## Quadratic and a Cubic- Operations with Polynomials Day 2 - Section 2: Exploring Operations with Polynomial using Graphing Technology

*Quadratic and a Cubic- Operations with Polynomials Day 2*

# Operations with Polynomials Day 2 of 2

Lesson 4 of 15

## Objective: Students will be able to add and subtract polynomial equations graphically and algebraically.

## Big Idea: Students explore and make conclusions about functions operations using graphing technology.

*50 minutes*

#### Warm up and Homework Review

*10 min*

I include **Warm ups **with a **Rubric **as part of my daily routine. My goal is to allow students to work on **Math Practice 3 **each day. Grouping students into homogeneous pairs provides an opportunity for appropriately differentiated math conversations. This lesson’s Warm Up- Operations with Polynomials Day 2 asks students to determine whether two polynomials have been added correctly.

I also use this time to correct and record any past Homework.

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This is the second day of a two day lesson. We now move on to exploring functions with TI-84 graphing calculators. Please see the Calculator Notes in slide #2 from the PowerPoint for specific instructions on using TI-84s.

I have students look first at Two Quadratics and then at a Quadratic and a Cubic to explore the effect on the degree of the sum or the difference of the polynomials (**Math Practice 7**). As they learn to accurately predict the degree of the resulting polynomial functions under addition or subtraction, I ask them to create their own polynomials whose sum or difference produces a specific characteristic. For example, I might ask them to identify two cubic functions whose sum produces a line function. In my video I describing another problem and getting students to think outside of the box a bit (**Math Practice 1**). Depending on my remaining time, I may ask specific students to write their functions on a note card so the class can see and discuss multiple solutions. This is a great, non-threatening way of allowing the students to analyze each other’s work (**Math Practice 3**).

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#### Lesson Summary

*17 min*

The concluding activity has the students do two things.

- Summarize the outcome when you find the sum or difference of polynomial functions with the same degree.
- Summarize the outcome when you find the sum or difference of polynomial functions with different degrees.

I have the students work on these in pairs and then we discuss it as a class.

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#### Exit Ticket

*3 min*

I use an exit ticket each day as a quick formative assessment to judge the success of the lesson.

Today's Exit Ticket asks students to find the sum of two functions.

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My Operations with Polynomial Functions assignment provides the students with an opportunity to find the sum and difference of polynomial functions both graphically and algebraically. It also assesses their understanding of the outcomes when adding polynomials (**Math Practice 7**). Finally, it provides them with a profit modeling exercise (**Math Practice 4**).

*note: I have students tape the half-sheet into their notebooks and work on separate paper. You can reformat the handout if you wanted to have students work directly on it.*

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- UNIT 1: Modeling with Expressions and Equations
- UNIT 2: Modeling with Functions
- UNIT 3: Polynomials
- UNIT 4: Complex Numbers and Quadratic Equations
- UNIT 5: Radical Functions and Equations
- UNIT 6: Polynomial Functions
- UNIT 7: Rational Functions
- UNIT 8: Exponential and Logarithmic Functions
- UNIT 9: Trigonometric Functions
- UNIT 10: Modeling Data with Statistics and Probability
- UNIT 11: Semester 1 Review
- UNIT 12: Semester 2 Review

- LESSON 1: Laws of Exponents
- LESSON 2: Sorting Polynomial Equations and Identities
- LESSON 3: Operations with Polynomials Day 1 of 2
- LESSON 4: Operations with Polynomials Day 2 of 2
- LESSON 5: Products of Polynomial Functions
- LESSON 6: Factoring GCF and Grouping
- LESSON 7: Factoring Trinomials
- LESSON 8: Special Factoring Situations
- LESSON 9: Polynomial Quiz and Factoring Puzzle
- LESSON 10: Factoring Completely
- LESSON 11: Modeling Equations and Functions with Factoring
- LESSON 12: Polynomial Inequalities
- LESSON 13: Polynomial Review Day 1
- LESSON 14: Polynomial Review Day 2
- LESSON 15: Polynomial Test