alg ii updated 8/7/2017 4:26 pm - jefferson parish...

ALG II Updated 8/7/2017 4:26 PM

1

UNIT 1 – PROPERTIES OF QUADRATIC FUNCTIONS (10 DAYS)

1. Overview

This unit will be a place to reengage students with the Algebra I concepts of factoring, completing the square, and solving quadratic equations (to find x-

intercepts). Beyond graphing, students will write the equation of quadratic functions given a focus and directrix. While working with quadratics, the

students will use function transformations, estimate rates of change, calculate average rates of change on an interval, and begin to explore the idea of

inverse functions. Specifically, students will

review solving quadratic equations by completing the square, square root analysis, factoring, and solving quadratic equations to find the x intercept.

calculate and interpret the average rate of change of a function. write the equation of quadratic functions given a focus and directrix. (graphing). explore the idea of inverse functions.

FOCUS

STANDARDS F-IF.B.6 Calculate and interpret the average rate of change of a function (presented symbolically or as a table)

over a specified interval. Estimate the rate of change from a graph.

F-BF.B.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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

F-BF.B.4a Find inverse functions.

Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the

inverse. For example, f(x) =2x3 or f(x) = x+1

x−1 for x ≠ 1.

STANDARDS FOR MATHEMATICAL

PRACTICE

MP1: Make sense of problems and persevere in solving them. MP2: Reason abstractly and quantitatively. MP3: Construct viable arguments and critique the reasoning of others. MP4: Model with mathematics. MP5: Use appropriate tools strategically. MP6: Attend to precision. MP7: Look for and make use of structure.


2

MP8: Look for and express regularity in repeated reasoning.


2. Resources = Major standard

= Supporting standard

= Additional standard

EUREKA and enVision A|G|A

Algebra 2 READY TOOLBOX PLATO

Resource: enVision A|G|A

A2: F-IF.B.6: SE/TE: 5-12, 133, 137-138, 321-326

A2: F-BF.B.3: SE/TE: 13-22, 73-79, 179-186, 193-200, 255-262, 321-326, 383-391, 393-399, 400-407

A2: F-BF.B.4a: SE/TE: 281-289, 314-320, 323, 326

EUREKA A2: F- IF .B.6

Module 3 Lessons 18 & 19 (Algebra II)

Module 3 Lessons 18 (Precalculus) Module 1 Lesson 15 (Algebra II)

Resource:

Resource: PLATO Course Algebra 1, Semester B,

v5.0, Unit 5

SUPPORTING RESOURCES

Resource: Illustrative Mathematics: (https://www.illustrativemathematics.org)

Activity (Alignments to Content Standard: F-IF.B.6 ): https://www.illustrativemathematics.org/content-standards/HSF/IF/B/6/tasks/686

https://www.illustrativemathematics.org/content-standards/HSF/IF/B/6/tasks/686

https://www.illustrativemathematics.org/content-standards/HSF/IF/B/6/tasks/686


3

Activity (Alignments to Content Standard: F-BF.B.3 ):https://www.illustrativemathematics.org/content-standards/HSF/BF/B/3/tasks/232

Activity(Alignments to Content Standard:F-BF.B.3 ):https://www.illustrativemathematics.org/content-standards/HSF/BF/B/3/tasks/695

Activity (Alignments to Content Standard: F-BF.B.4a): https://www.illustrativemathematics.org/content-standards/HSF/BF/B/4/tasks/1374

Activity (Alignments to Content Standard: F-BF.B.4a):https://www.illustrativemathematics.org/content-standards/HSF/BF/B/4/tasks/501

Khan Academy:(https://www.khanacademy.org)

Video: https://www.khanacademy.org/math/algebra2/manipulating-functions/shifting-functions/v/shifting-functions-examples Video: https://www.khanacademy.org/math/algebra2/manipulating-functions/stretching-functions/v/shifting-and-reflecting-functions Video: https://www.khanacademy.org/math/algebra2/manipulating-functions/stretching-functions/v/compressing-functions-example Video: https://www.khanacademy.org/math/algebra2/manipulating-functions/finding-inverse-functions/v/function-inverses-example-2 Video: https://www.khanacademy.org/math/algebra-home/algebra2/manipulating-functions#introduction-to-inverses-of-functions Video: https://www.khanacademy.org/math/algebra-home/algebra2/manipulating-functions#verifying-that-functions-are-inverses

Math Education Page: (http://www.mathedpage.org)

http://www.mathedpage.org/parabolas/moving.pdf 6666


3. Activities for Understanding

SUGGESTIONS Students will complete instructional task located at

http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/algebra-ii-instructional-tasks.pdf?sfvrsn=5 on page 234.

Students will: a) Complete a table in a way so that f could be invertible and so that g is definitely not invertible. b) Graph both functions and explain from the graph why f is invertible and g is not. c) Come up with two real life situations that f and g could be representing. d) Find and interpret the value f −1 (4) in terms of these contexts

https://www.illustrativemathematics.org/content-standards/HSF/BF/B/4/tasks/1374









https://www.khanacademy.org/math/algebra2/manipulating-functions/shifting-functions/v/shifting-functions-examples

https://www.khanacademy.org/math/algebra2/manipulating-functions/stretching-functions/v/shifting-and-reflecting-functions

https://www.khanacademy.org/math/algebra2/manipulating-functions/stretching-functions/v/compressing-functions-example

https://www.khanacademy.org/math/algebra2/manipulating-functions/finding-inverse-functions/v/function-inverses-example-2

https://www.khanacademy.org/math/algebra-home/algebra2/manipulating-functions#introduction-to-inverses-of-functions

https://www.khanacademy.org/math/algebra-home/algebra2/manipulating-functions#verifying-that-functions-are-inverses

http://www.mathedpage.org/parabolas/moving.pdf

http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/algebra-ii-instructional-tasks.pdf?sfvrsn=5

http://www.louisianabelieves.com/docs/default-source/teacher-toolbox-resources/algebra-ii-instructional-tasks.pdf?sfvrsn=5



4

UNIT 2 – COMPLEX NUMBERS (5 DAYS)

1. Overview

To connect with Unit 1, students will begin by exploring quadratics with no real zeroes to highlight the need for numbers beyond real numbers. The set of imaginary numbers will be introduced and combined with real numbers to form the set of complex numbers. Students will understand the concept of the imaginary unit i such that i 2 = -1 and solve quadratic equations with complex solutions. Additionally, students will use these concepts to perform operations with complex numbers (excluding division). Specifically, students will

solve quadratic equations with real coefficients that have complex solutions. know the concept of complex number. use the relation i2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation.

FOCUS

STANDARDS A-REI.B.4b Solve quadratic equations in one variable.

a. Solve quadratic equations by inspection (e.g., for x2 = 49), taking square roots, completing the square, the

quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b

N-CN.A.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.

N-CN.A.2 Use the relation i 2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

N-CN.C.7 Solve quadratic equations with real coefficients that have complex solutions.

STANDARDS FOR

MATHEMATICAL

PRACTICE

MP1: Make sense of problems and persevere in solving them. MP2: Reason abstractly and quantitatively. MP3: Construct viable arguments and critique the reasoning of others. MP4: Model with mathematics. MP5: Use appropriate tools strategically. MP6: Attend to precision. MP7: Look for and make use of structure. MP8: Look for and express regularity in repeated reasoning.


5

UNIT2 – Complex Numbers (5 DAYS)




EUREKA and enVision A|G|A READY TOOLBOX PLATO


A2: A-REI.B.4b: SE/TE: 103-109, 110-116

A2: N-CN.A.1 and A2: N-CN.A.2: SE/TE: 95-101

A2: N-CN.C.7: SE/TE: 103-109, 110-116

Eureka

N-CN.A.1 Module 1 Lesson 37 N-CN.A.2 Module 1 Lesson 37

N-CN.C.7 Module 1 Lesson 38

A-REI.B.4b Module 1 Lesson 38

Use the relation i 2 = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers

Resource:

Resource: PLATO Course Algebra 2, Semester A, v5.0,

Unit 3


Resource: Illustrative Mathematics: (https://www.illustrativemathematics.org)


6

Activity (Alignments to Content Standard A-REI.B.4b): https://www.illustrativemathematics.org/content-standards/HSA/REI/B/4/tasks/586



Activity (Alignments to Content Standard N-CN.C.7): https://www.illustrativemathematics.org/content-standards/HSN/CN/C/7/tasks/1690

Activity (Alignments to Content Standard N-CN.A.1) : https://www.illustrativemathematics.org/content-standards/HSN/CN/A/1/tasks/722

LearnZillion: (https://learnzillion.com)

Video game activity (Standard: A-REI.B.4b): https://learnzillion.com/lesson_plans/5383-solve-a-quadratic-equation-by-completing-the-square

Lesson with a video (Standard: A-REI.B.4b): https://learnzillion.com/lesson_plans/5399-solve-a-quadratic-equation-with-no-real-solutions-by-completing-the-square

Direct Instruction Video (Standard: N-CN.A.1): https://learnzillion.com/lesson_plans/6691-understand-the-number-i Direct Instruction Video (Standard: N-CN.C.7): https://learnzillion.com/lesson_plans/6908-graph-quadratic-functions-with-complex-

roots

Khan Academy: (https://www.khanacademy.org) Video: https://www.khanacademy.org/math/algebra2/introduction-to-complex-numbers-algebra-2/the-imaginary-numbers-algebra-

2/v/introduction-to-i-and-imaginary-numbers

Video: https://www.khanacademy.org/math/algebra2/introduction-to-complex-numbers-algebra-2/the-complex-numbers-algebra-

2/v/complex-number-intro

Video: https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/adding-and-subtracting-complex-

numbers/v/adding-complex-numbers

Video: https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/adding-and-subtracting-complex-

numbers/v/subtracting-complex-numbers

Video: https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/multiplying-complex-numbers/v/multiplying-

complex-numbers

Video: https://www.khanacademy.org/math/precalculus/conics-precalc/focus-and-directrix-of-a-parabola/v/focus-and-directrix-

introduction

https://www.illustrativemathematics.org/content-standards/HSA/REI/B/4/tasks/586






https://www.illustrativemathematics.org/content-standards/HSN/CN/C/7/tasks/1690

https://www.illustrativemathematics.org/content-standards/HSN/CN/C/7/tasks/1690

https://www.illustrativemathematics.org/content-standards/HSN/CN/A/1/tasks/722


https://learnzillion.com/lesson_plans/5383-solve-a-quadratic-equation-by-completing-the-square

https://learnzillion.com/lesson_plans/5383-solve-a-quadratic-equation-by-completing-the-square

https://learnzillion.com/lesson_plans/5399-solve-a-quadratic-equation-with-no-real-solutions-by-completing-the-square

https://learnzillion.com/lesson_plans/5399-solve-a-quadratic-equation-with-no-real-solutions-by-completing-the-square

https://learnzillion.com/lesson_plans/6691-understand-the-number-i

https://learnzillion.com/lesson_plans/6908-graph-quadratic-functions-with-complex-roots

https://learnzillion.com/lesson_plans/6908-graph-quadratic-functions-with-complex-roots

https://www.khanacademy.org/math/algebra2/introduction-to-complex-numbers-algebra-2/the-imaginary-numbers-algebra-2/v/introduction-to-i-and-imaginary-numbers

https://www.khanacademy.org/math/algebra2/introduction-to-complex-numbers-algebra-2/the-imaginary-numbers-algebra-2/v/introduction-to-i-and-imaginary-numbers

https://www.khanacademy.org/math/algebra2/introduction-to-complex-numbers-algebra-2/the-complex-numbers-algebra-2/v/complex-number-intro

https://www.khanacademy.org/math/algebra2/introduction-to-complex-numbers-algebra-2/the-complex-numbers-algebra-2/v/complex-number-intro

https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/adding-and-subtracting-complex-numbers/v/adding-complex-numbers

https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/adding-and-subtracting-complex-numbers/v/adding-complex-numbers

https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/adding-and-subtracting-complex-numbers/v/subtracting-complex-numbers

https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/adding-and-subtracting-complex-numbers/v/subtracting-complex-numbers

https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/multiplying-complex-numbers/v/multiplying-complex-numbers

https://www.khanacademy.org/math/precalculus/imaginary-and-complex-numbers/multiplying-complex-numbers/v/multiplying-complex-numbers

https://www.khanacademy.org/math/precalculus/conics-precalc/focus-and-directrix-of-a-parabola/v/focus-and-directrix-introduction

https://www.khanacademy.org/math/precalculus/conics-precalc/focus-and-directrix-of-a-parabola/v/focus-and-directrix-introduction


7

Video: https://www.khanacademy.org/math/precalculus/conics-precalc/focus-and-directrix-of-a-parabola/v/equation-for-parabola-from-

focus-and-directrix

Video: https://www.illustrativemathematics.org/content-standards/HSA/REI/B/4/tasks/586

UNIT 2 – Complex Numbers (10 DAYS)


SUGGESTIONS Students will apply knowledge of quadratics to complete a real-world task

http://map.mathshell.org/download.php?fileid=1736

Students will practice making calculations with complex numbers and to visualize what happens when two complex numbers are multiplied. https://www.illustrativemathematics.org/content-standards/HSN/CN/A/2/tasks/1689

https://www.khanacademy.org/math/precalculus/conics-precalc/focus-and-directrix-of-a-parabola/v/equation-for-parabola-from-focus-and-directrix

https://www.khanacademy.org/math/precalculus/conics-precalc/focus-and-directrix-of-a-parabola/v/equation-for-parabola-from-focus-and-directrix


http://map.mathshell.org/download.php?fileid=1736




8

UNIT 3 – POLYNOMIALS (5 DAYS)

1. Overview

In this unit working with polynomials will move beyond quadratics. Students will begin to work with polynomial expressions and equations and will prove polynomial identities. A common idea throughout the middle/high school math standards is using the structure of expressions to gain insight into equivalent expressions and insight into the meaning of the expressions. This will be the first application of this idea in the Algebra II course. Additionally, students will continue to develop and extend their understanding of factoring and will use the zero product property to solve polynomial equations. . In this unit the concept of systems will be continued and students will solve 3x3 systems of linear equations/inequalities and systems consisting of one linear and one quadratic equation. Additionally, students will explain why the x-coordinates of the points of intersection of y=f(x) and y=g(x) are the solutions to the equation f(x) = g(x). Graphical and algebraic methods will be used for linear/quadratic systems. Approximation techniques will be used for other function types. Specifically, students will

solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. solve 3x3 systems of linear equations/inequalities and systems consisting of one linear and one quadratic equation graph the solutions to a linear inequality in two variables as a half-plane.

FOCUS

STANDARDS A-SSE.A.2 Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 –

(y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2) (x2 + y2).

A-APR.C.4 Use polynomial identities to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 – y2)2 + (2xy) 2 can be used to generate Pythagorean triples.

A-REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

A-REI.D.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

STANDARDS FOR

MATHEMATICAL

PRACTICE

MP1: Make sense of problems and persevere in solving them. MP2: Reason abstractly and quantitatively. MP4: Model with mathematics. MP7: Look for and make use of structure


9

UNIT 3 – Polynomials (5 DAYS)





Resource: enVision A|G|A A2: A-SSE.A.2: SE/TE: 88-94, 154-161, 165-169, 210-216, 217-223, 224-231, 247-254, 327-332, 333-339, 463-471, and 480-488, 489-497 A2: A-APR.C.4: SE/TE: 146-153 A2: A-REI.C.6: SE/TE: 47-54 A-REI.D.12: N/A |A2: A-APR.C.4A

A-APR.C.4 Module 1: Lesson 1-7 pages 15-68

Resource:

Resource: PLATO Course Algebra 2, Semester A,

v5.0, Unit 1, 2


Resources:

EngageNY: (https://www.engageny.org) Algebra II Modules

https://www.engageny.org/resource/algebra-ii-module-1 Illustrative Math: (https://www.illustrativemathematics.org)

Activity (Alignments to Content Standards: A-APR.A.1) : https://www.illustrativemathematics.org/content-standards/tasks/1656 Activity (Alignments to Content Standards: A-APR.C.4) : https://www.illustrativemathematics.org/content-standards/tasks/594 Activity (Alignments to Content Standards: F-IF.C.7.c) : https://www.illustrativemathematics.org/content-standards/tasks/627 Activity (Alignments to Content Standards: A-APR.B.2) : https://www.illustrativemathematics.org/content-standards/tasks/787

https://www.engageny.org/resource/algebra-ii-module-1

https://www.illustrativemathematics.org/content-standards/tasks/1656





10

Learnzillion: (https://learnzillion.com) Lesson with a video (Standard: A-APR.C.4): https://learnzillion.com/lesson_plans/7003 Lesson with a video (Standard: A-REI.C.6): https://learnzillion.com/lesson_plans/93 Lesson with a video (Standard: A-APR.B.3, A-SSE.A.1a, A-SSE.A.2): https://learnzillion.com/lesson_plans/790

UNIT 3 – Polynomials (5 DAYS)


SUGGESTIONS Students will work two separate activities that will have them solve, create and critically think about ways polynomials can apply to the real world.

http://map.mathshell.org/lessons.php?unit=9115&collection=8 http://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/PolyPuzz-AS.pdf and

answers (http://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/6-8/PolyPuzz-AK.pdf)

https://learnzillion.com/lesson_plans/7003



http://map.mathshell.org/lessons.php?unit=9115&collection=8

http://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/PolyPuzz-AS.pdf

http://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/6-8/PolyPuzz-AK.pdf


11

UNIT 4 – RATIONAL EQUATIONS & EXPRESSIONS (7 DAYS)

1. Overview

In this unit students will begin to work with simple rational expressions and equations. Long division and inspection will be used to rewrite rational expressions. Rational equations will be created and used to solve problems. Additionally, students will explain the process of and justify the steps in solving rational equations. They will explain and provide examples of situations in which extraneous solutions may arise. (Students will not be expected to add, subtract, multiply, or divide rational expressions). Specifically, students will

solve simple rational and radical equations in one variable. rewrite simple rational expressions in different forms.

FOCUS

STANDARDS A-REI.A.1 Explain each step in solving an 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.

A-REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how

extraneous solutions may arise.

A-APR.D.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.

A-CED.A.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

STANDARDS FOR

MATHEMATICAL

PRACTICE

MP1: Make sense of problems and persevere in solving them. MP2: Reason abstractly and quantitatively. MP4: Model with mathematics. MP7: Look for and make use of structure. MP8: Look for and express regularity in repeated reasoning.



12






A2: A-REI.A.1: SE/TE: 224-231, 239-246, 263-271, 333-339

A2: A-REI.A.2: SE/TE: 263-271 A2: A-APR.D.6: SE/TE: 154-161 A2: A-CED.A.1: SE/TE: 40-46, 224-

231, 333-339 Eureka

A-REI.A.1 & A-CED.A.1: Rational Equation & Expression Module 1: Lesson 22-27 pages 245-312

Resource:

Resource:

PLATO Course Algebra 2, Semester A,

v5.0, Unit 1, 2


Resource: Illustrative Math: (https://www.illustrativemathematics.org)

Activity (Alignments to Content Standards: A-REI.D.11) : https://www.illustrativemathematics.org/content-standards/tasks/1925 Activity (Alignments to Content Standards: A-APR.D.6) : https://www.illustrativemathematics.org/content-standards/tasks/825 Activity (Alignments to Content Standards: A-REI.A.2) : https://www.illustrativemathematics.org/content-standards/tasks/1927

Learnzillion: (https://learnzillion.com)

Lesson with a video (Standard: A-APR.D.6): https://learnzillion.com/lesson_plans/5746 Lesson with a video (Standard: A-CED.A.1, F-BF.B.3): https://learnzillion.com/lesson_plans/793

Khan Academy: (https://www.khanacademy.org)







13

Video: https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/solving-rational-equations/v/ex-1-multi-step-equation

Video: https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/solving-rational-equations/v/solving-rational-equations-pjmt

Video: https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/solving-rational-equations/e/rational-equations-3

Video: https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/solving-rational-equations/v/rational-equations



SUGGESTIONS For this activity, student will have to be placed in groups of two or four. They will need to have paper, pencil, and calculator preferable a graphing calculator. Students will complete a table, discuss the results, discuss the behavior of the graphs, and critique each other’s work.

Trip to the Fair Activity: http://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-

12/LightItUp-AS-All.pdf

https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/solving-rational-equations/v/ex-1-multi-step-equation


https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/solving-rational-equations/v/solving-rational-equations-pjmt


https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/solving-rational-equations/e/rational-equations-3


https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/solving-rational-equations/v/rational-equations


http://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/LightItUp-AS-All.pdf

http://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/LightItUp-AS-All.pdf


14

UNIT 5 – RADICAL EQUATIONS & EXPRESSIONS (7 DAYS)

1. Overview

In this unit students will continue to master more sophisticated algebra skills. While the students will be familiar with simple radical functions from Algebra I, now they will work with more complicated radical equations. The expectations in this unit are analogous to Unit 4. Students will explain the process of and justify the steps in solving radical equations. They will explain and provide examples of situations in which extraneous solutions may arise. Specifically, students will

solve simple rational and radical equations in one variable and more complicated radical equations.

FOCUS

STANDARDS A-REI.A.1 Explain each step in solving an 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. A-REI.A.2 Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

STANDARDS FOR

MATHEMATICAL

PRACTICE








Resource:

Resource:


15

A2: A-REI.A.1: SE/TE: 224-231, 239-246, 263-271, 333-339 A2: A-REI.A.2: SE/TE: 263-271 Eureka

A-REI.A.2: Radical Equation & Expression Module 1: Lesson 28-29 pages 313 - 329

PLATO Course Algebra 2, Semester A, v5.0, Unit 1, 2



Activity (Alignments to Content Standards: A-REI.D.11) : https://www.illustrativemathematics.org/content-standards/tasks/1925 Activity (Alignments to Content Standards: A-APR.D.6) : https://www.illustrativemathematics.org/content-standards/tasks/825 Activity (Alignments to Content Standards: A-REI.A.2) : https://www.illustrativemathematics.org/content-standards/tasks/1927

Learnzillion: (https://learnzillion.com)

Lesson with a video (Standard: A-APR.D.6): https://learnzillion.com/lesson_plans/5746 Lesson with a video: (Standard: A-CED.A.1, F-BF.B.3): https://learnzillion.com/lesson_plans/793

Khan Academy: (https://www.khanacademy.org)

Video: https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/solving-rational-equations/v/ex-1-multi-step-equation

Video: https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/solving-rational-equations/v/solving-rational-equations-pjmt

Video: https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/solving-rational-equations/e/rational-equations-3

Video: https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/solving-rational-equations/v/rational-equations
















16


SUGGESTION S

Students will analyze and solve radical equations. Then, they put the solution steps in order as well as matching the reason to each step. Finally, they will copy the examples into their notebook (or glue pieces in their notebook) to have a discussion on their findings

http://www.wccusd.net/cms/lib03/CA01001466/Centricity/domain/60/lessons/algebra%20i%20lessons/SolvingRadicalEqationsV3.pdf




17

UNIT 6 – POLYNOMIAL FUNCTIONS (5 DAYS)

1. Overview

Now that students have more skill with algebraic manipulation, the focus will shift back to functions. In this unit, students will start to explore

polynomial functions. The connection between zeroes of a function and factors of that function will be explored. For quartic functions (and those with

lesser degree), students will use intercepts (when suitable factorizations are available) and end behavior to create rough graphs of the functions.

Additionally, for a function modeling real-life quantities, students will interpret key features of the function in terms of the provided context. Key

features could include intercepts, intervals where the function is increasing/decreasing/positive/negative, relative extreme, symmetries, end behavior,

etc.

Specifically, students will identify zeroes of polynomials when suitable factorizations are available, and use the zeroes to construct a rough graph of the function

defined by the polynomial.

know and apply the Remainder Theorem for a polynomial. (Dividing Polynomials)

review adding, subtracting, and multiplying polynomials.

graph polynomial functions, identifying zeroes when suitable factorizations are available, and showing end behavior, (function is

increasing/decreasing/positive/negative, relative extreme, symmetries, etc.).

FOCUS

STANDARDS A-APR.B.2 Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on

division by x – a is p (a), so p (a) = 0 if and only if (x – a) is a factor of p(x).

A-APR.B.3 Identify zeroes of polynomials when suitable factorizations are available, and use the zeroes to construct a rough graph of the function defined by the polynomial.

F-IF.B.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.

F-IF.C.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, determine which has the larger maximum.

F-IF.C.7c Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.


18

b. Graph polynomial functions, identifying zeroes when suitable factorizations are available, and showing end behavior.

STANDARDS FOR

MATHEMATICAL

PRACTICE








A2: A-APR.B.2: SE/TE: 154-161 A2: A-APR.B.3: SE/TE: 88-94, 162-

169, 171-178 A2: F-IF.B.4: SE/TE: 5-12, 73-79, 80-

87, 131-138, 255-262, 297-304, 393-399, 400-407

A2: F-IF.C.9: SE/TE: 139-145, 321-326

A2: F-IF.C.7c: SE/TE: 131-138, 162-169

EUREKAEUREKA

A-APR.B.3, F-IF.B.4, and F-IF.C.9 Polynomial Functions Module 1: Lesson 14-19 pages 152-233

Resource:


v5.0, Unit 3


19


Resource: Illustrative Math (https://www.illustrativemathematics.org)

Activity (Alignments to Content Standards: F-IF.C.7.c): https://www.illustrativemathematics.org/content-standards/tasks/627 Activity (Alignments to Content Standards: F-IF.C.7.c): https://www.illustrativemathematics.org/content-standards/tasks/1539 Activity ( Alignments to Content Standards: F-IF.B.4): https://www.illustrativemathematics.org/content-standards/tasks/2103

LearnZillion (https://learnzillion.com) Lesson with a video (Standard: F-IF.C.7c): https://learnzillion.com/lesson_plans/1212 Lesson with a video: (Standard: A-APR.B.2): https://learnzillion.com/lesson_plans/5835#lesson-tab Lesson with video: (Standard: https: A-APR.B.3): https://learnzillion.com/lesson_plans/5994 Lesson with a video (Standard: F-IF.C.7c): https://learnzillion.com/resources/9191?card_id=25626 Lesson with a video: (Standard: F-IF.C.7c): https://learnzillion.com/resources/9273?card_id=25628

Khan Academy (https://www.khanacademy.org)

Video: https://www.khanacademy.org/math/algebra2/polynomial-functions/finding-zeros-of-polynomials/v/finding-roots-or-zeros-of-polynomial-1

Video: https://www.khanacademy.org/math/algebra2/polynomial-functions/finding-zeros-of-polynomials/v/finding-roots-or-zeros-of-polynomial-2

Video: https://www.khanacademy.org/math/algebra2/polynomial-functions/zeros-of-polynomials-and-their-graphs/v/identifying-graph-based-on-roots

Video: https://www.khanacademy.org/math/algebra2/polynomial-functions/polynomial-end-behavior/v/polynomial-end-behavior Video: https://www.khanacademy.org/math/algebra2/polynomial-functions/symmetry-of-polynomial-functions/a/symmetry-of-polynomials



SUGGESTIONS Students will learn that the quadratic function has the same x-intercepts as the linear functions, which can be quite a revelation, and that the y-intercept of the quadratic function is the product of the y-intercepts of the linear functions





https://learnzillion.com/lesson_plans/5835#lesson-tab


https://learnzillion.com/resources/9191?card_id=25626


https://www.khanacademy.org/math/algebra2/polynomial-functions/finding-zeros-of-polynomials/v/finding-roots-or-zeros-of-polynomial-1




https://www.khanacademy.org/math/algebra2/polynomial-functions/zeros-of-polynomials-and-their-graphs/v/identifying-graph-based-on-roots

https://www.khanacademy.org/math/algebra2/polynomial-functions/zeros-of-polynomials-and-their-graphs/v/identifying-graph-based-on-roots

https://www.khanacademy.org/math/algebra2/polynomial-functions/polynomial-end-behavior/v/polynomial-end-behavior

https://www.khanacademy.org/math/algebra2/polynomial-functions/symmetry-of-polynomial-functions/a/symmetry-of-polynomials


20

http://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/BuildingPolys-AS-HigherDegree.pdf and answers to the activity (http://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/BuildingPolys-Answers.pdf)

http://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/BuildingPolys-AS-HigherDegree.pdf

http://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/BuildingPolys-AS-HigherDegree.pdf

http://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/BuildingPolys-Answers.pdf

http://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/BuildingPolys-Answers.pdf


21

UNIT 7 SYSTEMS OF EQUATIONS (5 DAYS)

1. Overview

Systems of equations are first introduced in 8th grade with 2x2 systems of linear equations. In Algebra I this concept is extended to include 2x2

systems of linear inequalities. In this unit the concept of systems will be continued and students will solve 3x3 systems of linear equations and

systems consisting of one linear and one quadratic equation. Additionally, students will explain why the x-coordinates of the points of intersection of

y=f(x) and y=g(x) are the solutions to the equation f(x) =g(x). Graphical and algebraic methods will be used for linear/quadratic systems.

Approximation techniques will be used for other function types.

Specifically students will

solve systems equations 2x2 systems of linear equations.

solve 3x3 systems of linear equations and systems consisting of one linear and one quadratic equation.

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)

FOCUS

STANDARDS A-REI.D.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.

A-REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), limited to systems of at most three equations and three variables with graphic solutions, systems are limited to two variables.

A-REI.C.7 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.

STANDARDS FOR

MATHEMATICAL

PRACTICE




22






A2: A-REI.D.11: SE/TE: 40-46, 117-123

A2: A-REI.C.6: SE/TE: 47-54 A2: A-REI.C.7: SE/TE: 117-123, 475,

477-478 EUREKA

A-REI.D.11, A-REI.C.6, and A-REI.C.7

Systems of Equations from Algebra I Module1: Lesson: 20 -24 pages 230 - 272

Resource:


v5.0, Unit 2


Resource: Illustrative Math (www.illustrativemathematics.org)

Task (Alignments to Content Standards: A-CED.A.3): https://www.illustrativemathematics.org/content-standards/tasks/220 Task (Alignments to Content Standards: A-CED.A A-REI.C.6): https://www.illustrativemathematics.org/content-

standards/tasks/462

LearnZillion (www.learnzillion.com) Lesson with a video (Standard: A-CED.A.3, A-REI.C.7, A-REI.D.11): https://learnzillion.com/lesson_plans/798#lesson-tab Lesson with a video (Standard: A-CED.A.3, A-REI.C.7, A-REI.D.11): https://learnzillion.com/lesson_plans/799 Lesson with a video (Standard: A-CED.A.3): https://learnzillion.com/resources/14186?card_id=2021 Lesson with a video (Standard: A-REI.C.6): https://learnzillion.com/lesson_plans/4729









23

Lesson with a video resource (Standard: A-REI.C.6): https://learnzillion.com/resources/10709?card_id=63077

Kuta Software (https://cdn.kutasoftware.com) System of Two Equations (Graphing)

https://cdn.kutasoftware.com/Worksheets/Alg2/Systems%20of%20Two%20Equations.pdf Systems of Equations Word Problems

https://cdn.kutasoftware.com/Worksheets/Alg2/Systems%20of%20Equations%20Word%20Problems.pdf Solving Systems of Three Equations w/ Elimination

https://cdn.kutasoftware.com/Worksheets/Alg2/Systems%20of%20Three%20Equations%20Elimination.pdf Solving Systems of Three Equations w/ Substitution

https://cdn.kutasoftware.com/Worksheets/Alg2/Systems%20of%20Three%20Equations%20Substitution.pdf Khan Academy (https://www.khanacademy.org)

Video: https://www.khanacademy.org/math/algebra-basics/core-algebra-systems/core-algebra-systems-tutorial/v/solving-linear-systems-by-graphing

Video: https://www.khanacademy.org/math/algebra-basics/core-algebra-systems/core-algebra-systems-tutorial/v/solving-linear-systems-by-substitution

Video: https://www.khanacademy.org/math/algebra-basics/core-algebra-systems/core-algebra-systems-tutorial/v/solving-systems-of-equations-by-multiplication

Video: https://www.khanacademy.org/math/algebra/systems-of-linear-equations/systems-of-linear-equations-word-problems/v/solving-systems-by-elimination

Video: https://www.khanacademy.org/math/algebra/systems-of-linear-equations/systems-of-linear-equations-word-problems/v/systems-word-problem-with-no-solution



SUGGESTIONS

(Content Standard: A-REI.C.6): Solve systems of linear equations exactly and approximately (e.g., with graphs), limited to systems of at most three equations and three variables with graphic solutions, systems are limited to two variables.


https://cdn.kutasoftware.com/Worksheets/Alg2/Systems%20of%20Two%20Equations.pdf

https://cdn.kutasoftware.com/Worksheets/Alg2/Systems%20of%20Equations%20Word%20Problems.pdf

https://cdn.kutasoftware.com/Worksheets/Alg2/Systems%20of%20Three%20Equations%20Elimination.pdf

https://cdn.kutasoftware.com/Worksheets/Alg2/Systems%20of%20Three%20Equations%20Substitution.pdf

https://www.khanacademy.org/

https://www.khanacademy.org/math/algebra-basics/core-algebra-systems/core-algebra-systems-tutorial/v/solving-linear-systems-by-graphing

https://www.khanacademy.org/math/algebra-basics/core-algebra-systems/core-algebra-systems-tutorial/v/solving-linear-systems-by-graphing

https://www.khanacademy.org/math/algebra-basics/core-algebra-systems/core-algebra-systems-tutorial/v/solving-linear-systems-by-substitution

https://www.khanacademy.org/math/algebra-basics/core-algebra-systems/core-algebra-systems-tutorial/v/solving-linear-systems-by-substitution

https://www.khanacademy.org/math/algebra-basics/core-algebra-systems/core-algebra-systems-tutorial/v/solving-systems-of-equations-by-multiplication

https://www.khanacademy.org/math/algebra-basics/core-algebra-systems/core-algebra-systems-tutorial/v/solving-systems-of-equations-by-multiplication

https://www.khanacademy.org/math/algebra/systems-of-linear-equations/systems-of-linear-equations-word-problems/v/solving-systems-by-elimination

https://www.khanacademy.org/math/algebra/systems-of-linear-equations/systems-of-linear-equations-word-problems/v/solving-systems-by-elimination

https://www.khanacademy.org/math/algebra/systems-of-linear-equations/systems-of-linear-equations-word-problems/v/systems-word-problem-with-no-solution

https://www.khanacademy.org/math/algebra/systems-of-linear-equations/systems-of-linear-equations-word-problems/v/systems-word-problem-with-no-solution


24

Activity Directions: Students will need to work in groups of two or four for this activity. Students will have to do the following read and analyze a scenario, construct an equation and solve the problem critically.

https://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/CandyProblemAS.pdf and answers (https://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/CandyProblemAK.pdf)

https://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/CandyProblemAS.pdf

https://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/CandyProblemAK.pdf

https://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/CandyProblemAK.pdf


25

UNIT 8 Rational Exponents (5 DAYS)

1. Overview

In Algebra I, students work with linear and exponential relationships; however, students do not graph exponential functions. Algebra I students can

only work with exponential functions with integer domains because the concept of rational exponents has not yet been introduced. In this unit,

students will be introduced to the concept of rational exponents and their connection to radicals to allow for work with exponential and logarithmic

functions in future units. The primary focus of this unit is to extend the properties of integer exponents to rational exponents, use those properties to

rewrite expressions in equivalent forms, and use the structure of expressions and equations with radicals or rational exponents in a real-world

context.

Specifically, students will

rewrite expressions involving radicals and rational exponents using the properties of exponents.

explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those

values, allowing for a notation for radicals in terms of rational exponents.

FOCUS

STANDARDS N-RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties

of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For

example, we define 51

3to be the cube root of 5 because we want (5

1

3)3 = 5(

1

3)3 to hold, so (5

1

3)3 must equal 5.

N-RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

A-SSE.B.3c Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

a. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

STANDARDS FOR

MATHEMATICAL

PRACTICE

MP1: Make sense of problems and persevere in solving them.

MP2: Reason abstractly and quantitatively.

MP4: Model with mathematics.

MP7: Look for and make use of structure.



26

UNIT 8 Rational Exponents (5 DAYS)






A2: N-RN.A.1: SE/TE: 239-246, 247-254

A2: N-RN.A.2: SE/TE: 239-246, 247-254

A2: A-SSE.B.3c: SE/TE: 305-312 EUREKA

N-RN.A.1, N-RN.A.2, and A-SSE.B.3c

Module 3: Lesson 1-3; pages: 14-43

Resource:


v5.0, Unit 6


Resource: Kuta Software

Radicals and Rational Exponents https://cdn.kutasoftware.com/Worksheets/Alg2/Radicals%20and%20Rational%20Exponents.pdf Simplifying Rational Exponents https://cdn.kutasoftware.com/Worksheets/Alg2/Simplifying%20Rational%20Exponents.pdf Simplifying Radicals https://cdn.kutasoftware.com/Worksheets/Alg2/Simplifying%20Radicals.pdf

https://cdn.kutasoftware.com/Worksheets/Alg2/Radicals%20and%20Rational%20Exponents.pdf

https://cdn.kutasoftware.com/Worksheets/Alg2/Simplifying%20Rational%20Exponents.pdf

https://cdn.kutasoftware.com/Worksheets/Alg2/Simplifying%20Radicals.pdf


27

Illustrative Math Task (Alignments to Content Standards: F-LE.A and N-RN.A.1): https://www.illustrativemathematics.org/content-

standards/tasks/385 Task (Alignments to Content Standards: F-LE.A.2) : https://www.illustrativemathematics.org/content-standards/tasks/2125

Learnzillion

Lesson with a video (Standard: N-RN.A.1): https://learnzillion.com/lesson_plans/486 Lesson with a video (Standard: N-RN.A.1): https://learnzillion.com/lesson_plans/490#description-tab Lesson with a video (Standard: N-RN.A.2): https://learnzillion.com/lesson_plans/6436-apply-exponents-to-physical-models Lesson with a video (Standard: N-RN.A.2): https://learnzillion.com/lesson_plans/5495

Khan Academy Video: https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/simplify-rational-

expressions/v/simplifying-rational-expressions-introduction Video: https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/simplify-rational-

expressions/v/simplifying-rational-expressions-w-common-monomial-factors Video: https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/simplify-rational-

expressions/v/simplifying-rational-expressions-w-two-variables Video: https://www.khanacademy.org/math/algebra/introduction-to-exponential-functions/solving-basic-exponential-models/v/word-

problem-solving-exponential-growth-and-decay Video: https://www.khanacademy.org/math/algebra/introduction-to-exponential-functions/comparing-exponential-and-polynomial-

functions/v/linear-exponential-models

UNIT 8 Rational Expression (5 days)


SUGGESTIONS

(Content Standard: A-SSE.B.3c): Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

The “M&M” Investigation Activity: For this activity, students will explore the patterns of exponential models in tables, graphs, and symbolic forms and to apply what they have learned to make predictions in a real situation. (Pages 11, 12, and 16)





https://learnzillion.com/lesson_plans/490#description-tab

https://learnzillion.com/lesson_plans/6436-apply-exponents-to-physical-models


https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/simplify-rational-expressions/v/simplifying-rational-expressions-introduction

https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/simplify-rational-expressions/v/simplifying-rational-expressions-introduction

https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/simplify-rational-expressions/v/simplifying-rational-expressions-w-common-monomial-factors

https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/simplify-rational-expressions/v/simplifying-rational-expressions-w-common-monomial-factors

https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/simplify-rational-expressions/v/simplifying-rational-expressions-w-two-variables

https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/simplify-rational-expressions/v/simplifying-rational-expressions-w-two-variables

https://www.khanacademy.org/math/algebra/introduction-to-exponential-functions/solving-basic-exponential-models/v/word-problem-solving-exponential-growth-and-decay

https://www.khanacademy.org/math/algebra/introduction-to-exponential-functions/solving-basic-exponential-models/v/word-problem-solving-exponential-growth-and-decay

https://www.khanacademy.org/math/algebra/introduction-to-exponential-functions/comparing-exponential-and-polynomial-functions/v/linear-exponential-models

https://www.khanacademy.org/math/algebra/introduction-to-exponential-functions/comparing-exponential-and-polynomial-functions/v/linear-exponential-models


28

http://www-tc.pbs.org/teachers/mathline/lessonplans/pdf/hsmp/rhinos.pdf

http://www-tc.pbs.org/teachers/mathline/lessonplans/pdf/hsmp/rhinos.pdf


29

UNIT 9 Functions as Sequences & Series (7 DAYS)

1. Overview

In this unit, students will work with arithmetic and geometric sequences. The work with geometric sequences will be a basic introduction to exponential functions with various whole number bases. Students will recognize that sequences are functions (sometimes defined recursively) whose domain is a subset of the integers. The focus will be on determining recursively and/or explicitly defined sequences from information about a real-world context or to solve real-world problems. Students will also convert between recursively and explicitly defined sequences. Additionally, students will derive the formula for the sum of a finite geometric series and use the formula to solve problems. Specifically, students will

write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate

between the two forms.

write a function that describes a relationship between two quantities. apply the formula for the sum of a finite geometric series (when the common ratio is not 1), to solve problems. recognize the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.

FOCUS

STANDARDS A-SSE.B.4 Apply the formula for the sum of a finite geometric series (when the common ratio is not 1), to solve

problems. For example, calculate mortgage payments.

F-BF.A.1a Write a function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context.

F-BF.A.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

F-IF.A.3 Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.

F-LE.A.2 Given a graph, a description of a relationship, or two input-output pairs (include reading these from a table), construct linear and exponential functions, including arithmetic and geometric sequences, to solve multi-step problems.

STANDARDS FOR

MATHEMATICAL

PRACTICE




30




UNIT 9 Functions as Sequences & Series (7 DAYS)





Resource: enVision A|G|A A2: A-SSE.B.4: SE/TE: 340-348 A2: F-BF.A.1a: SE/TE: 31-39 A2: F-BF.A.2: SE/TE: 31-39, 340-348 A2: F-LE.A.2: SE/TE: 31-39, 340-348 Eureka

A-SSE.B.4, F-BF.A.1a, F-BF.A.2, and F-LE.A.2

Functions as Sequence & Series Module 3: Lesson 29-33 Pages 474-554

Resource:


v5.0, Unit


Resource: Kuta Software (https://cdn.kutasoftware.com) Introduction to Sequences

https://cdn.kutasoftware.com/Worksheets/Alg2/Introduction%20to%20Sequences.pdf Arithmetic Sequences

https://cdn.kutasoftware.com/Worksheets/Alg2/Arithmetic%20Sequences.pdf

https://cdn.kutasoftware.com/

https://cdn.kutasoftware.com/Worksheets/Alg2/Introduction%20to%20Sequences.pdf

https://cdn.kutasoftware.com/Worksheets/Alg2/Arithmetic%20Sequences.pdf


31

Geometric Sequences https://cdn.kutasoftware.com/Worksheets/Alg2/Geometric%20Sequences.pdf

Finite Geometric Series https://cdn.kutasoftware.com/Worksheets/Alg2/Finite%20Geometric%20Series.pdf

Comparing Arithmetic and Geometric Sequences https://cdn.kutasoftware.com/Worksheets/Alg2/Comparing%20Arithmetic%20and%20Geometric%20Sequences.pdf

Liberty.kernhigh.org (Arithmetic Sequence using Recursive and Explicit)

http://liberty.kernhigh.org/wp-content/uploads/2014/08/Adv-Alg-Arithmetic-Sequences-Recursive-Formula-Worksheet.pdf Grade a math help (www.gradeamathhelp.com)

(Title: Sequences and Series): http://www.gradeamathhelp.com/support-files/free-algebra2-worksheets-unit11.pdf with answers http://www.gradeamathhelp.com/support-files/free-algebra2-worksheets-unit11-answers.pdf

Illustrative Math (https://www.illustrativemathematics.org)

Task: (Alignments to Content Standards: F-LE.A.1 F-LE.A.2): https://www.illustrativemathematics.org/content-standards/tasks/1594 Task: (Alignments to Content Standards F-LE.A.2 F-IF.A.1): https://www.illustrativemathematics.org/content-standards/tasks/377

LearnZillion (https://learnzillion.com)

Lesson with a video (Standard: F-BF.A.1a, F-LE.A.2): https://learnzillion.com/lesson_plans/110 Lesson with a video (Standard: F-LE.A.2): https://learnzillion.com/lesson_plans/423


Video: https://www.khanacademy.org/math/integral-calculus/sequences-series-approx-calc#calculus-sequences https://www.khanacademy.org/math/precalculus/seq-induction/precalc-geometric-sequences/v/geometric-sequences-introduction

Video: https://www.khanacademy.org/math/integral-calculus/sequences-series-approx-calc/calculus-sequences/v/explicit-and-recursive-definitions-of-sequences

Video: https://www.khanacademy.org/math/integral-calculus/sequences-series-approx-calc/calculus-series/v/formula-for-arithmetic-series

UNIT 9 Functions as Sequences & Series (7 days)


https://cdn.kutasoftware.com/Worksheets/Alg2/Geometric%20Sequences.pdf

https://cdn.kutasoftware.com/Worksheets/Alg2/Finite%20Geometric%20Series.pdf

https://cdn.kutasoftware.com/Worksheets/Alg2/Comparing%20Arithmetic%20and%20Geometric%20Sequences.pdf

http://liberty.kernhigh.org/wp-content/uploads/2014/08/Adv-Alg-Arithmetic-Sequences-Recursive-Formula-Worksheet.pdf

http://www.gradeamathhelp.com/support-files/free-algebra2-worksheets-unit11.pdf

http://www.gradeamathhelp.com/support-files/free-algebra2-worksheets-unit11-answers.pdf






https://www.khanacademy.org/math/integral-calculus/sequences-series-approx-calc#calculus-sequences

https://www.khanacademy.org/math/precalculus/seq-induction/precalc-geometric-sequences/v/geometric-sequences-introduction

https://www.khanacademy.org/math/integral-calculus/sequences-series-approx-calc/calculus-sequences/v/explicit-and-recursive-definitions-of-sequences

https://www.khanacademy.org/math/integral-calculus/sequences-series-approx-calc/calculus-sequences/v/explicit-and-recursive-definitions-of-sequences

https://www.khanacademy.org/math/integral-calculus/sequences-series-approx-calc/calculus-series/v/formula-for-arithmetic-series

https://www.khanacademy.org/math/integral-calculus/sequences-series-approx-calc/calculus-series/v/formula-for-arithmetic-series


32

SUGGESTIONS

(Content Standard: F-LE.A.2): Given a graph, a description of a relationship, or two input-output pairs (include reading these from a table), construct linear and exponential functions, including arithmetic and geometric sequences, to solve multi-step problems. Activity 1: Students will identify the precision and accuracy of your U.S. and metric for sequential and series functional order. For this activity, students should be placed into groups of two to four. You will need: Metric Measuring Tape and U.S. Measuring Tape, graph paper and pencil

https://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/Fret-AS-ToFret.pdf

Activity 2: See attachment Dot Activity

https://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/Fret-AS-ToFret.pdf


33

UNIT 10 Exponential and Logarithmic functions (10 DAYS)

1. Overview

Information from previous units culminates in fully utilizing exponential and logarithmic functions. Students should be familiar with rational exponents

and experimenting with geometric sequences that will give them insight into functions with a variable as the exponent. Students will explore the

connection between exponential and logarithmic functions and will use logarithms to express solutions to exponential equations with bases 2, 10, or

e. Students will also graph exponential and logarithmic functions and will determine appropriate key features of the function and/or graph to solve

problems. Additionally, students will begin to fit functions to data and will informally assess the function type and fit it to the data.


solve and Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

will use logarithms to express solutions to exponential equations with bases 2, 10, or e.

interpret the parameters in a linear, quadratic, or exponential function in terms of a context.

represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

FOCUS

STANDARDS N-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling.

F-IF.C.7e Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. a. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric

functions, showing period, midline, and amplitude.

F-IF.C.8b Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function. a. Use the properties of exponents to interpret expressions for exponential functions. For example, identify

percent rate of change in functions such as y = (1.02) t, y = (0.97) t, y = (1.01)12t, y = (1.2) t/10, and classify them as representing exponential growth or decay.

F-LE.A.4 For exponential models, express as a logarithm the solution to a bct = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

S-ID.B.6a Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.


34

a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given

functions or choose a function suggested by the context. Emphasize exponential models.

F-LE.B.5 Interpret the parameters in a linear, quadratic, or exponential function in terms of a context.

STANDARDS FOR

MATHEMATICAL

PRACTICE











Resource:

A2: N-Q.A.2: SE/TE: 39 (#33), 54 (#32), 64 (#29), 79 (#35), 87(#26), 101 (#46), 145 (#27), 254 (#48), 271 (#42),289 (#33), 311 (#14), 391 (#20), 407 (#24), 471, (#23), 488 (#24), 536 (#31), 649 (#20).

A2: F-IF.C.7e: SE/TE: 297-304, 321-326 A2: F-IF.C.8b: SE/TE: 305-312

Resource:


v5.0, Unit 3


35

A2: F-LE.A.4: SE/TE: 297-304, 314-320, 327-332, 333-339

A2: F-LE.B.5: SE/TE: 297-304, 305-312 A2: S-ID.B.6a: SE/TE: 299-304, 305 312

F-LE.A.4, S-ID.B.6a, F-IF.C.8b, N-Q.A.2,

& F-IF.C.7e

Exponential and Logarithmic Module 3: Lesson 7-14: pages: 105 - 209


Resource: LearnZillion (https://learnzillion.com)

Lesson with a video (Standard: F-IF.A.2): https://learnzillion.com/lesson_plans/886 Lesson with a video (Standard: F-LE.A.4): https://learnzillion.com/lesson_plans/4927 Lesson with a video (Standard: S-ID.B.6a): https://learnzillion.com/lesson_plans/644#lesson-tab

Kuta Software (https://cdn.kutasoftware.com)

Graphing Exponential Functions https://cdn.kutasoftware.com/Worksheets/Alg2/Graphing%20Exponential%20Functions.pdf Graphing Logarithms https://cdn.kutasoftware.com/Worksheets/Alg2/Graphing%20Logarithms.pdf The Meaning Of Logarithms https://cdn.kutasoftware.com/Worksheets/Alg2/Meaning%20of%20Logarithms.pdf

Illustrative Math (https://www.illustrativemathematics.org) Task: (Alignments to Content Standards: F-IF.A.2) https://www.illustrativemathematics.org/content-standards/tasks/664 Task: (Alignments to Content Standards: S-ID.B.6, S-ID.C.7, S-ID.C.8, and S-ID.C.9):


Khan Academy (https://www.khanacademy.org) Video: https://www.khanacademy.org/math/algebra2/exponential-and-logarithmic-functions/introduction-to-logarithms/v/logarithms




https://cdn.kutasoftware.com/Worksheets/Alg2/Graphing%20Exponential%20Functions.pdf

https://cdn.kutasoftware.com/Worksheets/Alg2/Graphing%20Logarithms.pdf

https://cdn.kutasoftware.com/Worksheets/Alg2/Meaning%20of%20Logarithms.pdf



https://www.khanacademy.org/math/algebra2/exponential-and-logarithmic-functions/introduction-to-logarithms/v/logarithms


36

EngageNY (https://www.engageny.org)

Algebra II Modules

https://www.engageny.org/resource/algebra-ii-module-1e

Grade a math help (www.gradeamathhelp.com)

(Title: Exponential and Logarithmic Functions): http://www.gradeamathhelp.com/support-files/free-algebra2-worksheets-unit8.pdf



SUGGESTIONS

Activity 1: (Content Standard: F-IF.C.7e) Student will be analyzing the relationship between a Logarithmic Function and Its Inverse. Students will also have the opportunity to investigate the inverse of the logarithmic function and explore several uses of the logarithmic function and its inverse in real world applications. http://www.math.uakron.edu/amc/PreCalculusFoundationsToCalculus/Inverses/Logarithmic-ExponentialInverseRelat_84.doc.

Activity 2: (Content Standards: F-IF.C.8.b F-LE.B.5): Students will have to write a function defined by an

expression in different but equivalent forms to reveal and explain different properties of the function (exponential function) and apply it ti the real world. http://s3.amazonaws.com/illustrativemathematics/attachments/000/008/933/original/public_task_758.pdf?1462393591

https://www.engageny.org/resource/algebra-ii-module-1e

http://www.gradeamathhelp.com/support-files/free-algebra2-worksheets-unit8.pdf

http://www.math.uakron.edu/amc/PreCalculusFoundationsToCalculus/Inverses/Logarithmic-ExponentialInverseRelat_84.doc

http://www.math.uakron.edu/amc/PreCalculusFoundationsToCalculus/Inverses/Logarithmic-ExponentialInverseRelat_84.doc

http://s3.amazonaws.com/illustrativemathematics/attachments/000/008/933/original/public_task_758.pdf?1462393591

http://s3.amazonaws.com/illustrativemathematics/attachments/000/008/933/original/public_task_758.pdf?1462393591


37

UNIT 11 Trigonometric functions (10 DAYS)

1. Overview

As in Unit 10, students will continue to use many of the skills developed in previous units as they explore trigonometric functions. In Geometry,

students will have used basic trigonometric ratios to solve problems involving right triangles. This unit will be the first introduction to the concept of a

radian as an angle measure. Students will understand the radian measure of an angle as the length of the arc on the unit circle subtended by the

angle. Students will understand the unit circle and its usefulness to extend trigonometric functions to all real numbers. Additionally, students will

prove the Pythagorean identity sin2 (θ) + cos2 (θ) = 1. Finally, students will graph trigonometric functions, interpret key characteristics of the

function and/or graph, use the functions and/or graphs to solve problems, and fit trigonometric functions to given data.


have used basic trigonometric ratios to solve problems involving right triangles.

prove the Pythagorean identity sin2 (θ) + cos2 (θ) = 1.

graph trigonometric functions, interpret key characteristics of the function and/or graph, use the functions and/or graphs to solve

problems, and fit trigonometric functions to given data.

understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

FOCUS

STANDARDS F-IF.B.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.

F-IF.C.7e Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

a. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric

functions, showing period, midline, and amplitude.

F-TF.A.1 Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

F-TF.A.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.


38

F-TF.B.5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

F-TF.C.8 Prove the Pythagorean identity sin2 (θ) + cos2 (θ) = 1 and use it find sin (θ), cos (θ), or tan (θ) given sin (θ), cos (θ), or tan (θ) and the quadrant.

STANDARDS FOR

MATHEMATICAL

PRACTICE











Resource: enVision A|G|A A2: F-TF.A.1: SE/TE: 365-375 A2: F-TF.A.2: SE/TE: 376-382 A2: F-TF.B.5: SE/TE: 393-399, 400-407 A2: F-TF.C.8: SE/TE: 376-382 Eureka

F-TF.A.1, F-TF.A.2, F-TF.C.8, and F-TF.B.5

Trigonometric Functions: Module 2: Lesson 1- 10 pages 9-157

Resource:


v5.0, Unit 1



39

Resource: LearnZillion: (https://learnzillion.com)

Lesson with a video (Standard: F-TF.A.1): https://learnzillion.com/lesson_plans/712

Lesson with a video: Standard: F-TF.C.8): https://learnzillion.com/lesson_plans/731

Lesson with a video: (Standard: F-TF.C.8): https://learnzillion.com/lesson_plans/733

Lesson with a video: (Standard: F-TF.B.5): https://learnzillion.com/lesson_plans/735

Lesson with a video: (Standard: F-TF.A.2) https://learnzillion.com/lesson_plans/708

Kuta Software: (https://cdn.kutasoftware.com) Angles and Angle Measure

https://cdn.kutasoftware.com/Worksheets/Alg2/Angles%20and%20Angle%20Measure.pdf Arc Length and Sector Area

https://cdn.kutasoftware.com/Worksheets/Alg2/Arc%20Length%20and%20Sector%20Area.pdf Coterminal Angles and Reference Angles

https://cdn.kutasoftware.com/Worksheets/Alg2/Coterminal%20Angles%20and%20Reference%20Angles.pdf Illustrative Math: (https://www.illustrativemathematics.org)

Task: (Alignments to Content Standards: F-TF.C.8): https://www.illustrativemathematics.org/content-standards/tasks/1835


Video: https://www.khanacademy.org/math/geometry-home/right-triangles-topic/intro-to-the-trig-ratios-geo/v/basic-trigonometry

Video: https://www.khanacademy.org/math/geometry-home/right-triangles-topic/trig-solve-for-a-side-geo/v/example-trig-to-solve-the-

sides-and-angles-of-a-right-triangle



SUGGESTIONS

Trigonometry Square Activity 1 (Content Standard: F-TF.B.5) Students will apply trigonometry values for some common angles.

Prepare the activity sheet by cutting up the sheets into squares, and ideally laminating them. Directions: Place the sixteen squares in an envelope. Divide students into groups (groups of three work well). Give each group an envelope of squares, and instruct them to match equivalent






https://cdn.kutasoftware.com/Worksheets/Alg2/Angles%20and%20Angle%20Measure.pdf

https://cdn.kutasoftware.com/Worksheets/Alg2/Arc%20Length%20and%20Sector%20Area.pdf

https://cdn.kutasoftware.com/Worksheets/Alg2/Coterminal%20Angles%20and%20Reference%20Angles.pdf


https://www.khanacademy.org/math/geometry-home/right-triangles-topic/intro-to-the-trig-ratios-geo/v/basic-trigonometry

https://www.khanacademy.org/math/geometry-home/right-triangles-topic/trig-solve-for-a-side-geo/v/example-trig-to-solve-the-sides-and-angles-of-a-right-triangle

https://www.khanacademy.org/math/geometry-home/right-triangles-topic/trig-solve-for-a-side-geo/v/example-trig-to-solve-the-sides-and-angles-of-a-right-triangle


40

expressions to create one large square, lining up equivalent values. Students will review and learn common equivalents and will be better prepared to deal comfortably with trigonometric functions in more advanced studies. If a group seems to be having difficulty, suggest identifying one of the corner squares to get started. Sheet 1 and 2: These sheets are "answered" by the correct assembly of the puzzle. https://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/TrigDrills-AS-Square.pdf

Activity Sheet 2: https://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/TrigDrills-AS-Square2.pdf

Activity 2 (Content Standard: F-TF.C.8): Students will apply the Pythagorean Theorem and trigonometric ratios to find the measure of angle on the coordinate plane. Then they will write these measures in degree and radian form. Students also use trigonometric function to model natural phenomena, reflect on the accuracy of these models, and use them to make predictions about future events.

Activity Website (Please only print pages 4-6 for the activity and scoring rubric is pages 7-12) file:///C:/Users/class/Documents/g11_math_trigonometric_functions.pdf

https://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/TrigDrills-AS-Square.pdf

https://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/TrigDrills-AS-Square.pdf

https://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/TrigDrills-AS-Square2.pdf

https://illuminations.nctm.org/uploadedFiles/Content/Lessons/Resources/9-12/TrigDrills-AS-Square2.pdf


41

UNIT 12 Modeling Statistics (5 DAYS)

1. Overview

Students are first introduced to univariate statistics in 6th grade and work with univariate and/or bivariate statistics in 6th grade, 7th grade, 8th

grade, and Algebra I. In Algebra II, students will work with bivariate statistics as they fit data with different types of functions in Units 10 and 11. In

Unit 12 students will 1focus on univariate statistics. Students will explain the basis of statistics as predicting population characteristics from a sample

and will use sample data to make predictions about a population for normally distributed data. Students will understand the differences and

similarities among sample surveys, experiments, and observational studies and will explain the role of randomization in each. Also, students will

compare and evaluate given models with experimental data and use data and their knowledge of statistics to evaluate reports. Additionally, students

will use data to determine if a treatment has resulted in a significant difference between parameters.


summarize categorical data for two categories in two-way frequency tables. establish and distinguish between correlation and causation. compute (using technology) and interpret the correlation coefficient of a linear fit. interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). represent data on two quantitative variables on a scatter plot, and describe how the variables are related. recognize possible associations and trends in the data. define appropriate quantities for the purpose of descriptive modeling.

FOCUS

STANDARDS

S-ID.C.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

S-ID.C.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.

S-ID.C.9 Distinguish between correlation and causation.

F-BF.A.1a Write a linear, quadratic, or exponential function that describes a relationship between two quantities. a. Determine an explicit expression, a recursive process, or steps for calculation from a context.

N-Q.A.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.

N-Q.A.2 Define appropriate quantities for the purpose of descriptive modeling.


42

S-IC.B.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

S-IC.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use

given functions or choose a function suggested by the context. Emphasize linear and quadratic models.

b. Informally assess the fit of a function by plotting and analyzing residuals.

c. A linear function for a scatter plot that suggests a linear association.

STANDARDS FOR

MATHEMATICAL

PRACTICE











Resource: enVision A|G|A A2: S-IC.B.5: SE/TE: 589-596 A2: S-IC.B.6: SE/TE: 558-564, 573-580, 589-596 EUREKA

Resource:


v5.0, Unit 4


43

Statistics: Module 5: Lesson 1- 6 pages 8-91



Activity: (Alignments to Content Standards: S-ID.B.6 S-ID.C.7 S-ID.C.8 S-ID.C.9): https://www.illustrativemathematics.org/content-standards/HSS/ID/C/7/tasks/1307

Activity: (Alignments to Content Standards: S-ID.C.7 S-ID.B.6.a): https://www.illustrativemathematics.org/content-standards/HSS/ID/C/7/tasks/1554

Activity: (Alignments to Content Standards: S-ID.C.7): https://www.illustrativemathematics.org/content-standards/HSS/ID/C/7/tasks/1028

Activity: (Alignments to Content Standards: S-ID.C.7): https://www.illustrativemathematics.org/content-standards/HSS/ID/C/7/tasks/940

LearnZillion (https://learnzillion.com)

Lesson with a video (Standard: S-ID.B.5): https://learnzillion.com/lesson_plans/1031#lesson-tab Lesson with a video (Standard: S-ID.B.5): https://learnzillion.com/lesson_plans/1030#lesson-tab Lesson with a video (Standard: N-Q.A.2): https://learnzillion.com/lesson_plans/8504 Lesson with a video (Standard: N-Q.A.2): https://learnzillion.com/lesson_plans/8504-choose-appropriate-scales-for-graphs

Math Worksheets Land (http://www.mathworksheetsland.com)

Correlation vs. Causation Worksheet (Standard: S-ID.C.9 ): http://www.mathworksheetsland.com/stats/10corrvscause/ip.pdf Interpreting Slope and Rate of Change In Context (Standard: S-ID.C.7):

http://www.mathworksheetsland.com/stats/9interslope/ip.pdf

EngageNY (https://www.engageny.org) Algebra II Modules



https://www.illustrativemathematics.org/

https://www.illustrativemathematics.org/content-standards/HSS/ID/C/7/tasks/1307










https://learnzillion.com/lesson_plans/8504-choose-appropriate-scales-for-graphs

http://www.mathworksheetsland.com/stats/10corrvscause/ip.pdf

http://www.mathworksheetsland.com/stats/9interslope/ip.pdf



44


SUGGESTIONS

(Content Standard: S-ID.C.9): Distinguish between correlation and causation.

Activity 1: Students will read a brief article that summarizes research and complete the Class Activity: Correlation and Causation activity. In groups they identify different correlations and causations that are implied in the article. Each group will write down the correlations and causations they identified along with a justification/explanation of their thinking and put their findings on the whiteboards in class. Each group will then present their findings to the class: http://betterlesson.com/lesson/resource/1984628/class-activity-correlation-and-causation?from=lessonsection_narrative

(Content Standard: S-ID.C.9): Distinguish between correlation and causation.

Activity 2: Correlation and Causation Writing Activity: http://betterlesson.com/lesson/resource/1984630/independent-work-writing-activity-on-correlation-and-causation?from=lessonsection_narrative Rubric: http://betterlesson.com/lesson/resource/1984631/short-response-rubric-for-correlation-and-causation-writing-activity

http://betterlesson.com/lesson/resource/1984628/class-activity-correlation-and-causation

http://betterlesson.com/lesson/resource/1984628/class-activity-correlation-and-causation

http://betterlesson.com/lesson/resource/1984628/class-activity-correlation-and-causation?from=lessonsection_narrative

http://betterlesson.com/lesson/resource/1984628/class-activity-correlation-and-causation?from=lessonsection_narrative

http://betterlesson.com/lesson/resource/1984630/independent-work-writing-activity-on-correlation-and-causation?from=lessonsection_narrative

http://betterlesson.com/lesson/resource/1984630/independent-work-writing-activity-on-correlation-and-causation?from=lessonsection_narrative

http://betterlesson.com/lesson/resource/1984631/short-response-rubric-for-correlation-and-causation-writing-activity

http://betterlesson.com/lesson/resource/1984631/short-response-rubric-for-correlation-and-causation-writing-activity