Ceiling Tile Room Art: Rational Expressions – SCOPES Digital Fabrication

Lesson Details

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Author

JEFFREY CHRISTOPHER

Summary

Students will improve the learning environment in the 11th/12th grade math room by creating (12″x 24″) acrylic ceiling tiles that show a challenging rational function. The tile will have a rational function provided by the teacher, students will have to show on the tile how to simplify the expression, how to find the zeros, how to find the asymptotes, how to find points of discontinuity, how to describe the end behavior of the function, and will have a graph of the function detailing all of those features. Students will be grouped into groups of 2-3 based on performance from a previous factoring unit. They will also create a rational equation with 2 rational expressions and at least 2 solutions, then show how to solve the equation, and explain the features of the rational function that results in solving the equation.

The Instructions

Ceiling Tile Room Art: Rational Expressions

Follow all directions in the attachment.

Follow all directions in the attachment.

Standards

• (HSA.APR.A1): Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
• (HSA.APR.B2): Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x - a is p(a), so p(a) = 0 if and only if (x - a) is a factor of p(x).
• (HSA.APR.B3): Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.
• (HSA.APR.C4): Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x² + y²)² = (x² - y²)² + (2xy)² can be used to generate Pythagorean triples.
• (HSA.APR.C5): (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.1
• (HSA.APR.D6): Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
• (HSA.APR.D7): (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.