Post on 22-Dec-2021
transcript
Big Idea: Shapes Quadratics and
Conics
Enduring Understandings Essential Questions
The quadratic formula can be used to solve any quadratic equation.
The zero product property can be used to solve some quadratic equations.
The Fundamental Theorem of Algebra can be used to determine the number of
solutions to a polynomial.
Use technology to find the maximum and minimum of a quadratic function.
Completing the square can be used to solve a quadratic equation and put an
equation of a conic in standard form.
All parts of conic sections can be used to graph those conic sections.
What are the similarities and differences of imaginary and complex numbers?
From the given equation, how can you tell which conic section is represented?
What are the different ways to solve a quadratic equation?
What are the parts (foci, vertices, directrix, etc.) of each conic section?
How do you derive the quadratic formula?
Where would the application of a quadratic equation be used in real life?
CC/Learning Targets Core Vocabulary Links to Technology N.CN.1 N.CN.2 N.CN.7 N.CN.8 N.CN.9 A.SSE.1b A.SSE.2
A.APR.3 A.REI.11 F.IF.4 A2.3.2b A2.41a-d,f A2.4.2 A2.10.1
maximum/minimum imaginary/complex numbers Zero-Product Property foci
- Baseball - iFactor (app) - MathRefFree (app) - AlgebraGenie (app) - KhanAcademy (app) - FreeGraphingCalculator (app)
Bundle Performance Task(s) Our goal for this project will be to determine which method, changing the angle or changing the velocity, of your baseball throw makes hitting a target easier. When is a target impossible to hit? We will discover how the angle of a bat influences the distance that a ball travels among other exciting things. See the above link for more information!! The students will make a video to present their findings to the class. **If/when opening the pdf file, it may say that the file could conatin a virus etc. Ignore the warning and click “ok” to open the file.** (See the attached PDF document to hand out to students.)
Algebra 2 Math Bundle 3
Quarter 2 Oct - Nov
Algebra II
Algebra II – Bundle 3
CC/Learning Targets Resource of Ideas Evidence of Learning N.CN.1 (A2.3.1a) (A2.3.2a)
Know there is a complex number i such
that i2 = −1, and every complex number
has the form a + bi with a and b real.
-Prentice Hall Algebra II Lesson 5.6 - Pearson Algebra 2 iBook Lesson 4.8
-DMR -NearPod app -Varied Informal Assessments -Homework Packets (included in curriculum resources) -Test -Quizzes -Bundle Task Assessments
N.CN.2 (A2.3.1b-e)
Use the relation i2 = –1 and the
commutative, associative, and
distributive properties to add, subtract,
and multiply complex numbers.
-Prentice Hall Algebra II Lesson 5.6 - Pearson Algebra 2 iBook Lesson 4.8 Concept Byte (after section 4.9)
-DMR -NearPod app -Varied Informal Assessments -Homework Packets (included in curriculum resources) -Test -Quizzes -Bundle Task Assessments
N.CN.7 (A2.3.3a,b)
Solve quadratic equations with real
coefficients that have complex
solutions.
-Prentice Hall Algebra II Lesson 5.8 - Pearson Algebra 2 iBook Lesson 4.8
-DMR -NearPod app -Varied Informal Assessments -Homework Packets (included in curriculum resources) -Test -Quizzes -Bundle Task Assessments
N.CN.8 (A2.3.1d)
Extend polynomial identities to the
complex numbers. For example, rewrite
x2 + 4 as (x + 2i)(x – 2i).
-Prentice Hall Algebra II Lesson 5.6 - Pearson Algebra 2 iBook Lesson 4.8
-DMR -NearPod app -Varied Informal Assessments -Homework Packets (included in curriculum resources) -Test -Quizzes -Bundle Task Assessments
Algebra II
Algebra II – Bundle 3
N.CN.9 Know the Fundamental Theorem of
Algebra; show that it is true for
quadratic polynomials.
-Prentice Hall Algebra II Lesson 6.6
-DMR -NearPod app -Varied Informal Assessments -Homework Packets (included in curriculum resources) -Test -Quizzes -Bundle Task Assessments
A.SSE.1 b
(A2.2.4a,b
)
Interpret expressions that represent a
quantity in terms of its context.
b) Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)
n as the product of P and a factor
not depending on P.
-Prentice Hall Algebra II Lessons 5.1, 5.2, 5.3, 10.1, 10.2, 10.3, 10.4, 10.5, 10.6
-DMR -NearPod app -Varied Informal Assessments -Homework Packets (included in curriculum resources) -Test -Quizzes -Bundle Task Assessments
A.SSE.2 Use the structure of an expression to
identify ways to rewrite it. For example,
see x4 – y
4 as (x
2)2 – (y
2)2, thus
recognizing it as a difference of squares
that can be factored as (x2 – y
2)(x
2 + y
2).
-Prentice Hall Algebra II Lessons 5.7, 10.6 - Pearson Algebra 2 iBook Lesson 4.4
-DMR -NearPod app -Varied Informal Assessments -Homework Packets (included in curriculum resources) -Test -Quizzes -Bundle Task Assessments
A.APR.3 (A2.1.1a,d) (A2.1.5a-f) (A2.5.3b)
(A2.5.7a-
c)
Identify zeros of polynomials when
suitable factorizations are available, and
use the zeros to construct a rough
graph of the function defined by the
polynomial.
-Prentice Hall Algebra II Lessons 5.1, 5.2, 5.3, 5.4, 5.5 10.1, 10.2, 10.3, 10.4, 10.5, 10.6 - Pearson Algebra 2 iBook Lesson 4.5 Concept Byte (after section 4.8) - MathGraph (app)
-DMR -NearPod app -Varied Informal Assessments -Homework Packets (included in curriculum resources) -Test -Quizzes -Bundle Task Assessments
Algebra II
Algebra II – Bundle 3
A.REI.11 (A2.2.4c,d) (A2.3.7a,b) (A2.5.4a) (A2.5.5b) (A2.6.4a) (A2.7.4a,b)
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.
-Prentice Hall Algebra II Lessons 5.1, 5.2, 5.3, 5.5, 10.1, 10.2, 10.3, 10.4, 10.5, 10.6 - Pearson Algebra 2 iBook Lesson 4.9
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F.IF.4 For a function that models a relationship
between two quantities, interpret key
features of graphs and tables in terms
of the quantities, and sketch graphs
showing key features given a verbal
description of the relationship. Key
features include: intercepts; intervals
where the function is increasing,
decreasing, positive, or negative;
relative maximums and minimums;
symmetries; end behavior; and
periodicity.
-Prentice Hall Algebra II Lessons 5.1, 5.2, 5.3, 5.5, 10.1, 10.2, 10.3, 10.4, 10.5, 10.6 - Pearson Algebra 2 iBook Lesson 4.1, 4.2, 4.3
-DMR -NearPod app -Varied Informal Assessments -Homework Packets (included in curriculum resources) -Test -Quizzes -Bundle Task Assessments
A2.3.2
b. Plot complex numbers on the coordinate plane.
-Prentice Hall Algebra II Lesson 5.6
-DMR -NearPod app -Varied Informal Assessments -Homework Packets (included in curriculum resources) -Test -Quizzes -Bundle Task Assessments
A2.4.1
a. Identify parts of a circle. b. Identify the parts of an ellipse.
-Prentice Hall Algebra II Lessons 10.1, 10.2, 10.3, 10.4, 10.5, 10.6
-DMR -NearPod app
Algebra II
Algebra II – Bundle 3
c. Identify parts of a hyperbola. d. Compare circles, ellipses, parabolas, and hyperbolas. f. Write the equation of a conic based on given information.
- MathGraph (app)
-Varied Informal Assessments -Homework Packets (included in curriculum resources) -Test -Quizzes -Bundle Task Assessments
A2.4.2
a. Classify a conic section given its equation. b. Graph a conic section from its equation.
-Prentice Hall Algebra II Lessons 10.1, 10.2, 10.3, 10.4, 10.5, 10.6
-DMR -NearPod app -Varied Informal Assessments -Homework Packets (included in curriculum resources) -Test -Quizzes -Bundle Task Assessments
A2.10.1a
a. Use a variety of problem-solving strategies, such as drawing a diagram and writing an equation.
b. Use a variety of problem-solving strategies, such as drawing a diagram, guess-and-check, solving a simpler problem, writing an equation, and working backwards.
-Prentice Hall Algebra II Lessons 5.1, 5.2, 5.3, 5.4, 5.5, 5.7, 5.8, 10.1, 10.2, 10.3, 10.4, 10.5, 10.6
-DMR -NearPod app -Varied Informal Assessments -Homework Packets (included in curriculum resources) -Test -Quizzes -Bundle Task Assessments
Correlating CC/Learning Targets Teacher Notes
A.SSE.1 A.APR.1 A.CED.1 A.CED.2 A.CED.3
A.CED.4 F.IF.5 F.IF.9 F.BF.3
- Pearson Algebra 2 iBook Concept Byte after Lesson 4.5 (for CC standard A.CED.2) Lesson 4.6, 4.7 complete for review of completing the square