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# Dicey Functions Day 2: Piecewise functions are basic functions... just cut up!

Lesson 8 of 16

## Objective: SWBAT evaluate a piecewise function, graph piecewise and step functions, and write the equation of the graph of a piecewise or step function.

## Big Idea: Teams explore piecewise functions on Day 2 of this self-paced activity with built in checks for understanding.

*50 minutes*

Students should continue their work on the Piecewise Investigation packet. See below for reminders from yesterday....

**Environment: **I will have students work with their 2 tablemates to complete this work. After our discussion of the mathematical practice of the day, Mathematical Practice 2, I will take some time to review my classroom expectations for teamwork (see Basic Team Rules in the list of resources).

**Differentiation:** For students advancing through this work quickly, keep pushing them to finish this packet so that they can move on to the more interesting Moving Day Problem. I predict that more advanced student teams will be able to finish this packet today. And then, they can spend the whole class period tomorrow extending their understating of piecewise functions by solving the Moving Day Problem.

For struggling students, I feel like there are already many scaffolds built in throughout the worksheet. The work was designed to step students though the problems so that they can learn the material without it being modeled for them first. Therefore, I predict most of their struggles are going to come from a lack of understanding of what the question is even asking. So I plan to start by helping students to define the key words in the sentence and help them make more meaning of what I am even asking. For example, in question 6, I think that question is very straight forward as long as students recall what a ray is. In question 8, students may not yet know minimum and maximum values of a function (even though most will know this intuitively). So the first line of defense: help students understand what the question is asking. Then ask students to ask you some questions to help them clarify anything else they don’t know after they have confirmed that they understand what we are asking.

**Narrative continued from video: **Be sure to close out today’s learning using the clicker questions (pages 3-6 of Flipchart - Piecewise Functions) for the sections in the worksheet that your students have completed. I plan to chunk it and give a ‘closure question’ about every 10 minutes or so to keep pushing students through the sections. I predict that my slowest student should be able to complete the first 2-3 parts today and will finish the rest tomorrow. Although I am ending ‘today's’ lesson here, students should continue to work until the end of the period even if they finish this section. We want to push students to finish as much as they can so we can hopefully have time to look at the moving day problem tomorrow.

*expand content*

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: Getting to Know You, Getting to Know All About You...
- LESSON 2: Ahoy team! What can you see? Finding functions.
- LESSON 3: Function Zoo - Basic Function Families
- LESSON 4: Parent Functions
- LESSON 5: Shifting Functions: How do they move?
- LESSON 6: Shifting Functions: How can we describe them?
- LESSON 7: Dicey Functions Day 1: Piecewise functions are basic functions... just cut up!
- LESSON 8: Dicey Functions Day 2: Piecewise functions are basic functions... just cut up!
- LESSON 9: Fun with Functions: Basic Inverse and Function Operations
- LESSON 10: Compositions in Context
- LESSON 11: Inundated with Inverses: Restricting the Range of an Inverse (Day 1 of 2)
- LESSON 12: Inundated with Inverses: Algebraic Inverse and Composition to Verify (Day 2 of 2)
- LESSON 13: Jeopardy: Basic Functions
- LESSON 14: Review Day
- LESSON 15: Test Review
- LESSON 16: Basic Functions Test