##
* *Reflection: Problem-based Approaches
Problem Solving Assessment - Section 1: Problem Solving Activity

**STUDENT WORK A**: This student failed to create the correct optimization equation, and instead created an inequality. Figuring out why this happened is a tough one, and I am going to have to conference with the student to see what was going through their head at the time. The remainder of the assessment wasn't bad, the incorrect initial equation lead them to an incorrect optimal solution.

**STUDENT WORK B**: When in doubt, put both answers! This is the philosophy of many students, and I always get a kick out of it on a test. The student's inability to chose one or the other crippled them and they were unable to get the correct answer. In my follow up conversations, I will encourage them to try BOTH equations (set them up accordingly) and see which answer makes sense.

**STUDENT WORK C**: An excellent job setting up the proper optimization equation (or objective function). This particular student only mixed up a couple of constraints... they failed to realize that there is both an upper AND a lower bound on acreage, and that profit is not a constraint but rather something that we are trying to maximize.

*NOTE: Disregard the point values shown at the top of the exam. This test was given in conjunction with another assessment required at out school. *

*Problem-based Approaches: Student Work Samples*

# Problem Solving Assessment

Lesson 10 of 11

## Objective: SWBAT showcase their growth in setting up and solving a complex problem!

*45 minutes*

#### Problem Solving Activity

*25 min*

I circulate this short, 20-30 minutes*, Problem Solving Assessment for the students to complete in class. There is no warm up prior to the assessment. I have also included a modified version that includes the final graph needed (MP1, MP5). I use this version **only** when students do not have access to a graphing utility or equivalent technology and I do not want to make graphing by hand a requirement.

**This version does not have a final graph. Students will either use technology to graph the constraints OR have them do it by hand on graph paper. If you choose to have them graph by hand (MP1), expect the completion time to increase by 10-15 minutes*

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#### Makin' the Rounds

*10 min*

As the students begin to finish up the exam, I take time to personally collect it as they finish. As I do, I quietly whisper to the students to tell me how they have bettered their problem solving skills over the last two weeks. As the students share their thoughts with me, I make note of them on a piece of paper. I will use this data with the class in the closing discussion.

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To conclude the final few minutes of class, I ask the students to elaborate on what we talked about when they turned in the test. My students are know at the start of class to check their online agenda for the day, but I also put a friendly reminder of this on the board. In my agenda is a link to a journal that I would like for them to respond to. The journal asks the following:

*In a well written paragraph, please explain how your problem solving tactics and strategies have evolved over the last two weeks. What small new tools, tricks, and strategies work for you when solving a non-routine problem? You might also choose to elaborate on the importance of collaboration, and how constructing arguments and critiquing the reasoning of others has helped you to become a better problem solver. *

I collect this journal as I would any other homework assignment, and set the due date on my online course web page to after homeroom of the following day. This allows the students to work on it in the morning during their homeroom classes if they do not have internet access at home. This is important to consider if the students do not have time to finish it after the problem solving assessment.

Following the lesson, I share in my video narrative a strategy to give meaningful feedback and how to "coach up" students.

#### Resources

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- UNIT 1: Culture Building Unit - Welcome to the New Year!
- UNIT 2: Exponential and Logarithmic Functions
- UNIT 3: Sequences and Series
- UNIT 4: Statistics: Something for Everyone
- UNIT 5: Review Lessons
- UNIT 6: Writing Prompts in Mathematics
- UNIT 7: Trig Tidbits
- UNIT 8: Functions, Problem Solving, and 21st Century Skills
- UNIT 9: Polynomials and Problem Solving
- UNIT 10: Probability
- UNIT 11: Imagine This! Imaginary and Complex Numbers
- UNIT 12: Let's Explore Radicals!

- LESSON 1: Mission Impossible: Roll Out
- LESSON 2: Mission Impossible: Day #2
- LESSON 3: Mission Impossible: Mission Complete!
- LESSON 4: Mission Possible - 5 Scenarios in 5 Days: Day #1
- LESSON 5: Mission Possible - 5 Scenarios in 5 Days: Day #2
- LESSON 6: Mission Possible - 5 Scenarios in 5 Days: Day #3
- LESSON 7: Mission Possible - 5 Scenarios in 5 Days: Day #4
- LESSON 8: Mission Possible - 5 Scenarios in 5 Days: Day #5
- LESSON 9: Mission Possible - 5 Scenarios in 5 Days: Business Meetings!
- LESSON 10: Problem Solving Assessment
- LESSON 11: A Confidence Builder! Problem Solving and Reflection