D AY 151 – V ISUAL U NDERSTANDING OF P ROOFS
Algebra tiles can be used to visualize how a perfect square trinomial can be formed. The tiles could be used by students or simply used by the teacher as a warm-up to this concept.
E XAMPLE 1: What is needed to create a perfect square trinomial for: 𝑦 2 + 4𝑦 + ____ Use the algebra tiles to create a square . What tiles will be needed to complete the square?
E XAMPLE 1: After viewing several examples, help students to see the pattern for finding the needed constant term. "Take half of the coefficient of the x -term and square it .“ 𝑦 2 + 4𝑦 + 𝟓
E XAMPLE 2: What is needed to create a perfect square trinomial for: 𝑦 2 − 6𝑦 + ______ Use the algebra tiles to create a square . Red tiles represent negative values. What tiles will be needed to complete the square? What will be the sign of these needed tiles?
E XAMPLE 2: This example should solidify the concept that the needed constant term will be a positive value. 𝑦 2 − 6𝑦 + 𝟘
E XAMPLE 3: S OLVE BY COMPLETING THE SQUARE 𝑦 2 + 6𝑦 + 1 = 0 Keep all x related terms on one side. Move the constant to the right. Get ready to create a perfect square on the left. Balance the equation. Take half of the x -term coefficient and square it. Add this value to both sides. Factor and write the perfect square on the left. Take the square root of both sides. Be sure to allow for both plus and minus. Solve for x.
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