Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Subject
Subchapter
Course
Publisher
Program Title
Program ISBN
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(A) apply mathematics to
problems arising in everyday
life, society, and the
workplace
(i) apply mathematics to
problems arising in everyday
lifeInstruction 9781457300615 291 #1
Instruction 9781457300615 580 #1 - 4
Review 9781457300615 285 #15
Review 9781457300615 546 #12
Activity 9781457300615 506 #1
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(A) apply mathematics to
problems arising in everyday
life, society, and the
workplace
(ii) apply mathematics to
problems arising in society
Instruction 9781457300615 320 Example A, Try These A
Instruction 9781457300615 323 #9
Review 9781457300615 323 #9
Activity 9781457300615 538 #4
Assessment 9781457300615 203 #1
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(A) apply mathematics to
problems arising in everyday
life, society, and the
workplace
(iii) apply mathematics to
problems arising in the
workplaceInstruction 9781457300615 79 - 81 #2 - 7
Instruction 9781457300615 433 - 434 #1 - 4
Instruction 9781457300615 539 #1, 2
Review 9781457300615 541 #15
Assessment 9781457300615 237 #1 - 5
(a) General requirements. Students shall be awarded one credit for successful completion of this course. Prerequisite: Algebra I.
Correlations to the Texas Essential Knowledge and Skills (TEKS): Teacher Material
Chapter 111. Mathematics
Subchapter C. High School
§111.41. Geometry, Adopted 2012 (One Credit).
The College Board - SpringBoard
SpringBoard® Geometry
9781457300400
(c) Knowledge and Skills.
(5) Statements that contain the word "including" reference content that must be mastered, while those containing the phrase "such as" are intended as possible illustrative examples.
(4) These standards are meant to provide clarity and specificity in regards to the content covered in the high school geometry course. These standards are not meant to limit the methodologies used to convey this knowledge to students. Though the
standards are written in a particular order, they are not necessarily meant to be taught in the given order. In the standards, the phrase "to solve problems" includes both contextual and non-contextual problems unless specifically stated.
(3) In Geometry, students will build on the knowledge and skills for mathematics in Kindergarten-Grade 8 and Algebra I to strengthen their mathematical reasoning skills in geometric contexts. Within the course, students will begin to focus on more
precise terminology, symbolic representations, and the development of proofs. Students will explore concepts covering coordinate and transformational geometry; logical argument and constructions; proof and congruence; similarity, proof, and
trigonometry; two- and three-dimensional figures; circles; and probability. Students will connect previous knowledge from Algebra I to Geometry through the coordinate and transformational geometry strand. In the logical arguments and constructions
strand, students are expected to create formal constructions using a straight edge and compass. Though this course is primarily Euclidean geometry, students should complete the course with an understanding that non-Euclidean geometries exist. In
proof and congruence, students will use deductive reasoning to justify, prove and apply theorems about geometric figures. Throughout the standards, the term "prove" means a formal proof to be shown in a paragraph, a flow chart, or two-column
formats. Proportionality is the unifying component of the similarity, proof, and trigonometry strand. Students will use their proportional reasoning skills to prove and apply theorems and solve problems in this strand. The two- and three-dimensional
figure strand focuses on the application of formulas in multi-step situations since students have developed background knowledge in two- and three-dimensional figures. Using patterns to identify geometric properties, students will apply theorems
about circles to determine relationships between special segments and angles in circles. Due to the emphasis of probability and statistics in the college and career readiness standards, standards dealing with probability have been added to the
geometry curriculum to ensure students have proper exposure to these topics before pursuing their post-secondary education.
(2) The process standards describe ways in which students are expected to engage in the content. The placement of the process standards at the beginning of the knowledge and skills listed for each grade and course is intentional. The process
standards weave the other knowledge and skills together so that students may be successful problem solvers and use mathematics efficiently and effectively in daily life. The process standards are integrated at every grade level and course. When
possible, students will apply mathematics to problems arising in everyday life, society, and the workplace. Students will use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution,
justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution. Students will select appropriate tools such as real objects, manipulatives, paper and pencil, and technology and techniques such as mental
math, estimation, and number sense to solve problems. Students will effectively communicate mathematical ideas, reasoning, and their implications using multiple representations such as symbols, diagrams, graphs, and language. Students will use
mathematical relationships to generate solutions and make connections and predictions. Students will analyze mathematical relationships to connect and communicate mathematical ideas. Students will display, explain, or justify mathematical ideas
and arguments using precise mathematical language in written or oral communication.
(1) The desire to achieve educational excellence is the driving force behind the Texas essential knowledge and skills for mathematics, guided by the college and career readiness standards. By embedding statistics, probability, and finance, while
focusing on fluency and solid understanding, Texas will lead the way in mathematics education and prepare all Texas students for the challenges they will face in the 21st century.
(b) Introduction.
Page 1 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(B) use a problem-solving
model that incorporates
analyzing given information,
formulating a plan or
strategy, determining a
solution, justifying the
solution, and evaluating the
problem-solving process
and the reasonableness of
the solution
(i) use a problem-solving
model that incorporates
analyzing given information,
formulating a plan or
strategy, determining a
solution, justifying the
solution, and evaluating the
problem-solving process
Instruction 9781457300615 68 Example C
Instruction 9781457300615 377 #2
Instruction 9781457300615 539 #1 - 3
Assessment 9781457300615 179 #1- 3
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(B) use a problem-solving
model that incorporates
analyzing given information,
formulating a plan or
strategy, determining a
solution, justifying the
solution, and evaluating the
problem-solving process
and the reasonableness of
the solution
(ii) use a problem-solving
model that incorporates
analyzing given information,
formulating a plan or
strategy, determining a
solution, justifying the
solution, and evaluating the
reasonableness of the
solution
Instruction 9781457300615 26 #4
Assessment 9781457300615 179 #1 - 3
Instruction 9781457300615 27 Example A
Instruction 9781457300615 258 #4
Instruction 9781457300615 411 #3
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(C) select tools, including
real objects, manipulatives,
paper and pencil, and
technology as appropriate,
and techniques, including
mental math, estimation,
and number sense as
appropriate, to solve
problems
(i) select tools, including real
objects as appropriate, to
solve problems
Instruction 9781457300615 183 #11
Instruction 9781457300615 213 #2
Instruction 9781457300615 257 #1
Review 9781457300615 352 #12
Assessment 9781457300615 414 #7
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(C) select tools, including
real objects, manipulatives,
paper and pencil, and
technology as appropriate,
and techniques, including
mental math, estimation,
and number sense as
appropriate, to solve
problems
(ii) select tools, including
manipulatives as
appropriate, to solve
problems
Instruction 9781457300615 19 #4 - 6
Instruction 9781457300615 287 #3
Instruction 9781457300615 479 #1, 2
Review 9781457300615 452 #19
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(C) select tools, including
real objects, manipulatives,
paper and pencil, and
technology as appropriate,
and techniques, including
mental math, estimation,
and number sense as
appropriate, to solve
problems
(iii) select tools, including
paper and pencil as
appropriate, to solve
problems
Instruction 9781457300615 336 #4 - 8
Instruction 9781457300615 79 - 81 #2, 4, 6
Activity 9781457300615 50 #2
Instruction 9781457300615 197 #15
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(C) select tools, including
real objects, manipulatives,
paper and pencil, and
technology as appropriate,
and techniques, including
mental math, estimation,
and number sense as
appropriate, to solve
problems
(iv) select tools, including
technology as appropriate,
to solve problems
Instruction 9781457300615 193 #9
Assessment 9781457300615 338 #13
Review 9781457300615 344 #15, 16
Review 9781457300615 456 #24
Instruction 9781457300615 123 #7 - 10
Page 2 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(C) select tools, including
real objects, manipulatives,
paper and pencil, and
technology as appropriate,
and techniques, including
mental math, estimation,
and number sense as
appropriate, to solve
problems
(v) select techniques,
including mental math as
appropriate, to solve
problems
Instruction 9781457300615 18 #1 - 3
Review 9781457300615 17 #11
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(C) select tools, including
real objects, manipulatives,
paper and pencil, and
technology as appropriate,
and techniques, including
mental math, estimation,
and number sense as
appropriate, to solve
problems
(vi) select techniques
including estimation as
appropriate, to solve
problems
Instruction 9781457300615 89 #1
Activity 9781457300615 289 #6
Assessment 9781457300615 57 #5
Instruction 9781457300615 553 #1
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(C) select tools, including
real objects, manipulatives,
paper and pencil, and
technology as appropriate,
and techniques, including
mental math, estimation,
and number sense as
appropriate, to solve
problems
(vii) select techniques,
including number sense as
appropriate, to solve
problems
Instruction 9781457300615 284 #4
Activity 9781457300615 330 #1
Activity 9781457300615 35 #9
Assessment 9781457300615 284 #6
Instruction 9781457300615 324 #4
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(D) communicate
mathematical ideas,
reasoning, and their
implications using multiple
representations, including
symbols, diagrams, graphs,
and language as
appropriate
(i) communicate
mathematical ideas using
multiple representations,
including symbols as
appropriateInstruction 9781457300615 5 Example A, Try These A a, b
Instruction 9781457300615 324 #4
Assessment 9781457300615 6 #16, 17, 19
Assessment 9781457300615 10 #12, 13
Assessment 9781457300615 12 #1, 3, 9, 12, 13
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(D) communicate
mathematical ideas,
reasoning, and their
implications using multiple
representations, including
symbols, diagrams, graphs,
and language as
appropriate
(ii) communicate
mathematical ideas using
multiple representations,
including diagrams as
appropriateInstruction 9781457300615 3 #1 - 7
Instruction 9781457300615 7 #1
Instruction 9781457300615 85 #4
Review 9781457300615 10 #10
Assessment 9781457300615 6 #20
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(D) communicate
mathematical ideas,
reasoning, and their
implications using multiple
representations, including
symbols, diagrams, graphs,
and language as
appropriate
(iii) communicate
mathematical ideas using
multiple representations,
including graphs as
appropriateInstruction 9781457300615 244 #15 - 17
Instruction 9781457300615 305 #5
Review 9781457300615 247 #28, 29
Assessment 9781457300615 98 #3 - 6
Page 3 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(D) communicate
mathematical ideas,
reasoning, and their
implications using multiple
representations, including
symbols, diagrams, graphs,
and language as
appropriate
(iv) communicate
mathematical ideas using
multiple representations,
including language as
appropriateInstruction 9781457300615 3 #1 - 7
Instruction 9781457300615 7 #2
Review 9781457300615 6 #16, 17 , 19
Review 9781457300615 10 #11, 14
Activity 9781457300615 12 #4, 5, 6, 7, 8, 19
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(D) communicate
mathematical ideas,
reasoning, and their
implications using multiple
representations, including
symbols, diagrams, graphs,
and language as
appropriate
(v) communicate
mathematical reasoning
using multiple
representations, including
symbols as appropriateInstruction 9781457300615 4 #4
Instruction 9781457300615 7 #10
Review 9781457300615 133 #15
Assessment 9781457300615 5 #11
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(D) communicate
mathematical ideas,
reasoning, and their
implications using multiple
representations, including
symbols, diagrams, graphs,
and language as
appropriate
(vi) communicate
mathematical reasoning
using multiple
representations, including
diagrams as appropriateInstruction 9781457300615 4 #9
Instruction 9781457300615 544 #7
Activity 9781457300615 203 #1
Assessment 9781457300615 10 #15
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(D) communicate
mathematical ideas,
reasoning, and their
implications using multiple
representations, including
symbols, diagrams, graphs,
and language as
appropriate
(vii) communicate
mathematical reasoning
using multiple
representations, including
graphs as appropriateInstruction 9781457300615 241 #1 - 4
Instruction 9781457300615 394 #9
Activity 9781457300615 91 #11
Assessment 9781457300615 237 #1
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(D) communicate
mathematical ideas,
reasoning, and their
implications using multiple
representations, including
symbols, diagrams, graphs,
and language as
appropriate
(viii) communicate
mathematical reasoning
using multiple
representations, including
language as appropriateInstruction 9781457300615 9 #3, 7
Review 9781457300615 176 #4, 5
Assessment 9781457300615 6 #18
Assessment 9781457300615 12 #15
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(D) communicate
mathematical ideas,
reasoning, and their
implications using multiple
representations, including
symbols, diagrams, graphs,
and language as
appropriate
(ix) communicate
[mathematical ideas']
implications using multiple
representations, including
symbols as appropriateInstruction 9781457300615 3 #2
Activity 9781457300615 540 #7
Assessment 9781457300615 12 #11
Page 4 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(D) communicate
mathematical ideas,
reasoning, and their
implications using multiple
representations, including
symbols, diagrams, graphs,
and language as
appropriate
(x) communicate
[mathematical ideas']
implications using multiple
representations, including
diagrams as appropriateInstruction 9781457300615 393 #6
Activity 9781457300615 219 #16
Activity 9781457300615 290 #17
Assessment 9781457300615 593 #2
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(D) communicate
mathematical ideas,
reasoning, and their
implications using multiple
representations, including
symbols, diagrams, graphs,
and language as
appropriate
(xi) communicate
[mathematical ideas']
implications using multiple
representations, including
graphs as appropriateInstruction 9781457300615 198 #2
Instruction 9781457300615 249 #5
Instruction 9781457300615 373 #1, 2
Instruction 9781457300615 405 #1 - 3
Review 9781457300615 200 #13
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(D) communicate
mathematical ideas,
reasoning, and their
implications using multiple
representations, including
symbols, diagrams, graphs,
and language as
appropriate
(xii) communicate
[mathematical ideas']
implications using multiple
representations, including
language as appropriateInstruction 9781457300615 75 - 76 #5, 6
Review 9781457300615 10 #9
Assessment 9781457300615 12 #17
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(D) communicate
mathematical ideas,
reasoning, and their
implications using multiple
representations, including
symbols, diagrams, graphs,
and language as
appropriate
(xiii) communicate
[mathematical reasoning's]
implications using multiple
representations, including
symbols as appropriateInstruction 9781457300615 20 #7 - 9
Review 9781457300615 91 #8 - 10
Assessment 9781457300615 12 #20
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(D) communicate
mathematical ideas,
reasoning, and their
implications using multiple
representations, including
symbols, diagrams, graphs,
and language as
appropriate
(xiv) communicate
[mathematical reasoning's]
implications using multiple
representations, including
diagrams as appropriateInstruction 9781457300615 19 #5, 6
Review 9781457300615 7 #3
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(D) communicate
mathematical ideas,
reasoning, and their
implications using multiple
representations, including
symbols, diagrams, graphs,
and language as
appropriate
(xv) communicate
[mathematical reasoning's]
implications using multiple
representations, including
graphs as appropriateInstruction 9781457300615 249 #5
Instruction 9781457300615 373 #1 - 3
Instruction 9781457300615 405 #1, 2
Assessment 9781457300615 237 #2, 3, 5
Page 5 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(D) communicate
mathematical ideas,
reasoning, and their
implications using multiple
representations, including
symbols, diagrams, graphs,
and language as
appropriate
(xvi) communicate
[mathematical reasoning's]
implications using multiple
representations, including
language as appropriateInstruction 9781457300615 20 #10, 11
Activity 9781457300615 81 #7
Assessment 9781457300615 24 #16, 18
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(E) create and use
representations to organize,
record, and communicate
mathematical ideas
(i) create representations to
organize mathematical
ideas Instruction 9781457300615 169 - 173 #3 - 12
Assessment 9781457300615 174 #17
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(E) create and use
representations to organize,
record, and communicate
mathematical ideas
(ii) create representations to
record mathematical ideas
Instruction 9781457300615 151 #5
Activity 9781457300615 219 #16
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(E) create and use
representations to organize,
record, and communicate
mathematical ideas
(iii) create representations to
communicate mathematical
ideas Instruction 9781457300615 435 #6
Assessment 9781457300615 593 #2
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(E) create and use
representations to organize,
record, and communicate
mathematical ideas
(iv) use representations to
organize mathematical
ideas Instruction 9781457300615 450 #1
Activity 9781457300615 220 #17
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(E) create and use
representations to organize,
record, and communicate
mathematical ideas
(v) use representations to
record mathematical ideas
Instruction 9781457300615 479 #1
Review 9781457300615 43 #16
Assessment 9781457300615 290 #17
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(E) create and use
representations to organize,
record, and communicate
mathematical ideas
(vi) use representations to
communicate mathematical
ideas Instruction 9781457300615 169 - 173 #3 - 12
Instruction 9781457300615 480 #3
Assessment 9781457300615 237 #2, 5
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(F) analyze mathematical
relationships to connect and
communicate mathematical
ideas
(i) analyze mathematical
relationships to connect
mathematical ideasInstruction 9781457300615 518 #1, 4, 5
Assessment 9781457300615 520 #10
Page 6 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(F) analyze mathematical
relationships to connect and
communicate mathematical
ideas
(ii) analyze mathematical
relationships to
communicate mathematical
ideas
Instruction 9781457300615 67 - 68 Example B, Example C
Instruction 9781457300615 481 #7
Activity 9781457300615 523 #4
Assessment 9781457300615 520 #10
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(G) display, explain, and
justify mathematical ideas
and arguments using
precise mathematical
language in written or oral
communication
(i) display mathematical
ideas using precise
mathematical language in
written or oral
communication
Instruction 9781457300615 175 #1
Instruction 9781457300615 481 #6
Assessment 9781457300615 203 #1
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(G) display, explain, and
justify mathematical ideas
and arguments using
precise mathematical
language in written or oral
communication
(ii) display mathematical
arguments using precise
mathematical language in
written or oral
communication
Instruction 9781457300615 66 Example A
Instruction 9781457300615 169 #2
Assessment 9781457300615 178 #11
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(G) display, explain, and
justify mathematical ideas
and arguments using
precise mathematical
language in written or oral
communication
(iii) explain mathematical
ideas using precise
mathematical language in
written or oral
communication
Instruction 9781457300615 182 #7
Instruction 9781457300615 346 #2
Review 9781457300615 267 #8
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(G) display, explain, and
justify mathematical ideas
and arguments using
precise mathematical
language in written or oral
communication
(iv) explain mathematical
arguments using precise
mathematical language in
written or oral
communication
Instruction 9781457300615 284 #7
Instruction 9781457300615 413 #5f
Review 9781457300615 48 #11
Activity 9781457300615 50 #21
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(G) display, explain, and
justify mathematical ideas
and arguments using
precise mathematical
language in written or oral
communication
(v) justify mathematical
ideas using precise
mathematical language in
written or oral
communication
Instruction 9781457300615 250 #4c
Instruction 9781457300615 253 #8
Instruction 9781457300615 258 #4
Review 9781457300615 337 #11
Assessment 9781457300615 178 #7
(1) Mathematical process standards. The student
uses mathematical processes to acquire and
demonstrate mathematical understanding. The
student is expected to:
(G) display, explain, and
justify mathematical ideas
and arguments using
precise mathematical
language in written or oral
communication
(vi) justify mathematical
arguments using precise
mathematical language in
written or oral
communication
Instruction 9781457300615 81 #7
Instruction 9781457300615 342 #5
Activity 9781457300615 300 #14
Assessment 9781457300615 273 #3
Page 7 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(2) Coordinate and transformational geometry.
The student uses the process skills to understand
the connections between algebra and geometry
and uses the one- and two-dimensional coordinate
systems to verify geometric conjectures. The
student is expected to:
(A) determine the
coordinates of a point that is
a given fractional distance
less than one from one end
of a line segment to the
other in one- and two-
dimensional coordinate
systems, including finding
the midpoint
(i) determine the
coordinates of a point that is
a given fractional distance
less than one from one end
of a line segment to the
other in one-dimensional
coordinate systems,
including finding the
midpoint
Instruction 9781457300615 41 #12
Review 9781457300615 44 #21
Assessment 9781457300615 42 #13
(2) Coordinate and transformational geometry.
The student uses the process skills to understand
the connections between algebra and geometry
and uses the one- and two-dimensional coordinate
systems to verify geometric conjectures. The
student is expected to:
(A) determine the
coordinates of a point that is
a given fractional distance
less than one from one end
of a line segment to the
other in one- and two-
dimensional coordinate
systems, including finding
the midpoint
(ii) determine the
coordinates of a point that is
a given fractional distance
less than one from one end
of a line segment to the
other in two-dimensional
coordinate systems,
including finding the
midpoint
Instruction 9781457300615 387 #4
Instruction 9781457300615 388 Example A
Review 9781457300615 58 #14
Activity 9781457300615 58 #20
(2) Coordinate and transformational geometry.
The student uses the process skills to understand
the connections between algebra and geometry
and uses the one- and two-dimensional coordinate
systems to verify geometric conjectures. The
student is expected to:
(B) derive and use the
distance, slope, and
midpoint formulas to verify
geometric relationships,
including congruence of
segments and parallelism or
perpendicularity of pairs of
lines
(i) derive the distance
formula
Instruction 9781457300615 53 #11 - 15
Instruction 9781457300615 374 #3
Review 9781457300615 54 #20
Activity 9781457300615 58 #5, 7, 13, 25b
(2) Coordinate and transformational geometry.
The student uses the process skills to understand
the connections between algebra and geometry
and uses the one- and two-dimensional coordinate
systems to verify geometric conjectures. The
student is expected to:
(B) derive and use the
distance, slope, and
midpoint formulas to verify
geometric relationships,
including congruence of
segments and parallelism or
perpendicularity of pairs of
lines
(ii) use the distance formula
to verify geometric
relationships, including
congruence of segments Instruction 9781457300615 53 #11 - 15
Instruction 9781457300615 223 #3
Review 9781457300615 54 20
(2) Coordinate and transformational geometry.
The student uses the process skills to understand
the connections between algebra and geometry
and uses the one- and two-dimensional coordinate
systems to verify geometric conjectures. The
student is expected to:
(B) derive and use the
distance, slope, and
midpoint formulas to verify
geometric relationships,
including congruence of
segments and parallelism or
perpendicularity of pairs of
lines
(iii) use the distance formula
to verify geometric
relationships, including
parallelism or
perpendicularity of pairs of
lines
Instruction 9781457300615 106 #1
Instruction 9781457300615 207 #6
Review 9781457300615 55 #26
Assessment 9781457300615 58 #5, 13
Instruction 9781457300615 374 #3
(2) Coordinate and transformational geometry.
The student uses the process skills to understand
the connections between algebra and geometry
and uses the one- and two-dimensional coordinate
systems to verify geometric conjectures. The
student is expected to:
(B) derive and use the
distance, slope, and
midpoint formulas to verify
geometric relationships,
including congruence of
segments and parallelism or
perpendicularity of pairs of
lines
(iv) derive the slope formula
Instruction 9781457300615 207 #6
Review 9781457300615 208 #8
Activity 9781457300615 236 #5
Instruction 9781457300615 224 #5
Instruction 9781457300615 228 #7
Page 8 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(2) Coordinate and transformational geometry.
The student uses the process skills to understand
the connections between algebra and geometry
and uses the one- and two-dimensional coordinate
systems to verify geometric conjectures. The
student is expected to:
(B) derive and use the
distance, slope, and
midpoint formulas to verify
geometric relationships,
including congruence of
segments and parallelism or
perpendicularity of pairs of
lines
(v) use the slope formula to
verify geometric
relationships, including
parallelism or
perpendicularity of pairs of
lines
Instruction 9781457300615 224 #5
Instruction 9781457300615 231 #6a
Activity 9781457300615 236 #1, 5
(2) Coordinate and transformational geometry.
The student uses the process skills to understand
the connections between algebra and geometry
and uses the one- and two-dimensional coordinate
systems to verify geometric conjectures. The
student is expected to:
(B) derive and use the
distance, slope, and
midpoint formulas to verify
geometric relationships,
including congruence of
segments and parallelism or
perpendicularity of pairs of
lines
(vi) derive the midpoint
formula
Instruction 9781457300615 223 #1, Math Tep
Activity 9781457300615 236 #1, 5
Instruction 9781457300615 224 #5
Instruction 9781457300615 233 #2
(2) Coordinate and transformational geometry.
The student uses the process skills to understand
the connections between algebra and geometry
and uses the one- and two-dimensional coordinate
systems to verify geometric conjectures. The
student is expected to:
(B) derive and use the
distance, slope, and
midpoint formulas to verify
geometric relationships,
including congruence of
segments and parallelism or
perpendicularity of pairs of
lines
(vii) use the midpoint
formula to verify geometric
relationships
Instruction 9781457300615 224 #5
Activity 9781457300615 236 #1, 5
Instruction 9781457300615 228 #7
Instruction 9781457300615 233 #2
(2) Coordinate and transformational geometry.
The student uses the process skills to understand
the connections between algebra and geometry
and uses the one- and two-dimensional coordinate
systems to verify geometric conjectures. The
student is expected to:
(C) determine an equation
of a line parallel or
perpendicular to a given line
that passes through a given
point
(i) determine an equation of
a line parallel or
perpendicular to a given line
that passes through a given
point
Instruction 9781457300615 92 #2 - 4
Review 9781457300615 94 #6 - 8
Assessment 9781457300615 96 #16 - 19
Assessment 9781457300615 98 #17, 18
Assessment 9781457300615 99 #3
(3) Coordinate and transformational geometry.
The student uses the process skills to generate
and describe rigid transformations (translation,
reflection, and rotation) and non-rigid
transformations (dilations that preserve similarity
and reductions and enlargements that do not
preserve similarity). The student is expected to:
(A) describe and perform
transformations of figures in
a plane using coordinate
notation
(i) describe transformations
of figures in a plane using
coordinate notation
Instruction 9781457300615 104 #4, 5
Instruction 9781457300615 245 #22
Review 9781457300615 241 - 243 #4, 7, 12
Activity 9781457300615 128 #1, 4
(3) Coordinate and transformational geometry.
The student uses the process skills to generate
and describe rigid transformations (translation,
reflection, and rotation) and non-rigid
transformations (dilations that preserve similarity
and reductions and enlargements that do not
preserve similarity). The student is expected to:
(A) describe and perform
transformations of figures in
a plane using coordinate
notation
(ii) perform transformations
of figures in a plane using
coordinate notation
Instruction 9781457300615 105 #6
Review 9781457300615 106 #9
Activity 9781457300615 109 #4, 5
Instruction 9781457300615 109 #2
Instruction 9781457300615 114 #6
Page 9 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(3) Coordinate and transformational geometry.
The student uses the process skills to generate
and describe rigid transformations (translation,
reflection, and rotation) and non-rigid
transformations (dilations that preserve similarity
and reductions and enlargements that do not
preserve similarity). The student is expected to:
(B) determine the image or
pre-image of a given two-
dimensional figure under a
composition of rigid
transformations, a
composition of non-rigid
transformations, and a
composition of both,
including dilations where the
center can be any point in
the plane
(i) determine the image or
pre-image of a given two-
dimensional figure under a
composition of rigid
transformations including
dilations where the center
can be any point in the
plane
Instruction 9781457300615 130 #2, 3
Instruction 9781457300615 132 Example A
Review 9781457300615 133 #11
(3) Coordinate and transformational geometry.
The student uses the process skills to generate
and describe rigid transformations (translation,
reflection, and rotation) and non-rigid
transformations (dilations that preserve similarity
and reductions and enlargements that do not
preserve similarity). The student is expected to:
(B) determine the image or
pre-image of a given two-
dimensional figure under a
composition of rigid
transformations, a
composition of non-rigid
transformations, and a
composition of both,
including dilations where the
center can be any point in
the plane
(ii) determine the image or
pre-image of a given two-
dimensional figure under a
composition of non-rigid
transformations, including
dilations where the center
can be any point in the
plane
Instruction 9781457300615 244 #16, 17
Assessment 9781457300615 245 #18, 19
(3) Coordinate and transformational geometry.
The student uses the process skills to generate
and describe rigid transformations (translation,
reflection, and rotation) and non-rigid
transformations (dilations that preserve similarity
and reductions and enlargements that do not
preserve similarity). The student is expected to:
(B) determine the image or
pre-image of a given two-
dimensional figure under a
composition of rigid
transformations, a
composition of non-rigid
transformations, and a
composition of both,
including dilations where the
center can be any point in
the plane
(iii) determine the image or
pre-image of a given two-
dimensional figure under a
composition of both,
including dilations where the
center can be any point in
the plane
Instruction 9781457300615 244 #16
Instruction 9781457300615 249 #5
Review 9781457300615 251 #11
Assessment 9781457300615 245 #8, 11
Assessment 9781457300615 256 #18, 19
(3) Coordinate and transformational geometry.
The student uses the process skills to generate
and describe rigid transformations (translation,
reflection, and rotation) and non-rigid
transformations (dilations that preserve similarity
and reductions and enlargements that do not
preserve similarity). The student is expected to:
(C) identify the sequence of
transformations that will
carry a given pre-image
onto an image on and off
the coordinate plane
(i) identify the sequence of
transformations that will
carry a given pre-image
onto an image on the
coordinate plane
Instruction 9781457300615 135 #6
Instruction 9781457300615 248 #3
Activity 9781457300615 273 #2
Assessment 9781457300615 251 #12
(3) Coordinate and transformational geometry.
The student uses the process skills to generate
and describe rigid transformations (translation,
reflection, and rotation) and non-rigid
transformations (dilations that preserve similarity
and reductions and enlargements that do not
preserve similarity). The student is expected to:
(C) identify the sequence of
transformations that will
carry a given pre-image
onto an image on and off
the coordinate plane
(ii) identify the sequence of
transformations that will
carry a given pre-image
onto an image off the
coordinate plane
Instruction 9781457300615 136 #9, 10
Review 9781457300615 136 #12
(3) Coordinate and transformational geometry.
The student uses the process skills to generate
and describe rigid transformations (translation,
reflection, and rotation) and non-rigid
transformations (dilations that preserve similarity
and reductions and enlargements that do not
preserve similarity). The student is expected to:
(D) identify and distinguish
between reflectional and
rotational symmetry in a
plane figure
(i) identify reflectional
symmetry in a plane figure
Instruction 9781457300615 117 #15
Instruction 9781457300615 125 #13a, b, c, d
Assessment 9781457300615 118 #17
Page 10 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(3) Coordinate and transformational geometry.
The student uses the process skills to generate
and describe rigid transformations (translation,
reflection, and rotation) and non-rigid
transformations (dilations that preserve similarity
and reductions and enlargements that do not
preserve similarity). The student is expected to:
(D) identify and distinguish
between reflectional and
rotational symmetry in a
plane figure
(ii) identify rotational
symmetry in a plane figure
Instruction 9781457300615 125 #13b, c, d
Review 9781457300615 126 #18
Assessment 9781457300615 126 #15
(3) Coordinate and transformational geometry.
The student uses the process skills to generate
and describe rigid transformations (translation,
reflection, and rotation) and non-rigid
transformations (dilations that preserve similarity
and reductions and enlargements that do not
preserve similarity). The student is expected to:
(D) identify and distinguish
between reflectional and
rotational symmetry in a
plane figure
(iii) distinguish between
reflectional and rotational
symmetry in a plane figure
Instruction 9781457300615 125 #13
Activity 9781457300615 128 #14
Assessment 9781457300615 126 #15c, d
(4) Logical argument and constructions. The
student uses the process skills with deductive
reasoning to understand geometric relationships.
The student is expected to:
(A) distinguish between
undefined terms, definitions,
postulates, conjectures, and
theorems
(i) distinguish between
undefined terms, definitions,
postulates, conjectures, and
theorems
Instruction 9781457300615 25 #1 - 3
Review 9781457300615 28 #10
Activity 9781457300615 22 #12
Assessment 9781457300615 36 #2, 3
(4) Logical argument and constructions. The
student uses the process skills with deductive
reasoning to understand geometric relationships.
The student is expected to:
(B) identify and determine
the validity of the converse,
inverse, and contrapositive
of a conditional statement
and recognize the
connection between a
biconditional statement and
a true conditional statement
with a true converse
(i) identify the validity of the
converse of a conditional
statement
Instruction 9781457300615 32 #1
Instruction 9781457300615 33 #5
Review 9781457300615 34 #15
Assessment 9781457300615 34 #9
(4) Logical argument and constructions. The
student uses the process skills with deductive
reasoning to understand geometric relationships.
The student is expected to:
(B) identify and determine
the validity of the converse,
inverse, and contrapositive
of a conditional statement
and recognize the
connection between a
biconditional statement and
a true conditional statement
with a true converse
(ii) identify the validity of the
inverse of a conditional
statement
Instruction 9781457300615 32 #1
Instruction 9781457300615 33 #5
Activity 9781457300615 36 #20
Assessment 9781457300615 37 #3
(4) Logical argument and constructions. The
student uses the process skills with deductive
reasoning to understand geometric relationships.
The student is expected to:
(B) identify and determine
the validity of the converse,
inverse, and contrapositive
of a conditional statement
and recognize the
connection between a
biconditional statement and
a true conditional statement
with a true converse
(iii) identify the validity of the
contrapositive of a
conditional statement
Instruction 9781457300615 32 #1
Instruction 9781457300615 33 #5
Activity 9781457300615 36 #20
Assessment 9781457300615 37 #3
Page 11 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(4) Logical argument and constructions. The
student uses the process skills with deductive
reasoning to understand geometric relationships.
The student is expected to:
(B) identify and determine
the validity of the converse,
inverse, and contrapositive
of a conditional statement
and recognize the
connection between a
biconditional statement and
a true conditional statement
with a true converse
(iv) determine the validity of
the converse of a
conditional statement
Instruction 9781457300615 32 #1
Instruction 9781457300615 33 #5
Review 9781457300615 34 #7
Assessment 9781457300615 36 #24
(4) Logical argument and constructions. The
student uses the process skills with deductive
reasoning to understand geometric relationships.
The student is expected to:
(B) identify and determine
the validity of the converse,
inverse, and contrapositive
of a conditional statement
and recognize the
connection between a
biconditional statement and
a true conditional statement
with a true converse
(v) determine the validity of
the inverse of a conditional
statement
Instruction 9781457300615 32 #1
Instruction 9781457300615 33 #5
Assessment 9781457300615 36 #21, 25
(4) Logical argument and constructions. The
student uses the process skills with deductive
reasoning to understand geometric relationships.
The student is expected to:
(B) identify and determine
the validity of the converse,
inverse, and contrapositive
of a conditional statement
and recognize the
connection between a
biconditional statement and
a true conditional statement
with a true converse
(vi) determine the validity of
the contrapositive of a
conditional statement
Instruction 9781457300615 32 #1
Instruction 9781457300615 33 #5
Review 9781457300615 34 #7
Assessment 9781457300615 36 #26
(4) Logical argument and constructions. The
student uses the process skills with deductive
reasoning to understand geometric relationships.
The student is expected to:
(B) identify and determine
the validity of the converse,
inverse, and contrapositive
of a conditional statement
and recognize the
connection between a
biconditional statement and
a true conditional statement
with a true converse
(vii) recognize the
connection between a
biconditional statement and
a true conditional statement
with a true converseInstruction 9781457300615 33 #3 - 5
Activity 9781457300615 36 #19
Assessment 9781457300615 37 #3
(4) Logical argument and constructions. The
student uses the process skills with deductive
reasoning to understand geometric relationships.
The student is expected to:
(C) verify that a conjecture
is false using a
counterexample
(i) verify that a conjecture is
false using a
counterexampleInstruction 9781457300615 29 #2
Instruction 9781457300615 32 #1
Review 9781457300615 31 #9
Assessment 9781457300615 36 #12
(4) Logical argument and constructions. The
student uses the process skills with deductive
reasoning to understand geometric relationships.
The student is expected to:
(D) compare geometric
relationships between
Euclidean and spherical
geometries, including
parallel lines and the sum of
the angles in a triangle
(i) compare geometric
relationships between
Euclidean and spherical
geometries, including
parallel lines
Instruction 9781457300615 533 #4, 5
Review 9781457300615 536 #20
Page 12 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(4) Logical argument and constructions. The
student uses the process skills with deductive
reasoning to understand geometric relationships.
The student is expected to:
(D) compare geometric
relationships between
Euclidean and spherical
geometries, including
parallel lines and the sum of
the angles in a triangle
(ii) compare geometric
relationships between
Euclidean and spherical
geometries, including the
sum of the angles in a
triangle
Instruction 9781457300615 534 #10e, f, 11, 12
Instruction 9781457300615 535 #13 - 15
Review 9781457300615 536 #20
(5) Logical argument and constructions. The
student uses constructions to validate conjectures
about geometric figures. The student is expected
to:
(A) investigate patterns to
make conjectures about
geometric relationships,
including angles formed by
parallel lines cut by a
transversal, criteria required
for triangle congruence,
special segments of
triangles, diagonals of
quadrilaterals, interior and
exterior angles of polygons,
and special segments and
angles of circles choosing
from a variety of tools
(i) investigate patterns to
make conjectures about
geometric relationships,
including angles formed by
parallel lines cut by a
transversal
Instruction 9781457300615 74 #3
Review 9781457300615 78 #19, 20
Activity 9781457300615 83 #15
(5) Logical argument and constructions. The
student uses constructions to validate conjectures
about geometric figures. The student is expected
to:
(A) investigate patterns to
make conjectures about
geometric relationships,
including angles formed by
parallel lines cut by a
transversal, criteria required
for triangle congruence,
special segments of
triangles, diagonals of
quadrilaterals, interior and
exterior angles of polygons,
and special segments and
angles of circles choosing
from a variety of tools
(ii) investigate patterns to
make conjectures about
geometric relationships,
including criteria required for
triangle congruence
Instruction 9781457300615 151 #5, 6
Activity 9781457300615 162 #4, 5
(5) Logical argument and constructions. The
student uses constructions to validate conjectures
about geometric figures. The student is expected
to:
(A) investigate patterns to
make conjectures about
geometric relationships,
including angles formed by
parallel lines cut by a
transversal, criteria required
for triangle congruence,
special segments of
triangles, diagonals of
quadrilaterals, interior and
exterior angles of polygons,
and special segments and
angles of circles choosing
from a variety of tools
(iii) investigate patterns to
make conjectures about
geometric relationships,
including special segments
of triangles
Instruction 9781457300615 193 #9
Activity 9781457300615 196 - 197 #11 - 13
(5) Logical argument and constructions. The
student uses constructions to validate conjectures
about geometric figures. The student is expected
to:
(A) investigate patterns to
make conjectures about
geometric relationships,
including angles formed by
parallel lines cut by a
transversal, criteria required
for triangle congruence,
special segments of
triangles, diagonals of
quadrilaterals, interior and
exterior angles of polygons,
and special segments and
angles of circles choosing
from a variety of tools
(iv) investigate patterns to
make conjectures about
geometric relationships,
including diagonals of
quadrilaterals
Instruction 9781457300615 211 #8
Instruction 9781457300615 213 #2, 3
Review 9781457300615 211 - 212 #10
Page 13 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(5) Logical argument and constructions. The
student uses constructions to validate conjectures
about geometric figures. The student is expected
to:
(A) investigate patterns to
make conjectures about
geometric relationships,
including angles formed by
parallel lines cut by a
transversal, criteria required
for triangle congruence,
special segments of
triangles, diagonals of
quadrilaterals, interior and
exterior angles of polygons,
and special segments and
angles of circles choosing
from a variety of tools
(v) investigate patterns to
make conjectures about
geometric relationships,
including interior angles of
polygons
Instruction 9781457300615 447 #3
Instruction 9781457300615 450 #6
Instruction 9781457300615 453 #1
Review 9781457300615 452 #19
Review 9781457300615 456 #24a, b
(5) Logical argument and constructions. The
student uses constructions to validate conjectures
about geometric figures. The student is expected
to:
(A) investigate patterns to
make conjectures about
geometric relationships,
including angles formed by
parallel lines cut by a
transversal, criteria required
for triangle congruence,
special segments of
triangles, diagonals of
quadrilaterals, interior and
exterior angles of polygons,
and special segments and
angles of circles choosing
from a variety of tools
(vi) investigate patterns to
make conjectures about
geometric relationships,
including exterior angles of
polygons
Instruction 9781457300615 183 #13
Instruction 9781457300615 455 #11
Review 9781457300615 456 #23, 24c
Activity 9781457300615 183 #10 - 12
(5) Logical argument and constructions. The
student uses constructions to validate conjectures
about geometric figures. The student is expected
to:
(A) investigate patterns to
make conjectures about
geometric relationships,
including angles formed by
parallel lines cut by a
transversal, criteria required
for triangle congruence,
special segments of
triangles, diagonals of
quadrilaterals, interior and
exterior angles of polygons,
and special segments and
angles of circles choosing
from a variety of tools
(vii) investigate patterns to
make conjectures about
geometric relationships,
including special segments
Instruction 9781457300615 339 #1
Instruction 9781457300615 342 #8
Assessment 9781457300615 337 #9, 10
Assessment 9781457300615 343 #13
(5) Logical argument and constructions. The
student uses constructions to validate conjectures
about geometric figures. The student is expected
to:
(A) investigate patterns to
make conjectures about
geometric relationships,
including angles formed by
parallel lines cut by a
transversal, criteria required
for triangle congruence,
special segments of
triangles, diagonals of
quadrilaterals, interior and
exterior angles of polygons,
and special segments and
angles of circles choosing
from a variety of tools
(viii) investigate patterns to
make conjectures about
angles of circles choosing
from a variety of tools
Instruction 9781457300615 353 #5
Instruction 9781457300615 354 #7
Instruction 9781457300615 366 #8
Assessment 9781457300615 357 #16, 17
Page 14 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(5) Logical argument and constructions. The
student uses constructions to validate conjectures
about geometric figures. The student is expected
to:
(B) construct congruent
segments, congruent
angles, a segment bisector,
an angle bisector,
perpendicular lines, the
perpendicular bisector of a
line segment, and a line
parallel to a given line
through a point not on a line
using a compass and a
straightedge
(i) construct congruent
segments using a compass
and a straightedge
Instruction 9781457300615 411 #3
Instruction 9781457300615 412 #4
Review 9781457300615 414 #7
Assessment 9781457300615 427 #1 - 3
(5) Logical argument and constructions. The
student uses constructions to validate conjectures
about geometric figures. The student is expected
to:
(B) construct congruent
segments, congruent
angles, a segment bisector,
an angle bisector,
perpendicular lines, the
perpendicular bisector of a
line segment, and a line
parallel to a given line
through a point not on a line
using a compass and a
straightedge
(ii) construct congruent
angles using a compass and
a straightedge
Instruction 9781457300615 411 #5
Review 9781457300615 413 #7
(5) Logical argument and constructions. The
student uses constructions to validate conjectures
about geometric figures. The student is expected
to:
(B) construct congruent
segments, congruent
angles, a segment bisector,
an angle bisector,
perpendicular lines, the
perpendicular bisector of a
line segment, and a line
parallel to a given line
through a point not on a line
using a compass and a
straightedge
(iii) construct a segment
bisector using a compass
and a straightedge
Instruction 9781457300615 414 #8
Review 9781457300615 417 #12
(5) Logical argument and constructions. The
student uses constructions to validate conjectures
about geometric figures. The student is expected
to:
(B) construct congruent
segments, congruent
angles, a segment bisector,
an angle bisector,
perpendicular lines, the
perpendicular bisector of a
line segment, and a line
parallel to a given line
through a point not on a line
using a compass and a
straightedge
(iv) construct an angle
bisector using a compass
and a straightedge
Instruction 9781457300615 414 #9
Review 9781457300615 417 #15
(5) Logical argument and constructions. The
student uses constructions to validate conjectures
about geometric figures. The student is expected
to:
(B) construct congruent
segments, congruent
angles, a segment bisector,
an angle bisector,
perpendicular lines, the
perpendicular bisector of a
line segment, and a line
parallel to a given line
through a point not on a line
using a compass and a
straightedge
(v) construct perpendicular
lines using a compass and a
straightedge
Instruction 9781457300615 419 #4
Review 9781457300615 420 #8
Activity 9781457300615 428 #2, 8
Page 15 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(5) Logical argument and constructions. The
student uses constructions to validate conjectures
about geometric figures. The student is expected
to:
(B) construct congruent
segments, congruent
angles, a segment bisector,
an angle bisector,
perpendicular lines, the
perpendicular bisector of a
line segment, and a line
parallel to a given line
through a point not on a line
using a compass and a
straightedge
(vi) construct the
perpendicular bisector of a
line segment using a
compass and a straightedge
Instruction 9781457300615 414 #8
Instruction 9781457300615 420 #9
Review 9781457300615 417 #12
Review 9781457300615 421 #10
(5) Logical argument and constructions. The
student uses constructions to validate conjectures
about geometric figures. The student is expected
to:
(B) construct congruent
segments, congruent
angles, a segment bisector,
an angle bisector,
perpendicular lines, the
perpendicular bisector of a
line segment, and a line
parallel to a given line
through a point not on a line
using a compass and a
straightedge
(vii) construct a line parallel
to a given line through a
point not on a line using a
compass and a straightedge
Instruction 9781457300615 418 #1
Review 9781457300615 420 #7
Activity 9781457300615 428 #7
(5) Logical argument and constructions. The
student uses constructions to validate conjectures
about geometric figures. The student is expected
to:
(C) use the constructions of
congruent segments,
congruent angles, angle
bisectors, and perpendicular
bisectors to make
conjectures about geometric
relationships
(i) use the constructions of
congruent segments to
make conjectures about
geometric relationships Instruction 9781457300615 412 #4d
Review 9781457300615 414 #8
(5) Logical argument and constructions. The
student uses constructions to validate conjectures
about geometric figures. The student is expected
to:
(C) use the constructions of
congruent segments,
congruent angles, angle
bisectors, and perpendicular
bisectors to make
conjectures about geometric
relationships
(ii) use the constructions of
congruent angles to make
conjectures about geometric
relationships Instruction 9781457300615 413 #5
Review 9781457300615 421 #14
(5) Logical argument and constructions. The
student uses constructions to validate conjectures
about geometric figures. The student is expected
to:
(C) use the constructions of
congruent segments,
congruent angles, angle
bisectors, and perpendicular
bisectors to make
conjectures about geometric
relationships
(iii) use the constructions of
angle bisectors to make
conjectures about geometric
relationships Instruction 9781457300615 415 #9
Review 9781457300615 417 #14
Review 9781457300615 426 #15
(5) Logical argument and constructions. The
student uses constructions to validate conjectures
about geometric figures. The student is expected
to:
(C) use the constructions of
congruent segments,
congruent angles, angle
bisectors, and perpendicular
bisectors to make
conjectures about geometric
relationships
(iv) use the constructions of
perpendicular bisectors to
make conjectures about
geometric relationships Instruction 9781457300615 414 #8
Review 9781457300615 417 #11, 12
Instruction 9781457300615 419 #4, 5
Instruction 9781457300615 420 #9
Page 16 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(5) Logical argument and constructions. The
student uses constructions to validate conjectures
about geometric figures. The student is expected
to:
(D) verify the Triangle
Inequality theorem using
constructions and apply the
theorem to solve problems
(i) verify the Triangle
Inequality theorem using
constructions Instruction 9781457300615 412 #4, Math Tip
Activity 9781457300615 428 #3, 4
Review 9781457300615 416 - 417 #11
(5) Logical argument and constructions. The
student uses constructions to validate conjectures
about geometric figures. The student is expected
to:
(D) verify the Triangle
Inequality theorem using
constructions and apply the
theorem to solve problems
(ii) apply the theorem to
solve problem
Instruction 9781457300615 412 #4
Activity 9781457300615 428 #3, 4
(6) Proof and congruence. The student uses the
process skills with deductive reasoning to prove
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(A) verify theorems about
angles formed by the
intersection of lines and line
segments, including vertical
angles, and angles formed
by parallel lines cut by a
transversal and prove
equidistance between the
endpoints of a segment and
points on its perpendicular
bisector and apply these
relationships to solve
problems
(i) verify theorems about
angles formed by the
intersection of lines
including vertical angles
Instruction 9781457300615 66 Example A
Assessment 9781457300615 88 #11, 17, 22
(6) Proof and congruence. The student uses the
process skills with deductive reasoning to prove
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(A) verify theorems about
angles formed by the
intersection of lines and line
segments, including vertical
angles, and angles formed
by parallel lines cut by a
transversal and prove
equidistance between the
endpoints of a segment and
points on its perpendicular
bisector and apply these
relationships to solve
problems
(ii) verify theorems about
angles formed by the
intersection of line
segments, including vertical
angles
Instruction 9781457300615 66 Example A
Review 9781457300615 68 - 69 Example C, Try These C a
Activity 9781457300615 72 #16
(6) Proof and congruence. The student uses the
process skills with deductive reasoning to prove
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(A) verify theorems about
angles formed by the
intersection of lines and line
segments, including vertical
angles, and angles formed
by parallel lines cut by a
transversal and prove
equidistance between the
endpoints of a segment and
points on its perpendicular
bisector and apply these
relationships to solve
problems
(iii) verify theorems about
angles formed by parallel
lines cut by a transversal
Instruction 9781457300615 74 - 75 #1 - 5
Review 9781457300615 77 #12
Review 78 #14
Page 17 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(6) Proof and congruence. The student uses the
process skills with deductive reasoning to prove
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(A) verify theorems about
angles formed by the
intersection of lines and line
segments, including vertical
angles, and angles formed
by parallel lines cut by a
transversal and prove
equidistance between the
endpoints of a segment and
points on its perpendicular
bisector and apply these
relationships to solve
problems
(iv) prove equidistance
between the endpoints of a
segment and points on its
perpendicular bisector
Instruction 9781457300615 85 #5
Instruction 9781457300615 198 #2
Activity 9781457300615 88 #18
Assessment 9781457300615 86 #8
Instruction 9781457300615 199 #4
(6) Proof and congruence. The student uses the
process skills with deductive reasoning to prove
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(A) verify theorems about
angles formed by the
intersection of lines and line
segments, including vertical
angles, and angles formed
by parallel lines cut by a
transversal and prove
equidistance between the
endpoints of a segment and
points on its perpendicular
bisector and apply these
relationships to solve
problems
(v) apply these relationships
to solve problems
Instruction 9781457300615 198 #2
Instruction 9781457300615 199 #4
Assessment 9781457300615 200 #14, 15
(6) Proof and congruence. The student uses the
process skills with deductive reasoning to prove
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(B) prove two triangles are
congruent by applying the
Side-Angle-Side, Angle-Side-
Angle, Side-Side-Side,
Angle-Angle-Side, and
Hypotenuse-Leg
congruence conditions
(i) prove two triangles are
congruent by applying the
Side-Angle-Side
congruence condition Instruction 9781457300615 152 Example A, Try These A
Instruction 9781457300615 169 #2
Review 9781457300615 153 #8
Review 9781457300615 159 #8
Activity 9781457300615 158 Example A, Try These A a
(6) Proof and congruence. The student uses the
process skills with deductive reasoning to prove
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(B) prove two triangles are
congruent by applying the
Side-Angle-Side, Angle-Side-
Angle, Side-Side-Side,
Angle-Angle-Side, and
Hypotenuse-Leg
congruence conditions
(ii) prove two triangles are
congruent by applying the
Angle-Side-Angle
congruence condition Instruction 9781457300615 161 #3
Instruction 9781457300615 167 Try These A
Review 9781457300615 153 #9
Activity 9781457300615 158 #7
Assessment 9781457300615 153 #13
(6) Proof and congruence. The student uses the
process skills with deductive reasoning to prove
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(B) prove two triangles are
congruent by applying the
Side-Angle-Side, Angle-Side-
Angle, Side-Side-Side,
Angle-Angle-Side, and
Hypotenuse-Leg
congruence conditions
(iii) prove two triangles are
congruent by applying the
Side-Side-Side congruence
condition Instruction 9781457300615 154 #1
Instruction 9781457300615 158 Example A
Instruction 9781457300615 167 Example A
Review 9781457300615 153 #12
Review 9781457300615 159 #9
(6) Proof and congruence. The student uses the
process skills with deductive reasoning to prove
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(B) prove two triangles are
congruent by applying the
Side-Angle-Side, Angle-Side-
Angle, Side-Side-Side,
Angle-Angle-Side, and
Hypotenuse-Leg
congruence conditions
(iv) prove two triangles are
congruent by applying the
Angle-Angle-Side
congruence condition Instruction 9781457300615 161 #3
Review 9781457300615 153 #15
Review 9781457300615 164 #11
Activity 9781457300615 166 #16
Page 18 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(6) Proof and congruence. The student uses the
process skills with deductive reasoning to prove
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(B) prove two triangles are
congruent by applying the
Side-Angle-Side, Angle-Side-
Angle, Side-Side-Side,
Angle-Angle-Side, and
Hypotenuse-Leg
congruence conditions
(v) prove two triangles are
congruent by applying the
Hypotenuse-Leg
congruence condition Instruction 9781457300615 163 #6
Review 9781457300615 164 #10
Activity 9781457300615 166 #19
Activity 9781457300615 178 #1
(6) Proof and congruence. The student uses the
process skills with deductive reasoning to prove
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(C) apply the definition of
congruence, in terms of rigid
transformations, to identify
congruent figures and their
corresponding sides and
angles
(i) apply the definition of
congruence, in terms of rigid
transformations, to identify
congruent figures Instruction 9781457300615 144 #1
Instruction 9781457300615 155 #1
Review 9781457300615 145 - 146 #4 - 6
(6) Proof and congruence. The student uses the
process skills with deductive reasoning to prove
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(C) apply the definition of
congruence, in terms of rigid
transformations, to identify
congruent figures and their
corresponding sides and
angles
(ii) apply the definition of
congruence, in terms of rigid
transformations, to identify
[congruent figures']
corresponding sides
Instruction 9781457300615 144 #2, 3
Instruction 9781457300615 147 #1a, b
Review 9781457300615 146 #6a, b, 7a, b
(6) Proof and congruence. The student uses the
process skills with deductive reasoning to prove
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(C) apply the definition of
congruence, in terms of rigid
transformations, to identify
congruent figures and their
corresponding sides and
angles
(iii) apply the definition of
congruence, in terms of rigid
transformations, to identify
[congruent figures']
corresponding angles
Instruction 9781457300615 144 #2, 3
Review 9781457300615 146 #6c, d, 7c, d
(6) Proof and congruence. The student uses the
process skills with deductive reasoning to prove
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(D) verify theorems about
the relationships in triangles,
including proof of the
Pythagorean Theorem, the
sum of interior angles, base
angles of isosceles
triangles, midsegments, and
medians, and apply these
relationships to solve
problems
(i) verify theorems about the
relationships in triangles,
including proof of the
Pythagorean Theorem
Instruction 9781457300615 283 #2
Instruction 9781457300615 284 #3, 4
Review 9781457300615 287 #3, 4
(6) Proof and congruence. The student uses the
process skills with deductive reasoning to prove
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(D) verify theorems about
the relationships in triangles,
including proof of the
Pythagorean Theorem, the
sum of interior angles, base
angles of isosceles
triangles, midsegments, and
medians, and apply these
relationships to solve
problems
(ii) verify theorems about the
relationships in triangles,
including the sum of interior
angles
Instruction 9781457300615 182 #6
Instruction 9781457300615 183 #13
Review 9781457300615 182 #7 - 9
Page 19 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(6) Proof and congruence. The student uses the
process skills with deductive reasoning to prove
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(D) verify theorems about
the relationships in triangles,
including proof of the
Pythagorean Theorem, the
sum of interior angles, base
angles of isosceles
triangles, midsegments, and
medians, and apply these
relationships to solve
problems
(iii) verify theorems about
the relationships in triangles,
including the base angles of
isosceles triangles
Instruction 9781457300615 186 #6
Instruction 9781457300615 187 #10
Review 9781457300615 188 #16
(6) Proof and congruence. The student uses the
process skills with deductive reasoning to prove
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(D) verify theorems about
the relationships in triangles,
including proof of the
Pythagorean Theorem, the
sum of interior angles, base
angles of isosceles
triangles, midsegments, and
medians, and apply these
relationships to solve
problems
(iv) verify theorems about
the relationships in triangles,
including of the
midsegments
Instruction 9781457300615 207 #6
Review 9781457300615 207 #7, 8
Review 9781457300615 208 #9, 10
(6) Proof and congruence. The student uses the
process skills with deductive reasoning to prove
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(D) verify theorems about
the relationships in triangles,
including proof of the
Pythagorean Theorem, the
sum of interior angles, base
angles of isosceles
triangles, midsegments, and
medians, and apply these
relationships to solve
problems
(v) verify theorems about
the relationships in triangles,
including the medians
Instruction 9781457300615 196 #11
Instruction 9781457300615 197 #12 - 14
Review 9781457300615 386 #12
Activity 9781457300615 202 #17
(6) Proof and congruence. The student uses the
process skills with deductive reasoning to prove
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(D) verify theorems about
the relationships in triangles,
including proof of the
Pythagorean Theorem, the
sum of interior angles, base
angles of isosceles
triangles, midsegments, and
medians, and apply these
relationships to solve
problems
(vi) apply these relationships
to solve problems
Instruction 9781457300615 184 Example A
Review 9781457300615 182 #8
Activity 9781457300615 187 #8, 9
Assessment 9781457300615 190 #20
(6) Proof and congruence. The student uses the
process skills with deductive reasoning to prove
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(E) prove a quadrilateral is
a parallelogram, rectangle,
square, or rhombus using
opposite sides, opposite
angles, or diagonals and
apply these relationships to
solve problems
(i) prove a quadrilateral is a
parallelogram, rectangle,
square, or rhombus using
opposite sides, opposite
angles, or diagonals
Instruction 9781457300615 223 #1, 2
Instruction 9781457300615 224 #5
Review 9781457300615 222 #8
Activity 9781457300615 225 #7
Assessment 9781457300615 226 #16, 17
(6) Proof and congruence. The student uses the
process skills with deductive reasoning to prove
and apply theorems by using a variety of methods
such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(E) prove a quadrilateral is
a parallelogram, rectangle,
square, or rhombus using
opposite sides, opposite
angles, or diagonals and
apply these relationships to
solve problems
(ii) apply these relationships
to solve problems
Instruction 9781457300615 214 #6
Review 9781457300615 219 #13
Assessment 9781457300615 222 #9, 10
Page 20 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(7) Similarity, proof, and trigonometry. The student
uses the process skills in applying similarity to
solve problems. The student is expected to:
(A) apply the definition of
similarity in terms of a
dilation to identify similar
figures and their
proportional sides and the
congruent corresponding
angles
(i) apply the definition of
similarity in terms of a
dilation to identify similar
figures Instruction 9781457300615 250 #8
Instruction 9781457300615 258 #4b
Review 9781457300615 251 #12
Assessment 9781457300615 258 #4b, c
(7) Similarity, proof, and trigonometry. The student
uses the process skills in applying similarity to
solve problems. The student is expected to:
(A) apply the definition of
similarity in terms of a
dilation to identify similar
figures and their
proportional sides and the
congruent corresponding
angles
(ii) apply the definition of
similarity in terms of a
dilation to identify their
proportional sides Instruction 9781457300615 253 #4
Review 9781457300615 254 #11
Assessment 9781457300615 254 #5
(7) Similarity, proof, and trigonometry. The student
uses the process skills in applying similarity to
solve problems. The student is expected to:
(A) apply the definition of
similarity in terms of a
dilation to identify similar
figures and their
proportional sides and the
congruent corresponding
angles
(iii) apply the definition of
similarity in terms of a
dilation to identify the
congruent corresponding
angles
Instruction 9781457300615 258 #4d
Review 9781457300615 254 #9
(7) Similarity, proof, and trigonometry. The student
uses the process skills in applying similarity to
solve problems. The student is expected to:
(B) apply the Angle-Angle
criterion to verify similar
triangles and apply the
proportionality of the
corresponding sides to solve
problems
(i) apply the Angle-Angle
criterion to verify similar
triangles Instruction 9781457300615 257 #2
Instruction 9781457300615 262 #1
Review 9781457300615 261 #10, 12
Activity 9781457300615 261 #8, 9
Assessment 9781457300615 258 #3
(7) Similarity, proof, and trigonometry. The student
uses the process skills in applying similarity to
solve problems. The student is expected to:
(B) apply the Angle-Angle
criterion to verify similar
triangles and apply the
proportionality of the
corresponding sides to solve
problems
(ii) apply the proportionality
of the corresponding sides
to solve problemsInstruction 9781457300615 262 #2
Instruction 9781457300615 263 Example A, Try These A a, b
Assessment 9781457300615 272 #2 - 4
(8) Similarity, proof, and trigonometry. The student
uses the process skills with deductive reasoning to
prove and apply theorems by using a variety of
methods such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(A) prove theorems about
similar triangles, including
the Triangle Proportionality
theorem, and apply these
theorems to solve problems
(i) prove theorems about
similar triangles, including
the Triangle Proportionality
theorem Instruction 9781457300615 266 #5
Activity 9781457300615 272 Additional Practice
Instruction 9781457300615 267 #7-8
(8) Similarity, proof, and trigonometry. The student
uses the process skills with deductive reasoning to
prove and apply theorems by using a variety of
methods such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(A) prove theorems about
similar triangles, including
the Triangle Proportionality
theorem, and apply these
theorems to solve problems
(ii) apply these theorems to
solve problems
Instruction 9781457300615 267 #6
Assessment 9781457300615 269 Check Your Understanding
268 #11-12
Page 21 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(8) Similarity, proof, and trigonometry. The student
uses the process skills with deductive reasoning to
prove and apply theorems by using a variety of
methods such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(B) identify and apply the
relationships that exist when
an altitude is drawn to the
hypotenuse of a right
triangle, including the
geometric mean, to solve
problems
(i) identify the relationships
that exist when an altitude is
drawn to the hypotenuse of
a right triangle, including the
geometric mean, to solve
problems
Instruction 9781457300615 278 #1-2, 3-4
Review 9781457300615 280 Assess
Instruction 9781457300615 280 Check Your Understanding
(8) Similarity, proof, and trigonometry. The student
uses the process skills with deductive reasoning to
prove and apply theorems by using a variety of
methods such as coordinate, transformational, and
axiomatic and formats such as two-column,
paragraph, and flow chart. The student is expected
to:
(B) identify and apply the
relationships that exist when
an altitude is drawn to the
hypotenuse of a right
triangle, including the
geometric mean, to solve
problems
(ii) apply the relationships
that exist when an altitude is
drawn to the hypotenuse of
a right triangle, including the
geometric mean, to solve
problems
Instruction 9781457300615 279 Example A
Review 9781457300615 280 Check Your Understanding
(9) Similarity, proof, and trigonometry. The student
uses the process skills to understand and apply
relationships in right triangles. The student is
expected to:
(A) determine the lengths of
sides and measures of
angles in a right triangle by
applying the trigonometric
ratios sine, cosine, and
tangent to solve problems
(i) determine the lengths of
sides in a right triangle by
applying the trigonometric
ratio sine to solve problemsInstruction 9781457300615 312 #2-3
Review 9781457300615 316 Assess
Instruction 9781457300615 313 #4
Instruction 9781457300615 314 Assess
(9) Similarity, proof, and trigonometry. The student
uses the process skills to understand and apply
relationships in right triangles. The student is
expected to:
(A) determine the lengths of
sides and measures of
angles in a right triangle by
applying the trigonometric
ratios sine, cosine, and
tangent to solve problems
(ii) determine the measures
of angles in a right triangle
by applying the
trigonometric ratio sine to
solve problems
Instruction 9781457300615 315 #1-2
Review 9781457300615 316 Assess
(9) Similarity, proof, and trigonometry. The student
uses the process skills to understand and apply
relationships in right triangles. The student is
expected to:
(A) determine the lengths of
sides and measures of
angles in a right triangle by
applying the trigonometric
ratios sine, cosine, and
tangent to solve problems
(iii) determine the lengths of
sides in a right triangle by
applying the trigonometric
ratio cosine to solve
problems
Instruction 9781457300615 312 #2-3
Review 9781457300615 316 Assess
Instruction 9781457300615 313 #4
Instruction 9781457300615 314 ADAPT
Assessment 9781457300615 314 Check Your Understanding
(9) Similarity, proof, and trigonometry. The student
uses the process skills to understand and apply
relationships in right triangles. The student is
expected to:
(A) determine the lengths of
sides and measures of
angles in a right triangle by
applying the trigonometric
ratios sine, cosine, and
tangent to solve problems
(iv) determine the measures
of angles in a right triangle
by applying the
trigonometric ratio cosine to
solve problems
Instruction 9781457300615 315 #1-2
Review 9781457300615 316 Assess
(9) Similarity, proof, and trigonometry. The student
uses the process skills to understand and apply
relationships in right triangles. The student is
expected to:
(A) determine the lengths of
sides and measures of
angles in a right triangle by
applying the trigonometric
ratios sine, cosine, and
tangent to solve problems
(v) determine the lengths of
sides in a right triangle by
applying the trigonometric
ratio tangent to solve
problems
Instruction 9781457300615 316 #3-5
Review 9781457300615 314 Assess
Review 9781457300615 316 Assess
Activity 9781457300615 318 Additional Practice
Page 22 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(9) Similarity, proof, and trigonometry. The student
uses the process skills to understand and apply
relationships in right triangles. The student is
expected to:
(A) determine the lengths of
sides and measures of
angles in a right triangle by
applying the trigonometric
ratios sine, cosine, and
tangent to solve problems
(vi) determine the measures
of angles in a right triangle
by applying the
trigonometric ratio tangent to
solve problems
Instruction 9781457300615 315 #1-2
Review 9781457300615 316 Additional Practice
Instruction 9781457300615 316 #3-5
(9) Similarity, proof, and trigonometry. The student
uses the process skills to understand and apply
relationships in right triangles. The student is
expected to:
(B) apply the relationships
in special right triangles 30°-
60°-90° and 45°-45°-90°
and the Pythagorean
theorem, including
Pythagorean triples, to solve
problems
(i) apply the relationships in
special right triangles 30°-
60°-90° to solve problems
Instruction 9781457300615 296 #4, 5, 6-7, 8, 9
Review 9781457300615 297 Check Your Understanding
Activity 9781457300615 297 Assess
Assessment 9781457300615 300 Additional Practice
(9) Similarity, proof, and trigonometry. The student
uses the process skills to understand and apply
relationships in right triangles. The student is
expected to:
(B) apply the relationships
in special right triangles 30°-
60°-90° and 45°-45°-90°
and the Pythagorean
theorem, including
Pythagorean triples, to solve
problems
(ii) apply the relationships in
special right triangles 45°-
45°-90° to solve problems
Instruction 9781457300615 291 #1a-c
Review 9781457300615 293 Check Your Understanding
Instruction 9781457300615 292 #1d, 2, 3, 4
Activity 9781457300615 294 Assess
Assessment 9781457300615 300 Additional Practice
(9) Similarity, proof, and trigonometry. The student
uses the process skills to understand and apply
relationships in right triangles. The student is
expected to:
(B) apply the relationships
in special right triangles 30°-
60°-90° and 45°-45°-90°
and the Pythagorean
theorem, including
Pythagorean triples, to solve
problems
(iii) apply the relationships in
the Pythagorean theorem,
including Pythagorean
triples, to solve problems Instruction 9781457300615 283 #1
Review 9781457300615 284 Check Your Understanding
Instruction 9781457300615 284 #7
Review 9781457300615 284 Assess
Assessment 9781457300615 290 Additional Practice
(10) Two-dimensional and three-dimensional
figures. The student uses the process skills to
recognize characteristics and dimensional changes
of two- and three-dimensional figures. The student
is expected to:
(A) identify the shapes of
two-dimensional cross-
sections of prisms,
pyramids, cylinders, cones,
and spheres and identify
three-dimensional objects
generated by rotations of
two-dimensional shapes
(i) identify the shapes of two-
dimensional cross-sections
of prisms
Instruction 9781457300615 483 #12
Review 9781457300615 484 Check Your Understanding
(10) Two-dimensional and three-dimensional
figures. The student uses the process skills to
recognize characteristics and dimensional changes
of two- and three-dimensional figures. The student
is expected to:
(A) identify the shapes of
two-dimensional cross-
sections of prisms,
pyramids, cylinders, cones,
and spheres and identify
three-dimensional objects
generated by rotations of
two-dimensional shapes
(ii) identify the shapes of two-
dimensional cross-sections
of pyramids
Instruction 9781457300615 484 #13
Review 9781457300615 484 Check Your Understanding
(10) Two-dimensional and three-dimensional
figures. The student uses the process skills to
recognize characteristics and dimensional changes
of two- and three-dimensional figures. The student
is expected to:
(A) identify the shapes of
two-dimensional cross-
sections of prisms,
pyramids, cylinders, cones,
and spheres and identify
three-dimensional objects
generated by rotations of
two-dimensional shapes
(iii) identify the shapes of
two-dimensional cross-
sections of cylinders
Instruction 9781457300615 486 #2-3
Page 23 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
Review 9781457300615 488 Check Your Understanding
Instruction 9781457300615 487 #6
Instruction 9781457300615 501 #4-5
Activity 9781457300615 494 Additional Practice
(10) Two-dimensional and three-dimensional
figures. The student uses the process skills to
recognize characteristics and dimensional changes
of two- and three-dimensional figures. The student
is expected to:
(A) identify the shapes of
two-dimensional cross-
sections of prisms,
pyramids, cylinders, cones,
and spheres and identify
three-dimensional objects
generated by rotations of
two-dimensional shapes
(iv) identify the shapes of
two-dimensional cross-
sections of cones
Instruction 9781457300615 487 #6, 7
Assessment 9781457300615 494 Additional Practice
(10) Two-dimensional and three-dimensional
figures. The student uses the process skills to
recognize characteristics and dimensional changes
of two- and three-dimensional figures. The student
is expected to:
(A) identify the shapes of
two-dimensional cross-
sections of prisms,
pyramids, cylinders, cones,
and spheres and identify
three-dimensional objects
generated by rotations of
two-dimensional shapes
(v) identify the shapes of two-
dimensional cross-sections
of spheres
Instruction 9781457300615 489 #1
Assessment 9781457300615 492 Assess
(10) Two-dimensional and three-dimensional
figures. The student uses the process skills to
recognize characteristics and dimensional changes
of two- and three-dimensional figures. The student
is expected to:
(A) identify the shapes of
two-dimensional cross-
sections of prisms,
pyramids, cylinders, cones,
and spheres and identify
three-dimensional objects
generated by rotations of
two-dimensional shapes
(vi) identify three-
dimensional objects
generated by rotations of
two-dimensional shapes
Instruction 9781457300615 490 #3
Review 9781457300615 492 Assess
Activity 9781457300615 491 #6
(10) Two-dimensional and three-dimensional
figures. The student uses the process skills to
recognize characteristics and dimensional changes
of two- and three-dimensional figures. The student
is expected to:
(B) determine and describe
how changes in the linear
dimensions of a shape
affect its perimeter, area,
surface area, or volume,
including proportional and
non-proportional
dimensional change
(i) determine how changes
in the linear dimensions of a
shape affect its perimeter,
area, surface area, or
volume, including
proportional dimensional
change
Instruction 9781457300615 540 #4
Review 9781457300615 541 Check Your Understanding
Instruction 9781457300615 543 #4, 5
Instruction 9781457300615 544 #6
Assessment 9781457300615 541 Assess
(10) Two-dimensional and three-dimensional
figures. The student uses the process skills to
recognize characteristics and dimensional changes
of two- and three-dimensional figures. The student
is expected to:
(B) determine and describe
how changes in the linear
dimensions of a shape
affect its perimeter, area,
surface area, or volume,
including proportional and
non-proportional
dimensional change
(ii) determine how changes
in the linear dimensions of a
shape affect its perimeter,
area, surface area, or
volume, including non-
proportional dimensional
change
Instruction 9781457300615 539 #2-3
Review 9781457300615 541 Check Your Understanding
Instruction 9781457300615 540 #5-6, 7
Activity 9781457300615 541 Assess
Instruction 9781457300615 544 #7
(10) Two-dimensional and three-dimensional
figures. The student uses the process skills to
recognize characteristics and dimensional changes
of two- and three-dimensional figures. The student
is expected to:
(B) determine and describe
how changes in the linear
dimensions of a shape
affect its perimeter, area,
surface area, or volume,
including proportional and
non-proportional
dimensional change
(iii) describe how changes in
the linear dimensions of a
shape affect its perimeter,
area, surface area, or
volume, including
proportional dimensional
change
Instruction 9781457300615 539 #2-3
Review 9781457300615 541 Check Your Understanding
Instruction 9781457300615 540 #5-6, 7
Page 24 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
Assessment 9781457300615 541 Assess
Instruction 9781457300615 544 #6, 7
(10) Two-dimensional and three-dimensional
figures. The student uses the process skills to
recognize characteristics and dimensional changes
of two- and three-dimensional figures. The student
is expected to:
(B) determine and describe
how changes in the linear
dimensions of a shape
affect its perimeter, area,
surface area, or volume,
including proportional and
non-proportional
dimensional change
(iv) describe how changes in
the linear dimensions of a
shape affect its perimeter,
area, surface area, or
volume, including non-
proportional dimensional
change
Instruction 9781457300615 471 #4
Review 9781457300615 541 Assess, Check Your Understanding
Instruction 9781457300615 539 #2-3
Instruction 9781457300615 540 #5-6, 7
Activity 9781457300615 548 Additional Practice
(11) Two-dimensional and three-dimensional
figures. The student uses the process skills in the
application of formulas to determine measures of
two- and three-dimensional figures. The student is
expected to:
(A) apply the formula for the
area of regular polygons to
solve problems using
appropriate units of
measure
(i) apply the formula for the
area of regular polygons to
solve problems using
appropriate units of
measure
Instruction 9781457300615 549 Example A
Assessment 9781457300615 460 Assess
(11) Two-dimensional and three-dimensional
figures. The student uses the process skills in the
application of formulas to determine measures of
two- and three-dimensional figures. The student is
expected to:
(B) determine the area of
composite two-dimensional
figures comprised of a
combination of triangles,
parallelograms, trapezoids,
kites, regular polygons, or
sectors of circles to solve
problems using appropriate
units of measure
(i) determine the area of
composite two-dimensional
figures comprised of a
combination of triangles,
parallelograms, trapezoids,
kites, regular polygons, or
sectors of circles to solve
problems using appropriate
units of measure
Instruction 9781457300615 433 #1
Review 9781457300615 435 Check Your Understanding
Instruction 9781457300615 435 #6
Activity 9781457300615 438 Check Your Understanding
Assessment 9781457300615 440 Assess
(11) Two-dimensional and three-dimensional
figures. The student uses the process skills in the
application of formulas to determine measures of
two- and three-dimensional figures. The student is
expected to:
(C) apply the formulas for
the total and lateral surface
area of three-dimensional
figures, including prisms,
pyramids, cones, cylinders,
spheres, and composite
figures, to solve problems
using appropriate units of
measure
(i) apply the formulas for the
total surface area of three-
dimensional figures,
including prisms, to solve
problems using appropriate
units of measure
Instruction 9781457300615 496 #5-6, 7
Review 9781457300615 499 Assess
Assessment 9781457300615 497 Check Your Understanding
Instruction 9781457300615 503 #8
(11) Two-dimensional and three-dimensional
figures. The student uses the process skills in the
application of formulas to determine measures of
two- and three-dimensional figures. The student is
expected to:
(C) apply the formulas for
the total and lateral surface
area of three-dimensional
figures, including prisms,
pyramids, cones, cylinders,
spheres, and composite
figures, to solve problems
using appropriate units of
measure
(ii) apply the formulas for the
total surface area of three-
dimensional figures,
including pyramids, to solve
problems using appropriate
units of measure
Instruction 9781457300615 507 #1, 3
Review 9781457300615 509 Check Your Understanding
Assessment 9781457300615 512 Assess
(11) Two-dimensional and three-dimensional
figures. The student uses the process skills in the
application of formulas to determine measures of
two- and three-dimensional figures. The student is
expected to:
(C) apply the formulas for
the total and lateral surface
area of three-dimensional
figures, including prisms,
pyramids, cones, cylinders,
spheres, and composite
figures, to solve problems
using appropriate units of
measure
(iii) apply the formulas for
the total surface area of
three-dimensional figures,
including cones, to solve
problems using appropriate
units of measure
Instruction 9781457300615 518 #1
Review 9781457300615 512 Check Your Understanding
Assessment 9781457300615 512 Assess
Page 25 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(11) Two-dimensional and three-dimensional
figures. The student uses the process skills in the
application of formulas to determine measures of
two- and three-dimensional figures. The student is
expected to:
(C) apply the formulas for
the total and lateral surface
area of three-dimensional
figures, including prisms,
pyramids, cones, cylinders,
spheres, and composite
figures, to solve problems
using appropriate units of
measure
(iv) apply the formulas for
the total surface area of
three-dimensional figures,
including cylinders, to solve
problems using appropriate
units of measure
Instruction 9781457300615 498 #15
Review 9781457300615 499 Check Your Understanding
Instruction 9781457300615 503 #8
Assessment 9781457300615 498 Assess
(11) Two-dimensional and three-dimensional
figures. The student uses the process skills in the
application of formulas to determine measures of
two- and three-dimensional figures. The student is
expected to:
(C) apply the formulas for
the total and lateral surface
area of three-dimensional
figures, including prisms,
pyramids, cones, cylinders,
spheres, and composite
figures, to solve problems
using appropriate units of
measure
(v) apply the formulas for the
total surface area of three-
dimensional figures,
including spheres, to solve
problems using appropriate
units of measure
Instruction 9781457300615 526 #1-2
Review 9781457300615 528 Assess
Instruction 9781457300615 540 #4
(11) Two-dimensional and three-dimensional
figures. The student uses the process skills in the
application of formulas to determine measures of
two- and three-dimensional figures. The student is
expected to:
(C) apply the formulas for
the total and lateral surface
area of three-dimensional
figures, including prisms,
pyramids, cones, cylinders,
spheres, and composite
figures, to solve problems
using appropriate units of
measure
(vi) apply the formulas for
the total surface area of
three-dimensional figures,
including composite figures,
to solve problems using
appropriate units of
measure
Instruction 9781457300615 496 #7
Review 9781457300615 512 Assess
Activity 9781457300615 523 Assessment Focus
Activity 9781457300615 528 Assess
Assessment 9781457300615 538 Additional Practice
(11) Two-dimensional and three-dimensional
figures. The student uses the process skills in the
application of formulas to determine measures of
two- and three-dimensional figures. The student is
expected to:
(C) apply the formulas for
the total and lateral surface
area of three-dimensional
figures, including prisms,
pyramids, cones, cylinders,
spheres, and composite
figures, to solve problems
using appropriate units of
measure
(vii) apply the formulas for
the lateral surface area of
three-dimensional figures,
including prisms, to solve
problems using appropriate
units of measure
Instruction 9781457300615 496 #4, 7
Review 9781457300615 497 Check Your Understanding
Review 9781457300615 499 Assess
Assessment 9781457300615 506 Additional Practice
(11) Two-dimensional and three-dimensional
figures. The student uses the process skills in the
application of formulas to determine measures of
two- and three-dimensional figures. The student is
expected to:
(C) apply the formulas for
the total and lateral surface
area of three-dimensional
figures, including prisms,
pyramids, cones, cylinders,
spheres, and composite
figures, to solve problems
using appropriate units of
measure
(viii) apply the formulas for
the lateral surface area of
three-dimensional figures,
including pyramids, to solve
problems using appropriate
units of measure
Instruction 9781457300615 508 #2c-d
Review 9781457300615 509 Check Your Understanding
Instruction 9781457300615 509 #2e-g, 3
Assessment 9781457300615 512 Assess
(11) Two-dimensional and three-dimensional
figures. The student uses the process skills in the
application of formulas to determine measures of
two- and three-dimensional figures. The student is
expected to:
(C) apply the formulas for
the total and lateral surface
area of three-dimensional
figures, including prisms,
pyramids, cones, cylinders,
spheres, and composite
figures, to solve problems
using appropriate units of
measure
(ix) apply the formulas for
the lateral surface area of
three-dimensional figures,
including cones, to solve
problems using appropriate
units of measure
Instruction 9781457300615 511 #9
Review 9781457300615 512 Check Your Understanding
Assessment 9781457300615 512 Assess
Page 26 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(11) Two-dimensional and three-dimensional
figures. The student uses the process skills in the
application of formulas to determine measures of
two- and three-dimensional figures. The student is
expected to:
(C) apply the formulas for
the total and lateral surface
area of three-dimensional
figures, including prisms,
pyramids, cones, cylinders,
spheres, and composite
figures, to solve problems
using appropriate units of
measure
(x) apply the formulas for the
lateral surface area of three-
dimensional figures,
including cylinders, to solve
problems using appropriate
units of measure
Instruction 9781457300615 498 #11-13
Review 9781457300615 499 Assess
Assessment 9781457300615 506 Assess
(11) Two-dimensional and three-dimensional
figures. The student uses the process skills in the
application of formulas to determine measures of
two- and three-dimensional figures. The student is
expected to:
(C) apply the formulas for
the total and lateral surface
area of three-dimensional
figures, including prisms,
pyramids, cones, cylinders,
spheres, and composite
figures, to solve problems
using appropriate units of
measure
(xi) apply the formulas for
the lateral surface area of
three-dimensional figures,
including spheres, to solve
problems using appropriate
units of measure
Instruction 9781457300615 526 #1-2
Activity 9781457300615 528 Assess
Instruction 9781457300615 540 4
(11) Two-dimensional and three-dimensional
figures. The student uses the process skills in the
application of formulas to determine measures of
two- and three-dimensional figures. The student is
expected to:
(C) apply the formulas for
the total and lateral surface
area of three-dimensional
figures, including prisms,
pyramids, cones, cylinders,
spheres, and composite
figures, to solve problems
using appropriate units of
measure
(xii) apply the formulas for
the lateral surface area of
three-dimensional figures,
including composite figures,
to solve problems using
appropriate units of
measure
Instruction 9781457300615 496 #7
Review 9781457300615 499 Assess
(11) Two-dimensional and three-dimensional
figures. The student uses the process skills in the
application of formulas to determine measures of
two- and three-dimensional figures. The student is
expected to:
(D) apply the formulas for
the volume of three-
dimensional figures,
including prisms, pyramids,
cones, cylinders, spheres,
and composite figures, to
solve problems using
appropriate units of
measure
(i) apply the formulas for the
volume of three-dimensional
figures, including prisms, to
solve problems using
appropriate units of
measure
Instruction 9781457300615 501 Example A
Review 9781457300615 504 Assess
Instruction 9781457300615 502 #7
(11) Two-dimensional and three-dimensional
figures. The student uses the process skills in the
application of formulas to determine measures of
two- and three-dimensional figures. The student is
expected to:
(D) apply the formulas for
the volume of three-
dimensional figures,
including prisms, pyramids,
cones, cylinders, spheres,
and composite figures, to
solve problems using
appropriate units of
measure
(ii) apply the formulas for the
volume of three-dimensional
figures, including pyramids,
to solve problems using
appropriate units of
measure
Instruction 9781457300615 515 Example A
Assessment 9781457300615 517 Assess
(11) Two-dimensional and three-dimensional
figures. The student uses the process skills in the
application of formulas to determine measures of
two- and three-dimensional figures. The student is
expected to:
(D) apply the formulas for
the volume of three-
dimensional figures,
including prisms, pyramids,
cones, cylinders, spheres,
and composite figures, to
solve problems using
appropriate units of
measure
(iii) apply the formulas for
the volume of three-
dimensional figures,
including cones, to solve
problems using appropriate
units of measure
Instruction 9781457300615 517 #10
Review 9781457300615 517 Check Your Understanding
Instruction 9781457300615 518 #1
Instruction 9781457300615 520 Assess
Assessment 9781457300615 517 Assess
Page 27 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(11) Two-dimensional and three-dimensional
figures. The student uses the process skills in the
application of formulas to determine measures of
two- and three-dimensional figures. The student is
expected to:
(D) apply the formulas for
the volume of three-
dimensional figures,
including prisms, pyramids,
cones, cylinders, spheres,
and composite figures, to
solve problems using
appropriate units of
measure
(iv) apply the formulas for
the volume of three-
dimensional figures,
including cylinders, to solve
problems using appropriate
units of measure
Instruction 9781457300615 501 Example A
Review 9781457300615 504 Assess
Instruction 9781457300615 502 #7
Assessment 9781457300615 506 Additional Practice
(11) Two-dimensional and three-dimensional
figures. The student uses the process skills in the
application of formulas to determine measures of
two- and three-dimensional figures. The student is
expected to:
(D) apply the formulas for
the volume of three-
dimensional figures,
including prisms, pyramids,
cones, cylinders, spheres,
and composite figures, to
solve problems using
appropriate units of
measure
(v) apply the formulas for the
volume of three-dimensional
figures, including spheres, to
solve problems using
appropriate units of
measure
Instruction 9781457300615 530 #10
Review 9781457300615 531 Check Your Understanding
Instruction 9781457300615 540 #4
Assessment 9781457300615 531 Assess
(11) Two-dimensional and three-dimensional
figures. The student uses the process skills in the
application of formulas to determine measures of
two- and three-dimensional figures. The student is
expected to:
(D) apply the formulas for
the volume of three-
dimensional figures,
including prisms, pyramids,
cones, cylinders, spheres,
and composite figures, to
solve problems using
appropriate units of
measure
(vi) apply the formulas for
the volume of three-
dimensional figures,
including composite figures,
to solve problems using
appropriate units of
measure
Instruction 9781457300615 501 #6
Review 9781457300615 522 Additional Practice
Review 9781457300615 531 Assess
Activity 9781457300615 523 Assessment Focus
Assessment 9781457300615 538 Additional Practice
(12) Circles. The student uses the process skills to
understand geometric relationships and apply
theorems and equations about circles. The student
is expected to:
(A) apply theorems about
circles, including
relationships among angles,
radii, chords, tangents, and
secants, to solve non-
contextual problems
(i) apply theorems about
circles, including
relationships among angles,
radii, chords, tangents, and
secants, to solve non-
contextual problems
Instruction 9781457300615 335 #3
Review 9781457300615 342 Check Your Understanding
Instruction 9781457300615 336 #4-6, 7-8
Review 9781457300615 354 #6
Assessment 9781457300615 348 Additional Practice
(12) Circles. The student uses the process skills to
understand geometric relationships and apply
theorems and equations about circles. The student
is expected to:
(B) apply the proportional
relationship between the
measure of an arc length of
a circle and the
circumference of the circle
to solve problems
(i) apply the proportional
relationship between the
measure of an arc length of
a circle and the
circumference of the circle
to solve problems
Instruction 9781457300615 468 #3-5
Activity 9781457300615 469 Assess
Assessment 9781457300615 469 Check Your Understanding
(12) Circles. The student uses the process skills to
understand geometric relationships and apply
theorems and equations about circles. The student
is expected to:
(C) apply the proportional
relationship between the
measure of the area of a
sector of a circle and the
area of the circle to solve
problems
(i) apply the proportional
relationship between the
measure of the area of a
sector of a circle and the
area of the circle to solve
problems
Instruction 9781457300615 467 #1-2
Review 9781457300615 469 Check Your Understanding
Activity 9781457300615 469 Assess
(12) Circles. The student uses the process skills to
understand geometric relationships and apply
theorems and equations about circles. The student
is expected to:
(D) describe radian
measure of an angle as the
ratio of the length of an arc
intercepted by a central
angle and the radius of the
circle
(i) describe radian measure
of an angle as the ratio of
the length of an arc
intercepted by a central
angle and the radius of the
circle
Instruction 9781457300615 472 #7-8
Review 9781457300615 474 Check Your Understanding
Assessment 9781457300615 474 Assess
Page 28 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(12) Circles. The student uses the process skills to
understand geometric relationships and apply
theorems and equations about circles. The student
is expected to:
(E) show that the equation
of a circle with center at the
origin and radius r is x2 +
y2 = r
2 and determine the
equation for the graph of a
circle with radius r and
center (h , k ), (x - h )2 + (y -
k )2 =r
2
(i) show that the equation of
a circle with center at the
origin and radius r is x2 +
y2 = r
2
Instruction 9781457300615 335 #1-2, 3
Assessment 9781457300615 400 Additional Practice
(12) Circles. The student uses the process skills to
understand geometric relationships and apply
theorems and equations about circles. The student
is expected to:
(E) show that the equation
of a circle with center at the
origin and radius r is x2 +
y2 = r
2 and determine the
equation for the graph of a
circle with radius r and
center (h , k ), (x - h )2 + (y -
k )2 =r
2
(ii) determine that the
equation for the graph of a
circle with radius r and
center (h , k ), (x - h )2 + (y -
k )2 =r
2Instruction 9781457300615 335 #3
Review 9781457300615 337 Check Your Understanding
(13) Probability. The student uses the process
skills to understand probability in real-world
situations and how to apply independence and
dependence of events. The student is expected to:
(A) develop strategies to
use permutations and
combinations to solve
contextual problems
(i) develop strategies to use
permutations to solve
contextual problems Instruction 9781457300615 625 #1-2
Review 9781457300615 626 Check Your Understanding
Instruction 9781457300615 626 #3, 4
Assessment 9781457300615 612 Additional Practice
(13) Probability. The student uses the process
skills to understand probability in real-world
situations and how to apply independence and
dependence of events. The student is expected to:
(A) develop strategies to
use permutations and
combinations to solve
contextual problems
(ii) develop strategies to use
combinations to solve
contextual problems Instruction 9781457300615 606 #7
Review 9781457300615 607 #8-9
Instruction 9781457300615 625 #1-2
Instruction 9781457300615 628 Check Your Understanding
Activity 9781457300615 607 Check Your Understanding
(13) Probability. The student uses the process
skills to understand probability in real-world
situations and how to apply independence and
dependence of events. The student is expected to:
(B) determine probabilities
based on area to solve
contextual problems
(i) determine probabilities
based on area to solve
contextual problems Instruction 9781457300615 621 #1
Review 9781457300615 623 Check Your Understanding
Instruction 9781457300615 622 #2-3
Activity 9781457300615 623 Assess
(13) Probability. The student uses the process
skills to understand probability in real-world
situations and how to apply independence and
dependence of events. The student is expected to:
(C) identify whether two
events are independent and
compute the probability of
the two events occurring
together with or without
replacement
(i) identify whether two
events are independent
Instruction 9781457300615 595 #1
Review 9781457300615 598 Check Your Understanding
Instruction 9781457300615 596 #2
(13) Probability. The student uses the process
skills to understand probability in real-world
situations and how to apply independence and
dependence of events. The student is expected to:
(C) identify whether two
events are independent and
compute the probability of
the two events occurring
together with or without
replacement
(ii) compute the probability
of the two events occurring
together with or without
replacementInstruction 9781457300615 608 #14
Review 9781457300615 609 Chreck Your Understanding
Page 29 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
Chapter 111. Mathematics §111.41. Geometry, Adopted 2012 (One Credit). Proclamation 2015
Knowledge and Skills Statement Student Expectation Breakout Citation Type Component ISBN Page (s) Specific Location
(13) Probability. The student uses the process
skills to understand probability in real-world
situations and how to apply independence and
dependence of events. The student is expected to:
(D) apply conditional
probability in contextual
problems
(i) apply conditional
probability in contextual
problems Instruction 9781457300615 595 #1
Review 9781457300615 596 Check Your Understanding
Instruction 9781457300615 596 #2
Instruction 9781457300615 601 #1
Assessment 9781457300615 603 Assess
(13) Probability. The student uses the process
skills to understand probability in real-world
situations and how to apply independence and
dependence of events. The student is expected to:
(E) apply independence in
contextual problems
(i) apply independence in
contextual problems
Instruction 9781457300615 613 #1
Review 9781457300615 616 Check Your Understanding
Instruction 9781457300615 614 #2
Review 9781457300615 618 Check Your Understanding
Page 30 of 30 The College Board - SpringBoard: 9781457300400 Teacher Material
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