
Skill Statement
Use coordinates to prove
G.GGPE4 Use coordinates to prove simple geometric theorems
G.GGPE4 Prove simple geometric theorems algebraically using
simple geometric theorems algebraically. For example, prove or disprove that a figure defined by coordinates
algebraically
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.GGPE5 Prove the slope criteria for parallel and perpendicular
lines and uses them to solve geometric problems (e.g., find the
equation of a line parallel or perpendicular to a given line that
passes through a given point)**
Circles
Translate between the
geometric description and
the equation for a conic
section
Understand and apply
theorems about circles
G.GGPE6 Find the point on a directed line segment between two
given points that partitions the segment in a given ratio
G.GGPE7 Use coordinates to compute perimeters of polygons and
areas of triangles and rectangles, e.g., using the distance formula**
G.GGPE5 Prove the slope criteria for parallel lines
G.GGPE5 Prove the slope criteria for perpendicular lines
G.GGPE5 Solve geometric problems using the slope criteria for
parallel lines
G.GGPE5 Solve geometric problems using the slope criteria for
perpendicular lines
G.GGPE6 Find the point on a directed line segment between two
given points that partitions the segment in a given ratio
G.GGPE7 Compute perimeters of polygons using coordinates
G.GGPE7 Compute areas of triangles and rectangles
G.GGPE2 Derive the equation of a parabola given a focus and
directrix
G.GGPE2 Derive the equation of a parabola given a focus and
directrix
G.GC1 Prove that all circles are similar
G.GC1 Prove that all circles are similar
G.GC2 Identify and describe relationships among inscribed angles, G.GC2 Identify and describe relationships among inscribed angles,
radii, and chords. Include the relationship between central, inscribed, radii, and chords
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.GC3 Construct the inscribed and circumscribed circles of a
triangle, and prove properties of angles for a quadrilateral inscribed
in a circle
Find arc lengths and areas
of sectors of circles
Conditional
Probability and
the rules of
Probability
Understand independence
and conditional probability
and use them to interpret
data
G.GC4 (+) Construct a tangent line from a point outside a given
circle to the circle
G.GC5 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.GC3 Construct the inscribed and circumscribed circles of a
triangle
G.GC3 Prove properties of angles for a quadrilateral inscribed in a
circle
G.GC4 (+) Construct a tangent line from a point outside a given
circle to the circle
G.GC5 Derive using similarity the fact that the length of the arc
intercepted by an angle is proportional to the radius
G.GC5 Define the radian measure of the angle as the constant of
proportionality
G.GC5 Derive the formula for the area of a sector
G.SCP1 Describe events as subsets of a sample space (the set of
outcomes) using characteristics (or categories) of the outcomes
G.SCP1 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”)
G.SCP1 Describe events as subsets of a sample space (the set of
outcomes) using unions, intersections, or complements of other
events (“or,” “and,” “not”)
G.SCP2 Understand that two events A and B are independent if the G.SCP2 Recognize that the probability of two independent events A
probability of A and B occurring together is the product of their
and B occurring together is the product of their probabilities
probabilities, and use this characterization to determine if they are
independent
G.SCP2 Recognize if the probability of events A and B occurring
together is the product of their probabilities, then events A and B are
independent
4 of 7
Resources
Core
Connections
Geometry, 2012,
College
Preparatory
Mathematics
(CPM)
Content
Conditional
Probability and
the rules of
Probability
(cont'd)
Cluster Standard
Understand independence
and conditional probability
and use them to interpret
data (cont'd)
Use the rules of
probability to compute
probabilities of
compound events in
a uniform probability
model
Standard
G.SCP3 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
Skill Statement
G.SCP3 Recognize the conditional probability of A given B as P(A
and B)/P(B)
G.SCP3 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
G.SCP4 Construct and interpret two-way frequency tables of data
G.SCP4 Construct and interpret two-way frequency tables of data
when two categories are associated with each object being
when two categories are associated with each object being
classified. Use the two-way table as a sample space to decide if
classified
events are independent and to approximate conditional probabilities. G.SCP4 Determine if events are independent by using a two-way
For example, collect data from a random sample of students in your table as a sample space to approximate conditional probabilities
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
G.SCP5 Recognize and explain the concepts of conditional
probability and independence in everyday 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
G.SCP5 Recognize the concepts of conditional probability and
independence in everyday language and everyday situations
G.SCP5 Explain the concepts of conditional probability and
independence in everyday language and everyday situations
G.SCP6 Find the conditional probability of A given B as the fraction
of B’s outcomes that also belong to A, and interpret the answer in
terms of the model
G.SCP6 Calculate the conditional probability of A given B as the
fraction of B’s outcomes that also belong to A
G.SCP6 Interpret the conditional probability in terms of the model
G.SCP7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and G.SCP7 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
B)
G.SCP7 Interpret the Addition Rule in terms of the model
G.SCP8 (+) Apply the general Multiplication Rule in a uniform
G.SCP8 (+) 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
probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B)
interpret the answer in terms of the model
G.SCP8 (+) Interpret the Multiplication Rule in terms of the model
G.SCP9 (+) Use permutations and combinations to compute
probabilities of compound events and solve problems
Using
Probability
to Make
Decisions
**Fluency
G.SCP9 (+) Compute probabilities of compound events and solve
problems using permutations
G.SCP9 (+) Compute probabilities of compound events and solve
problems using combinations
Use probability to evaluate G.SMD6 (+) Use probabilities to make fair decisions (e.g., drawing G.SMD6 (+) Make fair decisions using probabilities (e.g., drawing by
outcomes of decisions
by lots, using a random number generator)
lots, using a random number generator)
G.SMD7 (+) Analyze decisions and strategies using probability
G.SMD7 (+) Analyze decisions and strategies using probability
concepts (e.g., product testing, medical testing, pulling a hockey
concepts (e.g., product testing, medical testing, pulling a hockey
goalie at the end of a game)
goalie at the end of a game)
Prove theorems involving
G.GSRT5 Use congruence and similarity criteria for triangles to
G.GSRT5 Apply congruence and similarity criteria for triangles to
similarity
solve problems and to prove relationships in geometric figures
solve problems
Use coordinates to prove
G.GGPE4 Use coordinates to prove simple geometric theorems
G.GGPE4 Prove simple geometric theorems algebraically using
simple geometric theorems algebraically. For example, prove or disprove that a figure defined by coordinates
algebraically
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)
5 of 7
Resources
Core
Connections
Geometry, 2012,
College
Preparatory
Mathematics
(CPM)
Content
**Fluency
(cont'd)
Cluster Standard
Standard
Use coordinates to prove
G.GGPE5 Prove the slope criteria for parallel and perpendicular
simple geometric theorems lines and uses them to solve geometric problems (e.g., find the
algebraically (cont'd)
equation of a line parallel or perpendicular to a given line that
passes through a given point)
G.GGPE7 Use coordinates to compute perimeters of polygons and
areas of triangles and rectangles, e.g., using the distance formula
Interpreting
Categorical and
Quantitative
Data
Skill Statement
G.GGPE5 Prove the slope criteria for parallel lines
G.GGPE5 Prove the slope criteria for perpendicular lines
G.GGPE5 Solve geometric problems using the slope criteria for
parallel lines
G.GGPE5 Solve geometric problems using the slope criteria for
perpendicular lines
G.GGPE7 Compute perimeters of polygons using coordinates
G.GGPE7 Compute areas of triangles and rectangles
Make geometric
constructions
G.GCO12 Make formal geometric constructions with a variety of
G.GCO12 Create formal geometric constructions with a variety of
tools and methods (compass and straightedge, string, reflective
tools and methods (compass and straightedge, string, reflective
devices, paper folding, dynamic geometric software, etc.). Copying a devices, paper folding, dynamic geometric software, etc.)
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
Summarize, represent, and
interpret data on a single
count of measurement
variable
A.SID1 Represent data with plots on the real number line (dot plots,
histograms, and box plots)
A.SID2 Use statistics appropriate to the shape of the data
distribution to compare center (median, mean) and spread
(interquartile range, standard deviation) of two or more different data
sets
A.SID3 Interpret differences in shape, center, and spread in the
context of the data sets, accounting for possible effects of extreme
data points (outliers)
Summarize, represent, and A.SID5 Summarize categorical data for two categories in two-way
interpret data on two
frequency tables Interpret relative frequencies in the context of the
categorical and quantitative data (including joint, marginal, and conditional relative frequencies)
variables
Recognize possible associations and trends in the data
A.SID6 Represent data on two quantitative variables on a scatter
plot, and describe how the variables are related
A.SID6a Fit a function to the data; use functions fitted to data to
solve problems in the context of the data Use given functions or
choose a function suggested by the context Emphasize linear and
exponential models
Interpret linear models
A.SID6b Informally assess the fit of a function by plotting and
analyzing residuals
A.SID6c Fit a linear function for a scatter plot that suggests a linear
association
A.SID7 Interpret the slope (rate of change) and the intercept
(constant term) of a linear model in the context of the data
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T2.A.SID1 Represent data with plots on the real number line
T2.A.SID2 Utilize statistics appropriate to the shape of the data
distribution to compare center (median, mean) of two or more
different data sets
T2.A.SID2 Utilize statistics appropriate to the shape of the data
distribution to compare spread (interquartile range, standard
deviation) of two or more different data sets
T2.A.SID3 Interpret differences in shape, center, and spread in the
context of the data sets, accounting for possible effects of extreme
data points (outliers)
T2.A.SID5 Summarize categorical data for two categories in two-way
frequency tables
T2.A.SID5 Interpret relative frequencies in the context of the data
T2.A.SID5 Recognize possible associations and trends in the data
T2.A.SID6 Represent linear data on two quantitative variables on a
scatter plot
T2.A.SID6 Describe how the variables are related linearly
T2.A.SID6a Fit a linear function to the data
T2.A.SID6a Utilize linear functions fitted to data to solve problems in
the context of the data
T2.A.SID6b Informally assess the fit of a function by plotting and
analyzing residuals
T2.A.SID6c Fit a linear function for a scatter plot that suggests a
linear association
T2.A.SID7 Interpret the slope (rate of change) of a linear model in
the context of the data
T2.A.SID7 Interpret the intercept (constant term) of a linear model in
the context of the data
Resources
Core
Connections
Geometry, 2012,
College
Preparatory
Mathematics
(CPM)
Content
Cluster Standard
Interpreting
Interpret linear models
Categorical and (cont'd)
Quantitative
Data (cont'd)
Literacy of Math Craft and Structure
Integration of Knowledge
and Ideas
Text Type and Purposes
Standard
A.SID8 Compute (using technology) and interpret the correlation
coefficient of a linear fit
Skill Statement
T2.A.SID8 Compute (using technology) the correlation coefficient of
a linear fit
T2.A.SID8 Interpret the correlation coefficient of a linear fit
A.SID9 Distinguish between correlation and causation
T2.A.SID9 Distinguish between correlation and causation
G.RST4 Interpret words and phrases as they are used in a text,
9/10.RST4 Determine the meaning of symbols, key terms, and other
including determining technical, connotative, and figurative
domain-specific words and phrases as they are used in a specific
meanings, and analyze how specific word choices shape meaning or scientific or technical context
tone
G.RST7 Integrate and evaluate content presented in diverse media 9/10.RST7 Translate quantitative or technical information expressed
and formats, including visually and quantitatively, as well as in words in words in a text into visual form (e.g., a table or chart) and translate
information expressed visually or mathematically (e.g., in an
equation) into words
G.WHST2 Write informative/explanatory texts to examine and
9/10.WHST2 Write informative/explanatory texts, including the
convey complex ideas and information clearly and accurately
narration of historical events, scientific procedures/ experiments, or
through the effective selection, organization, and analysis of content technical processes
9/10.WHST2a Introduce a topic and organize ideas, concepts, and
information to make important connections and distinctions; include
formatting (e.g., headings), graphics (e.g., figures, tables), and
multimedia when useful to aiding comprehension
9/10.WHST2b Develop the topic with well-chosen, relevant, and
sufficient facts, extended definitions, concrete details, quotations, or
other information and examples appropriate to the audience’s
knowledge of the topic
9/10.WHST2c Use varied transitions and sentence structures
to link the major sections of the text, create cohesion, and clarify the
relationships among ideas and concepts
9/10.WHST2d Use precise language and domain-specific
vocabulary to manage the complexity of the topic and convey a style
appropriate to the discipline and context as well as to the expertise
of likely readers
9/10.WHST2e Establish and maintain a formal style and
objective tone while attending to the norms and conventions of the
discipline in which they are writing
9/10.WHST2f Provide a concluding statement or section
that follows from and supports the information or explanation
presented (e.g., articulating implications or the significance of the
topic)
MP1 Make sense of problems and persevere in solving them
MP2 Reason abstractly and quantitatively
MP3 Construct viable arguments and critique the reasoning of
others
MP4 Model with mathematics
MP5 Use appropriate tools strategically
MP6 Attend to precision
MP7 Look for and make use of structure
MP8 Look for and express regularity in repeated reasoning
Mathematical
Practices
7 of 7
Resources
Core
Connections
Geometry, 2012,
College
Preparatory
Mathematics
(CPM)