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# Problem Solving with Polynomials - Welcome Algebra I Students!

Lesson 8 of 8

## Objective: SWBAT to apply polynomial factoring in a real world context. SWBAT to present mathematical concepts to Algebra I students.

#### Workshop Requests

*5 min*

The opening stage of this lesson will be filled with collaborative student activity (MP3)! I begin class by reminding students they have approximately 20 minutes to wrap up their problem and powerpoint slides prior to the arrival of the Algebra I class. This certainly kicks the class into overdrive!

This is an outstanding opportunity to show younger math students that math classrooms can, indeed, be very high energy. Although the Algebra I students show up for the latter half of the block, the initial energy and class productivity carries over throughout the whole period. In the past, Algebra I kids say that they are amazed at what they saw considering that the Algebra II students only had about 35-40 class minutes to work. The Algebra I teacher almost always sees an increased level of productivity in the days following the visit, and my students take a great deal of pride in the professional environment that they create.

While students get rockin' and rolling, I visit groups address any workshop (support) requests. Students might need help continuing their problem or they may have technical questions that need to be answered. Based on the exit ticket from yesterday, if anything shows up more than once I will call those students together to efficiently answer the question(s).

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#### Work Time!

*20 min*

I work hard to spend most of my time working with the students who are struggling. Many "high flying" students will have the essentials of the PowerPoint wrapped up, and will be working on fine-tuning their product.

Should it become clear that a group of students is NOT going to finish before the Algebra I students come, encourage them to still highlight the important victories they have made in the problem, as well as the dead ends that they have taken. It is good for Algebra I students to see this modeled and that it is not always just about the right answer! It is also great to then have these students come in and finish before/after school one day. After all, the mathematical practice standards call for us to teach resiliency and perseverance when working on a math problem! (MP1)

#### Resources

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#### Welcome Algebra I Students!

*20 min*

I pre-arrange with the Algebra I teacher for his/her students to arrive 25 minutes before the final bell. This allows the visiting students to enter the room during the flurry of activity phase and feel the energy in the classroom. While I talk briefly with our guests, I first inform my Algebra II kids that they need to wrap up in the next couple of minutes, and prepare to share out what they have completed with the Algebra I students.

When meeting with the Algebra I kids, I tell them what we have been working on and how their math teacher and I decided to collaborate. We hope to be modeling for both our classes an important college and career readiness skill. If students see teachers collaborating, then hopefully they will be more likely to collaborate themselves! I also tell the Algebra I students to focus on the problem solving process in the presentations and not to be overwhelmed by the content. My goal is to ease any concerns and highlight problem solving as a skill that transcends any level of mathematics. "Good problem solving is good problem solving, I tell them, you'll know it when you see it!"

HOW THIS LOOKS IN ACTION:

- 2-3 Algebra I students are paired with a a group of 2 Algebra II students.
- The students spend approximately 10 minutes in conversation with each other about the problem. The Algebra I teacher and I encourage the Algebra I students to be active participants in the conversations and to speak up if they have questions.
- After 9-10 minutes are up, we "carousel" around the classroom so that the students have the opportunity to see at least one other presentation. This will help them formulate what a good mathematical presentation looks like, and it is part of the reason that the Algebra I teacher wished to bring the students in the first place. If they left seeing only one problem, it would be difficult for them to gauge what they liked/didn't like.

AN OPTION FOR THE "SHY STUDENT":

Although presenting to freshman is not as intimidating as presenting to peers or community members, I still provide the option for shy students to run the presentation like a question/answer session. Ultimately this is the dialogue that I hope takes place anyways. As these students "present" their work, I try to spend some time in their group helping the freshman "break the ice" and get the questions flowing.

As a concluding activity, it is important to capture student perceptions and feedback. To do this, after the class visit, the Algebra I teacher has his/her students complete a journal for a grade and my students follow up by reviewing their entries. I also have my students complete a journal assignment.

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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!