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

# Real Number Exponents

Lesson 2 of 15

## Objective: Students will be able to simplify real number exponents and solve equations with real number exponents.

*47 minutes*

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- Real Number Exponents asks students to correct the thinking of a fictional person who is doing a rational exponent problem. This warm up highlights one of the most common problems surrounding student understanding of multiplying exponents.

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

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#### Real Number System

*10 min*

Th

The goal of today’s lesson is to extend the student’s knowledge of exponents into real number exponents. Our first task is to construct a diagram of the relationship between real numbers (**Math Practice 7**). This is a conversation that has happened earlier in the year so it should be a review.

I give the students a couple of minutes. If they all seem to be floundering, then I provide some hints as to what real numbers are. I then pick a couple that have fairly different samples and have them put them on the board making sure to include someone how has irrational numbers. This is a great time to pick students who are reluctant to talk in class. Sometimes, I help a student who usually struggles to get a good example and then ask them to put it on the board. Please check out my Video Narrative about this task.

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#### Real Number Exponents

*30 min*

The remainder of the lesson involves Guided Practice of the specific skills important to the fruition of the day's objective. I have found this method to work the best for me when it comes to introducing students to new skills.

I start with something they know or give a basic introduction so they have some confidence. Each successive problem either reinforces a new that skill or strategy or adds a new twist. This works well since they go into each problem feeling like they already have some skill. It is also extremely important to follow to needs of a particular class. I regularly skip through problems or add more as needed. By the time we are done, they have had experience solving a wide range of problems for a particular skill. I try to include an extension in the homework that was not part of the day's instruction as this forces them to do some synthesis of what they have already done.

Detailed presentation notes can be found in the PowerPoint.

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This Assignment includes a variety of expressions and equations that include real number exponents.

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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 solve an equation similar to the problems worked on in the guided practice.

#### Resources

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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: Rational Exponents
- LESSON 2: Real Number Exponents
- LESSON 3: Exponential Models Day 1 of 2
- LESSON 4: Exponential Models Day 2 of 2
- LESSON 5: Exponential Functions
- LESSON 6: Exponential Decay Functions
- LESSON 7: Simplifying Logarithms
- LESSON 8: Exponential and Logarithmic Equations
- LESSON 9: Logarithmic Functions
- LESSON 10: Exponential Growth and Interest Day 1 of 2
- LESSON 11: Exponential Growth and Interest Day 2 of 2
- LESSON 12: Natural Logarithms
- LESSON 13: Exponential and Logarithmic Functions Review Day 1
- LESSON 14: Exponential and Logarithmic Functions Review Day 2
- LESSON 15: Exponential and Logarithmic Functions Test