Download Integrated Math 2 Course Guide 2013-2014

Palm Springs Unified School District
Integrated Math 2 Course Guide
2013 - 2014
INTEGRATED MATH 2
Table of Contents
Preface - Important Note to Teachers………………………………………………….……..3
Using the Released Test Questions..........................................................................................4
Purpose and Use of Pacing Guide……………………………………………………….…...5
National Educational Technology Standards Grades Pre-K - 12.............................................6
California Standards Test (CST) Blueprint……………………………………………….….8
California Content Standards at a Glance…………………………………………….…......11
California Content Standards Unpacked…………………………………………….….......12
Instructional Segments………………………………………………………………..…….15
Benchmark Exams at a Glance………………………….……………………………….….19
Vocabulary by Instructional Segments……………………….……………………….…….20
Vocabulary in Spanish by Instructional Segments………………………...……….……….21
Pacing Guide………………………………………………………………….…………….22
Please direct any questions or comments to:
Cinthia Ruiz
K-12 Math Specialist
[email protected]
(760) 285-5528
Sandi Enochs
Coordinator, Assessment and Data Analysis
[email protected]
(760) 416-6066
2
IMPORTANT!
THIS PACING GUIDE IS INTENDED TO BE FLEXIBLE!!!!
Although a Pacing Guide has been created with a suggested order for teaching the textbook lessons,
site curricular teams may change the order of the lessons being taught WITHIN an Instructional
Segment. The only requirement is that all lessons within each Instructional Segment be completed
(and standards mastered) prior to that Instructional Segment’s Closing Date. This is the absolute
last date by which the Segment’s Assessment must be administered and results entered into OARS.
These are OARS deadline dates, not just dates by which the exams must be administered to
students. Feel free to administer the Assessment any time prior to this date.
Please note: Benchmark Exam #3 has been replaced with a CST Mirror Test. During the time
between the administration of the CST Mirror Test and the administration of the actual CST
teachers will continue to teach new content while providing interventions as indicated by the results
of the CST Mirror Test. This Course Guide is NOT suggesting that all content be taught prior to the
CST Mirror Test administration date.
Throughout this document, Key Standards are highlighted in bold print. These represent the high
impact standards and comprise a minimum of 70% of the California Standards Test (CST).
A Scope and Sequence of the National Educational Technology Standards, Grades Pre-K - 12, has
been added to all Course Guides. It clearly identifies the Technology Standards that should be
integrated into all subject areas at the appropriate grade levels.
The Textbook column of the Pacing Guide refers to our adopted textbook, Integrated Mathematics
2, by McDougal Littell. The Teacher Notes on the side margin of the Teacher’s Edition are a
necessary read. There are California Content Standards that are not adequately addressed by this
textbook. To deal with this concern, SUPP will appear in the textbook column. This indicates that
you will need to supplement the textbook with a resource of your own. This would provide a
wonderful opportunity to work collaboratively with your team to develop appropriate materials.
“KC”, followed by page numbers, indicates pages from the California Standards Key Concept
Book, a McDougal Littell supplement. “SB”, followed by page numbers, denotes the Skills Bank,
an Integrated Math 2 supplement. “TS”, followed by page numbers, refers to the Teacher’s
Resource for Transfer Students, an Integrated Math 2 supplement.
A new column, entitled RTQ’s (Released Test Questions), has been added to the California
Standards Test Blueprint. It references the specific Released Test Question(s) that align to each
assessed standard. To obtain a copy of the STAR Released Test Questions, please download them
from the CDE websites:
http://www.cde.ca.gov/ta/tg/sr/documents/cstrtqalgebra.pdf
http://www.cde.ca.gov/ta/tg/sr/documents/cstrtqgeomapr15.pdf
http://www.cde.ca.gov/ta/tg/sr/documents/cstrtqalgebra2.pdf
Please see the following page for some suggestions of how to use the RTQ’s.
3
Using the Released Test Questions throughout the School Year
It is highly recommended that you use the Released Test Questions as a wrap-up of instruction on a
particular standard. Close the lesson with “Now let’s see how the state might test this concept (or
standard)”. After the students have answered the question(s) and selected their responses, thoroughly
review the question and answer choices with them. Discover how many (and which) students answered
the question(s) correctly. Then have a frank and open discussion about the distracters and why each
student chose a particular distracter




Did they totally not understand the concept (standard)?
Did they not know a particular vocabulary word (academic or content-specific)?
Did they miss a step in the process of solving the problem?
Did they not finish solving the problem, because one of the distracters was the answer they
received when they were only part-way through solving the problem?
 Did they arrive at a perfectly good answer, but it was not the answer to the problem?
Try and discover all errors and misconceptions now, so that they can be corrected immediately and not
continue throughout the school year.
Please keep in mind that most standards encompass several (if not many) concepts, as evidenced by the
Unpacked Standards in your Course Guide. These Released Test Questions may only assess some of these
concepts. That does not mean that these are the only aspects of the standard that will be tested on the CST.
These are the questions that CDE chose to release at this point in time. This is not necessarily an
indication of which concepts to stress or an indication of which part of the standard will be tested. You
may need to generate or find additional questions to assess the other portions of the standard.
These questions (and the students’ responses to the questions) should be a focus of your PLC
collaborative discussions. They will generate a wealth of information to be shared by the team. Here are
some facts quoted from Robert Marzano’s book Classroom Assessment and Grading that Work (pp.5 –
6):
 When students receive feedback on a classroom assessment that simply tells them whether their
answers are correct or incorrect, learning is negatively influenced.
 When students are provided with the correct answer, learning is influenced in a positive direction.
This practice is associated with a gain of 8.5 percentile points in student achievement.
 Providing students with explanations as to why their responses are correct or incorrect is
associated with a gain of 20 percentile points in student achievement.
 Asking students to continue responding to an assessment until they correctly answer the items is
associated with a gain of 20 percentile points.
 Displaying assessment results graphically can go a long way to helping students take control of
their own learning. However, this practice can also help teachers more accurately judge students’
levels of understanding and skill. It is associated with a gain of 26 percentile points in student
achievement.
 Teachers within a school or a district should have rigorous and uniform ways of interpreting the
results of classroom assessments. If the interpretation of assessment results is done by a set of
rules, student achievement is enhanced by 32 percentile points.
4
Purpose and Use of this Pacing Guide
1. This pacing guide is a work in progress and will be revised, along with the Benchmark
assessments, each year. Please note its strengths and weaknesses as you utilize this document
throughout the school year.
2. Emphasis for 2013-2014:
a. Emphasis is being placed on the Key Standards, which are completely aligned with the
CST High Impact Standards.
b. There are four common Instructional Segments, reconfigured to accommodate CST review
and testing.
c. The assessment data will provide teachers with information to improve and drive
instruction through team and department collaboration.
d. The assessment data may be used to provide information to assist with grading, but should
not be the only data used in determining grades.
3. Course Guide Format:
a. A scope and sequence of the National Educational Technology Standards has been
included to assist with the integration of the appropriate technology standards into
Integrated Math 2 lessons.
b. The actual CST Blueprint from the California Department of Education has been
reproduced for this document. It lists all the Integrated Math 2 standards and the number of
items per standard that are on the CST. It also identifies with an asterisk the Key Standards
(high impact standards) which comprise a minimum of 70% of the test. We have added a
column entitled RTQ’s. This column lists the CST Released Test Questions that
correspond to each standard.
c. Immediately following this official document is an “At a Glance” version of the standards,
which provides a one-page abbreviated summary of the standards.
d. The next section, CA Content Standards Unpacked, restates the standards, followed by a
listing of the individual skills and/or objectives encompassed by each standard. This may
be utilized as a checklist, to check off all components of each standard as they are
mastered. Teachers may even reproduce this section as a checklist for students to keep in
their notebook to keep track of their individual progress.
e. The Pacing Guide is separated into four Instructional Segments. An overview of the four
Instructional Segments is placed at the beginning of the next section. Each Instructional
Segment includes the Main Topics, a group of Standards and Essential Skills that must be
taught prior to the Benchmark Assessment.
f. This is followed by Benchmark Exams at a Glance. This chart lists the CA content
standards tested on each Benchmark Exam, along with the number of questions per
standard on each assessment.
g. The CA content standards (with correlated textbook sections) to be mastered before each
benchmark exam are clearly shown on the pacing guide. This pacing guide focuses on the
textbook lessons needed to teach the Integrated Math 2 CA content standards and includes
an alignment to the Released Test Questions. Therefore, the lessons that are outside of this
scope have been omitted.
5
National Educational Technology Standards Grades Pre-K - 12
Scope and Sequence (H = Help / I = Introduce / D = Develop / IU = Independent Use)
Integration and Projects
PK K 1 2 3 4 5
Create developmentally appropriate multimedia
products with support from teachers or student
H
partners
Use technology resources for problem solving,
communication, & illustration of thoughts, ideas
H
& stories
Work responsibly, independently & as part of a
group in developing projects
Use teacher-created rubric for assessment of
project
Use technology for individual & collaborative
writing, communication & publishing activities to
create knowledge products for audiences inside &
outside the classroom.
Determine when technology is useful & select the
appropriate tools & technology resources to
address a variety of tasks & problems
Use information literacy skills to research &
evaluate the accuracy, relevance, appropriateness,
comprehensiveness & bias of information sources
concerning real-world problems
Save, find & retrieve work in different formats via
email, network & online sources for project work
Develop & use student-created rubrics for
assessment
Take on specific role & manage different group
activities & rotation strategies as part of a project
Develop essential & subsidiary questions as part
of projects
Properly cite all information sources
Design, develop, publish & present real-world
products using technology resources that
demonstrate & communicate curriculum concepts
to audiences inside & outside the classroom
Select appropriate technology tools for research,
information analysis, problem-solving &
decision-making in content learning as part of
project-based learning
Compile projects in electronic portfolio
6
7
8
9 10 11 12
H I D D D IU IU IU IU IU IU IU IU
H I D D D D IU IU IU IU IU IU IU
H I D D D IU IU IU IU IU IU IU
H I D D D D IU IU IU IU IU IU
H H I D D D IU IU IU IU IU IU
H H H I D D D IU IU IU IU IU
H H H I
D D D IU IU IU IU
H H H I
D D D IU IU IU IU
H H H I
D D D IU IU IU IU
H H H
I
D D D IU IU IU
H H H
I
D D D IU IU IU
H H H
I
D D D IU IU IU
H H H
I
D D D D IU
H H H
I
D D D D IU
H H H
I
D D D D
6
National Educational Technology Standards Grades Pre-K - 12
Scope and Sequence ( H = Help / I = Introduce / D = Develop / IU = Independent Use)
Social & Ethical Use
Understand and follow rules & procedures for
technology use
Work cooperatively & collaboratively with
others when using technology in the classroom
Demonstrate positive social & ethical behaviors
when using technology
Practice responsible use of technology systems
& software
Discuss responsible use of technology &
information & describe consequences of
inappropriate use
Demonstrate knowledge of current changes in
information technologies & the effect those
changes have on the workplace & society
Exhibit legal & ethical behaviors when using
information & technology & discuss
consequences of misuse
Understand & follow proper use of copyrighted
material & use netiquette when using email
Cite resources properly
Identify capabilities & limitations of emerging
technology resources & assess the potential of
these systems & services to address personal,
lifelong learning, & workplace needs
Access & use primary & secondary sources of
information for an activity
Demonstrate & advocate for legal & ethical
behaviors among peers, family & community
regarding the use of technology & information
PK K 1 2 3 4
5
6
7
8
9 10 11 12
H
I D D D IU IU IU IU IU IU IU IU IU
H
I D D D IU IU IU IU IU IU IU IU IU
H H I D D D IU IU IU IU IU IU IU IU
H H I D D
D
IU IU IU IU IU IU IU
H H H I D
D
D IU IU IU IU IU IU
H H H I
D
D
D IU IU IU IU IU
H H H H
I
D
D D IU IU IU IU
H H H
H
I
D D D IU IU IU
H H H
H
I
D D D IU IU IU
H H
H
H
I
D D D IU IU
H
H
H
I
D D D IU IU
H
H
H
I
D D D IU
7
CALIFORNIA STANDARDS TEST
INTEGRATED MATHEMATICS 2
(Blueprint adopted by the State Board of Education 10/02)
CALIFORNIA CONTENT STANDARDS
Algebra I
# of Items
20 (31%)
3.0
Students solve equations and inequalities involving absolute
values.
9.0* Students solve a system of two linear equations in two variables
algebraically and are able to interpret the answer graphically.
Students are able to solve a system of two linear inequalities in
two variables and to sketch the solution sets.
15.0* Students apply algebraic techniques to solve rate problems, work
problems, and percent mixture problems
16.0 Students understand the concepts of a relation and a function,
determine whether a given relation defines a function, and give
pertinent information about given relations and functions.
17.0 Students determine the domain of independent variables and the
range of dependent variables defined by a graph, a set of ordered
pairs, or a symbolic expression.
18.0 Students determine whether a relation defined by a graph, a set
of ordered pairs, or a symbolic expression is a function and
justify the conclusion.
21.0* Students graph quadratic functions and know that their roots are
the x-intercepts.
22.0 Students use the quadratic formula or factoring techniques or
both to determine whether the graph of a quadratic function will
intersect the x-axis in zero, one, or two points.
23.0* Students apply quadratic equations to physical problems, such as
the motion of an object under the force of gravity.
Standard Set 24.0 Students use and know simple aspects
of a logical argument:
24.1 Students explain the difference between inductive and deductive
reasoning and identify and provide examples of each.
24.2 Students identify the hypothesis and conclusion in logical
deduction.
24.3 Students use counterexamples to show that an assertion is false
and recognize that a single counterexample is sufficient to refute
an assertion.
*
**
Released Test
Questions
1
7, 8
5
40, 41, 42, 43,
44, 45, 46
4
86, 87, 88,
89, 90, 91
1/2**
92, 93
1
94, 95
1/2**
96
3
69, 70, 71, 72
1
73
3
74, 75, 76
1/3**
19
1/3**
20, 21
1/3**
Key standards comprise a minimum of 70% of the test
Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years;
1/3 = rotated every three years)
© California Department of Education
22
8
CALIFORNIA STANDARDS TEST
INTEGRATED MATHEMATICS 2
(Blueprint adopted by the State Board of Education 10/02)
CALIFORNIA CONTENT STANDARDS
Geometry
Released Test
Questions
40 (61%)
1.0* Students demonstrate understanding by identifying and giving
examples of undefined terms, axioms, theorems, and inductive
and deductive reasoning.
2.0* Students write geometric proofs, including proofs by
contradiction.
3.0* Students construct and judge the validity of a logical argument
and give counterexamples to disprove a statement.
4.0* Students prove basic theorems involving congruence and
similarity.
5.0 Students prove that triangles are congruent or similar, and they
are able to use the concept of corresponding parts of congruent
triangles.
7.0* Students prove and use theorems involving the properties of
parallel lines cut by a transversal, the properties of
quadrilaterals, and the properties of circles.
13.0 Students prove relationships between angles in polygons by
using properties of complementary, supplementary, vertical, and
exterior angles.
14.0* Students prove the Pythagorean theorem.
15.0 Students use the Pythagorean theorem to determine distance and
find missing lengths of sides of right triangles.
16.0* Students perform basic constructions with a straightedge and
compass, such as angle bisectors, perpendicular bisectors, and
the line parallel to a given line through a point off the line.
18.0* Students know the definitions of the basic trigonometric
functions defined by the angles of a right triangle. They also
know and are able to use elementary relationships between them.
For example, tan(x) = sin(x)/cos(x), (sin (x))2 + (cos (x))2 = 1.
19.0* Students use trigonometric functions to solve for an unknown
length of a side of a right triangle, given an angle and a length of
a side.
20.0 Students know and are able to use angle and side relationships in
problems with special right triangles, such as 30°, 60°, and 90°
triangles and 45°, 45°, and 90° triangles.
22.0* Students know the effect of rigid motions on figures in the
coordinate plane and space, including rotations, translations, and
reflections.
*
**
# of Items
2
1, 2, 3
3
4, 5, 6, 7
4
8, 9, 10, 11, 12
5
13, 14, 15, 16,
17, 18, 19, 20
2
21, 22, 23
5 2/3**
26, 27, 28, 29,
30, 31, 32
2
57, 58, 59
1/3**
60
2
61, 62, 63
4
64, 65, 66, 67, 68
3
74, 75, 76, 77, 78
3
79, 80, 81, 82, 83
1
84, 85, 86
3
93, 94, 95, 96
Key standards comprise a minimum of 70% of the test
Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years;
1/3 = rotated every three years)
© California Department of Education
9
CALIFORNIA STANDARDS TEST
INTEGRATED MATHEMATICS 2
(Blueprint adopted by the State Board of Education 10/02)
CALIFORNIA CONTENT STANDARDS
Algebra II/ Probability and Statistics
# of
Items
Released Item #
5 (8%)
Released Item #
2
77, 78, 79
2
80
1
90. 91.92
18.0* Students use fundamental counting principles to compute
combinations and permutations.
19.0* Students use combinations and permutations to compute
probabilities.
Probability and Statistics
1.0
Students know the definition of the notion of independent events
and can use the rules for addition, multiplication, and
complementation to solve for probabilities of particular events in
finite sample spaces.
INTEGRATED 2 TOTAL
*
**
65 (100%)
Key standards comprise a minimum of 70% of the test
Fractional values indicate rotated standards (e.g., 1/2 = rotated every two years;
1/3 = rotated every three years)
© California Department of Education
10
# of
Items on
CST
20
Integrated Math 2 Standards at a Glance
ALGEBRA I - 31%
1
5
4
1/2
1
1/2
3
1
3
1/3
1/3
1/3
3.0
9.0*
15.0*
16.0
17.0
18.0
21.0*
22.0
23.0*
24.1
24.2
24.3
40
GEOMETRY - 61%
2
3
4
5
2
5 2/3
2
1/3
2
4
3
3
1
3
1.0*
2.0*
3.0*
4.0*
5.0
7.0*
13.0
14.0*
15.0
16.0*
18.0*
19.0*
20.0
22.0*
Absolute Value Equations and Inequalities
Systems of Linear Equations and Inequalities - Algebraically and Graphically
Rate, Work and Percent Mixture Problems
Relation and Function Concepts
Domain and Range of Graphs, Ordered Pairs, or Symbolic Expressions
Determine if Graph, Ordered Pairs, or Symbolic Expression is a Function and Justify
Graph Quadratic Functions
Graph of Quadratic Function - Number of x-intercepts
Quadratic Equation Word Problems - Motion and Gravity
Inductive and Deductive Reasoning
Hypothesis and Conclusion
Counterexamples
Undefined Terms, Axioms, Theorems, Inductive and Deductive Reasoning
Proofs, including by Contradiction
Judge Validity of a Logical Argument or Disprove by Counterexample
Prove Theorems involving Congruency and Similarity
Prove Congruency or Similarity of Triangles and Use CPCTC
Prove and Use Theorems involving Parallel Lines, Quadrilaterals and Circles
Prove Angle Relationships within Polygons
Prove the Pythagorean Theorem
Use the Pythagorean Theorem
Basic Geometric Constructions
Basic Trigonometric Functions
Solve Problems Using Basic Trigonometric Functions
Special Right Triangles
Rotations, Translations and Reflections
4
ALGEBRA II - 6%
2
2
18.0* Counting Principles to Compute Combinations and Permutations:
19.0* Combinations and Permutation to Compute Probability
1
PROBABILITY and STATISTICS - 2%
1
1.0
Independent Events
11
STD
Integrated Math 2
CA Content Standards Unpacked
# of
Items on
CST
ALGEBRA I - 31%
3.0
20
1
Equations and Inequalities involving Absolute Values
Solve absolute value linear equations
Solve absolute value linear inequalities
9.0*
Systems of Linear Equations and Inequalities
5
Solve systems of linear equations in two variables algebraically
Graph systems of linear equations in two variables and interpret the answer
Solve systems of linear inequalities in two variables and graph the solution sets
15.0*
Rate, Work and Percent Mixture Problems
4
Solve rate problems algebraically
Solve work problems algebraically
Solve percent mixture problems algebraically
16.0
1/2
Relation and Function Concepts
Understand the concepts of a relation and a function
Determine whether a given relation defines a function
Give pertinent information about given relations and functions
17.0
1
Domain and Range of Graphs, Ordered Pairs, or Symbolic Expressions
Understand the concept of domain of independent variables
Understand the concept of range of dependent variables
Determine the domain defined by a graph, ordered pairs, or symbolic expression
Determine the range defined by a graph, ordered pairs, or symbolic expression
18.0
Determine if Graph, Ordered Pairs, or Symbolic Expression is a Function
and Justify
1/2
Determine whether a relation defined by a graph is a function, justify the conclusion
Determine whether a relation defined by a set of ordered pairs is a function, justify the
conclusion
Determine whether a relation defined by a symbolic expression is a function, justify
the conclusion
21.0*
Graph Quadratic Functions
3
Graph quadratic functions
Know that the x-intercepts are the roots
22.0
1
Number of x-Intercepts for the Graph of a Quadratic Function
Use the quadratic formula to determine the number of x-intercepts for the graph of a
quadratic function
Use factoring techniques to determine the number of x-intercepts for the graph of a
quadratic function
23.0*
Quadratic Equation Word Problems - Motion and Gravity
3
Apply quadratic equations to physical problems, including gravity and motion
24.1
1/3
Inductive and Deductive Reasoning
Explain the difference between inductive and deductive reasoning
Identify and provide examples of inductive and deductive reasoning
12
24.2
1/3
Hypothesis and Conclusion
Identify the hypothesis in logical deduction
Identify the conclusion in logical deduction
24.3
1/3
Counterexamples
Use counterexamples to show that an assertion is false
Recognize that a single counterexample is sufficient to refute an assertion
1.0*
GEOMETRY - 61%
Undefined Terms, Axioms, Theorems, Inductive and Deductive Reasoning
40
2
Identify and give examples of undefined terms
Identify and give examples of axioms
Identify and give examples of theorems
Identify and give examples of inductive reasoning
Identify and give examples of deductive reasoning
2.0*
Proofs, including by Contradiction
3
Write geometric proofs
Write geometric proofs by contradiction
3.0*
Judge Validity of a Logical Argument or Disprove by Counterexample
4
Construct a logical argument
Judge the validity of a logical argument
Give counterexamples to disprove a statement
4.0*
Prove Theorems involving Congruency and Similarity
5
Prove basic theorems involving congruence
Prove basic theorems involving similarity
5.0
2
Prove Congruency or Similarity of Triangles and Use CPCTC
Prove basic theorems involving congruence
Use the concept of corresponding parts of congruent triangles
Prove basic theorems involving similarity
7.0*
Prove Congruency or Similarity of Triangles and Use CPCTC
5 2/3
Prove and use theorems involving the properties of parallel lines cut by a transversal
Prove and use theorems involving the properties of quadrilaterals
Prove and use theorems involving the properties of circles
13.0
2
Prove Angle Relationships within Polygons
Prove relationships between angles in polygons by using properties of complementary
angles
Prove relationships between angles in polygons by using properties of supplementary
angles
Prove relationships between angles in polygons by using properties of vertical angles
Prove relationships between angles in polygons by using properties of exterior angles
14.0
1/3
Prove the Pythagorean Theorem
Prove the Pythagorean Theorem
15.0*
Use the Pythagorean Theorem
Use the Pythagorean Theorem to find distance and measure lengths
Use the Pythagorean Theorem to find lengths of sides of right triangles
13
16.0*
Basic Geometric Constructions
4
Perform basic constructions of angle bisectors with a straightedge and compass
Perform basic constructions of perpendicular bisectors with straightedge and compass
Perform basic constructions of a line parallel to a given line with a straightedge and
compass
18.0*
Basic Trigonometric Functions
3
Know the definition of sine
Know the definition of cosine
Know the definition of tangent
Use the elementary relationships between the basic trigonometric functions
19.0*
Solve Problems Using Basic Trigonometric Functions
3
Use the basic trigonometric functions to solve a right triangle
20.0
1
Special Right Triangles
Know the angle and side relationships of special right triangles
Use the angle and side relationships of 30°, 60°, and 90° right triangles
Use the angle and side relationships of 45°, 45°, and 90° right triangles
22.0*
Rotations, Translations and Reflections
3
Know the effect of rotations
Know the effect of translations
Know the effect of reflections
ALGEBRA II - 6%
18.0*
4
2
Counting Principles to Compute Combinations and Permutations
Use fundamental counting principles to compute combinations
Use fundamental counting principles to compute permutations
19.0*
Combinations and Permutation to Compute Probability
2
Use combinations to compute basic probability
Use permutations to compute basic probability
PROBABILITY and STATISTICS - 2%
1.0
1
1
Independent Events
Know the definition of independent events
Use the rules for addition to solve probability problems.
Use the rules for multiplication to solve probability problems.
Use the rules for complementation to solve probability problems.
14
Instructional Segment 1 – Integrated Math 2
Benchmark Exam 1 Closing Date: November 1, 2013


Main Topics
Linear Systems - Chapter 3
Quadratic Functions - Chapter 4
Standards









A3.0 Students solve equations and inequalities involving absolute values.
A9.0* Students solve a system of two linear equations in two variables algebraically and
are able to interpret the answer graphically. Students are able to solve a system of two
linear inequalities in two variables and to sketch the solution sets.
A15.0* Students apply algebraic techniques to solve rate problems, work problems, and
percent mixture problems.
A16.0 Students understand the concepts of a relation and a function, determine whether a
given relation defines a function, and give pertinent information about given relations and
functions.
A17.0 Students determine the domain of independent variables and the range of dependent
variables defined by a graph, a set of ordered pairs, or a symbolic expression.
A18.0 Students determine whether a relation defined by a graph, a set of ordered pairs, or a
symbolic expression is a function and justify the conclusion.
A21.0* Students graph quadratic functions and know that their roots are the xintercepts.
A22.0 Students use the quadratic formula or factoring techniques or both to determine
whether the graph of a quadratic function will intersect the x-axis in zero, one, or two points.
A23.0* Students apply quadratic equations to physical problems, such as the motion of
an object under the force of gravity.
Essential Skills









Solve absolute value equations and inequalities
Solve systems of linear equations and inequalities in two variables
Graph systems of linear equations and inequalities in two variables
Solve rate, work and percent mixture problems algebraically
Understand the concepts of a relation and a function, including domain and range
Determine whether a relation is a function
Graph quadratic functions
Determine the number of x-intercepts for the graph of a quadratic function
Apply quadratic equations to physical problems
15
Instructional Segment 2 – Integrated Math 2
Benchmark Exam 2 Closing Date: January 24, 2014



Main Topics
Coordinate Geometry - Chapter 5
Counting Strategies and Probability - Chapter 6
Logical Arguments - Chapter 1
Standards








A24.1 Students explain the difference between inductive and deductive reasoning and
identify and provide examples of each.
A24.2 Students identify the hypothesis and conclusion in logical deduction.
A24.3 Students use counterexamples to show that an assertion is false and recognize that a
single counterexample is sufficient to refute an assertion.
G15.0 Students use the Pythagorean Theorem to determine distance and find missing
lengths of sides of right triangles.
G22.0* Students know the effect of rigid motions on figures in the coordinate plane and
space, including rotations, translations, and reflections.
AII18.0* Students use fundamental counting principles to compute combinations and
permutations.
AII19.0* Students use combinations and permutations to compute probabilities.
PS1.0 Students know the definition of the notion of independent events and can use the rules
for addition, multiplication, and complementation to solve for probabilities of particular
events in finite sample spaces.
Essential Skills









Understand the difference between inductive and deductive reasoning
Identify the hypothesis and conclusion
Understand and use counterexamples
Use the Pythagorean Theorem
Understand the effects or transformations
Use fundamental counting principles
Use combinations and permutations
Understand the difference between independent and dependent events
Solve for probabilities
16
Instructional Segment 3 – Integrated Math 2
CST Mirror Test Closing Date: March 21, 2014
Please Note: It is not imperative that this entire Instructional Segment be
completed before the administration of the CST Mirror Test. However, it
MUST be completed before the administration of the actual CST.
Main Topics



Logical Arguments and Geometric Proofs - Chapter 7
Similar and Congruent Triangles - Chapter 8
Basic Geometric Constructions - Chapter 8

G1.0* Students demonstrate understanding by identifying and giving examples of
undefined terms, axioms, theorems, and inductive and deductive reasoning.
G2.0* Students write geometric proofs, including proofs by contradiction.
G3.0 Students construct and judge the validity of a logical argument and give
counterexamples to disprove a statement.
G4.0* Students prove basic theorems involving congruence and similarity.
G5.0 Students prove that triangles are congruent or similar, and they are able to use the
concept of corresponding parts of congruent triangles.
G7.0* Students prove and use theorems involving the properties of parallel lines cut by
a transversal, the properties of quadrilaterals, and the properties of circles.
G14.0 Students prove the Pythagorean Theorem.
G15.0 Students use the Pythagorean Theorem to determine distance and find missing
lengths of sides of right triangles.
G16.0* Students perform basic constructions with a straightedge and compass, such as
angle bisectors, perpendicular bisectors, and the line parallel to a given line through a
point off the line.
G18.0* Students know the definitions of the basic trigonometric functions defined by
the angles of a right triangle. They also know and are able to use elementary
relationships between them. For example, tan(x) = sin(x)/cos(x), (sin (x))2+(cos (x))2 = 1.
G19.0 Students use trigonometric functions to solve for an unknown length of a side of a
right triangle, given an angle and a length of a side.
G20.0 Students know and are able to use angle and side relationships in problems with
special right triangles, such as 30°, 60°, and 90° triangles and 45°, 45°, and 90° triangles.
Standards


















Essential Skills
Write geometric proofs
Judge the validity of a logical argument
Prove and use theorems involving congruence, similarity, properties of parallel lines,
quadrilaterals and circles
Prove and use the Pythagorean Theorem
Perform basic geometric constructions
Know and use the basic trigonometric functions
Know and use the angle and side relationships of special tight triangles
17
Instructional Segment 4 – Integrated Math 2
Site-Based End of Year Assessments/Projects
Closing Date: June 13, 2014
Main Topics


Polynomial and Rational Functions - Chapter 9
Coordinates and Figures in Space - Chapter 10
Standards








A2.0 Students understand and use such operations as taking the opposite, finding the
reciprocal, taking a root, and raising to a fractional power. They understand and use the rules
of exponents.
A10.0 Students add, subtract, multiply, and divide monomials and polynomials. Students
solve multistep problems, including word problems, by using these techniques.
A11.0 Students apply basic factoring techniques to second-and
simple third-degree
polynomials. These techniques include finding a common factor for all terms in a
polynomial, recognizing the difference of two squares, and recognizing perfect squares of
binomials.
A12.0 Students simplify fractions with polynomials in the numerator and denominator by
factoring both and reducing them to the lowest terms.
G8.0 Students know, derive, and solve problems involving perimeter, circumference, area,
volume, lateral area, and surface area of common geometric figures.
G22.0* Students know the effect of rigid motions on figures in the coordinate plane and
space, including rotations, translations, and reflections.
AII 2.0 Students solve systems of linear equations and inequalities (in two or three variables)
by substitution, with graphs, or with matrices.
AII 17.0 Given a quadratic equation of the form ax2 + by2 + cx + dy + e = 0, students can use
the method for completing the square to put the equation into standard form and can
recognize whether the graph of the equation is a circle, ellipse, parabola, or hyperbola.
Students can then graph the equation.
Essential Skills






Understand and use the power and quotient rules of exponents
Solve rational equations involving polynomials
Graph and solve cubic equations
Solve parametric equations
Explore figures and rotations in space
Explore coordinates and the distance formula in three dimensions
18
INTEGRATED MATH 2 BENCHMARK EXAMS AT A GLANCE
Benchmark Exam 1 Deadline: November 1, 2013
# of
Items
3
6
3
1
1
3
3
2
3
STD
A3.0
A9.0*+
A15.0*
A16.0
A17.0
A18.0
A21.0*
A22.0
A23.0*
STANDARD
Absolute Value Equations and Inequalities
System of Equations/Inequalities
Rate, Work, Percent Mixture
Relation and Function Concepts
Domain and Range
Determine if Relation is a Function
Graph Quadratic Functions
Graph of Quadratic Function - Number of x-intercepts
Quadratic Equation Word Problems: Motion and Gravity
Benchmark Exam 2 Deadline: January 24, 2014
# of
Items
2
3
2
2
2
2
2
3
5
3
3
2
+One
STD
A9.0*
A15.0*+
A21.0*
A23.0*
A24.1
A24.2
A24.3
G15.0
G22.0*
AII 18.0*
AII 19.0*
PS1.0
STANDARD
System of Equations/Inequalities
Rate, Work, Percent Mixture
Graph Quadratic Functions
Quadratic Equation Word Problems: Motion and Gravity
Inductive and Deductive Reasoning
Hypothesis and Conclusion
Counterexamples
Use the Pythagorean Theorem
Rotations, Reflections, Translations
Counting Principles
Combinations and Permutations
Independent Events
question for this standard is an open-ended, constructed response question.
19
INTEGRATED MATH 2 VOCABULARY
INSTRUCTIONAL SEGMENT 1
x-intercept
y-intercept
consistent system
inconsistent system
rate
absolute value
equation
inequality
relation
function
domain
range
vertical line test
x-y notation
function notation
dependent variable
independent variable
linear
growth graph
decay graph
constant graph
parabola
quadratic function
standard form
vertex
maximum
minimum
monomial
trinomial
zero-product property
quadratic formula
discriminant
INSTRUCTIONAL SEGMENT 2
rhombus
kite
reflection
rotation
standard position
diagonal
symmetry
transformation
translation
tree diagram
outcome
event
factorial
permutation
mutually exclusive events
complementary events
odds
compound events
independent events
dependent events
sample space
combination
conjecture
inductive reasoning
counterexample
Venn diagram
deductive reasoning
converse
proof
postulate
axiom
theorem
INSTRUCTIONAL SEGMENT 3
conjunction
disjunction
negation
hypothesis
conclusion
implication
conditional
premise
valid argument
direct argument
biconditional
two-column proof
complementary angles
supplementary angles
vertical angles
transversal
alternate interior angles
diameter
circumference
arc
arc length
central angle
sector
congruent
similar
bisector
isosceles triangle
equiangular
altitude
sine
cosine
tangent
INSTRUCTIONAL SEGMENT 4
polynomial
degree
rational equation
extraneous solution
cubic function
zero of a function
double zero
parametric equations
parameter
space figure
cross section
plane figure
axis of rotation
equidistant
ordered triple
20
INTEGRATED MATH 2 VOCABULARY IN SPANISH
INSTRUCTIONAL SEGMENT 1
intercepción con el eje x
intercepción con el eje y
sistema congruente
sistema incongruente
tasa
valor absoluto
ecuación
desigualdad
relación
función
dominio
gama
prueba de línea vertical
notación x-y
notación de una función
variable dependiente
variable independiente
lineal
gráfica del crecimiento
gráfica del decrecimiento
gráfica constante
parábola
función cuadrática
forma estándar
vértice
máximo
mínimo
monomio
trinomio
propiedad del producto cero
fórmula cuadrático
discriminante
INSTRUCTIONAL SEGMENT 2
rombo
cometa
reflexión
rotación
posición estándar
diagonal
simetría
transformación
traslación
diagrama de árbol
resultado
suceso
factorial
permutación
sucesos mutuamente excluyentes
sucesos complementarios
probabilidades
sucesos compuestos
sucesos independientes
sucesos dependientes
espacio de muestra
combinación
conjetura
razonamiento inductivo
contraejemplo
Diagrama de Venn
razonamiento deductivo
recíproco
prueba
postulado
axioma
teorema
INSTRUCTIONAL SEGMENT 3
conjunción
disyunción
negación
hipótesis
conclusión
implicación
condicional
premise
argumento válido
argumento directo
bicondicional
prueba de dos columnas
ángulos complementarios
ángulos suplementarios
ángulos verticales
transversal
ángulos internos alternos transversal
diámetro
circumferencia
arco
longitud de arco
ángulo central
sector
congruente
semejante
bisectriz
triángulo isósceles
equiángulo
altura
seno
coseno
tangente
INSTRUCTIONAL SEGMENT 4
polinomio
grado
ecuación racional
solución extraña
función cúbica
cero de una función
doble cero
ecuaciónes paramétricas
parámetro
cuerpo volumétrico
sección transversal
figura plana
eje de rotación
equidistante
terna ordenada
21
Cut # CST
Items
STD
INTEGRATED MATH 2 PACING GUIDE 2013-2014
IM 2
Text
INSTRUCTIONAL SEGMENT 1
Other Resources
# of
Days
Vocabulary List 1
Linear Systems
pp 118120
Unit and Project Introduction
5
A9.0*
Review
4
A15.0*
Students solve a system of two linear equations in two variables
algebraically and are able to interpret the answer graphically. Students are
able to solve a system of two linear inequalities in two variables and to
sketch the solution sets.
Solve systems of linear equations and inequalities by graphing
3.1
Solve systems of linear equations by substitution
3.2
Determine the nature and number of solutions of a system of linear equations
3.3
Solve systems of linear equations by using addition or subtraction
3.4
Mid-Chapter Review/Checkpoint
Pg 150
Students apply algebraic techniques to solve rate problems, work
problems, and percent mixture problems.
KC
pp S78-S80
KC
pp S81-S83
KC
pp S84-S86
Solve rate problems
Solve work problems
Solve percent mixture problems
1
A3.0
Students solve equations and inequalities involving absolute values.
Absolute value equations
SUPP
Absolute value inequalities
SUPP
pp 180183
Project completion and presentations/review/reteach/enrich/assess
22
Cut # CST
Items
STD
INTEGRATED MATH 2 PACING GUIDE 2013-2014
IM 2
Text
Other Resources
# of
Days
Quadratic Functions and Graphs
pp 184186
Unit and Project Introduction
1/2
A16.0
1
A17.0
1/2
A18.0
Students understand the concepts of a relation and a function, determine
whether a given relation defines a function, and give pertinent information
about given relations and functions.
Students determine the domain of independent variables and the range of
dependent variables defined by a graph, a set of ordered pairs, or a
symbolic expression.
Students determine whether a relation defined by a graph, a set of ordered
pairs, or a symbolic expression is a function and justify the conclusion.
TS
pp 59-62
2.1 and
Understand functions and their graphs
pg 649
Students graph quadratic functions and know that their roots are the xintercepts.
Students use the quadratic formula or factoring techniques or both to
determine whether the graph of a quadratic function will intersect the xaxis in zero, one, or two points.
Students apply quadratic equations to physical problems, such as the
motion of an object under the force of gravity.
Graph quadratic functions
4.1
Understand functions and relations
3
A21.0*
1
A22.0
3
A23.0*
Review
Translate parabolas
4.2
Solve quadratic equations using square roots
4.3
Solve quadratic equations using factoring
4.4
Mid-Chapter Review/Checkpoint
Solve quadratic equations by using the quadratic formula
KC
pp S88-S91
pg 213
4.5
23
Cut # CST
Items
STD
IM 2
Other Resources
Text
4.6
Explore the discriminant of a quadratic equation (Discriminant only)
pp 236Project completion and presentations/review/reteach/enrich/assess
239
INTEGRATED MATH 2 PACING GUIDE 2013-2014
BENCHMARK EXAM #1 CLOSING DATE: November 1, 2013
# of
Days
Vocabulary List 1
BENCHMARK 1 DATA ANALYSIS AND INTERVENTIONS
INSTRUCTIONAL SEGMENT 2
Vocabulary List 2
Coordinate Geometry, Quadrilaterals and Circles
pp 240242
Unit and Project Introduction
5 2/3


2
3
G7.0*
G15.0
Students prove and use theorems involving the properties of parallel lines
cut by a transversal, the properties of quadrilaterals, and the properties of
circles.
Properties of quadrilaterals
5.1
Students use the Pythagorean theorem to determine distance and find
missing lengths of sides of right triangles.
Use the Pythagorean Theorem to determine distance
5.2
The Midpoint Formula
5.3
Review
Mid-Chapter Review/Checkpoint
G22.0*
Students know the effect of rigid motions on figures in the coordinate plane
and space, including rotations, translations, and reflections.
pg 265
5.4,
pp 662-664,
Transformations
SB pp 2830
24
Cut # CST
Items
5 2/3
STD
G7.0*
INTEGRATED MATH 2 PACING GUIDE 2013-2014
IM 2
Text
Students prove and use theorems involving the properties of parallel lines
cut by a transversal, the properties of quadrilaterals, and the properties of
circles.
Properties of quadrilaterals
5.5
Coordinate geometry and properties of polygons
Project completion and presentations/review/reteach/enrich/assess
Other Resources
# of
Days
5.6
pp 287291
Counting Strategies and Probability
pp 292294
Unit and Project Introduction
2
2
1
AII
18.0*
AII
19.0*
PS1.0
Students use fundamental counting principles to compute combinations
and permutations.
Students use combinations and permutations to compute probabilities.
Students know the definition of the notion of independent events and can
use the rules for addition, multiplication, and complementation to solve for
probabilities of particular events in finite sample spaces.
Fundamental counting principles
6.1
Permutations
6.2
Complementary events
6.3
Independent and dependent events
6.4
Combinations
6.5
Project completion and presentations/review/reteach/enrich/assess
pp 358361
Logical Arguments
1/3
A24.1
Students explain the difference between inductive and deductive reasoning
and identify and provide examples of each.
25
Cut # CST
Items
STD
1/3
A24.2
1/3
A24.3
INTEGRATED MATH 2 PACING GUIDE 2013-2014
IM 2
Text
Other Resources
# of
Days
Students identify the hypothesis and conclusion in logical deduction.
Students use counterexamples to show that an assertion is false and
recognize that a single counterexample is sufficient to refute an assertion.
Inductive reasoning and counterexamples
1.5
Deductive reasoning
1.6
Errors in logical reasoning
1.7
Logical reasoning
Review/reteach/enrich/assess
S92 - S95
pp 53-54
BENCHMARK EXAM #2 CLOSING DATE: January 24, 2014
Vocabulary List 2
BENCHMARK 2 DATA ANALYSIS AND INTERVENTIONS
INSTRUCTIONAL SEGMENT 3
Vocabulary List 3
It is not imperative that this entire Instructional Segment be completed before the administration of the
CST Mirror Test. However, it MUST be completed before the administration of the actual CST.
Logical Arguments and Proofs
Unit and Project Introduction
2
G1.0*
4
G3.0*
Students demonstrate understanding by identifying and giving examples of
undefined terms, axioms, theorems, and inductive and deductive
reasoning.
Students construct and judge the validity of a logical argument and give
counterexamples to disprove a statement.
Construct a logical argument
Identify hypothesis and conclusion, use counterexamples, and judge the validity
of a logical argument
pp 362364
7.1
7.2
26
Cut # CST
Items
STD
INTEGRATED MATH 2 PACING GUIDE 2013-2014
Judge the validity of a logical argument
Mid-Chapter Review/Checkpoint
Review
Construct a logical argument and judge the validity of a logical argument
4
5 2/3
G2.0*
G7.0*
IM 2
Text
Other Resources
# of
Days
7.3
pg 385
7.4
Students write geometric proofs, including proofs by contradiction.
Students prove and use theorems involving the properties of parallel lines
cut by a transversal, the properties of quadrilaterals, and the properties of
circles.
Introduction to proofs
7.5
Use postulates to write proofs
7.6
Mid-Chapter Review/Checkpoint
Review
pg 407
Write geometric proofs
7.7
Prove and use theorems involving the properties of parallel lines and
quadrilaterals
7.8
Properties of circles
Project completion and presentations/review/reteach/enrich/assess
TS pp
81-86
pp 423427
Similar and Congruent Triangles
pp 428430
Unit and Project Introduction
4
G2.0*
5 2/3
G7.0*
Students write geometric proofs, including proofs by contradiction.
Students prove and use theorems involving the properties of parallel lines
cut by a transversal, the properties of quadrilaterals, and the properties of
circles.
Parallel lines cut by a transversal
8.1
Properties of quadrilaterals
8.2
27
Cut # CST
Items
STD
5
G4.0*
2
G5.0
4
G16.0*
INTEGRATED MATH 2 PACING GUIDE 2013-2014
IM 2
Text
Students prove that triangles are congruent or similar, and they are able to
use the concept of corresponding parts of congruent triangles.
Students perform basic constructions with a straightedge and compass,
such as angle bisectors, perpendicular bisectors, and the line parallel to a
given line through a point off the line.
Triangle similarity and corresponding parts
Mid-Chapter Review/Checkpoint
8.3
pg 457
Triangle congruence and corresponding parts
8.4
Triangle congruence, corresponding parts, and basic constructions
8.5
Triangle congruence, corresponding parts, and construction of perpendicular
bisector
8.6
Basic constructions
Mid-Chapter Review/Checkpoint
Review
5
G4.0*
Students prove basic theorems involving congruence and similarity.
2
G5.0
Students prove that triangles are congruent or similar, and they are able to
use the concept of corresponding parts of congruent triangles.
1/3
G14.0*
Students prove the Pythagorean theorem.
2
G15.0
Students use the Pythagorean theorem to determine distance and find
missing lengths of sides of right triangles.
SB pp8994
pg 480
KC
pp T22-25
Proof of the Pythagorean Theorem
Triangle similarity, corresponding parts, the Pythagorean Theorem
G18.0*
# of
Days
Students prove basic theorems involving congruence and similarity.
Review
3
Other Resources
8.7
Students know the definitions of the basic trigonometric functions defined
by the angles of a right triangle. They also know and are able to use
elementary relationships between them. For example, tan(x) = sin(x)/cos(x),
(sin(x))2 + (cos(x))2 = 1.
28
Cut # CST
Items
STD
3
G19.0*
1
G20.0
INTEGRATED MATH 2 PACING GUIDE 2013-2014
IM 2
Text
Students use trigonometric functions to solve for an unknown length of a
side of a right triangle, given an angle and a length of a side.
Students know and are able to use angle and side relationships in problems
with special right triangles, such as 30°, 60°, and 90° triangles and 45°, 45°,
and 90° triangles.
Trigonometric functions and special right triangles
8.8
Project completion and presentations/review/reteach/enrich/assess
Other Resources
# of
Days
pp 497501
It is not imperative that this entire Instructional Segment be completed before the administration of the
CST Mirror Test. However, it MUST be completed before the administration of the actual CST.
CST MIRROR TEST DEADLINE: March 21, 2014
CST MIRROR TEST DATA ANALYSIS AND INTERVENTIONS
SUGGESTIONS FOR CST REVIEW
65
5
4
3
3
2
ALL
CST RELEASED ITEMS and any or all of the following for the Key
Standards:
Students solve a system of two linear equations in two variables
algebraically and are able to interpret the answer graphically. Students are
A9.0*
able to solve a system of two linear inequalities in two variables and to
sketch the solution sets.
Students apply algebraic techniques to solve rate problems, work
A15.0*
problems, and percent mixture problems.
Students graph quadratic functions and know that their roots are the xA21.0*
intercepts.
Students apply quadratic equations to physical problems, such as the
A23.0*
motion of an object under the force of gravity.
Students demonstrate understanding by identifying and giving examples of
G1.0* undefined terms, axioms, theorems, and inductive and deductive
reasoning.
KC
pp S48-S55
KC pg S87
pg 620
#1-20
4.5
SUPP
29
Cut # CST
Items
STD
INTEGRATED MATH 2 PACING GUIDE 2013-2014
3
G2.0*
Students write geometric proofs, including proofs by contradiction.
4
G3.0*
Students construct and judge the validity of a logical argument and give
counterexamples to disprove a statement.
5
G4.0*
Students prove basic theorems involving congruence and similarity.
2
G5.0
5 2/3
G7.0*
2
G13.0
2
G15.0
4
G16.0*
3
G18.0*
3
G19.0*
3
G22.0*
2
2
AII
18.0*
AII
19.0*
IM 2
Text
SB pp
74-77
Other Resources
# of
Days
SUPP
SB pp
65-68
SB pp
Students prove that triangles are congruent or similar, and they are able to
78-80
use the concept of corresponding parts of congruent triangles.
pp 673-676,
Students prove and use theorems involving the properties of parallel lines
SB pp 57cut by a transversal, the properties of quadrilaterals, and the properties of
60, TS pp
circles.
71-74
TS pp
Students prove relationships between angles in polygons by using
63-67
properties of complementary, supplementary, vertical, and exterior angles.
Students use the Pythagorean theorem to determine distance and find
pg 661
missing lengths of sides of right triangles.
Students perform basic constructions with a straightedge and compass,
SB pp
such as angle bisectors, perpendicular bisectors, and the line parallel to a
89-94
given line through a point off the line.
Students know the definitions of the basic trigonometric functions defined
TS pp
by the angles of a right triangle. They also know and are able to use
elementary relationships between them. For example, tan(x) = sin(x)/cos(x), 99-104
(sin(x))2 + (cos(x))2 = 1.
pp 659 Students use trigonometric functions to solve for an unknown length of a
660
side of a right triangle, given an angle and a length of a side.
TS
Students know the effect of rigid motions on figures in the coordinate plane
pp 105-111,
and space, including rotations, translations, and reflections.
115 - 118
pp 623 Students use fundamental counting principles to compute combinations
624
and permutations.
pp 623 Students use combinations and permutations to compute probabilities.
624
30
Cut # CST
Items
STD
INTEGRATED MATH 2 PACING GUIDE 2013-2014
IM 2
Text
INSTRUCTIONAL SEGMENT 4
Other Resources
# of
Days
Vocabulary List 4
Polynomial and Rational Functions
pp 502504
Unit and Project Introduction
A10.0
A2.0
A12.0
Students add, subtract, multiply, and divide monomials and polynomials.
Students solve multistep problems, including word problems, by using
these techniques.
Polynomial models
9.1
Students understand and use such operations as taking the opposite,
finding the reciprocal, taking a root, and raising to a fractional power.
They understand and use the rules of exponents.
Power and quotient rules
9.2
Students simplify fractions with polynomials in the numerator and
denominator by factoring both and reducing them to the lowest terms.
Solving rational equations
Review
A11.0
Mid-Chapter Review/Checkpoint
9.3
pg 527
Students apply basic factoring techniques to second-and simple thirddegree polynomials. These techniques include finding a common factor for
all terms in a polynomial, recognizing the difference of two squares, and
recognizing perfect squares of binomials.
Graphing cubic functions
9.4
Solving cubic equations
9.5
Parametric equations
9.6
Project completion and presentations/review/reteach/enrich/assess
pp 549 553
31
Cut # CST
Items
STD
INTEGRATED MATH 2 PACING GUIDE 2013-2014
IM 2
Text
Other Resources
# of
Days
Coordinates and Figures in Space
pp 554556
Unit and Project Introduction
G8.0
G22.0
Students know, derive, and solve problems involving perimeter,
circumference, area, volume, lateral area, and surface area of common
geometric figures.
Figures in space
10.1
Students know the effect of rigid motions on figures in the coordinate plane
and space, including rotations, translations, and reflections.
Rotations in space
10.2
Points that fit conditions
10.3
Mid-Chapter Review/Checkpoint
Review
AII 2.0
Students solve systems of equations and inequalities (in two or three
variables) by substitution, with graphs, or with matrices.
Coordinates in three dimensions
10.4
Distance formula in three dimensions
10.5
ax2
AII 17.0
pg 577
by2
Given a quadratic equation of the form
+
+ cx + dy + e = 0, students
can use the method for completing the square to put the equation into
standard form and can recognize whether the graph of the equation is a
circle, ellipse, parabola, or hyperbola. Students can then graph the
equation.
Circles and spheres
Project completion and presentations/review/reteach/enrich/assess
10.6
pp 549 553
SITE-BASED END OF YEAR ASSESSMENTS/PROJECTS CLOSING DATE: JUNE 13, 2014
END OF YEAR DATA ANALYSIS
32