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