## Working Backwards - Section 2: Investigation: Working Backwards and Polys of Degree 3

# Building Connections: Building Polynomials (Day 2 of 2)

Lesson 3 of 15

## Objective: SWBAT find an equation that could represent the function given the graph of a polynomial (limited to 2nd and 3rd degree).

Present the polynomial puzzler warm-up problem to students from page 2 of the flipchart. Depending on the pacing of your students from yesterday’s lesson you may want to just skip this warm-up and spend more time on the classwork today.

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Today students will finish the NCTM Illuminations lesson Building Connections. The lesson is outlined in great detail on their website so be sure to check out the link above. Today I expect students to finish the worksheet, Working Backwards, and the worksheet, Higher Degree Polynomials I have only allotted 30 minutes for this (why? I thought if we really built up students’ understanding of yesterday’s activity then today would go much smoother) so I don’t know that all students will finish both worksheets. It is important that all students complete at least the working backwards worksheet. The higher degree polynomials worksheet could be used as just an extension although I hope that all my students get through both.

This lesson does a great job at having students work toward becoming better mathematicians. While working through this activity many of the mathematical practice standards will be addressed. I am going to encourage my students to be aware of how they are practicing the following two standards as we discussed yesterday:

**Mathematical practice 2: Reason abstractly and quantitatively**

**Mathematical practice 7: Look for and make use of structure**

I definitely recommend working through the worksheet yourself before having students complete it. Check out the video in the section below (which is a bit long, sorry… you may be better just working through the activity!) for an overview of today’s activity and some tips on differentiation.

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#### Closure: Pair-Share

*5 min*

Present page 3 of the flipchart and have students summarize their findings today by doing a pair-share. (No time for the ‘think’ today! Just kidding, I really just want students to discuss with a partner their findings and not just think about it on their own) Teams should share their findings with the class.

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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