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# Step Functions

Lesson 17 of 24

## Objective: Students will be able to write and graph step functions

#### Warm up and Homework Check

*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- Step Functions asks students to write a piecewise function given a scenario.

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

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This lesson begins with a simple step function scenario: *AT&T offers a 10¢ per minute cell phone plan.* I ask the students to both graph and write an equation for this situation (**Math Practice 4**). Most students will want to do f(x)=0.10x along with the corresponding graph. Once they have had some time to work, I put this situation on the board and tell them that there is a problem with this model. I then ask them to do a think-pair-share to figure out the problem. It is important to clarify at this point that talking for 2 minutes and 1 second will be counted as 3 minutes. I have them redraw this graph up through five minutes including the proper open and closed end points.

Now that they have a graph of this situation, I show how to write it as a floor function. We also talk about ceiling functions and the difference between the two.

I then give them another scenario to model with a function and a graph: *The seniors are going on a field trip. Each bus has a capacity of 60 students*. This will help solidify this new concept. I also have them find the domain, range and intercepts for this function. It is good to compare the graph for this specific scenario to the general graph of the function.

#### Resources

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#### Is this a Step Function?

*8 min*

The next scenario isn’t really a step function although it does share similarities with one.

*I took my dog to the groomer to get a bath. Here is the pricing: 0-30 pounds $15 31-70 pounds $25 > 70 pounds $35*

I give this to my students without a warning that it is different. Once they have had a chance to work on it a bit, there is a good opportunity for some discussions about the similarities and differences between this and a step function (**Math Practice 7**). They will then write a piecewise function and graph this scenario.

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#### Write your own Step Function

*15 min*

The last activity in this lesson begins with a brainstorming session on situations that can be modeled as step functions. Students will come up with examples as pairs and then we will make a list as a class. Each student will then create their own step function scenario which they will switch with their partner to graph and write a function (**Math Practice 2**). This activity will help students deepen their understanding of step functions vs. other piecewise functions.

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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 student to write a step function from a real life scenario.

#### Resources

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This short assignment gives the students 4 scenarios that are either step or piecewise functions. Students need to determine whether they are step or piecewise** **(**Math Practice 7**), write a function to match the scenario and graph it on a coordinate plane.

#### 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