##
* *Reflection: Student Portfolios
Grandpa's Sweet Corn Problem: Day 2 of 2 - Section 2: Reviewing Student Responses

The **student responses** included in this lesson represent a collection of student work over two different years. This year, for a third year, I will be adding to the collection, as students continue to try various methods of solution. Early on in my math teaching career, I never taught the same course more than once. I started teaching 5 different classes my first year, and took on 2 entirely new ones the following year. Algebra II now is the only class that I have had the good fortune of teaching more than one year consecutively. For this reason, I have made it a point to be extremely diligent about saving student work and documenting progress. The reality is that it is just too hard to do in all of the other classes that I teach, and I only have a finite amount of energy to devote to the task and still create quality lessons. Through my efforts, the administrative team at my high school has recognized how much I have poured into my Algebra II curriculum. When they come into my classroom and see me talking about a PowerPoint of student work from 3, 4, or even 5 years ago, they have no doubt how passionate I am about what I do in the course. All though schedules may continue to change, I feel confident that I will have a place teaching Algebra II for as long as I desire.

Lesson learned: Sometimes a desire to teach students in creative ways has unintended, positive implications.

*Student Portfolios: Save Student Responses from Year to Year!*

# Grandpa's Sweet Corn Problem: Day 2 of 2

Lesson 2 of 8

## Objective: SWBAT examine flawed solutions and faulty reasoning.

#### Homework Questions

*10 min*

I begin class by accepting homework questions from the students prior to collection. As the students enter the classroom, I simply have written "Homework Question #'s" on the board. The students see this and proceed to write their questions on the board. As the students write the problems #'s up, I ask them to add commentary. For example, rather than simply putting "#13" the students should specify what issue they had with the problem. Other students then have the opportunity to write beside the commentary if they too ran into the same trouble.

Once we transition into homework questions, for each instance of finding the zeros I enter the graph of the function into Desmos so that the students can see where we are shooting for, before we algebraically get there. In many cases, the students will be able to see the mistake in their factors prior to ever even attacking in algebraically. This teaches them the value of understanding the nature of the problems through a variety of lenses.

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#### Reviewing Student Responses

*30 min*

After answering homework questions and collecting the assignment, it is time to jump back into the Grandpa's Sweet Corn Problem. Yesterday, we rolled out the problem, but that was essentially the extent of what we accomplished. Today, I ask the students to review student work from previous years. These are shown in the attached PowerPoint. I take them through several slides and provide detail on how I structure this section of the lesson in the attached video narrative. It is important to note that I am taking students through INCORRECT solutions first. My goal is to model to them what they might experience if they attempt a difficult math problem - they may gets stuck 4-5 times, but eventually they will continue to build to the correct answer. Wrong steps do not have to be backwards steps!

After discussing several wrong answers, I allow the students to try to solve the problem correctly based on what we have seen. It is an excellent enactment of MP3, MP4, and MP6!

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#### Journal Reflection

*5 min*

To close class, I have my students reflect briefly on the following journal prompt:

Albert Einstein once said, “If I had an hour to solve a problem I'd spend 55 minutes thinking about the problem and 5 minutes thinking about solutions.”

As we have explored a wide variety of problem solving techniques and strategies this semester, and again this this Grandpa's Sweet Corn Problem. **QUESTION**: *How have you grown in your approach?*

* My sincere hope is that the students are learning to DE-emphasize just finding the "right answer" and focus on the method of solution. I work hard the entire period to drive this home to the students as I seek to teach problem solving strategy. This journal helps me see if I have been successful in my approach.

I post the journal on our online learning platform, and the students respond by typing on their iPads and submitting.

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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: Grandpa's Sweet Corn Problem: Day 1 of 2
- LESSON 2: Grandpa's Sweet Corn Problem: Day 2 of 2
- LESSON 3: Properties of Exponents
- LESSON 4: What really is "Factoring"? - Factor by Grouping
- LESSON 5: Daily Desmos and Factoring Day 1 of 2
- LESSON 6: Daily Desmos and Factoring Day 2 of 2
- LESSON 7: Problem Solving with Polynomials
- LESSON 8: Problem Solving with Polynomials - Welcome Algebra I Students!