##
* *Reflection:
Puzzling Polynomials and Quizzical Quadratics - Section 3: Closure: Cliff Notes Jr.

I think this part of the lesson was crucial. After all of the hustle and bustle of stations, it was really important to have students stop and reflect on their learning. I found it interesting the different ‘hints’ that my students wrote to themselves in their Cliff Notes Jr activity. (see Student Work Samples - Cliff Notes Jr here) I like to see how they put things in their own words; phrases like “put the equation in order” showed me that students analyzed their learning and made notes that would actually help them based on their mistakes/learnings from the stations.

Also, I learned by doing this activity that many of my students didn’t know what Cliff Notes even are. So I had to take some time to talk about that. Many were familiar with Spark Notes though. So maybe I should call this a Spark Notes Jr.?

# Puzzling Polynomials and Quizzical Quadratics

Lesson 1 of 15

## Objective: SWBAT solve to find the exact answer to quadratic equations and will determine the best method for solving a quadratic equation.

## Big Idea: Review polynomial operations with NCTM’s polynomial puzzlers and then practice solving quadratic equations by moving through stations.

*51 minutes*

To help students do a quick review of polynomial operations, I am going to have them complete some polynomial puzzlers as a warm-up and as homework. I found these puzzles on the Illuminations website of the National Council of Teachers of Mathematics which has so many great activities, lessons, interactive applets, and interesting articles. Check out this link to this specific lesson on polynomial puzzlers. Although the concept of polynomial multiplication and division should now be quite routine for our students by their senior year, I still see students make the very common typical mistakes; for example, when multiplying binomials they multiply only the first term to the first term and the last to the last but then miss their middle terms. So I am hoping that by having this structure of the puzzle that students will catch their mistakes and have plenty of practice with multiplying and dividing polys for homework.

First present page 2 of the flipchart to students and demonstrate how the polynomial puzzlers work. So basically each row and column is multiplied and the product is put on the right (for rows) or bottom (for columns). On page 3, students text in their answer to this very basic puzzler. This is just to see if they get how to solve the puzzlers. Now for the actual warm-up problem on page 4, students should text in their answer for the bottom right corner. This will insure they have solved every section of the puzzle. While students work on this, I will now do my beginning of class routines.

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#### Closure: Cliff Notes Jr.

*5 min*

**Preperation: **Students will need an index card for today's closure.

To close out today’s lesson, present page 5 of the flipchart and have students complete a Cliff Notes, Jr**. **It is important for students to take a few minutes to summarize all the review they just had and to formalize an individual plan for how they will attack solving quadratic equations in this class. I plan to remind my students again here about Math Practice 7: Look for and make use of structure**. **I want them to include in their summary how the structure of a quadratic equation can affect the method of solving we choose.

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#### Homework

*1 min*

Assign Homework 1 Polynomial Puzzler from NCTM’s illuminations to help students review basic binomial multiplication and factoring.

Click here for NCTM's description of the lesson resources.

#### Resources

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- UNIT 1: Basic Functions and Equations
- UNIT 2: Polynomial Functions and Equations
- UNIT 3: Rational Functions and Equations
- UNIT 4: Exponential Functions and Equations
- UNIT 5: Logarithmic Functions and Equations
- UNIT 6: Conic Sections
- UNIT 7: Rotations and Cyclical Functions
- UNIT 8: Cyclical Patterns and Periodic Functions
- UNIT 9: Trigonometric Equations
- UNIT 10: Matrices
- UNIT 11: Review
- UNIT 12: Fundamentals of Trigonometry

- LESSON 1: Puzzling Polynomials and Quizzical Quadratics
- LESSON 2: Building Connections: Building Polynomials (Day 1 of 2)
- LESSON 3: Building Connections: Building Polynomials (Day 2 of 2)
- LESSON 4: Detailed Descriptions of our Puzzling Polynomials
- LESSON 5: Got zeros? Polynomials do! Multiplicity of Zeros (Day 1 of 3)
- LESSON 6: Got zeros? Polynomials do! Multiplicity of Zeros (Day 2 of 3)
- LESSON 7: Got zeros? Polynomials do! Multiplicity of Zeros (Day 3 of 3)
- LESSON 8: Long, Synthetic, and Square! Oh my! Polynomial Division
- LESSON 9: Rational Roots and Remainders: Important Theorems of Polynomials
- LESSON 10: Polynomials with Complexes… Complex Zeros that is!
- LESSON 11: Putting the Pieces of Polynomials Together (Day 1 of 2)
- LESSON 12: Putting the Pieces of Polynomials Together (Day 2 of 2)
- LESSON 13: Roller Coaster Polynomials
- LESSON 14: Test Review
- LESSON 15: Polynomials Unit Test