Break it Down 5 Copyright © 2026 Pearson Education, Inc. Break it Down (50 – 60 minutes) Learning Objective(s): Students will add, subtract, multiply, and divide polynomials with integer coefficients. Students will interpret and rewrite algebraic expressions into equivalent forms. Students will apply polynomial operations to realworld packaging problems. Material needed: Student pages: Break it Down Calculator Lesson Procedure: Warm–Up 10 minutes Prompt: Polynomials are often used to represent changing quantities, such as cost, area, or volume. Can you think of a real-life situation where a polynomial might be useful for modeling or solving a problem? What might the variables represent, and why would simplifying the expression help? Discuss: polynomial, variable, operations Guided Instruction 15 minutes Present: scenario for Break it Down. Example: A company uses the expression (x + 2)2 to model the area of one square face of a small box, where x is the length in inches. Expand the expression to find the area of one face. x2+ 4x + 4 Find the total surface area of the cube 6 • (x2+ 4x + 4) = 6x2+ 24x + 24 Review: key terms – expand, expression, distribute, simplify, surface area expand: to rewrite an expression, often using the Distributive Property expression: a combination of numbers, variables, and operations that represents a value distribute: to multiply a term by each term within a set of parentheses simplify: to rewrite an expression in a less complex, more concise form while maintaining its original value surface area: total area of the outer surface of a three-dimensional object Independent Practice 20 minutes Distribute: student activity Break it Down Allow students to work individually or in pairs. Closure 10–15 minutes Review Answers: 1. 7x2 + x + 8 2. 4x2 + 2x + 5 3. x2 + 5x + 6 4. a. 2x2 + 13x + 15; b. (2x2 + 13x + 15)(x + 1); c. 2x3 + 15x2 + 28x + 15 5. a. 2x + 6; b. 1.25(2x + 6) = 2.5x + 7.5 6. a. 6x(x + 2); b. 0.75(6x2 + 12x) = 4.5x2 + 9x 7. a. 10x2 + 12x + 18; b. 20x2 + 24x + 36 Discuss: How can simplifying and rewriting polynomial expressions help businesses make better decisions about cost, materials, or time?
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