Polynomial Operations

Objective

By the end of this 30-minute lesson, 7th-grade students will be able to confidently add and subtract polynomials, identify like terms, and simplify polynomial expressions, aligning with the US Common Core Standards: CCSS.MATH.CONTENT.7.EE.A.1 - Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Materials Needed

• Whiteboard and markers
• Printed handouts with practice problems
• Sets of algebra tiles for each group
• Colored pencils
• Exit tickets for assessment

Introduction (5 minutes)

Engage Students

Begin with a quick warm-up question on the board:

Simplify: 3x + 2x = ?

Ask students to solve the problem individually in their notebooks. Use this as a springboard to introduce the concept of combining like terms.

Briefly explain that today, they will expand on this idea by adding and subtracting polynomials, which are foundational skills in algebra.

Direct Instruction (10 minutes)

Explanation of Concepts

1. Define Polynomials:

   • A polynomial is an expression made up of variables, coefficients, and exponents arranged in terms.

2. Adding Polynomials:

   • Demonstrate combining like terms using the example: ( (3x^2 + 4x + 7) + (2x^2 + 5x + 3) )
   • Show how to align and add the coefficients of like terms.

3. Subtracting Polynomials:

   • Illustrate how subtraction changes signs: ( (5x^2 + 3x - 4) - (2x^2 + 7x + 6) )
   • Walk through each step carefully, ensuring clarity in sign changes when subtracting.

Use Visual Aids:

Have sets of algebra tiles to visualize adding and subtracting polynomials. Show students how different tiles can represent different terms.

Guided Practice (7 minutes)

Activity: Practicing with Algebra Tiles

Divide students into small groups and distribute algebra tiles. Provide each group with a simple addition and subtraction problem:

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

Instruct groups to model and solve these problems using the tiles, connecting the tangible representation to the symbolic expressions.

Walk around the classroom and offer guidance, confirming correct alignment and simplification with personalized feedback.

Independent Practice (5 minutes)

Distribute handouts with practice problems. Students will independently solve:

1. ( (x^2 + 3x + 4) + (2x^2 + 5x + 1) )
2. ( (3x^2 + 6x + 9) - (x^2 + 2x + 3) )

Encourage students to color code like terms if that aids their understanding.

Provide additional practice for advanced students.

Conclusion (3 minutes)

Review & Reflect

Summarize key points: Combining like terms, aligning them vertically, mindful subtraction of coefficients.

Exit Ticket

Have each student answer the following on an index card:

Simplify: (2x^2 + 3x) + (x^2 - x)

Collect these as students leave to assess understanding and plan next steps.

Differentiation and Extensions

• Support: For students needing extra help, offer simplified expressions and provide step-by-step guides.
• Challenge: Advanced students can explore multiplying polynomials as an extension.

Evaluation

Assess student understanding through observation during activities, accuracy of independent practice, and exit ticket responses. Use this data to identify students who may require further support or additional challenges.