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# Mathematical Modeling: Properties of Functions Day 2 of 2

Lesson 2 of 24

## Objective: Students will be able to model functions and identify their important features.

*45 minutes*

#### Warm up

*5 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- Modeling Functions Day 2 asks students to write a linear function given a chart of values (**Math Practice 5**).

The next introductory partner question is: *What is the first dream you can remember?*

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This is the second day of a two part lesson. I have included the last activity from the previous day as each class may end up in separate places. This will be skipped if already finished.

I present them with a definition for a function and then we look at a non-linear model (**Math Practice 4**). *Write an equation that relates the side of a square to its area.* The students write an equation, make a table and graph it, and then identify the x-intercept, y-intercept, domain, range, and independent/dependent variables of both the graph and the situation. This helps them solidify some of these introductory concepts discussed in the first example.

#### Resources

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#### Modeling Function Activity

*22 min*

In this Activity, each pair of students come up with three situations that compare two values and write them on note cards. As they finish, they bring the cards up to me so I can check that they are reasonable and contain adequate information. I return them for corrections if they don't contain enough information. Pairs that finish quickly can aid their peers. I may hold a brain storming session for ideas, as a scaffolding measure, if my students are struggling to come up with ideas.

Once all of the cards have been collected, I shuffle them and pass three to each pair. It doesn't matter if they get one of their own. Please seem my video on differentiation in this activity.

Each student will need to complete the following steps for each of the three problems they received:

*You will be creating complete mathematical model information profiles for each of the three problem situation cards. To do this you will need to:*

*The equation in function notation.*

*A chart of five values.*

*A graph.*

*Identify the independent and the dependent variables.*

*Identify the x-intercept, y-intercept, domain, and range. Explain what each means to the situation. *

*Write two questions that can be answered from this situation.*

Once the students have copied down their situations, I collect them because they will be used in another activity. I walk around the classroom providing support and encouraging the students to get a sense of each problem before leaving the class. Rather than giving answers, I ask questions that will lead to the solution. Anything not finished will be homework.

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#### Exit Ticket

*3 min*

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

This Exit Ticket, located in the PowerPoint in Section 2, gives the students a simple situation to model with function notation. It also asks them to find f(4). The purpose of this exit ticket is to assess their understanding of both evaluating function notation and rewriting equations as functions.

#### 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: Mathematical Modeling: Properties of Functions Day 1 of 2
- LESSON 2: Mathematical Modeling: Properties of Functions Day 2 of 2
- LESSON 3: Mathematical Modeling: Linear Functions
- LESSON 4: Mathematical Modeling: Linear Functions Design Project
- LESSON 5: Finding Equations of Parallel and Perpendicular Lines
- LESSON 6: Inverse Functions
- LESSON 7: System of Equations Day 1 of 2
- LESSON 8: Systems of Equations Day 2 of 2
- LESSON 9: Modeling Systems of Equations
- LESSON 10: Function Review
- LESSON 11: Function Mid Test
- LESSON 12: The Tortoise and The Hare Project Day 1
- LESSON 13: The Tortoise and The Hare Project Day 2
- LESSON 14: The Tortoise and The Hare Project Day 3
- LESSON 15: The Tortoise and the Hare Project Day 4
- LESSON 16: The Tortoise and the Hare Piece-wise Functions
- LESSON 17: Step Functions
- LESSON 18: Absolute Value Equations
- LESSON 19: Absolute Value Inequalities
- LESSON 20: Absolute Value Functions: Transformations Day 1
- LESSON 21: Absolute Value Functions: Transformations Day 2
- LESSON 22: Functions Test Review Day 1
- LESSON 23: Functions Test Review Day 2
- LESSON 24: Functions Test