Download Topic 5 - Miami-Dade County Public Schools

MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
Pacing
Traditional
18
Block
9
Topic V Assessment Window
Topic V: Quadratic Functions, Equations, and Relations
MATHEMATICS FLORIDA STATE STANDARDS (MAFS) &
MATHEMATICAL PRACTICES (MP)
MAFS.912.N-CN.3.7: Solve quadratic equations with real coefficients that
have complex solutions. (MP.1, MP.7)
Also assesses:
MAFS.912.A-REI.2.4: Solve quadratic equations in one variable.
(MP.2, MP.7, MP.8)
MAFS.912.A-REI.1.1: Explain each step in solving a simple equation as
following from the equality of numbers asserted at the previous step,
starting from the assumption that the original equation has a solution.
Construct a viable argument to justify a solution method. (MP.1, MP.2,
MP.3, MP.7) *NO CALCULATOR*
MAFS.912. F-IF.3.8: Write a function defined by an expression in different
but equivalent forms to reveal and explain different properties of the
function. (MP.2, MP.7)
MAFS.912.N-CN.1.2: Use the relation – and the commutative, associative,
and distributive properties to add, subtract, and multiply complex numbers.
(MP.2, MP.7, MP.8) *NO CALCULATOR*
Also assesses:
MAFS.912.N-CN.1.1: Know there is a complex number, 𝑖, such that
𝑖 2 = −1, and every complex number has the form 𝑎 + 𝑏𝑖 with a and b
real (MP.2, MP.6) *NO CALCULATOR*
MAFS.912.A-CED.1.4: Rearrange formulas to highlight a quantity of
interest, using the same reasoning as in solving equations. For example,
rearrange Ohm’s law V = IR to highlight resistance R. (MP.1, MP.2, MP.4,
MP.5) (Assessed with A-CED.1.1)
MAFS.912.G-GPE.1.2: Derive the equation of a parabola given a focus
and directrix. (MP.2, MP.3, MP.7, MP.8)
MAFS.912.A-REI.4.11: Explain why the x-coordinates of the points where
the graphs of the equations y = f(x) and y = g(x) intersect are the solutions
of the equation f(x) = g(x); find the solutions approximately, e.g., using
technology to graph the functions, make tables of values, or find
successive approximations. Include cases where f(x) and/or g(x) are
linear, polynomial, rational, absolute value, exponential, and logarithmic
functions. (MP.2, MP.4, MP.5, MP.6)
Division of Academics - Department of Mathematics
Topic V Second Nine Weeks
Date(s)
11/10/16 – 12/09/16
11/10/16 – 12/09/16
12/05/16 – 12/09/16
ESSENTIAL CONTENT
OBJECTIVES (from Item Specifications)
A. Quadratic Equations
1. Solving Quadratic
Equations by Taking
Square Roots.
2. Solving Equations by
Completing the Square
(A1-22.2)
3. Complex Numbers
4. Finding Complex Solutions
of Quadratic Equations
I can:
 Rewrite a quadratic equation in vertex form by completing the
square.
 Solve a quadratic equation by choosing an appropriate method
(i.e., completing the square, the quadratic formula, or
factoring).
 Complete an algebraic proof to explain steps for solving a
simple equation.
 Construct a viable argument to justify a solution method.
 Calculate and interpret the average rate of change of a
continuous function that is represented algebraically, in a table
of values, on a graph, or as a set of data with a real-world
context.
 Identify zeros, extreme values, and symmetry of a quadratic
function written symbolically.
 Add, subtract, and multiply complex numbers and use 𝑖 2 = −1
to write the answer as a complex number.
 Solve multi-variable formulas or literal equations for a specific
variable.
 Write the equation of a parabola when given the focus and
directrix.
 Find a solution or an approximate solution for 𝑓(𝑥) = 𝑔(𝑥)
using a graph.
 Find a solution or an approximate solution for 𝑓(𝑥) = 𝑔(𝑥)
using a table of values.
 Find a solution or an approximate solution for 𝑓(𝑥) =
𝑔(𝑥) using successive approximations that gives the solution
to a given place value.
 Demonstrate why the intersection of two functions is a solution
to 𝑓(𝑥) = 𝑔(𝑥).
B. Quadratic Relations and
Systems of Equations
1. Parabolas
2. Solving Linear Systems in
Three Variables
Page 1 of 18
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
MATHEMATICS FLORIDA STATE STANDARDS (MAFS) &
MATHEMATICAL PRACTICES (MP)
MAFS.912.A-CED.1.2: Create equations in two or more variables to
represent relationships between quantities; graph equations on coordinate
axes with labels and scales. (MP.1, MP.2, MP.4, MP.5)
Also assesses:
MAFS.912.A-CED.1.3: Represent constraints by equations or
inequalities, and by systems of equations and/or inequalities, and
interpret solutions as viable or non-viable options in a modeling context.
For example, represent inequalities describing nutritional and cost
constraints on combinations of different food. (MP.1, MP.2, MP.4, MP.5)
MAFS.912.A-REI.3.6: Solve systems of linear equations exactly and
approximately (e.g., with graphs), focusing on pairs of linear equations
in two variables. (MP.2, MP.4, MP.5, MP.6, MP.7, MP.8)
MAFS.912.A-REI.3.7: Solve a simple system consisting of a linear
equation and a quadratic equation in two variables algebraically and
graphically. (MP.2, MP.4, MP.5, MP.6, MP.7, MP.8)
Division of Academics - Department of Mathematics
Topic V Second Nine Weeks
Course Code: 120034001
ESSENTIAL CONTENT
OBJECTIVES (from Item Specifications)
I can:
 Identify the quantities in a real-world situation that should be
represented by distinct variables.
 Write constraints for a real-world context using equations,
inequalities, a system of equations, or a system of inequalities.
 Write a system of equations given a real-world situation.
 Graph a system of equations that represents a real-world
context using appropriate axis labels and scale.
 Solve systems of linear equations.
 Write a system of equations for a modeling context that is best
represented by a system of equations.
 Write a system of inequalities for a modeling context that is
best represented by a system of inequalities.
 Interpret the solution of a real-world context as viable or not
viable.
 Solve a simple system of a linear equation and a quadratic
equation in two variables algebraically.
 Solve a simple system of a linear equation and a quadratic
equation in two variables graphically.
Page 2 of 18
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
INSTRUCTIONAL TOOLS
Pacing
Core Text Book: Houghton Mifflin Harcourt – Algebra 2
Algebra 2 Honors Course Description
Algebra 2 Item Specifications
Date(s)
11/10/16 – 12/09/16
11/10/16 – 12/09/16
12/05/16 – 12/09/16
Traditional
18
Block
9
Topic V Assessment Window
Algebra 2 Honors – H.M.H. Resources
Unit Resources
Unit Tests – A, B, and C
Performance Assessment
Module Resources
Module Test B
Common Core Assessment Readiness
Advanced Learners – Challenge Worksheets
Additional Unit Resources
Math in Careers Video
Assessment Readiness (Mixed Review)
Lesson Resources
Lessons – Work text/Interactive Student Edition
Practice and Problem Solving: A/B
Advanced Learners - Practice and Problem Solving: C
Success for English Learners
PMT Preferences: Auto-assign for intervention and enrichment: YES
Test and Quizzes
Auto-assign
Homework for intervention and enrichment: NO
STANDARDS
MAFS.912.A-CED.1.2★
MAFS.912.A-CED.1.3★
MAFS.912.A-CED.1.4★
MAFS.912.A-REI.1.1
MAFS.912.A-REI.2.4
MAFS.912.A-REI.3.6
MAFS.912.A-REI.3.7
MAFS.912.F-IF.3.8
MAFS.912.G-GPE.1.2
MAFS.912.N-CN.1.1
MAFS.912.N-CN.1.2
MAFS.912.N-CN.3.7
PMT Preferences: Auto-assign for intervention and enrichment: YES
Auto-assign
for intervention
and enrichment: NO
Standard-Based
Intervention
Auto-assign
for intervention and enrichment: YES
Course Intervention
Daily Intervention
MODULES
TEACHER NOTES
Algebra 2 Honors Block Schedule – Suggested Pace
Module 3
Module 4
Day 1
Day 2
Day 3
Day 4
Day 5
Day 6
Day 7
Day 8
Day 9
3.1
A1-22.2
3.2
3.3
4.2
4.3
4.4
Review
Topic 5 Test
MAFS.912.A-REI.4.11★
Topic V Assessment: Quadratic Functions, Equations, and Relations
Division of Academics - Department of Mathematics
Topic V Second Nine Weeks
Page 3 of 18
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
INSTRUCTIONAL TOOLS
Reporting Category: Algebra and Modeling
% of Test
36%
Average % Correct 2015
29%
Average % Correct 2016
20%
Reporting Category: Functions and Modeling
% of Test
36%
Average % Correct 2015
24%
Average % Correct 2016
23%
Reporting Category: Statistics, Probability, and the Number System
% of Test
28%
Average % Correct 2015
17%
Average % Correct 2016
27%
MODELING CYCLE (★)
The basic modeling cycle involves:
1. Identifying variables in the situation and selecting those that represent essential features.
2. Formulating a model by creating and selecting geometric, graphical, tabular, algebraic, or statistical representations that describe relationships between the
variables.
3. Analyzing and performing operations on these relationships to draw conclusions.
4. Interpreting the results of the mathematics in terms of the original situation.
5. Validating the conclusions by comparing them with the situation, and then either improving the model or, if it is acceptable.
6. Reporting on the conclusions and the reasoning behind them.
Choices, assumptions, and approximations are present throughout this cycle.
http://www.cpalms.org/Standards/mafs_modeling_standards.aspx
Vocabulary: Directrix, focus of a parabola, linear equations in the three variables, matrix, ordered triple, complex number, imaginary unit, pure imaginary
number.
Algebra 2 Honors
REPORTING CATEGORY: ALGEBRA AND MODELING
PRACTICE ITEMS
1.
2.
1
𝑎𝑡 2
The formula 𝑠 =
represents the distance 𝑠 that a freefalling object will fall near a planet or the moon in a given time 𝑡. In the formula, 𝑎 represents the acceleration due to
2
gravity.
a) Solve the formula for 𝑡.
b) A free‐falling object near the moon drops 20.5. For how many second does the object is falling? Use 𝑎 = 1.6𝑚/𝑠 2.
The following equation represents a particle moving linearly, in three dimensions: 𝑟 =
Scientist 1:𝑣 = −2𝑟 − 2𝑟0 −
𝑎𝑡 2
and scientist 2: =
𝑟
𝑡
−
𝑎𝑡 2
2
−
𝑟0
𝑡
𝑎𝑡 2
2
+ 𝑣𝑡 + 𝑟0 . Two scientists solve the equation for 𝑣 and their equations are as follows:
. How did each scientist come up with the equation? Show the steps.
Division of Academics - Department of Mathematics
Topic V Second Nine Weeks
Page 4 of 18
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
INSTRUCTIONAL TOOLS
REPORTING CATEGORY: ALGEBRA AND MODELING
PRACTICE ITEMS
Solve the following quadratic equations. Explain each step.
a) 2𝑥 2 − 7𝑥 − 4 = 0
b) 4𝑥 2 + 12𝑥 + 9 = 0
c) 𝑥 2 + 6𝑥 + 2 = 0
4. The steps used to simplify an expression are shown. Identify the missing property that justifies each step.
Steps
Justification
3.
5𝑖 + 4(6 + 3𝑖)
5𝑖 + 24 + 12𝑖
24 + 5𝑖 + 12𝑖
24 + (5𝑖 + 12𝑖)
24 + 17𝑖
5.
6.
7.
8.
9.
Given Expression
Substitution Property
Which of the following quadratic equations has no real solutions?
A. 𝑥 2 + 3𝑥 − 5 = 0
B. 4𝑥 2 + 4𝑥 + 1 = 0
C. 2𝑥 2 − 4𝑥 + 3 = 0
D. 𝑥 2 − 6𝑥 − 2 = 0
Consider the quadratic equation 3𝑥 2 − 9𝑥 + 20 = 13.
a) What method should be used to most easily solve the equation over the set of complex numbers? Explain your reasoning.
b) Solve the equation using the method from part a). Show your work, and write the solutions using the imaginary unit 𝑖 as necessary.
Which points are on the parabola with focus (0.4) and directrix 𝑦 = −4?
 (8, −4)
 (0, −4)
 (0, 4)
 (4, 1)
 (9, 12)
 (12, 9)
1
Which focus and directrix correspond to a parabola described by y= 𝑥 2 ?
16
A. Focus (0, −4) and directrix 𝑦 = −4
B. Focus (0, 4) and directrix 𝑦 = 4
C. Focus (0, −4) and directrix 𝑦 = 4
D. Focus (0, 4) and directrix 𝑦 = −4
Which point is always on a parabola with focus 𝐹(0, 𝑝) and directrix 𝑦 = −𝑝?
A. (0, 0)
B. (0, 𝑝)
C. (𝑝, 0)
D. (𝑝, 𝑝)
Division of Academics - Department of Mathematics
Topic V Second Nine Weeks
Page 5 of 18
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
INSTRUCTIONAL TOOLS
REPORTING CATEGORY: ALGEBRA AND MODELING
PRACTICE ITEMS
10. Solve the following quadratic equations. Explain each step.
d) 2𝑥 2 − 7𝑥 − 4 = 0
e) 4𝑥 2 + 12𝑥 + 9 = 0
f)
𝑥 2 + 6𝑥 + 2 = 0
11. The steps used to simplify an expression are shown. Identify the missing property that justifies each step.
Steps
Justification
5𝑖 + 4(6 + 3𝑖)
Given Expression
5𝑖 + 24 + 12𝑖
24 + 5𝑖 + 12𝑖
24 + (5𝑖 + 12𝑖)
24 + 17𝑖
Substitution Property
12. Which of the following quadratic equations has no real solutions?
A. 𝑥 2 + 3𝑥 − 5 = 0
B. 4𝑥 2 + 4𝑥 + 1 = 0
C. 2𝑥 2 − 4𝑥 + 3 = 0
D. 𝑥 2 − 6𝑥 − 2 = 0
13. Consider the quadratic equation 3𝑥 2 − 9𝑥 + 20 = 13.
c) What method should be used to most easily solve the equation over the set of complex numbers? Explain your reasoning.
d) Solve the equation using the method from part a). Show your work, and write the solutions using the imaginary unit 𝑖 as necessary.
14. Which points are on the parabola with focus (0.4) and directrix 𝑦 = −4?
 (8, −4)
 (0, −4)
 (0, 4)
 (4, 1)
 (9, 12)
 (12, 9)
1
15. Which focus and directrix correspond to a parabola described by y= 𝑥 2 ?
16
A. Focus (0, −4) and directrix 𝑦 = −4
B. Focus (0, 4) and directrix 𝑦 = 4
C. Focus (0, −4) and directrix 𝑦 = 4
D. Focus (0, 4) and directrix 𝑦 = −4
16. Which point is always on a parabola with focus 𝐹(0, 𝑝) and directrix 𝑦 = −𝑝?
A. (0, 0)
B. (0, 𝑝)
C. (𝑝, 0)
D. (𝑝, 𝑝)
Division of Academics - Department of Mathematics
Topic V Second Nine Weeks
Page 6 of 18
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
INSTRUCTIONAL TOOLS
REPORTING CATEGORY: ALGEBRA AND MODELING
PRACTICE ITEMS
17. Which is one of the appropriate steps in finding the solutions for 𝑥 2 + 8𝑥 − 9 = 0 when solved by completing the square?
A. (𝑥 + 4)2 = 25
B. (𝑥 + 8)2 = 9
C. (𝑥 + 4)2 = 9
D. (𝑥 + 9)(𝑥 − 1) = 0
18. For the scenario below, use the model ℎ = −16𝑡 2 + 𝑣0 𝑡 + ℎ0 , where ℎ = height (in feet), ℎ0 = initial height (in feet), 𝑣0 = initial velocity (in feet per second), and t = time (in
seconds).
A cheerleading squad performs a stunt called a “basket toss” where a team member is thrown into the air and is caught moments later. During one performance, a cheerleader is
thrown upward, leaving her teammates’ hands 6 feet above the ground with an initial vertical velocity of 15 feet per second.
When the girl falls back, the team catches her at a height of 5 feet. How long was the cheerleader in the air?
1
A.
second
16
9
B. 1 second
16
C. 1 second
D. 2 seconds
2
19. If a + 2i is a root of the quadratic equation 2x + 6x + c = 0, find the values of the real numbers a and c .
20. For each of the following, determine if the statement is true or false. If false, explain your reasoning.
STATEMENTS
TRUE
FALSE
There is a parabola with focus of (2, 3), directrix 𝑦 = 1, and vertex (0, 0).


The parabola with focus of (0, ¼) and directrix y = -¼ has no x-intercepts.


(𝑥 + 4)2 = 29𝑦 − 4.5) has focus at (−4, 5) and directrix 𝑦 = 4


21. Which ordered pair is in the solution set of the system of equations shown below?
𝑦 2 − 𝑥 2 + 32 = 0
3𝑦 − 𝑥 = 0
A. (2, 6)
B. (3, 1)
C. (−1, −3)
D. (−6, −2)
22. The directrix of the parabola 12(𝑦 + 3) = (𝑥 − 4)2 has the equation 𝑦 = −6. Find the coordinates of the focus of the parabola.
23. Solve the system
6𝑥 − 2𝑦 − 4𝑧 = −8
3𝑥 − 5𝑦 + 5𝑧 = −14
𝑥 + 𝑦 − 5𝑧 = 6
Division of Academics - Department of Mathematics
Topic V Second Nine Weeks
Page 7 of 18
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
INSTRUCTIONAL TOOLS
REPORTING CATEGORY: STATISTICS, Probability, AND THE NUMBER SYSTEM
PRACTICE ITEMS
24. Which one of the following is in the simplest form of
A.
B.
C.
D.
-48 ?
−4𝑖√3
4√−3
−4√3
4𝑖√3
25. What does the imaginary number 𝑖 represent?
A. −1
B. √1
C. √−1
D. -√−1
26. Simplify each expression and tell whether it represents a real number or a non-real number.
a) √144 − √64
b) √144 + √−64
27. Let 𝑎, 𝑏, and 𝑐 be any real numbers. Find the product 𝑐𝑖(𝑎 + 𝑏𝑖).
Which of the following sums, differences, and products can be simplified to 6 − 3𝑖?
 (9 − 5𝑖) + (3 − 2𝑖)
 (4 + 2𝑖) + (2 − 5𝑖)
 (9 − 5𝑖) − (3 − 2𝑖)
 (4 + 2𝑖) − (2 − 5𝑖)
 3𝑖(−1 + 2𝑖)
 3𝑖(−1 − 2𝑖)
28. Consider the following expressions
i8 - i2
i 7 - i5
i6 - i
4i 4 - 2i 3
6i 4 - 2i2
a)
b)
Which of these expressions can be expressed as in the form a + 0i?
Which of these expressions can be expressed as an imaginary number 0 + bi?
Division of Academics - Department of Mathematics
Topic V Second Nine Weeks
Page 8 of 18
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
INSTRUCTIONAL TOOLS
REPORTING CATEGORY: STATISTICS, Probability, AND THE NUMBER SYSTEM
PRACTICE ITEMS
29. For which of the following operations will the complex numbers (4 – 3𝑖) and (1 + 2𝑖) produce a real solution? Find the solution.
A. Addition
B. Subtraction
C. Multiplication
D. Division
30. Given 𝑖 is the imaginary unit, (2 − 𝑦𝑖)2 in simplest form is
A. 𝑦 2 − 4yi + 4
B. −𝑦 2 − 4yi + 4
C. 𝑦 2 + 4
D. −𝑦 2 + 4
STEM Lessons - Model Eliciting Activity
STEM Lessons
N/A
CPALMS Perspectives Videos
Professional/Enthusiasts
Gear Heads and Gear Ratios
Hurricane Dennis & Failed Math Models
Solving Systems of Equations, Oceans & Climate
Determining Strengths of Shark Models based on Scatterplots and Regression
Expert
Problem Solving with Project Constraints
Using Mathematics to Optimize Wing Design
Division of Academics - Department of Mathematics
Topic V Second Nine Weeks
Page 9 of 18
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
MATHEMATICS FLORIDA STANDARDS
MATHEMATICAL PRACTICES
DESCRIPTION
MAFS.K12.MP.1
Make sense of problems and
persevere in solving them.
MAFS.K12.MP.2
Reason abstractly and
quantitatively.
MAFS.K12.MP.3
Construct viable arguments
and critique the reasoning of
others.
MAFS.K12.MP.4
Model with mathematics.
Mathematically proficient students will be able to:
Explain the meaning of a problem and looking for entry points to its solution.
Analyze givens, constraints, relationships, and goals.
Make conjectures about the form and meaning of the solution and plan a solution pathway.
Consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution.
Monitor and evaluate their progress and change course if necessary.
Explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search
for regularity or trends.
 Check answers to problems using a different method, and continually ask, “Does this make sense?”
 Identify correspondences between different approaches.











Mathematically proficient students will be able to:
Make sense of quantities and their relationships in problem situations.
Decontextualize—to abstract a given situation and represent it symbolically.
Contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols
Create a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them.
Know and be flexible using different properties of operations and objects.
Mathematically proficient students will be able to:
Understand and use stated assumptions, definitions, and previously established results in constructing arguments.
Make conjectures and build a logical progression of statements to explore the truth of their conjectures.
Analyze situations by breaking them into cases, and can recognize and use counterexamples.
Justify their conclusions, communicate them to others, and respond to the arguments of others.
Reason inductively about data, making plausible arguments that take into account the context from which the data arose.
Compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain
what it is.
 Determine domains to which an argument applies.












Mathematically proficient students will be able to:
Apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.
Use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another.
Apply what they know and feel comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later.
Identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas.
Analyze relationships mathematically to draw conclusions.
Interpret mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its
purpose.
Division of Academics - Department of Mathematics
Topic V Second Nine Weeks
Page 10 of 18
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
MATHEMATICS FLORIDA STANDARDS
MATHEMATICAL PRACTICES
DESCRIPTION
MAFS.K12.MP.5
Use appropriate tools
strategically.
MAFS.K12.MP.6
Attend to precision.
MAFS.K12.MP.7
Look for and make use
of structure.
MAFS.K12.MP.8
Look for and express
regularity in repeated
reasoning.
Mathematically proficient students will be able to:
 Consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a
spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software.
 Make sound decisions about when each of the tools appropriate for their grade or course might be helpful, recognizing both the insight to be gained and their




limitations. Example: High school students analyze graphs of functions and solutions using a graphing calculator.
Detect possible errors by strategically using estimation and other mathematical knowledge.
Know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data.
Identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems.
Use technological tools to explore and deepen their understanding of concepts
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
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Mathematically proficient students will be able to:
Communicate precisely to others.
Use clear definitions in discussion with others and in their own reasoning.
State the meaning of the symbols they choose, including using the equal sign consistently and appropriately.
Be careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem.
Calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context.
Mathematically proficient students will be able to:
 Discern a pattern or structure. Example: In the expression x2 + 9x + 14, students can see the 14 as 2 × 7 and the 9 as 2 + 7.
 Recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. Step back for an overview
and shift perspective.
 See complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. Example: They can see 5 – 3(x – y)2 as 5
minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y.
Mathematically proficient students will be able to:
 Notice if calculations are repeated, and look both for general methods and for shortcuts. Example: Noticing the regularity in the way terms cancel when expanding (x1)(x+1),(x-1)(x2+x+1),and(x-1)(x3 +x2+x+1)might lead them to the general formula for the sum of a geometric series.
 Maintain oversight of the process, while attending to the details as they work to solve a problem.
 Continually evaluate the reasonableness of their intermediate results.
Division of Academics - Department of Mathematics
Topic V Second Nine Weeks
Page 11 of 18
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
Domain: CREATING EQUATIONS
STANDARD CODE
STANDARD DESCRIPTION
Cluster 1: Create equations that describe numbers or relationships
Create
two
or more
to represent relationships between quantities; graph equations on coordinate axes with labels and
Understand solving equations as a process
of equations
reasoning in
and
explain
thevariables
reasoning
scales.
Context Complexity: Level 2: Basic Applications of Skills and Concepts
MAFS.912.A-CED.1.2
Assessed
Level 2
writes or chooses a system of linear
equations with integral coefficients for a
real-world context or writes a single
equation for a real-world context that
has at least three variables with integral
coefficients
Level 3
Level 4
Level 5
writes or chooses a system of two equations writes a system of three equations for employs the modeling cycle when
with rational coefficients, where one equation a real-world context.
writing equations that have at least
can be a simple quadratic equation for a realtwo variables.
world context; writes a single equation that
has at least three variables with rational
coefficients for a real-world context; identifies
the meaning of the variables
Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable
options in a modeling context.
Context Complexity: Level 3: Strategic Thinking
MAFS.912.A-CED.1.3
(Assessed with MAFS.912.ACED.1.2)
Level 2
Level 3
Level 4
identifies variables; writes constraints
models constraints using a combination of
explain why a solution is viable or
as a system of linear inequalities or
equations, inequalities, systems of equations, nonviable for a real-world context
linear equations for a real-world context systems of inequalities for a real-world
context; interprets solutions as viable or
nonviable based on the context
Level 5
employs the modeling cycle when
writing constraints
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR
to highlight resistance R.
MAFS.912.A-CED.1.4
(Assessed with MAFS.912.ACED.1.1)
Context Complexity: Level 1: Recall
Level 2
Level 3
solves a literal linear equation in a real- solves a literal equation that requires three
world context that requires two
procedural steps.
procedural steps
Division of Academics - Department of Mathematics
Topic V Second Nine Weeks
Level 4
solves a literal equation that requires
four or five procedural steps.
Level 5
solves a literal equation that requires
six procedural steps.
Page 12 of 18
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
Domain: ALGEBRA: REASONING WITH EQUATIONS & INEQUALITIES
STANDARD CODE
STANDARD DESCRIPTION
Cluster 1: Understand solving equations as a process of reasoning and explain the reasoning
Understand solving equations as a process of reasoning and explain the reasoning
Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the
assumption
that the
original
equation
has a solution. Construct a viable argument to justify a solution method.
Understand solving equations as a process
of reasoning
and
explain
the reasoning
Context Complexity: Level 3: Strategic Thinking & Complex Reasoning
MAFS.912.A-REI.1.1
Assessed
Level 2
chooses the correct justifications for the
steps in solving a simple quadratic
equation, where a = 1, containing integer
coefficients
Level 3
Level 4
chooses the correct justifications for the justifies the steps in solving a quadratic
steps in solving a quadratic equation,
equation with complex solutions
where a does not equal 1,
containing rational coefficients
Level 5
constructs a viable argument to justify
the steps in solving radical, rational,
and exponential equations (with
bases 2, 10, or e)
Cluster 2: Solve equations and inequalities in one variable
Solve quadratic equations in one variable.
Context Complexity: Level 2: Basic Application of Skills & Concepts
MAFS.912.A-REI.2.4
(Assessed with MAFS.912.NCN.3.7)
Level 2
Level 3
solves quadratic equations of the form ax2 solves quadratic equations of the form
+ bx + c = d with integral coefficients
ax2 + bx + c = d with integral
coefficients, where b/a is an integer
Level 4
solves quadratic equations of the form
ax2 + bx + c = d with rational
coefficients
Level 5
[intentionally left blank]
Cluster 3: Solve systems of equations
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Context Complexity: Level 1: Recall
MAFS.912.A-REI.3.6
(Assessed with MAFS.912.ACED.1.2)
Level 2
explains whether a system of equations
has one, infinitely many, or no solutions;
solves a system of equations by graphing
or substitution (manipulation of equations
may be required) or elimination in the form
of ax+ by = c and dx + ey = f, where
multiplication is required for both
equations
Division of Academics - Department of Mathematics
Topic V Second Nine Weeks
Level 3
Level 4
solves a system that consists of linear [intentionally left blank]
equations in two variables with rational
coefficients by graphing, substitution, or
elimination; interprets solutions in a
real- world context or mathematical
context
Level 5
[intentionally left blank]
Page 13 of 18
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
Domain: ALGEBRA: REASONING WITH EQUATIONS & INEQUALITIES
STANDARD CODE
STANDARD DESCRIPTION
Cluster 3: Solve systems of equations
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the
points of intersection between the line y = –3x and the circle x² + y² = 3.
Context Complexity: Level 2: Basic Application of Skills & Concepts
Level 2
MAFS.912.A-REI.3.7
(Assessed with MAFS.912.ACED.1.2)
Level 3
solves a simple system consisting of a
solves a simple system consisting of a
linear equation and a quadratic equation in linear equation, where the slope and
two variables, when given a graph
the y- intercept are integers and a
univariate quadratic with integral
coefficients by graphing; solves a
simple system, consisting of a linear
equation of the form y = kx and a circle
centered at (0, 0) by graphing and
algebraically; solves a simple system
consisting of a linear equation of the
form y = kx and a univariate quadratic
algebraically
Level 4
solves a simple system consisting of a
linear equation, where the slope and
the y- intercept are rational numbers
and a univariate quadratic with rational
coefficients by graphing; solves a
simple system, consisting of a linear
equation and a circle by graphing and
algebraically; solves a simple system
consisting of a linear equation of the
form Ax + By = C, where A, B, and C
are integers and a bivariate quadratic
algebraically
Level 5
solves a simple system consisting of
a linear equation and a bivariate
quadratic algebraically and
graphically
Cluster 4: Represent and solve equations and inequalities graphically
Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) =
g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations.
Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions
Context Complexity: Level 2: Basic Application of Skills & Concepts
MAFS.912.A-REI.4.11
Assessed
Level 2
determines an integral solution or
approximate solution using successive
approximations for f(x) = g(x) given a
graph or table of linear, quadratic, or
exponential functions
Division of Academics - Department of Mathematics
Topic V Second Nine Weeks
Level 3
determines a solution or an
approximate solution for f(x) = g(x)
using a graph, table of values, or
successive approximations, where f(x)
and g(x) are an exponential with a
rational exponent, polynomial degree
greater than two, rational, absolute
value, and logarithmic
Level 4
completes an explanation on how to
find a solution for f(x) = g(x)
Level 5
employs the modeling cycle when
validating that the intersection of two
functions is a solution to f(x) = g(x)
Page 14 of 18
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
Domain: FUNCTIONS: INTERPRETING FUNCTIONS
STANDARD CODE
STANDARD DESCRIPTION
Cluster 3: Analyze functions using different representations
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
a.
Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the
graph, and interpret these in terms of a context.
Understand solving equations as a process of reasoning and explain the reasoning
b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in
functions such as y =
,y=
,y=
,y=
, and classify them as representing exponential growth or decay
Context Complexity: Level 2: Basic Applications of Skills and Concepts
MAFS.912.F-IF.3.8
Assessed
Level 2
factors difference of two squares with a
degree of 2, and trinomials with a degree
of 2 whose leading coefficent has up to 4
factors and interprets the zeros; completes
the square when the leading coefficent is 1;
interprets the extreme values.
Level 3
Level 4
interprets key features of quadratics by interprets symmetry of a quadratic
factoring or completing the square.
function written symbolically for a realworld context.
Level 5
[intentionally left blank]
Domain: GEOMETRY: EXPRESSING GEOMETRIC PROPERTIES WITH EQUATIONS
STANDARD CODE
STANDARD DESCRIPTION
Cluster 1: Translate between the geometric description and the equation for a conic section
Derive
equation
of explain
a parabola
given a focus and directrix.
Understand solving equations as a process
of the
reasoning
and
the reasoning
Context Complexity: Level 2: Basic Applications of Skills and Concepts
MAFS.912.G-GPE.1.2
Assessed
Level 2
[intentionally left blank]
Division of Academics - Department of Mathematics
Topic V Second Nine Weeks
Level 3
derives the equation of a parabola
given a focus and directrix, parallel to
the y-axis, on the coordinate grid
Level 4
derives the equation of a parabola
given a focus and directrix, parallel to
the y-axis with an integral value
Level 5
derives the equation of a parabola
given a focus and directrix
Page 15 of 18
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
Domain: NUMBER & QUANTITY: THE COMPLEX NUMBER SYSTEM
STANDARD CODE
STANDARD DESCRIPTION
Cluster 1: Perform arithmetic operations with complex numbers.
Knowofthere
is a complex
number
such that i² = –1, and every complex number has the form a + bi with a and b real
Understand solving equations as a process
reasoning
and explain
the ireasoning
Context Complexity: Level 1: Recall
MAFS.912.N-CN.1.1
(Assessed with MAFS.912.N-CN.1.2)
Level 2
Level 3
recognizes that a negative square root is not converts simple “perfect” squares to
a real number
complex number form (bi), such as the
square root of -25 is 5i
Level 4
assimilates that there is a complex
number i such that i2
= -1, and identifies the proper a + bi
form (with a and b real)
Level 5
generalizes or develops a rule that
explains complex numbers and their
properties
Use the relation i² = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
Context Complexity: Level 2: Basic Applications of Skills and Concepts
Level 2
MAFS.912.N-CN.1.2
Assessed
adds, subtracts, or multiplies simple
complex numbers, with up to two steps
Level 3
Level 4
uses the commutative, associative, or
evaluates sums or products of complex
distributive properties to identify
numbers for multistep problems
products or sums of complex numbers,
with up to three steps
Level 5
generalizes rules for abstract
problems, such as explaining what
type of expression results, when
given (a + bi)(c + di)
Cluster 3: Use complex numbers in polynomial identities and equations.
Solveofquadratic
equations
withthe
realreasoning
coefficients that have complex solutions.
Understand solving equations as a process
reasoning
and explain
Context Complexity: Level 1: Recall
MAFS.912.N-CN.3.7
Assessed
Level 2
solves quadratic equations of the form ax2
+ b = c, where c- b is a negative integer
Division of Academics - Department of Mathematics
Topic V Second Nine Weeks
Level 3
solves quadratic equations where the
discriminant is a negative perfect
square
Level 4
solves quadratic equations (with any
real coefficients) that have complex
solutions
Level 5
[intentionally left blank]
Page 16 of 18
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
TECHNOLOGY TOOLS
CPALM RESOURCES
LESSON PLANS
Ranking Sports Players (Quadratic Equations Practice)
Where did the answers go? Oh, they're imaginary!
Selling Fuel Oil at a Loss
The Quadratic Quandary
TUTORIAL
MAFS.912.N-CN.1.2
Adding Complex Numbers
How to Subtract Complex Numbers
Multiplying Complex Numbers
MAFS.912.A-REI.2.4
Learning How to Complete the Square
Solving Quadratic Equations by Square Roots
Solving Quadratic Equations Using the Quadratic Formula
VIRTUAL MANIPULATIVE
Fractal Tool
Equation Grapher
PROBLEM-SOLVING TASK
Two Squares Are Equal
A Linear and Quadratic System
The Circle and The Line
GRAPHING CALCULATOR CORRELATION
TEXAS INSTRUMENT MATH ACTIVITY TITLE
Solving Systems involving Quadratic Equations: Systems of Conics
Quadratic Equations
Graphing Quadratic Equations
Investigating the Graphs of Quadratic Equations
Division of Academics - Department of Mathematics
Topic V Second Nine Weeks
Page 17 of 18
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
GIZMOS CORRELATION
GIZMO TITLE
Roots of a Quadratic
Points in the Complex Plane
2
Modeling the Factorization of ax +bx+c
TOPIC V
VIDEO TITLE
DISCOVERY EDUCATION CORRELATION
Quadratic Equations: Fire in the Sky
Applications of Quadratic Equations
Types of Numbers
Solving Systems of Quadratic Equations
MATH EXPLANATION TITLE
The Quadratic Formula
Working with Imaginary Numbers
MATH OVERVIEW
Solving a System of Two Conics
Division of Academics - Department of Mathematics
Topic V Second Nine Weeks
Page 18 of 18