Dicey Functions Day 1: Piecewise functions are basic functions... just cut up!

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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

Working in teams, students explore piece-wise functions in this self-paced activity that emphasizes MP2: Reasoning Abstractly and Quantitatively.

Warm-up: Evaluating Functions

3 minutes

There is a clicker question built into page 2 of the flipchart that just has students review function notation and what it means to evaluate a function for a given value of x. Students will just text in their numeric answers so you can check to be sure all students understand this basic function notation before moving onto evaluating piecewise functions.

Homework Quiz

10 minutes

In my class, we do a  Homework Quiz every Monday. So for my calendar this lesson is landing on a Monday, so we will take about 10 minutes out of class to do that. I am not posting my homework quizzes at this time because I like to be selective of the problems I put on the quiz based on what is happening in the classroom. If students are really struggling on a particular topic as a whole then I won’t put that question on the quiz. Or if we have gone over a problem in class, I won’t put that on the quiz but would probably choose a similar problem. So for minimal prep work, I would recommend having students do a written homework quiz. Just make a list of problems that you want to check in more detail and give students an allotment of time to copy down their work and answer for this problem. I also sometimes have students do their homework quizzes in their clickers. I will share an example of that, once one is made.

Overview: Mathematical Practice of the Day

2 minutes

Overview: Investigating Piecewise Functions

33 minutes

Investigation: Piecewise functions

1 minutes

Environment: I will be having students work with their 2 other tablemates to complete this work. After our discussion of the mathematical practice of the day (Mathematical Practice 2: reason abstractly and quantitatively), I will take some time once again to review the expectations for teamwork. (see Basic Team Rules pdf)  

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 our more advanced student teams will be able to finish this packet today. And then 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 built into pages 3-6 of the flipchart for the sections in the worksheet that you feel that your students have successfully worked through. 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 ‘todays’ 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.


1 minutes

Assign homework 3 from this unit at the end of today’s lesson. Even though we will be continuing this lesson tomorrow, students can start acticing what they know and then if we feel the need we can assign the Moving Day problem for homework tomorrow.