Radical Equations and Relationships - Unit 8 Bundle - Texas Algebra 2 Curriculum

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10th - 12th
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137 pages + keys
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  1. Get a complete, ready-to-print curriculum covering topics from the Algebra 2 TEKS.This curriculum bundle contains guided notes handouts, practice worksheets, exit tickets, warm-ups, reviews, mid-unit assessments, tests, and concept organizers - all aligned to the Texas Algebra 2 state standards (TEK
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Description

Get a complete, ready-to-print unit covering topics from the Algebra 2 TEKS including square root, cube root, and cubic function transformations; solving radical equations; solving equations with rational exponents; find and graph the inverse of quadratic/square root and cubic/cube root functions.


UNIT OVERVIEW:

This unit extends students' knowledge of function transformations to square root functions y = (x), cubic functions y = x³. and cube root functions y = ∛(x). Students will write equations of transformed functions and describe transformations including vertical stretch and compression, horizontal stretch and compression, vertical and horizontal translation, and reflection about the x-axis and y-axis.

This unit also introduces solving radical equations, including square root equations, cube root equations, and equations involving rational exponents. Students will identify extraneous solutions of square root functions.

Finally, students will build on their knowledge of inverse functions by finding and graphing the inverse of cubic, cube root, quadratic, and square root functions including domain restrictions when necessary.

These no-prep resources include 7 lessons with guided notes, an exit ticket, a next-day warm-up, and 2 extra practice assignments per lesson.  The unit also includes mid-unit and end-of-unit reviews, mid-unit and end-of-unit editable assessments, and concept organizers. Increase student engagement with 10 TEKS-aligned activities!

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TEACHERS LOVE the worked-out keys included with the lessons notes. Feel confident delivering instruction on these sometimes tricky topics! It is a major time-saver if you don’t have quite enough time to create your own guided notes key for the day.

STUDENTS LOVE the reduced note-taking burden with the guided notes handouts. Fill-in-the-blank vocabulary improves the accuracy of students’ notes and frees up more time for showing mathematical steps. 

TEACHERS LOVE the multiple versions of each practice worksheet, review, and assessment and they take full advantage of the EDITABLE versions of the mid-unit assessment form and unit test.

STUDENTS LOVE the complementary concept organizers that help them organize concepts and procedures.  

TEACHERS LOVE the pre-made exit tickets and next-day warm-ups that support skills from every lesson in the unit. Print 4-per-page or project on the board and record answers on scratch paper.

STUDENTS LOVE the variety of fun and engaging activities!  

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Most resources are in non-editable PDF format.

  • Editable versions of the mid-unit assessment and test are also included in .docx format for MS Word.
  • 5 digital activities compatible with Google Slides and Google Classroom™ are included. (Printable versions of the digital activities are included in PDF format.)
  • 5 paper-based activities in PDF format are included.

UNIT 8 INCLUDES THE FOLLOWING LESSONS:

Lesson 1: Transformations I

Students will:

  • formulate the equation of transformed square root, cubic, and cube root functions
  • describe single function transformations performed on y = (x), y = x^3, and y = ∛(x)

Lesson 2: Transformations II

Students will:

  • formulate the equation of transformed square root, cubic, and cube root functions
  • describe composite function transformations performed on y = (x), y = x^3, and y = ∛(x)

Lesson 3: Solving Radical Equations

Students will:

  • solve square root and cube root equations
  • check for extraneous solutions

Lesson 4: Solving Equations with Rational Exponents

Students will:

  • solve equations involving rational exponents

Lesson 5: Cubic-Cube Root Relationship

Students will:

  • find the inverse of cubic and cube root functions algebraically
  • graph inverse functions
  • verify functions using the composition of functions

Lesson 6: Quadratic-Square Root Relationship

Students will:

  • find the inverse of quadratic and square root functions algebraically, including domain restrictions
  • graph inverse functions
  • verify functions using the composition of functions

Lesson 7: Inverse Function Study

Students will:

  • write and graph inverses of cubic, cube root, quadratic, and square root functions
  • verify functions using the composition of functions
  • describe and analyze the relationship between a function and its inverse using multiple representations

EACH LESSON CONTAINS THE FOLLOWING ELEMENTS:

  • The Lesson Notes are designed for use as a note-taking guide combined with guided practice.
  • Practice A and Practice B are suitable for use as in-class practice and homework. Two comparable forms are included for increased versatility.
  • The Exit Ticket is designed for a quick concept check at the end of the class period.
  • The Warm-Up is designed for next-day use to reinforce the previous day’s learning.
  • One-page display versions of the exit ticket and warm-up are included. Display the PDF page on a screen for student viewing and have students record their responses on notebook paper or scratch paper to save on printing.

ADDITIONAL RESOURCES EXCLUSIVELY AVAILABLE IN UNIT 8 INCLUDE:

  • 3 Concept Organizers offer a complementary alternative for note-taking or post-lesson concept reinforcement.
  • The Mid-Unit Review (Forms A and B) provides an opportunity for students to practice the concepts they learned in the first part of the unit.
  • The Mid-Unit Assessment (Forms A and B) may be used as a test, quiz, or daily assignment to meet the specific needs of your students. Editable versions of Forms A and B are included as a .docx file for MS Word.
  • The Unit Review (Forms A and B) helps students focus on the key concepts studied throughout the unit.
  • The Unit Test (Forms A, B, and C) comes in two comparable multiple-choice forms (A and B) and one free-response form (C). The test key includes TEKS alignment for each question to facilitate easy data analysis. Editable versions of Forms A and B are included as a .docx file for MS Word.

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5 PAPER-BASED ACTIVITIES ARE INCLUDED IN THIS BUNDLE:

5 DIGITAL ACTIVITIES FOR GOOGLE SLIDES ARE INCLUDED IN THIS BUNDLE:

(Each digital activity also includes a printable version.)

Please view the previews in the bundle section for more detail.

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This unit and activity bundle is perfect for providing a complete TEKS-aligned unit or for supplementing existing resources. Use every resource or pick-and-choose from the many options to meet the needs of your students!

TEACHERS LIKE YOU SAID…

⭐️⭐️⭐️⭐️⭐️ “Amazing! I only wish I had it earlier.”

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Supports Algebra 2 Texas Essential Knowledge and Skills (TEKS)

Standards: 2A.2B, 2A.2C, 2A.2D, 2A.4C, 2A.4F, 2A.4G, 2A.6A, 2A.6B, 2A.7H

A note from Allison at Math Beach Solutions about standards alignment: This resource was designed from the ground up to provide ready-made resources for Texas teachers to implement to facilitate their students’ mastery of the Algebra 2 TEKS (Texas Essential Knowledge and Skills TAC §111.40). A considerable effort has been made to ensure the TEKS are addressed thoroughly, but these resources will reflect my understanding of the TEKS. As always, continue to use your professional judgment and experience when lesson planning.

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⭐️ Bundle & save for a discount ⭐️

Purchase the Texas Algebra 2 Curriculum to get all 12 units and activities. The curriculum lasts the entire year. It also includes an editable mid-term and editable final exam!

You may also like...

Looking for a long-term homework solution? Check out Algebra 2 Skill Spirals Review Workbook for a year-long solution for homework, warm-ups, or tutorial session resources. It supports the Texas Algebra 2 TEKS, too!

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Having difficulty with a file?

Visit the FAQs section, submit a help ticket, or email allison@mathbeach.com before leaving feedback. 

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Copyright © Math Beach Solutions LLC.

Permission to copy for single classroom use only. 

Please purchase additional licenses if you intend to share this product.

Total Pages
137 pages + keys
Answer Key
Included
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Standards

to see state-specific standards (only available in the US).
Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.
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.
Identify the effect on the graph of replacing 𝘧(𝘹) by 𝘧(𝘹) + 𝘬, 𝘬 𝘧(𝘹), 𝘧(𝘬𝘹), and 𝘧(𝘹 + 𝘬) for specific values of 𝘬 (both positive and negative); find the value of 𝘬 given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
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) =2 𝘹³ or 𝘧(𝘹) = (𝘹+1)/(𝘹–1) for 𝘹 ≠ 1.

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