Discipline: Mathematics

Professional Commentary: How many toothpicks does it take to make an n x n square composed of 1 x 1 squares? The lesson begins with a review of transformations of quadratic functions--vertical and horizontal shifts, and stretches and shrinks....

Discipline: Mathematics

Professional Commentary: Students must solve a quadratic equation whose roots are irrational. This constructed-response question is a sample test item used in grade 12 in the 1990 National Assessment of Educational Progress (see About NAEP)....

Discipline: Mathematics

Professional Commentary: Algebra tiles are used to show the square of a + b, the square of a - b, and the product of a + b and a - b. The explanations are step-by-step and easy to follow....

Discipline: Mathematics

Professional Commentary: This online tutorial discusses the standard and polar forms for complex numbers and the basic operations in each system. Euler's Equation presents the link between the two representations....

Discipline: Mathematics

Professional Commentary: Students must find the zeros of a quadratic equation, given its graph. This multiple-choice question is a sample item used in the 2005 Ohio Grade 8 Achievement Test (see Overview of Ohio's Assessment System)....

Discipline: Mathematics

Professional Commentary: Students must identify the graph of a quadratic equation. This multiple-choice question is a sample item used in the 2005 Ohio Graduation Test (see Overview of Ohio's Assessment System)....

Discipline: Mathematics

Professional Commentary: Students must select the equation that represents the relationship between values for x and y shown in a table. This multiple-choice question is a sample item used in the 2004 Ohio Graduation Test (see Overview of Ohio's Assessment System)....

Discipline: Mathematics

Professional Commentary: Students use quadratic functions to describe the relationship of the height of a football thrown in a parabolic path to its distance from the goal line. Working with graphing calculators, students collect and organize data, make a scatterplot, fit a curve to the appropriate parent function, and interpret the results. Discussion questions, an activity sheet, an extension...

Discipline: Mathematics

Professional Commentary: Both ends of a small chain are attached to a board with a grid on it to form a catenary curve, similar to a parabola. Students choose three points along the curve and use them to identify an equation....

Discipline: Mathematics

Professional Commentary: In this set of lessons, students analyze the number line and the relationships among the different sets of numbers in the real number system. Activities help students understand different sizes of infinity, the unique qualities of zero, the behavior of a positional number system, the behavior of zero in multiplication and division, and the role of...

Discipline: Mathematics

Professional Commentary: The short course covers the history as well as the mathematics of complex numbers. The development of the imaginary unit i and the proof of the Fundamental Theorem of Algebra are followed by explorations of the complex plane....

Discipline: Mathematics

Professional Commentary: Here is an extension of some basic factoring methods. Although factoring has been lessened in importance in recent years, it is extremely helpful in maintaining algebraic skills and extending logical thinking and problem-solving skills....

Discipline: Mathematics

Professional Commentary: Commercial fireworks must be carefully timed to ignite as intended. The process involves projectile motion that can be modeled with the quadratic function (ignoring air resistance), as found in the study of dynamics in physics: h = –16t2 + v0t + h0....

Discipline: Mathematics

Professional Commentary: Students determine a plan to maximize profit on a donut sale using data provided. The parabolic graphs of selling price vs....