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Polynomial Power-Up!

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Lesson Plan

Polynomial Power-Up!

Students will learn to accurately add and subtract polynomials, applying properties of like terms and distributing negative signs. This lesson helps students build foundational algebra skills crucial for advanced mathematics.

Understanding polynomials is essential for solving complex equations, graphing functions, and excelling in higher-level math courses. Mastering these operations builds confidence and problem-solving abilities.

Audience

11th Grade Students

Time

30 minutes (plus 45-minute activity)

Approach

Direct instruction followed by an interactive, movement-based activity.

Materials

Smartboard or Projector, Polynomial Power-Up! Slide Deck, Polynomial Power-Up! Activity Cards, and Activity Recording Sheet

Prep

Teacher Preparation

15 minutes

Step 1

Warm-Up: What's a Like Term?

5 minutes

  • Display the first slide of the Polynomial Power-Up! Slide Deck which asks students to identify like terms.
    - Ask students to briefly discuss with a partner what 'like terms' are and why they are important when combining expressions.
    - Call on a few students to share their answers with the class.

Step 2

Direct Instruction: Adding Polynomials

10 minutes

  • Use the Polynomial Power-Up! Slide Deck to explain how to add polynomials.
    - Focus on combining like terms, emphasizing organization and careful calculation.
    - Work through 2-3 examples together as a class, ensuring student understanding before moving on.

Step 3

Direct Instruction: Subtracting Polynomials

10 minutes

  • Continue using the Polynomial Power-Up! Slide Deck to explain how to subtract polynomials.
    - Highlight the crucial step of distributing the negative sign to all terms in the second polynomial.
    - Work through 2-3 examples together, including at least one with multiple terms in the second polynomial.

Step 4

Activity Introduction: Polynomial Power-Up!

5 minutes

  • Explain the Polynomial Power-Up! Activity to students. Distribute the Activity Recording Sheet.
    - Inform them that various polynomial expressions will be posted around the room.
    - Students will work in pairs or small groups to find these cards, identify two expressions, add or subtract them as instructed on their recording sheet, and record their answers.
    - Emphasize the importance of showing all work clearly on their sheets.
    - Transition to the Polynomial Power-Up! Activity which will take approximately 45 minutes and is intended to be done after the direct instruction.

Step 5

Closure/Review (Post-Activity)

5 minutes

  • (To be conducted after the 45-minute activity).
    - Bring the class back together.
    - Review a few challenging problems from the activity, focusing on common errors.
    - Answer any lingering questions students may have.
    - Assign additional practice as needed.
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Slide Deck

Polynomial Power-Up!

Level Up Your Algebra Skills!

Today, we're mastering how to add and subtract polynomials – essential skills for conquering advanced math!

Welcome students and introduce the exciting journey into polynomial operations! Briefly explain the day's objective.

Warm-Up: What are Like Terms?

Discuss with a partner:

  • What makes two terms 'like terms'?
  • Why is it important to combine only like terms when adding or subtracting expressions?




Engage students with a warm-up. Ask them to think individually for a moment, then discuss with a partner. Encourage sharing definitions and examples of like terms and why they are important for combining expressions.

Adding Polynomials: The Basics

When adding polynomials, we combine like terms.

Like terms have the same variables raised to the same powers.

Example 1:
(3x + 5) + (2x - 3)

Step 1: Identify like terms.
(3x and 2x) & (5 and -3)

Step 2: Combine like terms.
(3x + 2x) + (5 - 3)

Step 3: Simplify.
5x + 2

Introduce adding polynomials. Emphasize the concept of combining 'like terms' and guide students through the first example step-by-step. Encourage questions.

Adding Polynomials: Another Example

Example 2:

(4x^2 + 2x - 7) + (x^2 - 6x + 1)

Step 1: Identify like terms.
(4x^2 and x^2), (2x and -6x), (-7 and 1)

Step 2: Combine like terms.
(4x^2 + x^2) + (2x - 6x) + (-7 + 1)

Step 3: Simplify.
5x^2 - 4x - 6

Work through a slightly more complex addition example, encouraging students to anticipate the steps. Pay attention to terms with different powers.

Subtracting Polynomials: A Key Rule

When subtracting polynomials, remember to distribute the negative sign!

Example 1:
(5x + 8) - (2x + 3)

Step 1: Distribute the negative sign.
5x + 8 - 2x - 3

Step 2: Identify like terms.
(5x and -2x) & (8 and -3)

Step 3: Combine like terms.
(5x - 2x) + (8 - 3)

Step 4: Simplify.
3x + 5

Introduce subtracting polynomials. Stress the importance of distributing the negative sign to every term in the second polynomial. This is a common error point.

Subtracting Polynomials: Let's Try One!

Example 2:

(6x^2 - 3x + 1) - (2x^2 + 5x - 4)

Step 1: Distribute the negative sign.
6x^2 - 3x + 1 - 2x^2 - 5x + 4

Step 2: Identify like terms.
(6x^2 and -2x^2), (-3x and -5x), (1 and 4)

Step 3: Combine like terms.
(6x^2 - 2x^2) + (-3x - 5x) + (1 + 4)

Step 4: Simplify.
4x^2 - 8x + 5

Present a more challenging subtraction problem. Have students try to apply the distribution step themselves before revealing the solution. Reinforce careful attention to signs.

Time to Power-Up! Your Polynomial Skills

Get Ready to Move!

Now that we've reviewed adding and subtracting polynomials, it's time to put your skills to the test with our Polynomial Power-Up! Activity.

  • Find the activity cards around the room.
  • Work with your group to solve the problems.
  • Show all your work on your recording sheet!

Let's get started!

Introduce the activity. Explain that students will apply what they've learned in a movement-based activity. Briefly explain the setup and handout. This slide serves as a transition to the main activity.

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Activity

Polynomial Power-Up! Activity Cards

Instructions for Teacher: Print these cards, cut them out, and post them around the classroom. Students will use these cards in conjunction with the Activity Recording Sheet.

Card A

Expression 1: 5x + 3
Expression 2: 2x + 7

Card B

Expression 1: 4x² - 2x
Expression 2: x² + 5x

Card C

Expression 1: (3x - 1) - (x + 4)
Expression 2: (6x + 2) + (-2x - 5)

Card D

Expression 1: 7x³ + 2x - 9
Expression 2: 3x³ - 4x + 1

Card E

Expression 1: (10y - 4) - (3y - 6)
Expression 2: (-5y + 2) + (7y + 8)

Card F

Expression 1: 2x² + 3xy - y²
Expression 2: 4x² - xy + 2y²

Card G

Expression 1: (8m - 3n) - (2m + 5n)
Expression 2: (4m + 7n) + (m - 2n)

Card H

Expression 1: 9x²y + 5xy - x
Expression 2: -3x²y + 2xy + 4x

Card I

Expression 1: (11a² + 6a) + (-4a² - 2a)
Expression 2: (7a - 3) - (2a + 5)

Card J

Expression 1: -x³ + 4x² - 6
Expression 2: 2x³ - 3x² + 10

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Worksheet

Polynomial Power-Up! Activity Recording Sheet

Name(s):



Date:


Instructions: Go around the room and find the Polynomial Power-Up! Activity Cards. For each problem below, locate the specified cards, perform the indicated operation, and show all your work clearly. Then, write your final simplified answer in the space provided.

Problem 1: Add Card A and Card B

Card A Expression 1:





Card B Expression 1:




Work:












Simplified Answer:



Problem 2: Subtract Card B (Expression 2) from Card A (Expression 2)

Card A Expression 2:





Card B Expression 2:




Work:












Simplified Answer:



Problem 3: Add Card C (Expression 1) and Card D (Expression 1)

Card C Expression 1:





Card D Expression 1:




Work:












Simplified Answer:



Problem 4: Subtract Card D (Expression 2) from Card C (Expression 2)

Card C Expression 2:





Card D Expression 2:




Work:












Simplified Answer:



Problem 5: Add Card E (Expression 1) and Card F (Expression 1)

Card E Expression 1:





Card F Expression 1:




Work:












Simplified Answer:



Problem 6: Subtract Card F (Expression 2) from Card E (Expression 2)

Card E Expression 2:





Card F Expression 2:




Work:












Simplified Answer:



Problem 7: Add Card G (Expression 1) and Card H (Expression 1)

Card G Expression 1:





Card H Expression 1:




Work:












Simplified Answer:



Problem 8: Subtract Card H (Expression 2) from Card G (Expression 2)

Card G Expression 2:





Card H Expression 2:




Work:












Simplified Answer:



Problem 9: Add Card I (Expression 1) and Card J (Expression 1)

Card I Expression 1:





Card J Expression 1:




Work:












Simplified Answer:



Problem 10: Subtract Card J (Expression 2) from Card I (Expression 2)

Card I Expression 2:





Card J Expression 2:




Work:












Simplified Answer:



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Answer Key

Polynomial Power-Up! Activity Answer Key

Here are the step-by-step solutions for the Activity Recording Sheet problems.

Problem 1: Add Card A and Card B

Card A Expression 1: 5x + 3
Card B Expression 1: 4x² - 2x

Thought Process:

  1. Identify the expressions: (5x + 3) and (4x² - 2x).
  2. Combine them with an addition sign: (5x + 3) + (4x² - 2x).
  3. Remove parentheses and reorder by degree: 4x² + 5x - 2x + 3.
  4. Identify like terms: 5x and -2x.
  5. Combine like terms: 4x² + (5x - 2x) + 3.
  6. Simplify.

Simplified Answer: 4x² + 3x + 3

Problem 2: Subtract Card B (Expression 2) from Card A (Expression 2)

Card A Expression 2: 2x + 7
Card B Expression 2: x² + 5x

Thought Process:

  1. Identify the expressions: (2x + 7) and (x² + 5x).
  2. Set up the subtraction: (2x + 7) - (x² + 5x).
  3. Distribute the negative sign to the second polynomial: 2x + 7 - x² - 5x.
  4. Reorder by degree: -x² + 2x - 5x + 7.
  5. Identify like terms: 2x and -5x.
  6. Combine like terms: -x² + (2x - 5x) + 7.
  7. Simplify.

Simplified Answer: -x² - 3x + 7

Problem 3: Add Card C (Expression 1) and Card D (Expression 1)

Card C Expression 1: (3x - 1) - (x + 4) = 3x - 1 - x - 4 = 2x - 5
Card D Expression 1: 7x³ + 2x - 9

Thought Process:

  1. First simplify Card C (Expression 1): 3x - 1 - x - 4 = 2x - 5.
  2. Identify the expressions: (2x - 5) and (7x³ + 2x - 9).
  3. Combine them with an addition sign: (2x - 5) + (7x³ + 2x - 9).
  4. Remove parentheses and reorder by degree: 7x³ + 2x + 2x - 5 - 9.
  5. Identify like terms: 2x and 2x; -5 and -9.
  6. Combine like terms: 7x³ + (2x + 2x) + (-5 - 9).
  7. Simplify.

Simplified Answer: 7x³ + 4x - 14

Problem 4: Subtract Card D (Expression 2) from Card C (Expression 2)

Card C Expression 2: (6x + 2) + (-2x - 5) = 6x + 2 - 2x - 5 = 4x - 3
Card D Expression 2: 3x³ - 4x + 1

Thought Process:

  1. First simplify Card C (Expression 2): 6x + 2 - 2x - 5 = 4x - 3.
  2. Identify the expressions: (4x - 3) and (3x³ - 4x + 1).
  3. Set up the subtraction: (4x - 3) - (3x³ - 4x + 1).
  4. Distribute the negative sign: 4x - 3 - 3x³ + 4x - 1.
  5. Reorder by degree: -3x³ + 4x + 4x - 3 - 1.
  6. Identify like terms: 4x and 4x; -3 and -1.
  7. Combine like terms: -3x³ + (4x + 4x) + (-3 - 1).
  8. Simplify.

Simplified Answer: -3x³ + 8x - 4

Problem 5: Add Card E (Expression 1) and Card F (Expression 1)

Card E Expression 1: (10y - 4) - (3y - 6) = 10y - 4 - 3y + 6 = 7y + 2
Card F Expression 1: 2x² + 3xy - y²

Thought Process:

  1. First simplify Card E (Expression 1): 10y - 4 - 3y + 6 = 7y + 2.
  2. Identify the expressions: (7y + 2) and (2x² + 3xy - y²).
  3. Combine them with an addition sign: (7y + 2) + (2x² + 3xy - y²).
  4. Remove parentheses and reorder: 2x² + 3xy - y² + 7y + 2. (No like terms to combine after simplification).

Simplified Answer: 2x² + 3xy - y² + 7y + 2

Problem 6: Subtract Card F (Expression 2) from Card E (Expression 2)

Card E Expression 2: (-5y + 2) + (7y + 8) = -5y + 2 + 7y + 8 = 2y + 10
Card F Expression 2: 4x² - xy + 2y²

Thought Process:

  1. First simplify Card E (Expression 2): -5y + 2 + 7y + 8 = 2y + 10.
  2. Identify the expressions: (2y + 10) and (4x² - xy + 2y²).
  3. Set up the subtraction: (2y + 10) - (4x² - xy + 2y²).
  4. Distribute the negative sign: 2y + 10 - 4x² + xy - 2y².
  5. Reorder by degree/variable: -4x² - 2y² + xy + 2y + 10. (No like terms to combine).

Simplified Answer: -4x² - 2y² + xy + 2y + 10

Problem 7: Add Card G (Expression 1) and Card H (Expression 1)

Card G Expression 1: (8m - 3n) - (2m + 5n) = 8m - 3n - 2m - 5n = 6m - 8n
Card H Expression 1: 9x²y + 5xy - x

Thought Process:

  1. First simplify Card G (Expression 1): 8m - 3n - 2m - 5n = 6m - 8n.
  2. Identify the expressions: (6m - 8n) and (9x²y + 5xy - x).
  3. Combine them with an addition sign: (6m - 8n) + (9x²y + 5xy - x).
  4. Remove parentheses. (No like terms to combine after simplification).

Simplified Answer: 9x²y + 5xy - x + 6m - 8n

Problem 8: Subtract Card H (Expression 2) from Card G (Expression 2)

Card G Expression 2: (4m + 7n) + (m - 2n) = 4m + 7n + m - 2n = 5m + 5n
Card H Expression 2: -3x²y + 2xy + 4x

Thought Process:

  1. First simplify Card G (Expression 2): 4m + 7n + m - 2n = 5m + 5n.
  2. Identify the expressions: (5m + 5n) and (-3x²y + 2xy + 4x).
  3. Set up the subtraction: (5m + 5n) - (-3x²y + 2xy + 4x).
  4. Distribute the negative sign: 5m + 5n + 3x²y - 2xy - 4x.
  5. Reorder by variable/degree. (No like terms to combine).

Simplified Answer: 3x²y - 2xy - 4x + 5m + 5n

Problem 9: Add Card I (Expression 1) and Card J (Expression 1)

Card I Expression 1: (11a² + 6a) + (-4a² - 2a) = 11a² + 6a - 4a² - 2a = 7a² + 4a
Card J Expression 1: -x³ + 4x² - 6

Thought Process:

  1. First simplify Card I (Expression 1): 11a² + 6a - 4a² - 2a = 7a² + 4a.
  2. Identify the expressions: (7a² + 4a) and (-x³ + 4x² - 6).
  3. Combine them with an addition sign: (7a² + 4a) + (-x³ + 4x² - 6).
  4. Remove parentheses and reorder. (No like terms to combine after simplification).

Simplified Answer: -x³ + 4x² + 7a² + 4a - 6

Problem 10: Subtract Card J (Expression 2) from Card I (Expression 2)

Card I Expression 2: (7a - 3) - (2a + 5) = 7a - 3 - 2a - 5 = 5a - 8
Card J Expression 2: 2x³ - 3x² + 10

Thought Process:

  1. First simplify Card I (Expression 2): 7a - 3 - 2a - 5 = 5a - 8.
  2. Identify the expressions: (5a - 8) and (2x³ - 3x² + 10).
  3. Set up the subtraction: (5a - 8) - (2x³ - 3x² + 10).
  4. Distribute the negative sign: 5a - 8 - 2x³ + 3x² - 10.
  5. Reorder by degree/variable: -2x³ + 3x² + 5a - 8 - 10.
  6. Identify like terms: -8 and -10.
  7. Combine like terms: -2x³ + 3x² + 5a + (-8 - 10).
  8. Simplify.

Simplified Answer: -2x³ + 3x² + 5a - 18

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Polynomial Power-Up! • Lenny Learning