Chino Valley Unified School District
Integrated I Pacing Guide
(2015-2016)
Math I
(2015-2016)
Essential Ideas
This course needs to be taught around “Essential Ideas”. Unlike previous courses where chapters and skills were taught in isolation
and it was not apparent why students studied certain skills, there is a need to connect concepts and skills and teach them in multiple
perspectives. So for example, a “Essential Idea” would be on Functions. Functions can be linear or non-linear. All functions involve
five perspectives that are taken into consideration: Data Tables, Equations, Graphs, Word Problems, and Pictorial Representations. So
students would take this “Essential Idea” and apply it to linear, quadratic, exponential, step, logarithmic and trigonometric functions.
In Integrated 1, we focus on linear and exponential functions. Therefore there is a purpose and a connection made around these
perspectives rather than teaching each function as something totally separate. Keeping this in mind, as you incorporate the Essential
Ideas that are listed below. Be sure to explicitly model the Standards for Mathematical Practice listed in the next pages. When students
explain their reasoning have them justify their responses by using the Standards for Mathematical Practice they become familiar with
them.
TRIMESTER ONE
Essential Idea #1: Linear Functions
Key Question: Given one representation of a linear function, how do you get the other representations?
How do you graph and write equations of lines?
Chapter: 1, 2, 3, 4
Essential Idea #2: Linear Inequalities
Key Question: How do you graph and solve linear inequalities?
Chapter: 5
TRIMESTER TWO
Essential Idea #3: Systems of Linear Equations and Inequalities
Key Question: How are systems of equations or inequalities used to determine unknowns?
Chapter: 6
Essential Idea #4: Exponential and Radical Functions
Key Questions: How do you distinguish a linear from a non-linear function?
What is the difference between a geometric progression and an arithmetic progression?
Chapter: 7, 8-1~8-4
Essential Idea #5: Statistics
Key Questions: How do you apply a linear model to data that exhibits a linear trend?
How do you use regression techniques to describe approximately linear relationships among quantities?
How do you use graphical representations and knowledge of the context to make judgments about the
appropriateness of linear models?
How do you look at residuals to analyze the accuracy of the linear models?
Chapter: 9
Essential Idea #6: Geometry
Key Questions: How do you find the length and midpoint of a segment in a 1- or 2-dimensional coordinate system?
Chapter: 10
TRIMESTER THREE
Essential Idea #7: Geometry
Key Questions: How do you apply the Pythagorean Theorem in the coordinate plane?
How do you prove that lines are parallel or perpendicular?
How do you use transformations to prove congruence and similarity?
Chapter: 11, 14, 12
Essential Idea # 8: Preview of Integrated II
Key Questions: How do you factor polynomials?
How do you graph quadratic functions and solve quadratic equations?
How do you solve rational equations?
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Math I
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Integrated II: Chapter 1, 2, 3; Integrated I: 8-5~8-7
STANDARDS FOR MATHEMATICAL PRACTICE (SMP)
SMP
STANDARD
Examples of each practice in Mathematics I
#1
Make sense of problems and
persevere in solving them.
#2
Reason abstractly and
quantitatively.
#3
Construct viable arguments
and critique the reasoning of
others. Students build proofs
by induction and proofs by
contradiction.
Model with mathematics.
Students persevere when attempting to understand the differences
between linear and exponential functions. They make diagrams of
geometric problems to help them make sense of the problems.
Quantitative reasoning entails habits of creating a coherent
representation of the problem at hand; considering the units involved;
attending to the meaning of quantities, not just how to compute them; and
knowing and flexibly using different properties of operations and objects.
Students reason through the solving of equations, recognizing that
solving an equation is more than simply a matter of rote rules and
steps. They use language such as “if… then...” when explaining
their solution methods.
#4
Students apply their mathematical understanding of linear and
exponential functions to many real-world problems, such as linear and
exponential growth. Students also discover mathematics through
experimentation and examining patterns in data from real-world contexts.
#5
Use appropriate tools
strategically.
Students develop a general understanding of the graph of an equation or
function as a representation of that object, and they use tools such as
graphing calculators or graphing software to create graphs in more
complex examples, understanding how to interpret the result.
#6
Attend to precision.
Students use clear definitions in discussion with others and in their
own reasoning. They state the meaning of the symbols they choose,
including using the equal sign consistently and appropriately. They
are careful about specifying units of measure, and labeling axes to
clarify the correspondence with quantities in a problem.
#7
Look for and make use of
structure.
#8
Look for and make use of
regularity in repeated
reasoning.
Students recognize the significance of an existing line in a geometric
figure and can use the strategy of drawing an auxiliary line for solving
problems. They also can step back for an overview and shift perspective.
They can see complicated things, such as some algebraic expressions,
as single objects or as being composed of several objects.
Students see that the key feature of a line in the plane is an equal
difference in outputs over equal intervals of inputs, and that the result of
evaluating the expression y 2  y1 for points on the line is always equal to a
x 2  x1
certain number 𝑚. Therefore, if (𝑥,) is a generic point on this line, the
equation m 

y 2  y1
, will give a general equation of that line.
x 2  x1
Source: California Mathematics Framework, 2014
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TRIMESTER ONE
Chapter 1: Expressions, Equations, and Function
Time: August 24th – September 10th
How can mathematical ideas be represented?
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Lesson 1-1: Variables and Expressions
[A.SSE.1a, 2]
Lesson 1-2: Order of Operations
[A.SSE.1b, 2]
Lesson 1-3: Properties of Numbers
Extend Lesson: Algebra Lab (Accuracy)
[A.SSE.1b, 2, N.Q.3]
Lesson 1-4: Distributive Property
[A.SSE.1b, 2]
Lesson 1-5: Equations
[A.CED.1, A.REI.3]
Lesson 1-6: Relations
[A.REI.10, F.IF.1]
Lesson 1-7: Functions
[F.IF.1, A.CED.2]
Chapter 1 Review and Test
Find Project on McGraw Hill under Resources
Notes:
 Focus on Independent and Dependent Variables (1-6)
 When is a graph a function? (Vertical Line Test)
 How do you match a scenario to a graph?
Chapter Project (Want to be Your Own Boss): Students use what they have learned about
expressions to complete a project. This chapter project addresses entrepreneurial literacy as well as
several specific skills identified as being essential to student success by the Framework for 21st Century
Learning. Visit connected.mcgraw-hill.com for student and teacher handouts. Go to Menu, Resources,
Chapter 1, Worksheets, and Chapter 1 Project.
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Chapter 2: Linear Equations
Time: September 11th – September 28th
Why is it helpful to represent the same
mathematical idea in different ways?
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Lesson 2-1: Writing Equations
[A.CED.1]
Lesson 2-2: Solving One Step Equations
Explore Lesson 2-3: Algebra Lab (Solving MultiStep Equations)
Lesson 2-3: Solving Multi-Step Equations
[A.REI.1, 3]
Lesson 2-4: Solving Equations with the Variable
on Each Side
[A.REI.1, 3]
Lesson 2-5: Solving Equations Involving
Absolute Value
[A.REI.1, 3]
Lesson 2-8: Literal Equations and Dimensional
Analysis
[A.CED.4, A.REI.3]
Chapter 2 Review and Test
Find Project on McGraw Hill under Resources
Notes:
 Describe functional relationships for given problem situations and write equations
to answer questions arising from the situations.
 Find specific function values and transform and solve equations in problem
situations.
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Chapter 3: Linear Equations
Time: September 29th – October 9th
How are linear graphs useful in representing
linear functions based on a word problem?
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Lesson 3-1: Graphing Linear Equations
Lesson 3-2: Solving Linear Equations by
Graphing
Lesson 3-3: Rate of Change
Lesson 3-5: Arithmetic Sequences
Lesson 3-6: Proportional and Non-proportional
relationships
Chapter 3Review and Test
End of grading period Project
Find Project on McGraw Hill under Resources
Notes:
 Develop the concept of slope as a rate of change and determine the slope from
graphs, tables and algebraic representations.
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Math I
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Chapter 4: Equations of Linear Functions
Time: October 12th – October 23rd
Why is math used to model real-world situations?
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Lesson 4-1: Graphing Equations in SlopeIntercept Form
Extend Lesson 4-1: Graphing Technology Lab
(The Family of Linear Graphs)
[F.IF.7a, S.ID.7, F.BF.3]
Lesson 4-2: Writing Equations in slope-Intercept
Form
[F.BF.1, F.LE.2]
Lesson 4-3: Writing Equations in Point-Slope
Form
[F.IF.2, F.LE.2]
Lesson 4-4: Parallel and Perpendicular Lines
[F.LE.2, S.ID.7]
Chapter 4 Review and Test
Find Project on McGraw Hill under Resources
Notes:
 You may want to supplement with additional application problems.
 Interpret and make decisions, predictions, and critical judgements from functional
relationships.
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Math I
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Chapter 5: Linear Inequalities
Time: October 26th – November 6th
 Lesson 5-1: Solving Inequalities by Addition and
How can you find the solution to a math problem?

Subtraction
Lesson 5-2: Solving Inequalities by
Multiplication and Division
Lesson 5-3: Solving Multi-step Inequalities
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Lesson 5-4: Solving Compound Inequalities
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Lesson 5-5: Inequalities involving Absolute
Value
Lesson 5-6: Graphing Inequalities in Two
Variables
Lesson 6-6: Systems of Inequalities
Extend Lesson 6-6: Graphing Technology Lab:
(Systems of Inequalities)
[A.REI.12]
Chapter 5 and Section 6-6 Review and Test
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Notes:
 Investigate methods for solving linear inequalities using the properties of inequality.
TRIMESTER ONE BENCHMARK REVIEW AND TEST
Time: November 9th – November 13th
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TRIMESTER TWO
Chapter 6: Systems of Linear Equations and Inequalities
Time: November 16th – December 4th
What does the break-even point mean in the
situation?
Use desmos.com (apple) or Wabbitemu
(android) to demonstrate system of
equations. Very useful online graphing
program.
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Lesson 6-1: Graphing Systems of Equations
Lesson 6-2: Substitution Method
Lesson 6-3: Elimination Using Addition and
Subtraction
Lesson 6-4: Elimination Using Multiplication
Lesson 6-5: Applying System of Linear
Equations
Chapter 6 Review and Test
Notes:
 Remember you have 1 week off for Thanksgiving from Nov. 23rd to Nov. 27th.
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Math I
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Chapter 7: Exponents and Exponential Functions
Time: December 7th – December 18th
 Lesson 7-1: Multiplication Properties of
How can you find the solution to a math problem?
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Exponents
Lesson 7-2: Division Properties of Exponents
Lesson 7-3: Rational Exponents
Explore Lesson 7-5: Graphing Technology Lab:
(Family of Exponential Functions)
Lesson 7-5: Exponential Functions
[F.IF.7e, F.BF.3, F.LE.2, A.REI.11]
Extend Lesson 7-5: Graphing Technology Lab:
(Solving Exponential Equations and
Inequalities)
Lesson 7-6: Growth and Decay
[F.IF.8b, F.LE.2, A.SSE.3c]
Lesson 7-7: Geometric Sequences as Exponential
Functions
Extend Lesson 7-7: Algebra Lab: Average Rate of
Change of Exponential Functions
[F.BF.2, F.LE.1]
Lesson 7-8: Recursive Formulas
[F.IF.3, F.BF.2]
Chapter 7 Exponents Review and Test
Notes:
 Simplify polynomial expressions and apply the laws of exponents in problem-
solving functions.
 Graph and analyze exponential functions.
 Analyze data and represent situations involving exponential growth and decay using
tables, graphs, or algebraic methods.
Chapter Project (INTERE$T-ing Thing About Credit Cards…): Students use what they have
learned about exponential functions to complete a project. This chapter project addresses
financial literacy, as well as several specific skills identified as being essential to student success
by the Framework for 21st Century Learning. Visit connectED.mcgraw-hill.com for student and
teacher handouts.
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Math I
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Chapter 8-1 ~ 8-4: Radical Functions
Time: January 4th – January 12th
How do you simplify and utilize radical
expressions?
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Lesson 8-1: Square Root Functions
[F.IF.4]
Lesson 8-2: Simplifying Radical Expressions
[A.REI.4a]
Lesson 8-3: Operations with Radical
Expressions [N.RN.2]
Lesson 8-4: Radical Equations [N.RN.2, A.CED.2]
Review and Test
Notes:
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Math I
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Chapter 9: Statistics and Probability
Time: January 13th – January 29h
How can mathematical ideas be represented?
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Lesson 0-12: Measures of Center, Variation and
Position (Mean, Median, Mode, Interquartile
Range and Range; Outliers; Spread)
Lesson 0-13: Representing Data (Histogram,
Dot Plots, Stem-and-Leaf Plot, Box-and-Whisker
Plot, Frequency Tables, Line Graph)
Lesson 9-1: Statistics and Parameters (Variance
and Standard Deviation)
Lesson 9-2: Distributions of Data
Lesson 9-3: Comparing Sets of Data
Statistics Review and Test
Notes:
 You can allow for an 1 week Project on Statistics or move ahead to Geometry.
Chapter Project (Want to be Your Own Boss): Students use what they have learned about
expressions to complete a project. This chapter project addresses entrepreneurial literacy as well as
several specific skills identified as being essential to student success by the Framework for 21st Century
Learning. Visit connected.mcgraw-hill.com for student and teacher handouts.
Math I
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Math I
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Chapter 10: Tools of Geometry
Time: February 7th – February 19th
Why are geometry and measurement important in
the real-world?
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Lesson 10-1: Points, Lines, and Planes
[G.CO.1, G.MG.1]
Lesson 10-2: Linear Measure
Extend Lesson 10-2: Extension Lesson:
(Precision and Accuracy)
[G.CO.1, 12]
Lesson 10-3: Distance and Midpoints
[G.CO.1, 12]
Lesson 10-4: Angle Measure
[G.CO.1, 12]
Extend Lesson 10-5: Geometry Lab:
(Constructing Perpendiculars)
Lesson 10-6: Two-Dimensional Figures
Chapter 10 Review and Test
Notes:
 Make sure to do CONSTRUCTIONS in the Extend Lessons!!!
 Skip proofs. 
Chapter Project (Map Your Town): Students use what they have learned about points, lines, planes,
and polygons to create a map of a fictitious town and connect the parts of the map to the geometry
figures they represent.
(1) Have students create a map grid and label the horizontal and vertical axes. Students should also
name the town.
(2) Students place important landmarks of their town on the grid represented by a 3-dimensional
polygon. Each of the polygons discussed in this chapter should be used at least one time.
Landmarks may include the school, Post Office, library, park, home, etc. and should be indicated
by a labeled point at its location.
(3) Next, students use line segments to build the road system of their town and name the major
roadways.
(4) Lastly, students should write a short paper that describes all of the geometric figures and
concepts used to create the map. You may want to remind students that the map itself is a plane.
TRIMESTER TWO BENCHMARK REVIEW AND TEST
Time: February 22nd – February 26th
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TRIMESTER THREE
Chapter 11: Parallel and Perpendicular Lines
Time: February 29th – March 11th
 Lesson 11-1: Parallel Lines and Transversals
How can you determine if lines are parallel or
[G.CO.1]
perpendicular?
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How are the concepts of parallel and perpendicular
lines used in real life?
Use desmos.com to demonstrate parallel
and perpendicular lines. Very useful online
graphing program.
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Lesson 11-2: Angles and Parallel Lines
[G.CO.1, 9, 12]
Lesson 11-3: Slopes of Lines
[G.GPE.5]
Lesson 11-4: Equations of Lines
Extend Lesson 11-4: Geometry Lab: (Equations
of Perpendicular Bisectors)
[G.GPE.5]
Lesson 11-5: Proving Lines Parallel
[G.CO.9, 12]
Lesson 11-6: Perpendiculars and Distance
[G.CO.12, G.MG.3]
Chapter 11 Review and Test
Notes:
 Lesson 11-6: Make sure to do CONSTRUCTIONS of parallel and perpendicular lines.
Chapter Project (Function of Lines in Construction): Students use what they have learned about
parallel and perpendicular lines to make connection in building technology.
Your students will research the design of the Golden Gate Bridge in San Francisco, California, to see how
parallel and perpendicular lines play an important role in design engineering.
Questions for research and discussion:
(1) How many different areas on the bridge show examples of parallel and perpendicular lines?
(2) How can you prove that the cable lines that hold up the road are parallel? How can you prove that
they are perpendicular to the road surface?
(3) Can you find the diagonal pieces of steel that transverse the parallel supports that make up the
road section? How can you prove that these are parallel?
(4) Write a report of your research and findings to present to the class.
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Math I
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Chapter 14: Similarity, Transformations, and Symmetry
Time: March 14th – April 8th
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Lesson 14-4: Reflections
[G.CO.4, 5]
Lesson 14-5: Translations
[G.CO.4, 5]
Explore Lesson 14-6: Geometry Lab: Rotations
Lesson 14-6: Rotations
[G.CO.2, 4, 5, G.GMD.4]
Lesson 14-7: Compositions of Transformations
[G.CO.2, 5]
Extend Lesson 14-7: Geometry Lab: Tessellations
Lesson 14-8: Symmetry
[G.CO.3, 12]
Lesson 14-9: Dilations
[G.CO.2, G.SRT.1]
Lesson 14-3: Similarity Transformations
[G.SRT.2, G.SRT.5]
Lesson 14-1: Similar Triangles
[G.SRT.4, G.SRT.5]
Lesson 14-2: Parallel Lines and Proportional Parts
[G.SRT.4, G.SRT.5]
Chapter 14 Review and Test
Notes:
 Based on Common Core State Standards, congruency should be taught using
rigid motion. Therefore, 14-4 to 14-9 appear before 14-1 to 14-3.
 Extend lesson 14-7: Assign this as a take home project.
 Graph paper is highly recommended for this chapter.
Chapter Project (Time for a Rebound): Students incorporate what they have learned about similar triangles to
determine the path of a basketball when it is rolled into a wall at an angle.
(1) Students partner up with a classmate for this experiment and will need a basketball, or some other type of
similar ball, a meter stick, a paper cup, masking tape, and a marker.
(2) On a flat wall, mark a point near the ground with a piece of tape (point A). Measure over 4 meters and
mark a second piece of tape on the wall near the floor (point B). Measure over 2 more meters and mark a
third piece of tape on the wall near the floor again (point C).
(3) Next, from point A, measure out 5 meters perpendicular to the wall and place a piece of tape on the floor
and label it with “Start.”
(4) How can you use the properties of similar triangles to determine how far to place a paper cup
perpendicular to the wall at point C so that when you roll the ball from the starting point to point B, it will
rebound off the wall and knock over the cup?
(5) What happens when you change the distance of the starting point from the wall?
(6) Record your results, make a detailed scale drawing of your experiment and present to class.
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Math I
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Chapter 12: Congruent Triangles
Time: April 11th – April 29th
How can you prove that two triangles are
congruent?
What is a congruence transformation?
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Notes:
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Lesson 12-1: Classifying Triangles
Explore Lesson 12-2:
Geometry Lab: (Angles of Triangles)
[G.CO.12]
Lesson 12-2 Angles of Triangles
[G.CO.10]
Lesson 12-3: Congruent Triangles
[G.CO.7, G.SRT.5]
Lesson 12-4: Proving Triangles Congruent: SSS
and SAS
[G.CO.10, G.SRT.5]
Lesson 12-5: Proving Triangles Congruent: ASA
and AAS
[G.CO.10, G.SRT.5]
Explore Lesson 12-7: Graphing Technology Lab:
Congruence Transformations
Lesson 12-7: Congruence Transformations
[G.CO.5, 6, 7]
Explore 12-9A Geometry Lab: Constructing
Bisectors
Explore Lesson 12-9B: Geometry Lab:
Constructing Medians and Altitudes
Chapter 12 Review and Test
Lesson 12-2: Don’t do the proofs in this lesson
Lesson 12-3: Don’t do the proofs in this lesson
There will be construction questions on the assessment
If you have extra time, do 12-8 and 12-9, but these are not required under California
Common Core Standards.
Chapter Project (Classifying Triangles): Students use what they have learned about triangles to
classify the many different types used in sports and fitness equipment.
(1) Have students find examples of the use of triangles in sports and fitness equipment such as the
bike frames, soccer goals, hang gliders, etc. Which types of triangles are typical? How are these
shapes used? What do the triangle designs help to accomplish?
(2) Print out as many examples as you can and trace the triangle shapes incorporated in the designs
on a piece of paper. Discuss how the triangles are used in each piece of equipment.
(3) Finally, classify each triangle by its sides and its angles and present your findings to the rest of the
class.
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Math I
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Preview of Integrated II (Optional)
Time: May 2nd – May 27th
How do you factor polynomials?
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How do you graph quadratic functions and solve
quadratic equations?

How do you solve rational equations?
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Chapter 1: Quadratic Expressions and Equations
[A.APR.1, A.APR.3, A.SSE. 1a, A.SSE.2, A.SSE.3a,
A.REI.4b, N.CN.9]
Chapter 2: Quadratic Functions and Equations
[A.SSE. 3b, F.BF. 3, F.IF.4, F.IF.6, F.IF.7, F.IF.7a,
F.IF.7b, F.IF.8, F.IF.8a, F.LE.1, F.LE.2, A.REI.4,
A.REI.4b, A.REI.7, S.ID.6a]
Chapter 3: Quadratic Functions and Relations
[A.CED.1, A.CED.3, A.SSE.1b, A.SSE.2, F.BF.3,
F.IF.4, F.IF.6, F.IF.8a, N.CN.1, N.CN.2, N.CN.7]
Integrated I Lesson 8-5: Inverse Variation
Integrated I Lesson 8-6: Rational Functions
[A.CED.2]
Integrated I Lesson 8-7: Rational Equations
[A.CED.2]
Review and Test
Notes:
 Access Integrated II Textbook on
http://connected.mcgraw-hill.com/connected/login.do
END-OF-COURSE EXAM REVIEW AND TEST
Time: May 31st – June 2nd
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