Reading Apprenticeship Inspired Lesson

I have attached the handout that I used based on notes built collaboratively with colleagues using the James Stewart Calculus book. RA Course Final Project.pdf                                                   

I do not remember which online resources the graphs came from, so adjust those as you see fit.

Students will need a copy of the notes, graph paper, and a pencil with eraser.

You have tons of options of how you can grade this! 

You can have students turn in their sketch and their partners sketch with the criteria and grade them yourself.

You can have students grade each others and write a discussion post or grade their peer grading.                                                      

You can make it an informal class discussion and grade based on effort and participation. This last gradin strategy can help students feel less pressured and stress that creativity, effort, and self-reflection are key components to learning.

This lesson will take place within the first week or two of classes (depending on how much review you complete first). 

Students would learn first about the rules of left hand limits, right hand limits, and two-sided limits graphically. Students will also understand, graphically, when a limit does not exist.

After learning this lesson,  students will...                                                                       CREATE: Each student will be asked to sketch their own function with limit restrictions. I would recommend at least one place where the left and right hand limits differ, at least one infinite limit, one two-sided limit, and anything else you'd like to see.                                                                   

WRITTEN INTERPRETATION: Students will analyze their own sketch and create limit and points (both open and closed) "on" graph to give to another student.                    

EXCHANGE AND READING INTERPRETATION: Students exchange limit restrictions, they will attempt to sketch a graph that meets their partners criteria.        

ANALYZE AND REFLECTION: Students will return their work to the partner who wrote the directions. The student will grade their partners graph and put a check mark next to those that were met while circling and analyzing those that were not. This can be followed by a peer discussion and reflection.

This activity can take anywhere from 20 - 30 minutes depending on how much reflection you would like involved.

CREATE your function (5 minutes)   

WRITE and INTERPRET using mathematical notation (7 minutes)       *This allows for any adjustments needed on graph.

EXCHANGE GRAPH PAPER WITH LIMIT RULES (2 minutes)

PARTNER SKETCH (6 minutes)              Allows students time to interpret their criteria and sketch in pencil in case any corrections need to be made.     

(optional) GRADE PARTNER'S WORK + FEEDBACK SHARING  (5 - 10 minutes)   *You could also make this an online discussion or submission where they send the feedback through some form of online communication you want your students to get used to.

If the students are checking each others work, you can remind them that the sketch they receive might not look exactly like what the student drew initially. Multiple functions can meet these criteria.                    

I also recommend reminding students to verify that the graph passes the vertical line test and truly is a function. This tends to be a common mistake at first.