Modeling Polynomials with Algebra Tiles

This lesson teaches how to use algebra tiles to model polynomials by examining the area of patterned floors. It starts with a 10x10 floor design and generalizes it using a variable x to find the area of any size floor. The lesson clarifies common misunderstandings in polynomial addition and explores different floor sizes and their polynomial representations. It also adapts polynomial models for non-square floor designs, encouraging students to create their own designs.

What is a polynomial?

• A mathematical expression with one term

• A mathematical expression with many terms

• A mathematical expression with no terms

• A mathematical expression with two terms

How do you calculate the area of a center floor pattern that is 10 meters by 10 meters?

• 50 square meters

• 100 square meters

• 10 square meters

• 200 square meters

What is the total area of a floor with a center square of x meters and a 1-meter wide border?

• x squared plus 5x plus 5

• x squared plus 3x plus 3

• x squared plus 4x plus 4

• x squared plus 2x plus 2

If x equals 1/2 a meter, what is the total area of the floor?

• 8.25 square meters

• 7.25 square meters

• 6.25 square meters

• 5.25 square meters

What happens to the polynomial expression if the center floor size is doubled?

• It becomes 3x squared plus 5x plus 3

• It becomes 4x squared plus 8x plus 4

• It becomes x squared plus 4x plus 4

• It becomes 2x squared plus 6x plus 4

How does doubling the width of the border affect the polynomial expression?

• It becomes x squared plus 10x plus 20

• It becomes x squared plus 8x plus 16

• It becomes x squared plus 6x plus 12

• It becomes x squared plus 4x plus 4

What is the new polynomial expression if the length of the center section is tripled and the width is doubled?

• 4x squared plus 8x plus 2

• 5x squared plus 9x plus 3

• 6x squared plus 10x plus 4

• 7x squared plus 11x plus 5