##
* *Reflection: Student Ownership
Indentify That! - Section 3: Wrap it Up

One of my goals for my students is that they assume more responsibility for their own learning. To encourage this I try to regularly incorporate opportunities for conjecture and reflection into my lessons. These notecards show before and after thinking for two students. I selected these to share because they represent different opinions and levels of thinking. Student #1 doesn't have a mathematically solid reason for his opinion while student #2 is clearly working from an understanding of where complex numbers fit in the larger scheme of numbers. Their end-of-lesson reflections are also good examples of different levels of thinking as student #1 accepts that complex numbers "work like polynomials because they do" while student #2 shows confidence in his original reasoning as supported by the results of the lesson. I'll need to keep working with student #1 to strengthen his understanding of the coherence of mathematics and may need to find ways to enrich the lessons for student #2.

# Indentify That!

Lesson 5 of 8

## Objective: SWBAT extend polynomial identities to complex numbers.

## Big Idea: Identities can be complex and confusing...this lesson helps your students make sense of polynomial identities and complex numbers!

*55 minutes*

#### Set the Stage

*10 min*

I begin this lesson by referring to a previous lesson where my students worked with polynomial identities. I ask my students if they can recall any of the identities we worked with in our last unit and give a few hints like "Remember the Pythagorean Triples" or "Think about those polynomial shortcuts we studied". When they've suggested a few I ask them to reflect silently for a moment (actually about 30 seconds, which is a long time for teenagers to be silent) about whether or not they think the complex numbers will also fit the polynomial identities. After the reflection time I give my students each a notecard and tell them to write their opinion and also their supporting reasoning. **(MP3)** I collect these and tell them we'll look at them again later. I discuss why I choose to include this plus standard in my video.

#### Resources

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#### Put it into Action

*40 min*

*For this section you will want copies of the Polynomial identities handout. *I give my students a copy of the polynomial identities handout that we used in our algebraic arithmetic unit and tell them they will be working independently to check their conjecture about the identities and complex numbers. I tell them they should try at least five different complex numbers with each of the identities to confirm or refute their conjecture. **(MP1, MP3) ** As they're working I walk around offering encouragement and assistance as needed. My students are familiar with identities from earlier work, so they should be fairly comfortable expanding them to include complex numbers. I've included a **Resource **of possible numbers to "test" which might be used for students who need extra support for this unit.

After about 30 minutes or when everyone has finished I randomly select different students to share their opinions about one of the identities and support it mathematically. **(MP3)** When we've covered all the identities I ask if there are any questions about whether or not the polynomial identities should include complex numbers. Rather than answering any questions directly I first offer the other students the opportunity to give answers (including explanations, if needed). I clarify and answer those that are still stumping the class as a whole.

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#### Wrap it Up

*5 min*

To close this lesson I return the notecards written during the opener to my students. I ask them to consider the work they've just completed and decide whether they have supported or refuted their original opinion, then write out what they've learned. I clarify that what I'm interest in is whether or not they think their original reasoning which they based their conjecture on was mathematically sound. This gives them a chance to critique their own thinking and reasoning, a skill I believe is important to cultivate. ** (MP1, MP3)**

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- UNIT 1: First Week!
- UNIT 2: Algebraic Arithmetic
- UNIT 3: Algebraic Structure
- UNIT 4: Complex Numbers
- UNIT 5: Creating Algebraically
- UNIT 6: Algebraic Reasoning
- UNIT 7: Building Functions
- UNIT 8: Interpreting Functions
- UNIT 9: Intro to Trig
- UNIT 10: Trigonometric Functions
- UNIT 11: Statistics
- UNIT 12: Probability
- UNIT 13: Semester 2 Review
- UNIT 14: Games
- UNIT 15: Semester 1 Review