##
* *Reflection: High Expectations
Transformations of Rational Functions - Section 1: Warm up and Homework Review

One important measure we math teachers need to take, particularly in this transition to the Common Core, is to ensure that our students are writing about mathematics. This will be a requirement on both the SBAC and the PARCC standardized tests, and if your students are like mine, they need plenty of opportunities to practice this skill. One of my biggest struggles has been to get students to write in complete sentences. For example, Warm Up 2 is a correct response to today’s warm up. This student knew what she was doing but just listed the transformations rather than writing them down properly. Warm Up 1 did a much better job thoroughly explaining her work. While complete sentences are part of my rubric, I think some of my students have gotten a bit lazy. I think tomorrow I will review the rubric with them.

*High Expectations: The Importance of Complete Sentences*

# Transformations of Rational Functions

Lesson 3 of 15

## Objective: Students will be able to graph rational functions using transformations.

*50 minutes*

#### Warm up and Homework Review

*10 min*

I include **Warm ups** with a **Rubric** as part of my daily routine. My goal is to allow students to work on **Math Practice 3** each day. Grouping students into homogenous pairs provides an opportunity for appropriately differentiated math conversations. The Video Narrative explains this lesson’s Warm Up- Transformations of Rational Functions which asks students to describe the transformations on an absolute value function.

I also use this time to correct and record the previous day's Homework.

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We begin by looking at the two basic rational parent functions and their features. This is the basis for the rest of the lesson. The students create a table, graph each function, and determine the domain and range. We also look at the equations of each asymptotes and discuss why the function is undefined at these points (**Math Practice 2**).

Next, we investigate vertical reflections, and horizontal and vertical translations individually. Rather than identify the domain, range and asymptotes of each function we graph, I have the students identify any differences between its properties and the parent function.

The students then graph several functions with multiple transformations. Finally, the students find the function given information or a graph which deepens their understanding of transformations on rational functions.

Detailed presentation notes are located in the PowerPoint.

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#### Exit Ticket

*2 min*

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.

Today's Exit Ticket asks students to graph rational functions using transformations.

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This Assignment begins with a small number of rational functions to graph. While brief, these problems reinforce the graphing skill. The final three problems look at these transformations in different ways to ensure that student understand their structure (**Math Practice 7**).

This assignment was created with Kuta Software, an amazing resource for secondary mathematics teachers.

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- UNIT 1: Modeling with Expressions and Equations
- UNIT 2: Modeling with Functions
- UNIT 3: Polynomials
- UNIT 4: Complex Numbers and Quadratic Equations
- UNIT 5: Radical Functions and Equations
- UNIT 6: Polynomial Functions
- UNIT 7: Rational Functions
- UNIT 8: Exponential and Logarithmic Functions
- UNIT 9: Trigonometric Functions
- UNIT 10: Modeling Data with Statistics and Probability
- UNIT 11: Semester 1 Review
- UNIT 12: Semester 2 Review

- LESSON 1: Quotients of Monomials
- LESSON 2: Modeling Rational Functions
- LESSON 3: Transformations of Rational Functions
- LESSON 4: Properties of Rational Functions Investigation Day 1 of 2
- LESSON 5: Properties of Rational Functions Investigation Day 2 of 2
- LESSON 6: Rational Functions Quiz
- LESSON 7: Modeling and Simplifying Rational Expressions
- LESSON 8: Multiplying and Dividing Rational Expressions
- LESSON 9: Adding and Subtraction Rational Expressions
- LESSON 10: Complex Rational Expressions
- LESSON 11: Equations with Rational Coefficients
- LESSON 12: Rational Equations
- LESSON 13: Rational Functions Review Day 1
- LESSON 14: Rational Function Review Day 2
- LESSON 15: Rational Functions Test