Bundle 3 Algebra II

EAST ALLEN COUNTY SCHOOLS

Bundle 3

Algebra II

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

Baseball.pdf

http://itunes.apple.com/us/app/ifactor-quadratics/id369606383?mt=8

http://itunes.apple.com/us/app/math-ref-free/id312756358?mt=8

http://itunes.apple.com/us/app/algebra-genie/id481026577?mt=8

http://itunes.apple.com/us/app/khan-academy/id469863705?mt=8

http://itunes.apple.com/us/app/free-graphing-calculator/id378009553?mt=8

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)


N.CN.7 (A2.3.3a,b)

Solve quadratic equations with real

coefficients that have complex

solutions.



N.CN.8 (A2.3.1d)

Extend polynomial identities to the

complex numbers. For example, rewrite

x2 + 4 as (x + 2i)(x – 2i).



Algebra II


N.CN.9 Know the Fundamental Theorem of

Algebra; show that it is true for

quadratic polynomials.

-Prentice Hall Algebra II Lesson 6.6


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


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


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)


/%3ca%20href=%22http/::itunes.apple.com:us:app:mathgraph:id494113780?mt=8&uo=4%22%20target=%22itunes_store%22%3eMathGraph%20-%20Katherine%20Philip%3c:a%3e

Algebra II


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


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


A2.3.2

b. Plot complex numbers on the coordinate plane.

-Prentice Hall Algebra II Lesson 5.6


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


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


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


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

/%3ca%20href=%22http/::itunes.apple.com:us:app:mathgraph:id494113780?mt=8&uo=4%22%20target=%22itunes_store%22%3eMathGraph%20-%20Katherine%20Philip%3c:a%3e

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Bundle 3 Algebra II