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Mathematical Modeling: Properties of Functions Day 1 of 2
Lesson 1 of 24
Objective: Students will be able to model functions and identify their important features.

Warm Up
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. As seen in the video narrative, this lesson’s Warm Up- Modeling Functions asks students to model a linear situation which is the introductory example in today's lesson.
Since this is the first day of a new unit, my students are placed with new partners. Since they will be having a lot of conversations with this person, I provide them with a conversation starter at the beginning of the first several lessons in this unit. Today's starter is: "What was your favorite toy growing up?"
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The warm up is the introduction to today's lesson. I begin by talking about the expression from the warm up: Alvin has a pool that has 80 cm of water. He is emptying it at a rate of 12 cm per minute. This is a similar problem to the ones done in the first unit. I explain that we can rewrite this as a two variable situation: y = 80 – 12x where x represents minutes and y represents the depth of the pool.
I then introduce function notation as a different method for writing the same scenario and relate that f(x) is another method of writing y.
Now we review evaluating functions with function notation. I show them how to find f(1). Then the students try the second one, f(3), and the third one, f(10). I ask them to relate each answer back to the situation as this keeps their mind on the scenario which will deepen their understanding of how function notation works (Math Practice 7).
The students then make a table of the first five minutes of this situation and graph the ordered pairs. I make sure to have them label the intercepts with both the variable and the unit. Either a student that I choose or myself graph it on the white board to help with next portion of the activity.
Once they have a graph, we talk about some of the important terms associated to the graph of this function including x- intercept, y-intercept, domain, range, and independent/dependent variables. We define each of them and relate them back to both the graph and the situation (Math Practice 2).
I present them with a formal definition for a function and then we look at a non-linear model. 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.
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Exit Ticket
I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.
This Exit Ticket asks students to describe the difference between the independent and the dependent variables of a function.
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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