Reading Apprenticeship Inspired Assignment or Lesson 

This lesson takes place after reviewing intermediate algebra and after being introduced to functions. By this point, students have practiced identifying functions from relations (S, G) and should be familiar with function notation, evaluating functions, and finding the domain (S). They should also be familiar with writing in interval or set builder notation from the real number line.

S - Symbolic representation of functions (equations)

G - Graphical representation of functions

Metacognitive routines practiced up to this point: Think Aloud, Think-Pair-Share, Evidence and Interpretation (E&I) notetaker, Think Aloud Partner Problem Solving

To evaluate students’ understanding, they will complete an exit slip as a formative assessment. We care to see that students are interpreting and expressing interval or set builder notation accurately (writing from least to greatest, correct endpoints, inclusion/exclusion of endpoints), we also care about identifying characteristics of the graph and taking into account the discontinuities of the graph when formulating their answers.

Students will have completed an Evidence and Interpretation notetaker on two short videos prior to class. In class, we will debrief students’ insights from the E&I notetaker. 

After the debrief, students will work in pairs to analyze the graph of a function and identify a couple of its characteristics. This is followed by a class discussion where the instructor brings forth the student's mistakes to clear out misconceptions and the class can come to a consensus of the result. 

The students will repeat this portion of the activity two more times, each time identifying a couple more characteristics. Additionally, students will have direct links to OER texts as an additional resource. 

This activity is designed for a synchronous setting. See all the details at College Algebra Stretch I Reading Apprenticeship Plan

Videos (for pre-class assignment)

• video 1 -  Domain and Range of the graph of a function
•  video 2 - Introduction to increasing, decreasing, positive or negative intervals 

Graphs:  Graphs of any function (including piecewise functions). Graphs can be created using Demos or can be obtained from OER texts. 

Textbook: Openstax College Algebra

• Section 3.1 - Finding Function values from a graph - Ex. 12

• Section 3.2 - Domain and Range of the graph of a function (right after example 5)

• Section 3.3 - Using a graph to determine where the function is increasing, decreasing, or constant (after Try it #3) 

• Section 3.3 - Local and Absolute Extremas (only read after figure 3 to Example 7 and after figure 12 to Example 10)

• Section 3.2 - Using Notations to Specify Domain and Range (after Example 4 to Example 5)

Handout (“exit slip” question can be found in handout):

• Characteristics of Graphs of Functions