Algebra tiles can be used to visualize how a perfect square - - PowerPoint PPT Presentation

DAY 151 – VISUAL UNDERSTANDING OF PROOFS

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.

EXAMPLE 1:

What is needed to create a perfect square trinomial for: 𝑦2 + 4𝑦 + ____ Use the algebra tiles to create a square. What tiles will be needed to complete the square?

EXAMPLE 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.“

𝑦2 + 4𝑦 + 𝟓

EXAMPLE 2:

What is needed to create a perfect square trinomial for: 𝑦2 − 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?

EXAMPLE 2:

This example should solidify the concept that the needed constant term will be a positive value.

𝑦2 − 6𝑦 + 𝟘

𝑦2 + 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.

EXAMPLE 3: SOLVE BY COMPLETING THE SQUARE