# Examples

# Interactive Lectures Examples by Type

*Jump down to:* Think-Pair-Share Examples | ConcepTest Examples | Question of the Day Examples | Longer Activities

## Examples that Feature All Three Types in One

The following activities can be used as a Think-Pair-Share, ConcepTest, and/or Question of the Day.Effect of Coefficient of x

^{2}on Parabola Vertex (a < 0) 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}...

Effect of Coefficient of x on Parabola Vertex (b > 0) This 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}...

Effect of Coefficient of x

^{2}on Parabola Vertex (a > 0) College Algebra students are presented 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}...

Effect of Coefficient of x on Parabola Vertex (b < 0) 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...

Effect of Coefficient of x

^{2}on Parabola Shape This activity provides College Algebra students 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}...

Effect of Coefficient of x

^{0}on Parabola Vertex 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}...

Effect of Initial Value on Graph of Exponential Function (C > 0) College Algebra students are given 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)}...

Effect of Initial Value on Graph of Exponential Function (C < 0) 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)}...

Effect of Proportionality Constant on Exponential Graph (k > 0) This 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)}...

Effect of Proportionality Constant on Exponential Graph (k < 0) This classroom activity provides 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)}...

## Think-Pair-Share Examples

Volumes of Solids of Revolution This write-pair-share activity presents Calculus II students with a worksheet containing several exercises that require them to find the volume of solids of revolution using disk, washer and shell ...

How Much Work is Required: Intuition vs. Mathematical Calculation This classroom activity presents Calculus II students with some Flash tutorials involving work and pumping liquids and a simple question concerning the amount of work involved in pumping water out of ...

Riemann Sums and Area Approximations After covering the standard course material on area under acurve, Riemann sums and numerical integration, Calculus I students are given a write-pair-share activity that directs them to predict the ...

U.S. Population Growth: What Does the Future Hold? 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 ...

The Crusty Loaf of Bread: An Exploration of Area of a Surface of Revolution 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 ...

Partial Derivatives: Geometric Visualization 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 ...

Mathematical Curve Conjectures 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 ...

## ConcepTest Examples

How Much Work is Required: Intuition vs. Mathematical Calculation This classroom activity presents Calculus II students with some Flash tutorials involving work and pumping liquids and a simple question concerning the amount of work involved in pumping water out of ...

U.S. Population Growth: What Does the Future Hold? 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 ...

## Question of the Day Examples

How Much Work is Required: Intuition vs. Mathematical Calculation This classroom activity presents Calculus II students with some Flash tutorials involving work and pumping liquids and a simple question concerning the amount of work involved in pumping water out of ...

U.S. Population Growth: What Does the Future Hold? 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 ...

## Longer Activities

Back to TopThe Crusty Loaf of Bread: An Exploration of Area of a Surface of Revolution 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.

How Much Work is Required: Intuition vs. Mathematical Calculation 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.

Mathematical Curve Conjectures In this write-pair-share activity, a six-foot length of nylon rope is suspended at both ends to model a mathematical curve known as the hyperbolic cosine.

Partial Derivatives: Geometric Visualization 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.

Riemann Sums and Area Approximations 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.

U.S. Population Growth: What Does the Future Hold? 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.

Volumes of Solids of Revolution 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.