Download Topic 7 - Miami-Dade County Public Schools

MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
Topic VII: Rational Functions, Expressions, and Equations
MATHEMATICS FLORIDA STATE STANDARDS (MAFS) &
MATHEMATICAL PRACTICES (MP)
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)
MAFS.912.A-REI.1.2: Solve simple rational and radical equations in one
variable, and give examples showing how extraneous solutions may arise.
(MP.1, MP.2, MP.3, MP.7) Assessed with A-CED.1.1
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) Assessed with A-CED.1.2
MAFS.912.F-BF.2.3: Identify the effect on the graph of replacing f(x) by
f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and
negative); find the value of k given the graphs. Experiment with cases and
illustrate an explanation of the effects on the graph using technology.
(MP.2, MP.4, MP.5, MP.6)
MAFS.912.F-IF.3.7d: Graph functions expressed symbolically and show
key features of the graph, by hand in simple cases and using technology
for more complicated cases.
d. Graph rational functions, identifying zeros and asymptotes when
suitable factorizations are available, and showing end behavior.
(MP.5, MP.6, MP 7) Assessed with F-IF.3.8
Pacing
Date(s)
Traditional
10
Block
5
Topic VII Assessment Window
01/24/17 – 02/06/17
01/24/17 – 02/06/17
01/30/17 - 02/06/17
ESSENTIAL CONTENT
A. Rational Functions
1. Graphing Simple Rational
Functions
2. Graphing More Complicated
Rational Functions
B. Rational Expressions and
Equations
1. Adding and Subtracting
Rational Expressions
2. Multiplying and Dividing
Rational Expressions
3. Solving Rational Equations
OBJECTIVES (from Item Specifications)
I can:
•
•
•
•
•
•
•
•
•
•
•
•
•
•
MAFS.912.A-APR.4.6: Rewrite simple rational expressions in different
forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x),
and r(x) are polynomials with the degree of r(x) less than the degree of
b(x), using inspection, long division, or, for the more complicated
examples, a computer algebra system. (MP.2, MP.5, MP.7, MP.8) *NO
CALCULATOR*
•
•
MAFS.912.A-APR.4.7: Understand that rational expressions form a
system analogous to the rational numbers, closed under addition,
subtraction, multiplication, and division by a nonzero rational expression;
add, subtract, multiply, and divide rational expressions. NOT Assessed.
•
Division of Academics - Department of Mathematics
Topic VII Third Nine Weeks
Complete an algebraic proof to explain steps for solving a
simple equation.
Construct a viable argument to justify a solution method.
Write and solve an equation that represents a real-world
context in one variable.
Solve a rational equation in one variable.
Justify algebraically why a solution is extraneous.
Write constraints for a real-world context using equations,
inequalities, a system of equations, or a system of
inequalities.
Determine the value of k when given a graph of the
function and its transformation.
Identify differences and similarities between a function
and its transformation.
Identify a graph of a function given a graph or a table of a
transformation and the type of transformation that is
represented.
Graph by applying a given transformation to a function.
Identify ordered pairs of a transformed graph.
complete a table for a transformed function
Recognize even and odd functions from their graphs and
equations.
Identify intercepts, asymptotes, and end behavior of a
rational function.
Graph a function using key features.
Identify and interpret key features of a graph within the
real-world context that the function represents.
Note: For F-IF.3.7d, the asymptotes of rational functions
are limited to no more than two vertical asymptotes and
no more than one horizontal asymptote.
Rewrite a rational expression as the quotient in the form of
a polynomial added to the remainder divided by the
divisor.
Page 1 of 15
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
Traditional
10
Block
5
Topic VII Assessment Window
Date(s)
01/24/17 – 02/06/17
01/24/17 – 02/06/17
01/30/17 - 02/06/17
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
Homework
STANDARDS
PMT Preferences: Auto-assign for intervention and enrichment: YES
Standard-Based Intervention
Course Intervention
Daily Intervention
MODULES
TEACHER NOTES
MAFS.912.A-REI.1.1
MAFS.912.A-REI.1.2
Module 8
MAFS.912.A-APR.4.6
Module 9
MAFS.912.A-APR.4.7
MAFS.912.A-CED.1.3★
Algebra 2 Honors Block Schedule – Suggested Pace
Day 1
Day 2
Day 3
Day 4
Day 5
8.1-8.2
9.1
9.2
9.3
Topic Test
MAFS.912.F-BF.2.3
MAFS.912.F-IF.3.7d★
Topic VII Assessment: Rational Functions, Expressions, and Equations
Division of Academics - Department of Mathematics
Topic VII Third Nine Weeks
Page 2 of 15
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%
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: Asymptote, constant of variation, parent function, rational function, closure, extraneous solutions, rational expression, reciprocal.
Algebra 2 – Algebra 2 Honors
REPORTING CATEGORY PRACTICE ITEMS
1. As a new element is heated, its temperature can be modeled with the function (𝑥𝑥) = √100𝑥𝑥 2 − 80𝑥𝑥 + 3500 , where 𝑥𝑥 represents the time in minutes and from when the element is
placed on top of a Bunsen burner, and 𝑇𝑇(𝑥𝑥) is the temperature, in degrees Celsius. When will the temperature be 100°C?
2. On Sally’s last quiz, she solved the following equation and found two solutions. When the quiz was scored and returned to her, she noticed that she did not receive full credit for
the problem. Explain why Sally’s answer is incorrect.
9x + 10 = x
( 9x + 10 ) = (x )
2
2
9x + 10 = x 2
x 2 − 9x − 10 = 0
(x − 10)(x + 1)= 0
x = 10, x = −1
Division of Academics - Department of Mathematics
Topic VII Third Nine Weeks
Page 3 of 15
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
INSTRUCTIONAL TOOLS
REPORTING CATEGORY PRACTICE ITEMS
3. Determine all the restriction of the following equation. Then solve.
(𝑥𝑥 − 1)
(𝑥𝑥 − 1)
�
�÷� 2
� = 17
(𝑥𝑥 − 5)
(𝑥𝑥 − 7𝑥𝑥 + 10)
4.
Working alone Kyle can clean his room in 15 minutes. Ally can clean the same room in 11 minutes. If they worked together, how long would it take them to clean the room? In
order to answer this, write a rational equation that models the situation and round your answer to the nearest thousandth.
5.
The function ℎ(𝑥𝑥) =
A.
B.
C.
D.
6.
4𝑥𝑥 2 − 1
has which of the following discontinuities?
Vertical asymptotes at 𝑥𝑥 = ±
1
2
Removable discontinuity at 𝑥𝑥 = ±
1
1
2
Vertical asymptote at 𝑥𝑥 = ; removable discontinuity at 𝑥𝑥 = −
2
1
Vertical asymptote at 𝑥𝑥 = − ; removable discontinuity at 𝑥𝑥 =
2
1
2
1
2
Which expression is equivalent to the following expression if no denominators equal zero?
A.
B.
C.
D.
7.
4𝑥𝑥 2 − 3𝑥𝑥 − 1
−
−
11 − 𝑤𝑤
30𝑤𝑤 2
𝑤𝑤 − 11
5𝑤𝑤 6
𝑤𝑤 4
6
6
𝑤𝑤 3
𝑤𝑤 3
6
6
𝑤𝑤 4
What are the apparent roots of the equation graphed on the coordinate grid?
3𝑥𝑥 − 4
3
=
2
𝑥𝑥
2𝑥𝑥
8
A. � �
3
8
B. � �
9
−2
C. �
3
−2
D. �
3
, 2�
2
, �
3
Division of Academics - Department of Mathematics
Topic VII Third Nine Weeks
Page 4 of 15
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
INSTRUCTIONAL TOOLS
REPORTING CATEGORY PRACTICE ITEMS
8.
The teacher assistant can grade homework papers by herself in 1 hour. If the teacher helps, the grading can be completed in 20 minutes. How long would it take the teacher to
grade the papers working alone?
9.
Graph the following rational function and determine each of the following characteristics of the graph. 𝑓𝑓(𝑥𝑥) =
2𝑥𝑥 2 +10𝑥𝑥+12
𝑥𝑥 2 +3𝑥𝑥+2
𝑥𝑥 −intercepts: _______________________
𝑦𝑦 −intercepts: _______________________
vertical asymptotes: __________________
horizontal asymptotes: ________________
10. Jim can paint a house in 25 hours. Alex can paint the same house in 20 hours.
Write an equation that can be used to find the time in hours, t, it would take Jim and Alex to paint the house together assuming they both work at the rates they work when working
alone.
11. What value of t makes the equation
2
𝑡𝑡+3
1
= true?
2
12. Select whether each equation has no real solutions, one real solution, or infinitely many real solutions.
No Real Solutions
−2𝑥𝑥 2 −
One Real Solution
Infinitely Many Real
Solutions
3
=0
𝑥𝑥
3
3
=
𝑥𝑥 𝑥𝑥 + 20
𝑥𝑥 2𝑥𝑥 + 10
=
−1
5
10
Division of Academics - Department of Mathematics
Topic VII Third Nine Weeks
Page 5 of 15
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
INSTRUCTIONAL TOOLS
REPORTING CATEGORY PRACTICE ITEMS
1
3
13. Beth is solving this equation: + 3 = .
𝑥𝑥
𝑥𝑥
2
She says, “I can multiply both sides by x and get the linear equation 1 + 3𝑥𝑥 = 3, whose solution is 𝑥𝑥 =
3
Which of the following statements makes this a correct argument?
A. All rational equations can be multiplied by 𝑥𝑥 to get a linear equation.
B. After multiplying both sides by 𝑥𝑥 you need to subtract 1 from both sides.
C. You cannot multiply both sides by 𝑥𝑥 because you do not know what 𝑥𝑥 is.
D. The equation is not linear, so you cannot use the methods normally used for solving linear equations.
14. Select all correct solutions of
𝑥𝑥+2
𝑥𝑥+5
=
2
.
𝑥𝑥−1
-5
-4
-3
1
3
4
𝑥𝑥+3
15. Select All the values that are NOT included in the domain of the function: 𝑔𝑔(𝑥𝑥) = (𝑥𝑥−2)(𝑥𝑥−5).
-5
-3
-2
2
3
5
16. Select All the asymptotes of the function 𝑝𝑝(𝑥𝑥) =
𝑥𝑥+1
𝑥𝑥 2 −4𝑥𝑥−5
+ 2.
𝑥𝑥 = 2
𝑦𝑦 = 2
𝑥𝑥 = 4.5
𝑦𝑦 = 4.5
𝑥𝑥 = 5
𝑦𝑦 = 5
17. The $1000 prize for a lottery is to be divided evenly among the winners. Initially there are 𝑥𝑥 winners, but then one more winner comes forward, causing each winner to receive $50
less. Create an equation that represents the situation and can be used to solve for 𝑥𝑥, the initial number of winners. Find the number of initial winners.
18. An excursion party had $2.00 to pay in total, but before the bill was paid 10 people from the party went away, and those that remained had each to pay 10 cents more. Write an
equation that can be used to find how many were in the party at first.
Division of Academics - Department of Mathematics
Topic VII Third Nine Weeks
Page 6 of 15
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
INSTRUCTIONAL TOOLS
REPORTING CATEGORY PRACTICE ITEMS
19. For the function below, select all of the following that are true:
The function has vertical asymptotes at 𝑥𝑥 = 3 and 𝑥𝑥 = 4
The function has a vertical asymptote only at 𝑥𝑥 = 3
The function has a hole at 𝑥𝑥 = 4
The function has a horizontal asymptote at 𝑦𝑦 = 0
The function’s domain is all real numbers.
𝑓𝑓(𝑥𝑥) =
𝑥𝑥 2 − 𝑥𝑥 − 12
𝑥𝑥 2 − 7𝑥𝑥 + 12
20. A rational function has a hole at 𝑥𝑥 = 2, a vertical asymptote at 𝑥𝑥 = −4 and a horizontal asymptote at 𝑦𝑦 = 3. Which of the following could be the function? Select all that apply.
𝑦𝑦 =
𝑦𝑦 =
𝑦𝑦 =
𝑦𝑦 =
𝑦𝑦 =
3𝑥𝑥(𝑥𝑥−2)
(𝑥𝑥−2)(𝑥𝑥+4)
𝑥𝑥 3 −2𝑥𝑥 2
𝑥𝑥 2 +2𝑥𝑥−8
3𝑥𝑥
𝑥𝑥 2 +2𝑥𝑥−8
𝑥𝑥−2
(𝑥𝑥−2)(𝑥𝑥+4)
3𝑥𝑥 2 −3𝑥𝑥−6
𝑥𝑥 2 +2𝑥𝑥−8
+3
21. What are the restrictions of this graph?
Division of Academics - Department of Mathematics
Topic VII Third Nine Weeks
Page 7 of 15
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
INSTRUCTIONAL TOOLS
STEM Lessons - Model Eliciting Activity
STEM Lessons
Looking for the best Employment Option: Technology. Mathematics
Sticks and Stones May Break My Bones: Science, Mathematics, Technology
Preserving Our Marine Ecosystems: Science, Mathematics, Technology
Alternative Fuel Systems: Science, Mathematics, Technology, Engineering
Efficient Storage: Mathematics, Technology,
CPALMS Perspectives Videos
Professional/Enthusiasts
Asymptotic Behavior in Shark Growth Research
Expert
Problem Solving with Project Constraints
Division of Academics - Department of Mathematics
Topic VII Third Nine Weeks
Page 8 of 15
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 VII Third Nine Weeks
Page 9 of 15
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
•
•
•
•
•
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 VII Third Nine Weeks
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MIAMI-DADE COUNTY PUBLIC SCHOOLS
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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
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.
MAFS.912.A-REI.1.1
Assessed
Content Complexity Rating: Level 3: Strategic Thinking and Complex Reasoning
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 steps
in solving a quadratic equation, where a does
not equal 1, containing rational coefficients
justifies the steps in solving a quadratic
equation with complex solutions
Level 5
constructs a viable argument to justify
the steps in solving radical, rational, and
exponential equations (with bases 2, 10,
or e)
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
Content Complexity Rating: Level 3: Strategic Thinking and Complex Reasoning
MAFS.912.A-REI.1.2
Assessed
Level 2
solves radical equations of the form
�(𝑘𝑘𝑘𝑘) = 𝑐𝑐 ; solves rational equations
1
= 𝑐𝑐.
of the form
(𝑘𝑘𝑘𝑘)
Level 3
Level 4
determines if a given solution is extraneous;
solves radical equations of the form
solves radical equations of the form
�(𝑘𝑘𝑘𝑘 + 𝑎𝑎) = �(𝑗𝑗𝑗𝑗 + 𝑏𝑏); solves rational
�(𝑘𝑘𝑘𝑘 + 𝑎𝑎) = 𝑏𝑏; solves rational equations of the equations of the form 𝑐𝑐 = 𝑑𝑑 ;
𝑐𝑐
(𝑘𝑘𝑘𝑘+𝑎𝑎)
(𝑗𝑗𝑗𝑗+𝑏𝑏)
form
= 𝑏𝑏.
(𝑘𝑘𝑘𝑘+𝑎𝑎)
eliminates extraneous solutions from the
solution set
Level 5
solves radical equations of the form
�(𝑘𝑘𝑘𝑘 + 𝑎𝑎) = 𝑗𝑗𝑗𝑗 + 𝑏𝑏, �(ℎ𝑥𝑥 2 + 𝑘𝑘𝑘𝑘 + 𝑎𝑎) =
𝑗𝑗𝑗𝑗 + 𝑏𝑏,, or �(ℎ𝑥𝑥 2 + 𝑘𝑘𝑘𝑘 + 𝑎𝑎) =
�𝑔𝑔𝑥𝑥 2 (𝑗𝑗𝑗𝑗 + 𝑏𝑏); solves rational equations
𝑐𝑐
𝑑𝑑
of the form (𝑘𝑘𝑘𝑘+𝑎𝑎) + 𝑤𝑤 = (𝑗𝑗𝑗𝑗+𝑏𝑏) + 𝑣𝑣;
justifies algebraically why a solution is
extraneous
Domain: Algebra: Creating Equations
STANDARD CODE
STANDARD DESCRIPTION
Cluster 1: Create equations that describe numbers or relationships
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 foods.
Content Complexity Rating: Level 3: Strategic Thinking and Complex Reasoning
MAFS.912.A-CED.1.3
Assessed
Level 2
identifies variables; writes constraints
as a system of linear inequalities or
linear equations for a real-world
context
Level 3
Level 4
Level 5
models constraints using a combination of
explain why a solution is viable or nonviable employs the modeling cycle when writing
equations, inequalities, systems of equations, for a real-world context
constraints
systems of inequalities for a real-world context;
interprets solutions as viable or nonviable
based on the context
Division of Academics - Department of Mathematics
Topic VII Third Nine Weeks
Page 11 of 15
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
Domain: Algebra: Arithmetic with Polynomials & Rational Expressions
STANDARD CODE
STANDARD DESCRIPTION
Cluster 4: Rewrite rational expressions
Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the
degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
Content Complexity Rating: Level 2: Basic Application of Skills and Concept
MAFS.912.A-APR.4.6
Assessed
MAFS.912.A-APR.4.7
NOT Assessed
Level 2
Level 3
Level 4
rewrites rational expressions, a(x)/b(x),
where a(x) is a univariate cubic with
integral coefficients and b(x) is a
univariate monomial with an integral
coefficient
rewrites rational expressions, a(x)/b(x), where
a(x) is a univariate cubic or quartic with integral
coefficients and b(x) is a univariate binomial
with an natural number coefficient and the
remainder is a constant; rewrites rational
expressions, a(x)/b(x), where a(x) is a
multivariate of a degree no greater than 8 and
b(x) can be multivariate monomial with a
degree no greater than 4
rewrites rational expressions, a(x)/b(x),
where a(x) is a univariate with a degree no
greater than 5 and b(x) is a univariate
binomial or trinomial with a degree no
greater than 2; rewrites rational expressions,
a(x)/b(x), where a(x) is a multivariate of a
degree no greater than 10 and b(x) can be a
factorable multivariate binomial with a
degree no greater than 6
Level 5
rewrites rational expressions, a(x)/b(x),
where a(x) is a univariate with a degree
no greater than 6 with integral
coefficients and b(x) is a univariate
binomial or trinomial with a degree no
greater than 3
Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational
expression; add, subtract, multiply, and divide rational expressions.
Content Complexity Rating: Level 2: Basic Application of Skills and Concept
Domain: Functions: Building Functions
STANDARD CODE
STANDARD DESCRIPTION
Cluster 2: Build new functions from existing functions
Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k
given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd
functions from their graphs and algebraic expressions for them.
Content Complexity Rating: Level 2: Basic Application of Skills and Concept
MAFS.912.F-BF.2.3
Assessed
Level 2
identifies the graph of a linear or
quadratic function with a vertical or
horizontal stretch or shrink; determines
the value of k given a graph and its
transformation; completes a table of
values for a function that has a vertical
or horizontal shift; graphs a function
with a vertical or horizontal shift
Level 3
Level 4
identifies the graph of an exponential function identifies differences and similarities
or radical function with at least two
between a function and its transformations
transformations; completes a table of values
for a function with at least two transformations;
recognizes even and odd functions given a
graph or equation; determines the value of k
when given a set of ordered pairs for two
functions or a table of values for two functions
Division of Academics - Department of Mathematics
Topic VII Third Nine Weeks
Level 5
justifies a transformation that has been
applied to a function, not limited to
linear, quadratic, exponential, or square
root
Page 12 of 15
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
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
4. Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.
Content Complexity Rating: Level 2: Basic Application of Skills and Concept
MAFS.912.F-IF.3.7d
Assessed
Level 2
Level 3
identifies the graph of a linear,
quadratic, or exponential function given
its equation; constructs the graph of a
linear or quadratic function given its
equation; constructs linear function
using x- and y-intercepts
constructs the graph of an exponential,
logarithmic, absolute value, polynomial, square
root, or cube root function given its equation;
constructs the graph of a quadratic function
given key features
Division of Academics - Department of Mathematics
Topic VII Third Nine Weeks
Level 4
constructs the graph of an exponential or
logarithmic function given key features;
constructs the graph of a rational function
given the equation
Level 5
constructs a graph of a piece- wise or
rational function given key features
Page 13 of 15
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
TECHNOLOGY TOOLS
CPALM RESOURCES
LESSON PLANS
Justly Justifying
A Rational Representation
Preserving Our Marine Ecosystems
Exploring Systems with Piggies, Pizzas and Phones
Predicting Your Financial Future
VIRTUAL MANIPULATIVE
Data Flyer
PROBLEM-SOLVING TASK
How does the solution change?
Radical Equations
Combined Fuel Efficiency
Dimes and Quarters
TUTORIAL
Solving Radical Equations
Simplifying Square Roots Containing Variables
GRAPHING CALCULATOR CORRELATION
TEXAS INSTRUMENT MATH ACTIVITY TITLE
Roots of Radical Equations
Asymptotes & Zeros
Families of Functions
Quadratic Functions and Stopping Distance
Asymptotes and Zeros of Rational Functions
GIZMOS CORRELATION
GIZMO TITLE
Modeling and Solving Two-Step Equations
Radical Functions
Linear Programming
Division of Academics - Department of Mathematics
Topic VII Third Nine Weeks
Page 14 of 15
MIAMI-DADE COUNTY PUBLIC SCHOOLS
District Pacing Guide
ALGEBRA 2 HONORS
Course Code: 120034001
GIZMOS CORRELATION
GIZMO TITLE
Exponential Functions
General Form of a Rational Function
TOPIC VII
VIDEO TITLE
DISCOVERY EDUCATION CORRELATION
The Power of Algebra: Polynomials and Equations
Algebra II: Solving Rational Equations and Inequalities
Converting from Fahrenheit to Celsius
Composite Functions -- Barbeque
MATH EXPLANATION TITLE
Algebra II: Finding All the Zeros
MATH OVERVIEW
Algebra II: Real Numbers and Their Number Operations
Algebra II: Graphing Square and Cube Root Functions
Division of Academics - Department of Mathematics
Topic VII Third Nine Weeks
Page 15 of 15