## Warm ups - Section 1: Warm up and Homework Review

# Rational Functions Review Day 1

Lesson 13 of 15

## Objective: Students will be able to model and graph rational functions.

*55 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 homogeneous pairs provides an opportunity for appropriately differentiated math conversations. This lesson’s Warm Up- Rational Functions Review Day 1, asks students to analyze the mistakes of a student simplifying an expression with a negative exponent. This warm up came from a website that highlights the mistakes students make with the hope of helping teachers better understand their students.

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

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#### Review Activity

*40 min*

The review for this unit has been split into two days with the first day focusing on modeling and graphing rational functions and the second day focusing on connecting rational expressions to the operations performed on rational numbers.

Today’s review looks at three major skills:

- graphing and interpreting rational functions through transformations
- writing rational functions given a set of constraints, and
- solving modeling problems with rational equations.

This activity is done with personal white boards. I give the students a problem, they solve it as best they can and then hold their solution for me to view.

At this point, I do one of two things. If most are correct, I give feedback individually to students. If there are multiple correct solutions and/or many incorrect answers, I write the variations on the board, and have the students analyze them in pairs. We then share out as a class, eliminating the incorrect ones until only the correct remain. This is an extremely powerful activity that allows students to critique each other’s reasoning (**Math Practice 3**) as well as view multiple models for a problem (**Math Practice 5**). As I move through the problems, I may skip some or add additional problems as seems right for my students.

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This Practice Test assignment is a common style of review that I use for all of my units. For more information, please check out this **document**.

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#### Exit Ticket

*5 min*

For today's exit ticket, I ask the student to describe how to find the domain of a rational function. This is one of the big ideas of this unit and hits on precision when solving problems involving rational functions (**Math Practice 6**).

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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