# James Rutledge

## St. Petersburg College

## Materials Contributed through SERC-hosted Projects

### Activities (50)

Effect of Coefficient of x^0 on Parabola Vertex part of Merlot Physics Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x^0 (i.e., the constant, c) on the vertex of a parabola where a and b are arbitrarily fixed values in f(x)=ax^2+bx+c. While students generally accept that the constant, c, produces a vertical shift in the graph of a parabola, most don't clearly understand why that happens. The project helps them to understand the nature of polynomial functions at a deeper level.

Effect of Coefficient of x^2 on Parabola Shape part of Merlot Biology Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x^2 on the shape of a parabola where b and c are arbitrarily fixed values in f(x)=ax^2+bx+c. The results are quite revealing and show that while students may have learned that the coefficient of x^2 affects the shape of a parabola (i.e., when a>0, the parabola opens upward, and when a<0, the parabola opens downward), most do not understand the reason why. The fact that the term with the highest degree is the dominant term in a polynomial is generally unfamiliar to them.

Effect of Coefficient of x^2 on Parabola Shape part of Merlot Math Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x^2 on the shape of a parabola where b and c are arbitrarily fixed values in f(x)=ax^2+bx+c. The results are quite revealing and show that while students may have learned that the coefficient of x^2 affects the shape of a parabola (i.e., when a>0, the parabola opens upward, and when a<0, the parabola opens downward), most do not understand the reason why. The fact that the term with the highest degree is the dominant term in a polynomial is generally unfamiliar to them.

Effect of Coefficient of x^2 on Parabola Shape part of Merlot Information Technology Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x^2 on the shape of a parabola where b and c are arbitrarily fixed values in f(x)=ax^2+bx+c. The results are quite revealing and show that while students may have learned that the coefficient of x^2 affects the shape of a parabola (i.e., when a>0, the parabola opens upward, and when a<0, the parabola opens downward), most do not understand the reason why. The fact that the term with the highest degree is the dominant term in a polynomial is generally unfamiliar to them.

Effect of Coefficient of x on Parabola Vertex (b < 0) part of Merlot Biology Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x on the vertex of a parabola where a>0, b<0 and a and c are arbitrarily fixed values in f(x)=ax^2+bx+c. Algebraically analyzing the effects requires a good bit of effort on the students' part, but the results are rewarding.

Effect of Coefficient of x on Parabola Vertex (b < 0) part of Merlot Math Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x on the vertex of a parabola where a>0, b<0 and a and c are arbitrarily fixed values in f(x)=ax^2+bx+c. Algebraically analyzing the effects requires a good bit of effort on the students' part, but the results are rewarding.

Effect of Coefficient of x on Parabola Vertex (b < 0) part of Merlot Information Technology Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x on the vertex of a parabola where a>0, b<0 and a and c are arbitrarily fixed values in f(x)=ax^2+bx+c. Algebraically analyzing the effects requires a good bit of effort on the students' part, but the results are rewarding.

Effect of Coefficient of x on Parabola Vertex (b < 0) part of Merlot Physics Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x on the vertex of a parabola where a>0, b<0 and a and c are arbitrarily fixed values in f(x)=ax^2+bx+c. Algebraically analyzing the effects requires a good bit of effort on the students' part, but the results are rewarding.

Effect of Coefficient of x^2 on Parabola Vertex (a>0) part of Merlot Biology Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x^2 on the vertex of a parabola where a>0, b>0 and b and c are arbitrarily fixed values in f(x)=ax^2+bx+c. The results are quite revealing and show that while students may have learned that the coefficient of x^2 affects the shape of a parabola, most do not realize that it also affects the position of the vertex when b is not equal to 0. Algebraically analyzing the effects requires a good bit of effort on the students' part, but the results are rewarding.

Effect of Coefficient of x^2 on Parabola Vertex (a>0) part of Merlot Math Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x^2 on the vertex of a parabola where a>0, b>0 and b and c are arbitrarily fixed values in f(x)=ax^2+bx+c. The results are quite revealing and show that while students may have learned that the coefficient of x^2 affects the shape of a parabola, most do not realize that it also affects the position of the vertex when b is not equal to 0. Algebraically analyzing the effects requires a good bit of effort on the students' part, but the results are rewarding.

Effect of Coefficient of x^2 on Parabola Vertex (a>0) part of Merlot Information Technology Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x^2 on the vertex of a parabola where a>0, b>0 and b and c are arbitrarily fixed values in f(x)=ax^2+bx+c. The results are quite revealing and show that while students may have learned that the coefficient of x^2 affects the shape of a parabola, most do not realize that it also affects the position of the vertex when b is not equal to 0. Algebraically analyzing the effects requires a good bit of effort on the students' part, but the results are rewarding.

Effect of Coefficient of x^2 on Parabola Vertex (a>0) part of Merlot Physics Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x^2 on the vertex of a parabola where a>0, b>0 and b and c are arbitrarily fixed values in f(x)=ax^2+bx+c. The results are quite revealing and show that while students may have learned that the coefficient of x^2 affects the shape of a parabola, most do not realize that it also affects the position of the vertex when b is not equal to 0. Algebraically analyzing the effects requires a good bit of effort on the students' part, but the results are rewarding.

Effect of Coefficient of x^2 on Parabola Shape part of Merlot Physics Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x^2 on the shape of a parabola where b and c are arbitrarily fixed values in f(x)=ax^2+bx+c. The results are quite revealing and show that while students may have learned that the coefficient of x^2 affects the shape of a parabola (i.e., when a>0, the parabola opens upward, and when a<0, the parabola opens downward), most do not understand the reason why. The fact that the term with the highest degree is the dominant term in a polynomial is generally unfamiliar to them.

Effect of Proportionality Constant on Exponential Graph (k>0) part of Merlot Biology Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the proportionality constant, k, on the y-intercept and position of an exponential graph where k>0 and C is an arbitrarily fixed value in f(x)=Ce^(kx). While students may have learned that the proportionality constant affects the shape of a exponential curve, most do not realize exactly how. Analyzing the effect requires some effort on the students' part but the results are rewarding.

Effect of Proportionality Constant on Exponential Graph (k>0) part of Merlot Math Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the proportionality constant, k, on the y-intercept and position of an exponential graph where k>0 and C is an arbitrarily fixed value in f(x)=Ce^(kx). While students may have learned that the proportionality constant affects the shape of a exponential curve, most do not realize exactly how. Analyzing the effect requires some effort on the students' part but the results are rewarding.

Effect of Proportionality Constant on Exponential Graph (k>0) part of Merlot Information Technology Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the proportionality constant, k, on the y-intercept and position of an exponential graph where k>0 and C is an arbitrarily fixed value in f(x)=Ce^(kx). While students may have learned that the proportionality constant affects the shape of a exponential curve, most do not realize exactly how. Analyzing the effect requires some effort on the students' part but the results are rewarding.

Effect of Proportionality Constant on Exponential Graph (k>0) part of Merlot Physics Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the proportionality constant, k, on the y-intercept and position of an exponential graph where k>0 and C is an arbitrarily fixed value in f(x)=Ce^(kx). While students may have learned that the proportionality constant affects the shape of a exponential curve, most do not realize exactly how. Analyzing the effect requires some effort on the students' part but the results are rewarding.

Effect of Coefficient of x on Parabola Vertex (b>0) part of Merlot Biology Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x on the vertex of a parabola where a>0, b>0 and a and c are arbitrarily fixed values in f(x)=ax^2+bx+c. Algebraically analyzing the effects requires a good bit of effort on the students' part, but the results are rewarding.

Effect of Proportionality Constant on Exponential Graph (k < 0) part of Merlot Information Technology Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the proportionality constant, k, on the y-intercept and position of an exponential graph where k<0 and C is an arbitrarily fixed value in f(x)=Ce^(kx). While students may have learned that the proportionality constant affects the shape of a exponential curve, most do not realize exactly how. Analyzing the effect requires some effort on the students' part but the results are rewarding.

Effect of Proportionality Constant on Exponential Graph (k < 0) part of Merlot Physics Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the proportionality constant, k, on the y-intercept and position of an exponential graph where k<0 and C is an arbitrarily fixed value in f(x)=Ce^(kx). While students may have learned that the proportionality constant affects the shape of a exponential curve, most do not realize exactly how. Analyzing the effect requires some effort on the students' part but the results are rewarding.

Effect of Initial Value on Graph of Exponential Function (C>0) part of Merlot Biology Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the initial value, C, on the y-intercept and position of an exponential graph where C>0 and k is an arbitrarily fixed value in f(x)=Ce^(kx). While students may have learned that the initial value affects the shape of a exponential curve, most do not realize exactly how or that it also affects the position of the y-intercept. Analyzing the effects requires some effort on the students' part but the results are rewarding.

Effect of Initial Value on Graph of Exponential Function (C>0) part of Merlot Math Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the initial value, C, on the y-intercept and position of an exponential graph where C>0 and k is an arbitrarily fixed value in f(x)=Ce^(kx). While students may have learned that the initial value affects the shape of a exponential curve, most do not realize exactly how or that it also affects the position of the y-intercept. Analyzing the effects requires some effort on the students' part but the results are rewarding.

Effect of Coefficient of x^2 on Parabola Vertex (a < 0) part of Merlot Physics Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x^2 on the vertex of a parabola where a<0, b>0 and b and c are arbitrarily fixed values in f(x)=ax^2+bx+c. The results are quite revealing and show that while students may have learned that the coefficient of x^2 affects the shape of a parabola, most do not realize that it also affects the position of the vertex when b is not equal to 0. Algebraically analyzing the effects requires a good bit of effort on the students' part, but the results are rewarding.

Effect of Initial Value on Graph of Exponential Function (C < 0) part of Merlot Biology Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the initial value, C, on the y-intercept and position of an exponential graph where C<0 and k is an arbitrarily fixed value in f(x)=Ce^(kx). While students may have learned that the initial value affects the shape of a exponential curve, most do not realize exactly how or that it also affects the position of the y-intercept. Analyzing the effects requires some effort on the students' part but the results are rewarding.

Effect of Initial Value on Graph of Exponential Function (C < 0) part of Merlot Math Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the initial value, C, on the y-intercept and position of an exponential graph where C<0 and k is an arbitrarily fixed value in f(x)=Ce^(kx). While students may have learned that the initial value affects the shape of a exponential curve, most do not realize exactly how or that it also affects the position of the y-intercept. Analyzing the effects requires some effort on the students' part but the results are rewarding.

Effect of Initial Value on Graph of Exponential Function (C < 0) part of Merlot Information Technology Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the initial value, C, on the y-intercept and position of an exponential graph where C<0 and k is an arbitrarily fixed value in f(x)=Ce^(kx). While students may have learned that the initial value affects the shape of a exponential curve, most do not realize exactly how or that it also affects the position of the y-intercept. Analyzing the effects requires some effort on the students' part but the results are rewarding.

Effect of Initial Value on Graph of Exponential Function (C < 0) part of Merlot Physics Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the initial value, C, on the y-intercept and position of an exponential graph where C<0 and k is an arbitrarily fixed value in f(x)=Ce^(kx). While students may have learned that the initial value affects the shape of a exponential curve, most do not realize exactly how or that it also affects the position of the y-intercept. Analyzing the effects requires some effort on the students' part but the results are rewarding.

Effect of Proportionality Constant on Exponential Graph (k < 0) part of Merlot Biology Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the proportionality constant, k, on the y-intercept and position of an exponential graph where k<0 and C is an arbitrarily fixed value in f(x)=Ce^(kx). While students may have learned that the proportionality constant affects the shape of a exponential curve, most do not realize exactly how. Analyzing the effect requires some effort on the students' part but the results are rewarding.

Effect of Proportionality Constant on Exponential Graph (k < 0) part of Merlot Math Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the proportionality constant, k, on the y-intercept and position of an exponential graph where k<0 and C is an arbitrarily fixed value in f(x)=Ce^(kx). While students may have learned that the proportionality constant affects the shape of a exponential curve, most do not realize exactly how. Analyzing the effect requires some effort on the students' part but the results are rewarding.

Effect of Coefficient of x on Parabola Vertex (b>0) part of Merlot Physics Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x on the vertex of a parabola where a>0, b>0 and a and c are arbitrarily fixed values in f(x)=ax^2+bx+c. Algebraically analyzing the effects requires a good bit of effort on the students' part, but the results are rewarding.

Effect of Coefficient of x^2 on Parabola Vertex (a < 0) part of Merlot Biology Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x^2 on the vertex of a parabola where a<0, b>0 and b and c are arbitrarily fixed values in f(x)=ax^2+bx+c. The results are quite revealing and show that while students may have learned that the coefficient of x^2 affects the shape of a parabola, most do not realize that it also affects the position of the vertex when b is not equal to 0. Algebraically analyzing the effects requires a good bit of effort on the students' part, but the results are rewarding.

Effect of Coefficient of x^2 on Parabola Vertex (a < 0) part of Merlot Math Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x^2 on the vertex of a parabola where a<0, b>0 and b and c are arbitrarily fixed values in f(x)=ax^2+bx+c. The results are quite revealing and show that while students may have learned that the coefficient of x^2 affects the shape of a parabola, most do not realize that it also affects the position of the vertex when b is not equal to 0. Algebraically analyzing the effects requires a good bit of effort on the students' part, but the results are rewarding.

Effect of Coefficient of x^2 on Parabola Vertex (a < 0) part of Merlot Information Technology Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x^2 on the vertex of a parabola where a<0, b>0 and b and c are arbitrarily fixed values in f(x)=ax^2+bx+c. The results are quite revealing and show that while students may have learned that the coefficient of x^2 affects the shape of a parabola, most do not realize that it also affects the position of the vertex when b is not equal to 0. Algebraically analyzing the effects requires a good bit of effort on the students' part, but the results are rewarding.

Effect of Coefficient of x on Parabola Vertex (b>0) part of Merlot Math Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x on the vertex of a parabola where a>0, b>0 and a and c are arbitrarily fixed values in f(x)=ax^2+bx+c. Algebraically analyzing the effects requires a good bit of effort on the students' part, but the results are rewarding.

Effect of Coefficient of x on Parabola Vertex (b>0) part of Merlot Information Technology Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x on the vertex of a parabola where a>0, b>0 and a and c are arbitrarily fixed values in f(x)=ax^2+bx+c. Algebraically analyzing the effects requires a good bit of effort on the students' part, but the results are rewarding.

Effect of Initial Value on Graph of Exponential Function (C>0) part of Merlot Information Technology Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the initial value, C, on the y-intercept and position of an exponential graph where C>0 and k is an arbitrarily fixed value in f(x)=Ce^(kx). While students may have learned that the initial value affects the shape of a exponential curve, most do not realize exactly how or that it also affects the position of the y-intercept. Analyzing the effects requires some effort on the students' part but the results are rewarding.

Effect of Initial Value on Graph of Exponential Function (C>0) part of Merlot Physics Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest and a Question of the Day activity concerning the effect of the initial value, C, on the y-intercept and position of an exponential graph where C>0 and k is an arbitrarily fixed value in f(x)=Ce^(kx). While students may have learned that the initial value affects the shape of a exponential curve, most do not realize exactly how or that it also affects the position of the y-intercept. Analyzing the effects requires some effort on the students' part but the results are rewarding.

Effect of Coefficient of x^0 on Parabola Vertex part of Merlot Biology Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x^0 (i.e., the constant, c) on the vertex of a parabola where a and b are arbitrarily fixed values in f(x)=ax^2+bx+c. While students generally accept that the constant, c, produces a vertical shift in the graph of a parabola, most don't clearly understand why that happens. The project helps them to understand the nature of polynomial functions at a deeper level.

Effect of Coefficient of x^0 on Parabola Vertex part of Merlot Math Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x^0 (i.e., the constant, c) on the vertex of a parabola where a and b are arbitrarily fixed values in f(x)=ax^2+bx+c. While students generally accept that the constant, c, produces a vertical shift in the graph of a parabola, most don't clearly understand why that happens. The project helps them to understand the nature of polynomial functions at a deeper level.

Effect of Coefficient of x^0 on Parabola Vertex part of Merlot Information Technology Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents College Algebra students with a ConcepTest, a Question of the Day, and a Write-pair-share activity concerning the effect of the coefficient of x^0 (i.e., the constant, c) on the vertex of a parabola where a and b are arbitrarily fixed values in f(x)=ax^2+bx+c. While students generally accept that the constant, c, produces a vertical shift in the graph of a parabola, most don't clearly understand why that happens. The project helps them to understand the nature of polynomial functions at a deeper level.

U.S. Population Growth: What Does the Future Hold? part of Merlot Math Pedagogic Collection:Interactive Lectures:Examples

College Algebra or Liberal Arts math students are presented with a ConcepTest, a Question of the Day and a write-pair-share activity involving U.S. population growth. The results are quite revealing and show that while students may have learned how to perform the necessary calculations, their conceptual understanding concerning exponential growth may remain faulty. Student knowledge (or lack thereof) of the size of our population and its annual growth rate may also be surprising.

Pythagorean Theorem Investigations part of Just in Time Teaching:Examples

Secondary Math Ed majors or Geometry students are directed to a Web site that contains a rich and extensive collection of proofs of the Pythagorean Theorem, some accompanied by Java applets. Each student then selects two proofs to prepare to present to the class (a geometric proof and a visual proof) and writes a detailed outline of each proof. The student also indicates one additional proof that was of particular interest and the reason(s) for its selection. In a subsequent class, students are selected to make their presentations, either individually or in teams; the number of presentations may be limited due to time constraints and can be selected by lottery or a similar system.

Partial Derivatives: Geometric Visualization part of Merlot Math Pedagogic Collection:Interactive Lectures:Examples

This write-pair-share activity presents Calculus III students with a worksheet containing several exercises that require them to find partial derivatives of functions of two variables. Afterwards, a series of Web-based animations are used to illustrate the surface of each function, the path of the indicated partial derivative for a specified value of the variable, and the value of the derivative at each point along the path. Students find it difficult if not impossible to visualize most three-dimensional surfaces without assistance; the Web-based animation gallery provides an excellent source of visual illustrations that allow students to connect their abstract mathematical computations with geometric representations.

Symmetry and Tilings: An Exploration part of Just in Time Teaching:Examples

Students are directed to read through a Web-based tutorial on Symmetry and Tilings in the form of an short and colorful article entitled Tilings and Tesselations; afterwards, they answer several questions on tilings (tessellations), tiling terminology, types of symmetry (isometries), periodic tilings and Penrose tilings. In addition, they are given opportunity to use an interactive Java applet in which various types of symmetry can be sketched and explored in the form of wallpaper groups, frieze groups and rosette groups. In a subsequent think-pair-share activity or write-pair-share activity, they analyze some tilings and apply their newly obtained knowledge.

part of Just in Time Teaching:Examples

Students are directed to visit the MacTutor History of Mathematics Archive and to read an extensive online article entitled History of Pi; in addition, they make use of an interactive simulation of Buffon's Needle experiment. Afterwards, they answer several questions on how mathematicians calculated approximations for the value of pi and on the formulas that they used. In a subsequent class session, the instructor demonstrates a Java applet that simulates Buffon's Needle experiment in a cumulative manner. In a think-pair-share activity or write-pair-share activity, students analyze and discuss Buffon's experiment and its relationship to the value of pi.

Riemann Sums and Area Approximations part of Merlot Math Pedagogic Collection:Interactive Lectures:Examples

After covering the standard course material on area under a curve, Riemann sums and numerical integration, Calculus I students are given a write-pair-share activity that directs them to predict the best area approximation methods for each of several different functions. Afterwards, the instructor employs a Web-based applet that visually displays each method and provides the corresponding numerical approximations.

Mathematical Curve Conjectures part of Merlot Math Pedagogic Collection:Interactive Lectures:Examples

In this activity, a six-foot length of nylon rope is suspended at both ends to model a mathematical curve known as the hyperbolic cosine. In a write-pair-share activity, students are asked to make a conjecture concerning the nature of the curve and then embark on a guided discovery in which they attempt to determine a precise mathematical description of the curve using function notation.

How Much Work is Required: Intuition vs. Mathematical Calculation part of Merlot Math Pedagogic Collection:Interactive Lectures:Examples

This classroom activity presents Calculus II students with some Flash tutorials involving work and pumping liquids along with a simple question concerning the amount of work involved in pumping water out of two full containers having the same shape and size but different spatial orientations. Students are given opportunities to address this question by means of a ConcepTest, a Question of the Day and a write-pair-share activity. The results are quite revealing and show that while students may have learned how to perform the necessary calculations, their conceptual understanding concerning work may remain faulty.

Volumes of Solids of Revolution part of Merlot Math Pedagogic Collection:Interactive Lectures:Examples

This write-pair-share activity presents Calculus II students with a worksheet containing several exercises that require them to find the volumes of solids of revolution using disk, washer and shell methods and to sketch three-dimensional representations of the resulting solids. Afterwards, a Web-based tool is used to produce graphs of the solids and an interactive applet provides additional practice and feedback. This activity inevitably brings to light student misunderstandings concerning the various radii involved and enables them to discover the cause of their misunderstandings and resultant errors. The write-pair-share mode is helpful in that it allows students to get immediate feedback from their partners on their attempts at drawing and labeling diagrams.

The Crusty Loaf of Bread: An Exploration of Area of a Surface of Revolution part of Merlot Math Pedagogic Collection:Interactive Lectures:Examples

This write-pair-share activity for Calculus II students involves a hypothetical hemispherical loaf of bread with a 12-inch diameter that has been sliced into twelve one-inch-thick slices. The objective is to determine which slice contains the most upper crust (i.e., most area of its surface of revolution). Contrary to students' intuition and conjectures, the answer is neither the slices at each end of the loaf nor the two congruent slices at the center of the loaf.