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Geometric Sequences & Series

Sequences, Series & Functions ... Students find common ratios of geometric sequences on a spreadsheet and create scatter plots of the sequences to see how each curve is related to the value of the common ratio and/or the sign of the first term of the sequence.

Working Hard or Hardly Working?

Data Analysis ... Analyze univariate and bivariate data. Questions are posed for discussion, further research, and algebraic problem solving.

Transformations With Lists

Transformational Geometry ... Students use list operations to perform reflections, rotations, translations and dilations on a figure, and graph the resulting image using a scatter plot.

All Systems Go!

Vectors and Matrices ... Students learn about inverse matrices in the context of encoding/decoding secret messages and then use inverse matrices to solve systems of equations.

What is Calculus?

Overview of Calculus ... Students answer self-check questions and investigate animations in this introduction and overview of calculus to get the big picture of what Calculus is about and its various applications.

Inference for Two-way Tables

Hypothesis Testing ... Students use the chi-square test to analyze whether two categorical variables are independent or dependent calculating expected frequencies, the test statistic and the critical values.

Transformations With Lists

Transformational Geometry ... Students use list operations to perform reflections, rotations, translations and dilations on a figure, and graph the resulting image using a scatter plot.

Geometric Sequences & Series

Working Hard or Hardly Working?

Data Analysis ... Analyze univariate and bivariate data. Questions are posed for discussion, further research, and algebraic problem solving.

All Systems Go!

Vectors and Matrices ... Students learn about inverse matrices in the context of encoding/decoding secret messages and then use inverse matrices to solve systems of equations.

What is Calculus?

Inference for Two-way Tables

Box Plots & Histograms

Data Analysis ... Create and explore a box plot and histogram for a data set. Then compare the two data displays and use the comparison to draw conclusions about the data.

Arithmetic Sequences & Series

Sequences, Series & Functions ... Use formulas to find the differences of the consecutive terms, plot a scatter plot of each sequence, and determine the shape of sequences with common differences. Then use a spreadsheet to display the first n terms and find the sum.

Reflections and Rotations

Transformational Geometry ... Students reflect figures over the x- and y-axes and rotate figures 90°, 180°, and 270° counterclockwise about the origin, writing rules for each reflection and rotation.

Transitions

Parametric and Rectangular Equations ... Students explore converting rectangular equations to polar form and vice versa. Familiar trigonometric identities and circle relationships are applied in making the conversions.

The Derivative of Logs

Formal Differentiation ... Finally, students will use the Chain Rule to find the derivative of more complex exponential and logarithmic functions.

What! A Mistake!

Hypothesis Testing ... Students learn about type I and type II errors. Then, for a given scenario, they calculate the probabilities of errors and the power of the test.

Box Plots & Histograms

Data Analysis ... Create and explore a box plot and histogram for a data set. Then compare the two data displays and use the comparison to draw conclusions about the data.

Arithmetic Sequences & Series

Reflections and Rotations

Transitions

The Derivative of Logs

Formal Differentiation ... Students use the graph of the natural logarithm function to estimate the graph of the inverse function by inspecting the slope of a tangent and using this information to construct a scatter plot.

What! A Mistake!

Hypothesis Testing ... Students learn about type I and type II errors. Then, for a given scenario, they calculate the probabilities of errors and the power of the test.

Perms and Combs?

Permutations and Combinations ... Review of the vocabulary and concepts of factorials, combinations, and permutations. Students use built-in commands to evaluate the expressions.

Average Orange

Statistics ... Explore the area under the normal curve between various x-values and use a model to find what percent of the area lies within 1, 2, and 3 standard deviations of the mean.

Scale Factor

Transformational Geometry ... Students dilate polygons and find the perimeter and area of both the pre image and image. Then they find the ratios of the perimeters and areas.

Spring Training

Parametric Equations ... Explore parametric equations, finding the horizontal and vertical distances traveled by a projectile. Parametric equations will be converted into quadratic equations.

Optimization

Applications of Derivatives ... Students will learn how to use the second derivative test to find maxima and minima in word problems and solve optimization in parametric functions.

Goodness-of-Fit Tests

Hypothesis Testing ... Students test claims of whether given distributions “fit” theoretical distributions. They use spreadsheets to calculate test statistics and the Integral tool to calculate P-values.

Perms and Combs?

Permutations and Combinations ... Review of the vocabulary and concepts of factorials, combinations, and permutations. Students use built-in commands to evaluate the expressions.

Average Orange

Statistics ... Explore the area under the normal curve between various x-values and use a model to find what percent of the area lies within 1, 2, and 3 standard deviations of the mean.

Scale Factor

Transformational Geometry ... Students dilate polygons and find the perimeter and area of both the pre image and image. Then they find the ratios of the perimeters and areas.

Spring Training

Parametric Equations ... Explore parametric equations, finding the horizontal and vertical distances traveled by a projectile. Parametric equations will be converted into quadratic equations.

Optimization

Applications of Derivatives ... Students will learn how to use the second derivative test to find maxima and minima in word problems and solve optimization in parametric functions.

Goodness-of-Fit Tests

AP Calculus Prep Exam

Exam Practice Questions ... Prepare for the AP Calculus exam by reviewing and gaining skills in graphing, finding intersections, zeros, derivatives at a point, and evaluating definite integrals.

Bewildered Babies

Data Analysis & Probability ... After making charts and using logic to list possible label arrangements, students compare their results with the output of the combinations formula and nCr command.

Perspective Drawings

3-D Geometry ... Draw figures in one- and two-point perspective, comparing and contrasting the two types of drawings. Then create an isometric drawing and compare it to the other drawings.

Modeling Probabilities

Statistics ... Use simulations and graphs to explore when the number of trials of a binomial experiments becomes large number.

Winter Conics

Conics ... Explore conic graphing using a polar notation equation and determine the effects the various variables on the graph.

Comparing Two Means

Hypothesis Testing ... Test hypotheses concerning means of two populations by calculating the test statistic and the critical values and graphing the critical region.

Winter Conics

Conics ... Explore conic graphing using a polar notation equation and determine the effects the various variables on the graph.

AP Calculus Prep Exam

Exam Practice Questions ... Prepare for the AP Calculus exam by reviewing and gaining skills in graphing, finding intersections, zeros, derivatives at a point, and evaluating definite integrals.

Bewildered Babies

Modeling Probabilities

Statistics ... Use simulations and graphs to explore when the number of trials of a binomial experiments becomes large number.

Perspective Drawings

3-D Geometry ... Draw figures in one- and two-point perspective, comparing and contrasting the two types of drawings. Then create an isometric drawing and compare it to the other drawings.

Comparing Two Means

Hypothesis Testing ... Test hypotheses concerning means of two populations by calculating the test statistic and the critical values and graphing the critical region.

Inverse Variation

Radical Equations & Functions ... Explore the inverse variation function with a geometric representation (a rectangle with fixed area), a table of values, an algebraic expression, and a graph.

Permutations and Combinations

Permutations, Combinations & Probability ... Students explore permutations and combinations by arranging letters when order does and does not make a difference. As an extension, they explore the handshake problem.

Torricelli�s Law

Applications of Integration ... Students will examine the velocity of water flowing through the tap of a tank, finding an equation to model the height of the water in the tank as the tank is drained.

Claims About Two Proportions

Hypothesis Testing ... Students test claims about two proportions by calculating test statistics, critical values, and P-values, for both one- and two-tailed tests.

Volume

3-D Geometry ... Defining right and oblique three dimensional figures and calculating the volume for prisms, pyramids, cylinders, and cones. Use multiple representations to explore properties of area and volume.

Properties of an Ellipse

Conics ... Discover properties of an ellipse, such as the set of all points such that the sum of the distances from these points to two fixed points is constant.

Inverse Variation

Radical Equations & Functions ... Explore the inverse variation function with a geometric representation (a rectangle with fixed area), a table of values, an algebraic expression, and a graph.

Permutations and Combinations

Torricelli�s Law

Applications of Integration ... Students will examine the velocity of water flowing through the tap of a tank, finding an equation to model the height of the water in the tank as the tank is drained.

Claims About Two Proportions

Hypothesis Testing ... Students test claims about two proportions by calculating test statistics, critical values, and P-values, for both one- and two-tailed tests.

Volume

Properties of an Ellipse

Conics ... Discover properties of an ellipse, such as the set of all points such that the sum of the distances from these points to two fixed points is constant.

STOP

Radical Equations & Functions ... Work with speeds in meters per second and stopping distances in meters, students will use an interactive page to evaluate a formula involving a square root. With a collection of data values, the scatter plot reveals a relationship and a shape to the students.

Binomial Probabilities

Permutations, Combinations & Probability ... Students simulate rolling a die and keeping track of the numbers of successes and failures by using the randBin command. Next, they find the theoretical probabilities and compare them with the experimental probabilities.

Exploring Cavalieri�s Principle

3-D Geometry ... Students will explore Cavalieri’s Principle for cross sectional area and volume.

Is It Standard?

Hypothesis Testing ... Students will test a claim about the standard deviation by comparing the χ² value to the critical value.

Laws of Sine and Cosine

Trigonometry ... Students explore the proofs of the Laws of Sine and Cosine, investigate various cases where they are utilized, and apply them to solve problems.

Mr. Taylor, I Presume?

Series & Taylor Polynomials ... Explore Taylor polynomials graphically and analytically, as well as graphically determine the interval where the Taylor polynomial approximates the function it models.

STOP

Is It Standard?

Hypothesis Testing ... Students will test a claim about the standard deviation by comparing the χ² value to the critical value.

Binomial Probabilities

Exploring Cavalieri�s Principle

3-D Geometry ... Students will explore Cavalieri’s Principle for cross sectional area and volume.

Laws of Sine and Cosine

Trigonometry ... Students explore the proofs of the Laws of Sine and Cosine, investigate various cases where they are utilized, and apply them to solve problems.

Mr. Taylor, I Presume?

Series & Taylor Polynomials ... Explore Taylor polynomials graphically and analytically, as well as graphically determine the interval where the Taylor polynomial approximates the function it models.

Double Tree

Exponential & Radical Functions ... In this activity, students model tree growth using the sequence 2ⁿ. They use the Line command to draw line segments, representing the height of a tree. The commands shown in the screenshot, draws lines from (1, 0) to (1, 2) and (2, 0) to (2, 4).

Parabola Construction

Conics & Polar Coordinates ... Students construct parabolas using the focus and directrix definition. They also explore how the location of the focus with respect to the directrix affects the shape of the parabola.

Exploring Circle Equations

Circles ... Students will discover the equation of circles of the form (x - h)² + (y - k)²

What�s the Difference?

Cosine Difference Identity ... The angle difference formula for cosine is explored.

Polar Necessities

Polar Equations ... Students will graphically and algebraically find the slope of the tangent line at a point on a polar graph. Finding the area of a region of a polar curve will be determined using the area formula.

Hypothesis Testing: Means

Hypothesis Testing ... Students test a claim about a mean with a large sample size at the five-percent significance level. The test statistic is found and compared to the critical value.

Parabola Construction

Double Tree

Exponential & Radical Functions ... Geometric sequences are explored visually by modeling the growth of a tree that doubles in height every year.

Exploring Circle Equations

Circles ... Students will discover the equation of circles of the form (x – h)² + (y – k)² = r², where (h, k) is the center of the circle and r is the radius of the circle.

What�s the Difference?

Cosine Difference Identity ... The angle difference formula for cosine is explored.

Polar Necessities

Hypothesis Testing: Means

Hypothesis Testing ... Students test a claim about a mean with a large sample size at the five-percent significance level. The test statistic is found and compared to the critical value.

The Box Method

Quadratic Functions ... Students will discover how to factor a quadratic function using the Box Method.

Constructing an Ellipse

Conics & Polar Coordinates ... Two different methods for constructing an ellipse are presented and explored. Students discover that the sum of the distances from a point on an ellipse to its foci is always constant.

Circle Product Theorems

Circles ... Students will use dynamic models to find patterns. These patterns are the Chord-Chord, Secant-Secant, and Secant-Tangent Theorems.

Find That Sine

Trigonometric Functions ... Sinusoidal regression is used to determine equations to model various data sets and the equations are used to make inferences.

Parametric Race & Slope

Parametric Equations ... Students will study the motion of two points and use calculus to determine the velocity and acceleration. The slope of parametric equations will be determined.

Testing Claims About Proportions

Statistical Inference ... Students find z-scores and critical values to test claims about proportions. To verify the results, they find P-values by finding the area under the curve.

Testing Claims About Proportions

Statistical Inference ... Students find z-scores and critical values to test claims about proportions. To verify the results, they find P-values by finding the area under the curve.

The Box Method

Quadratic Functions ... Students will discover how to factor a quadratic function using the Box Method.

Constructing an Ellipse

Circle Product Theorems

Circles ... Students will use dynamic models to find patterns. These patterns are the Chord-Chord, Secant-Secant, and Secant-Tangent Theorems.

Parametric Race & Slope

Parametric Equations ... Students will study the motion of two points and use calculus to determine the velocity and acceleration. The slope of parametric equations will be determined.

Find That Sine

Trigonometric Functions ... Sinusoidal regression is used to determine equations to model various data sets and the equations are used to make inferences.

Inscribed Angles Theorem

Circles ... Investigate at inscribed angles and central angles and work towards discovering a relationship among the two, the Inscribed Angle Theorem, and look at two corollaries.

Trigonometric Patterns

Trigonometry ... Students will use the unit circle to examine patterns in the six trigonometric functions.

Area � FOILed Again

Quadratic Functions ... Students will practice finding rectangular areas with algebraic expressions for the lengths of the sides.

Vertical and Phase Shifts

Trigonometric Functions ... Students explore vertical and phase shifts of sine and cosine functions and determine the effect that each change has upon the shape of the graph.

Gateway Arc Length

Applications of Integration ... Investigate the arc length of the Gateway Arch, using the Pythagorean Theorem to approximate and using Calculus to find the exact solution. Students also solve arc length questions.

How Far Am I Off

Statistical Inference ... Students calculate a confidence interval using the chi-square distribution to estimate a population variance.

Inscribed Angles Theorem

Circles ... Investigate at inscribed angles and central angles and work towards discovering a relationship among the two, the Inscribed Angle Theorem, and look at two corollaries.

Vertical and Phase Shifts

Trigonometric Functions ... Students explore vertical and phase shifts of sine and cosine functions and determine the effect that each change has upon the shape of the graph.

Trigonometric Patterns

Trigonometry ... Students will use the unit circle to examine patterns in the six trigonometric functions.

Area � FOILed Again

Quadratic Functions ... Students will practice finding rectangular areas with algebraic expressions for the lengths of the sides.

Gateway Arc Length

How Far Am I Off

Statistical Inference ... Students calculate a confidence interval using the chi-square distribution to estimate a population variance.

Quadratic Formula

Quadratic Functions ... Students make connections between the visual ways to find zeros of a parabola and algebraic ways with an emphasis on the quadratic formula.

Simple Harmonic Motion

Applications of Integration ... With an example of the motion of a child on a swing, the activity begins with the trigonometric function between time and displacement and differentiates up to acceleration. It concludes with integration from acceleration back to displacement.

Trig Transformations

Trigonometric & Logarithmic Functions ... Explore function notation and transformational graphing of trigonometric functions. For a related TI-84 Plus activity, see Solving Trigonometric Equations.

Angles & Arcs

Circles ... Students explore angles constructed in a circle and how their measures are related to the measures of the intercepted arcs.

Round and Round She Goes�

Unit Circle ... Explore relationships on the unit circle and identify coordinates of points given an angle measure in degrees.

Population Mean: Variance Unknown

Statistical Inference ... Calculate confidence intervals to estimate the true population mean when the standard deviation of the population is not known.

Quadratic Formula

Quadratic Functions ... Students make connections between the visual ways to find zeros of a parabola and algebraic ways with an emphasis on the quadratic formula.

Simple Harmonic Motion

Applications of Integration ... In this activity, students explore simple harmonic motion in terms of the motion on a swing. Students derive the defining formulas — first, beginning with the trigonometric relationship between time and displacement, and differentiation to the form for acceleration, and then by integration from acceleration back to displacement.

Population Mean: Variance Unknown

Statistical Inference ... Calculate confidence intervals to estimate the true population mean when the standard deviation of the population is not known.

Trig Transformations

Trigonometric & Logarithmic Functions ... Explore function notation and transformational graphing of trigonometric functions. For a related TI-84 Plus activity, see Solving Trigonometric Equations.

Angles & Arcs

Circles ... Students explore angles constructed in a circle and how their measures are related to the measures of the intercepted arcs.

Round and Round She Goes�

Unit Circle ... Explore relationships on the unit circle and identify coordinates of points given an angle measure in degrees.

The Impossible Task

Linear Systems ... Students write an inequality to represent a given manufacturing situation. They examine its solution setting by testing values of the variable on a spreadsheet and viewing its graph. Then a second constraint and a second variable are added to the situation.

Getting Triggy With It

Trigonometric & Logarithmic Functions ... Explore the effect of the coefficients on the graph of sine or cosine functions. Amplitude, period, frequency, phase shift, baseline, and vertical offset are introduced and calculated using the geometry and measurement tools.

Ratios of Similar Figures

Ratio, Proportion & Similarity ... Explore the ratio of perimeter, area, surface area, and volume of similar figures in two and three dimensional figures.

Can You Hear Me Now?

Logarithmic Functions ... Students will explore logarithmic equations relating to sound intensity and pH.

Charged Up

Differential Equations ... Use the deSolve command to find general and particular solutions to differential equations. Then dynamically explore the family of particular solution to a differential equation.

Means With Confidence

Statistical Inference ... Estimate the true mean of a population when the standard deviation is known by finding the sample mean, margin of error and confidence interval.

Getting Triggy With It

The Impossible Task

Getting Triggy With It

Ratios of Similar Figures

Ratio, Proportion & Similarity ... Explore the ratio of perimeter, area, surface area, and volume of similar figures in two and three dimensional figures.

Can You Hear Me Now?

Logarithmic Functions ... Students will explore logarithmic equations relating to sound intensity and pH.

Charged Up

Means With Confidence

Statistical Inference ... Estimate the true mean of a population when the standard deviation is known by finding the sample mean, margin of error and confidence interval.

Estimating a Population Proportion

Statistical Inference ... Find the confidence interval for a population proportion by first finding the critical value and the margin of error. Then find the required sample size given a confidence level and margin of error.

Bridge On The River Quad

Quadratic Functions ... Graph a quadratic function that models the shape of a bridge trestle and then solve the related quadratic equation by completing the square. This list of steps is generalized to deduce the quadratic formula.

Modeling Data

Exponential & Logarithmic Functions ... Graph data modeling exponential and logarithmic growth and find equations representing the data.

Side-Splitter Theorem

Ratio, Proportion & Similarity ... Explore the side-splitter theorem by collecting data from a triangle with a line parallel to one of its sides.

Change of Base

Logarithmic Functions ... Discover the change of base rule for logarithms by examining the ratio of two logarithmic functions with different bases.

Slope Fields Forever

Differential Equations ... Dynamically explore a particular solution to a differential equation for different initial conditions and investigate slope fields.

Bridge On The River Quad

Modeling Data

Exponential & Logarithmic Functions ... Graph data modeling exponential and logarithmic growth and find equations representing the data.

Side-Splitter Theorem

Ratio, Proportion & Similarity ... Explore the side-splitter theorem by collecting data from a triangle with a line parallel to one of its sides.

Change of Base

Logarithmic Functions ... Discover the change of base rule for logarithms by examining the ratio of two logarithmic functions with different bases.

Slope Fields Forever

Differential Equations ... Dynamically explore a particular solution to a differential equation for different initial conditions and investigate slope fields.

Estimating a Population Proportion

Manual Fit

Quadratic Functions ... Utilize the grab and move feature to manipulate parabolas so that the curve matches a set of data points. This activity will serve to reinforce understanding of the vertex form for a parabola.

The Geometric Mean

Ratio, Proportion & Similarity ... Establish that several triangles are similar and verify that one side is the geometric mean between two other segments.

Exponential Reflections

Exponential & Logarithmic Functions ... Reflect a point from the exponential function over the line y = x and find the locus of the reflection, which is the natural log function.

Is It Rare?

Distributions ... The Poisson distribution is used to determine the probabilities for various numbers of hurricanes hitting the United States in a given year. Students will also explore the graph of the Poisson distribution and how it behaves.

Volume by Cross Sections

Applications of Integration ... The concept of finding the volume of a solid formed by cross sections of a function that form certain shapes is explored. Students review areas of various shapes and use Geometry Trace to help get a “3D” visual of the volume under consideration.

Accelerated Returns

Finance with Exponential Functions ... Students will compare periodic and continuous compounding and apply continuous compounding to a variety of problem situations.

Manual Fit

The Geometric Mean

Ratio, Proportion & Similarity ... Establish that several triangles are similar and verify that one side is the geometric mean between two other segments.

Exponential Reflections

Exponential & Logarithmic Functions ... Reflect a point from the exponential function over the line y = x and find the locus of the reflection, which is the natural log function.

Is It Rare?

Volume by Cross Sections

Accelerated Returns

Finance with Exponential Functions ... Students will compare periodic and continuous compounding and apply continuous compounding to a variety of problem situations.

Angle Bisectors in a Triangle

Triangles and Their Centers ... In this activity, students will explore the relationships between an angle bisector and segments in a triangle. They will determine the distances from an angle bisector to the sides of the bisected angle. In a triangle, proportional relationships occur when an angle bisector divides the opposite side into two parts.

Exponential Growth

Exponential & Logarithmic Functions ... In this activity, students will find an approximation for the value of the mathematical constant e and to apply it to exponential growth and decay problems. They are asked to search for the base, b, that defines a function f(x) = bx with the property that at any point on the graph, the slope of the tangent line (instantaneous rate of change) is equal to f(x).

Applications of Parabolas

Quadratic Functions ... In this activity, students will look for both number patterns and visual shapes that go along with quadratic relationships. Two applications are introduced after some basic patterns in the first two problems.

Very Interesting

Nominal and Effective Rates ... In this activity, students will explore interest related to consumer loans, credit, and savings accounts. They will use the formulas as well as use tools available with TI-Nspire technology to convert nominal interest rates to annual rates and vice versa. Students will also use the Finance Solver function to determine monthly payments.

Area Accumulation

Average ... In this activity, students will numerically and graphically investigate the integral using area accumulation. Geometry Trace is used to see the family of functions produced by changing the value of a in the integral of f(x)dx from a to x. Also the kinematic relationships for integration are used with a piecewise function and with actual data.

Chi-Squared Distribution

Continuous Distributions ... In this activity, students first compare the chi-square distribution to the standard normal distribution. They will also determine how the Chi-Square distribution changes as they increase the degrees of freedom. Students then confirm critical values for given confidence levels and sample sizes they find in a chart.

Angle Bisectors in a Triangle

Exponential Growth

Applications of Parabolas

Very Interesting

Area Accumulation

Chi-Squared Distribution

F Distribution

Continuous Distributions ... In this activity, students study the characteristics of the F distribution and compare the distribution to others previously studied. Students then find probabilities and percentiles, verifying their values on a graph by using the Integral tool. They move on to find critical values and then compute a confidence interval.

Folding Parabolas

Quadratic Functions ... In this activity, students graph a quadratic function and investigate its symmetry by choosing pairs of points with the same y-value. They then calculate the average of the x-values of these points and discover that not only do all the points have the same x-value, but the average is equal to the x-value of the vertex.

Roots of Radical Equations

Rational & Radical Functions ... In this activity, students will solve radical equations graphically. Several square and cubic root equations are given for students to graph and find intersections with the x-axis. They will also use the distance formula to solve an extension problem.

Midsegments of Triangles

Ratio, Proportion & Similarity ... In this activity, students will explore the properties of the midsegment, a segment that connects the midpoints of two sides of a triangle. First, students will construct and investigate one midsegment and the relationship of the new small triangle to the original triangle. Then, all three midsegments will be constructed and this figure will be explored.

Coin Toss

Logarithmic Functions ... In this activity, students will run two experiments that involve simulating pouring out coins from a bag. They will collect the data and graph it, using different methods to find equations to model the data. Then students will find the inverse of the data and corresponding equation to model it.

Average Roller Coaster

Average Value ... In this activity, students will graphically discover how to find the average value of a function. This exploration uses animation and graphical observations to develop understanding. Additionally, students will review concepts like average rate of change and using the Trapezoid Rule to find the definite integral when given only data.

F Distribution

Continuous Distributions ... In this activity, students study the characteristics of the F distribution and compare the distribution to others previously studied. Students then find probabilities and percentiles, verifying their values on a graph by using the Integral tool. They move on to find critical values and then compute a confidence interval.

Midsegments of Triangles

Using Symmetry to Find the Vertex of a Parabola

Roots of Radical Equations

Coin Toss

Average Roller Coaster

Testing For Truth

Linear Systems ... In this short activity, students will identify whether points lie within a shaded region that is bounded by linear inequalities. The focus is on testing the points for truth in the inequality. Students will use a graph to verify their answers.

Living On The Edge

Rational & Radical Functions ... Students build a solution to a rather complex problem: Finding the edge length of an octahedron given its volume by solving two simpler problems first. First, they find a formula for the edge length of a square given its area. Then students find, test, and apply a formula for the edge length of a cube given its volume.

Angles in Polygons

Quadrilaterals & General Polygons ... In this activity, students measure interior angles in convex polygons and find the sum of the angle measures. They make and test a conjecture about the sum of the angle measures in an n-sided polygon. Finally, they measure exterior angles in convex polygons, find their sum, and write a proof for the sum of the exterior angles.

Logging In

Integration ... In this short activity, students will use integration by parts to integrate the natural log of x. In the homework/extension problems, they will use a similar process to integrate tan–1x. Self-check questions engage students and help deepen understanding. Multiple-choice exam-like questions are also included to apply what was learned.

It�s A Radical, Rational Universe

Rational and Radical Functions ... In this activity, students will explore values and optimization of rational and radical functions in real contexts by graphing and using spreadsheets. Problem 1 involves a radical function relating to acceleration due to gravity. Problem 2 involves a rational function relating to the dilution of a more concentrated solution with a less concentrated solution.

t Distribution

Continuous Distributions ... In this activity, students first compare the shape of the t distribution to the standard normal distribution. Students then use the invt command to find critical values for a t distribution and compare to those used for a normal distribution. They use the critical values and margins of error to construct confidence intervals.

Testing For Truth

Living On The Edge

Angles in a Quadrilateral

Quadrilaterals & General Polygons ... This activity allows students to use an interactive, investigative approach to determining the sum of the interior angles of a quadrilateral. Students will use Cabri Jr. to draw, measure, and calculate as they explore the angles of quadrilaterals.

Logging In

It�s A Radical, Rational Universe

t Distribution

Tri This!

Linear Systems ... In this activity, students will investigate a set of linear equations and a set of linear inequalities that form a triangle. They will determine which points are solutions to the systems. At the end of the activity, students will compare the differences between the systems of equations and the system of inequalities.

Airport Impact Study

Rational & Radical Functions ... Students perform a simulation to measure the sound intensity at different distances from the source of the noise, and then use the data to develop an inverse variation model. After verifying the model, students use it to map safe and unsafe zones based on sound-intensity restrictions.

Running Circles Around Quads

Quadrilaterals & General Polygons ... In this activity, students will explore various properties of cyclic quadrilaterals.

How Cool It Is!

Exponential Functions ... In this activity, students will use a temperature probe to generate a cooling curve and develop an appropriate regression equation to model collected data.

FTC Changed History

Fundamental Theorem of Calculus ... In this activity, students will graphically investigate the Fundamental Theorem of Calculus and properties of definite integrals. Self-check questions engage students and deepen understanding of the topic. Multiple choice exam-like questions are also included.

Introduction to the Central Limit Theorem

Sampling ... In this activity, students discover the Central Limit Theorem by simulating rolls of two, four, and seven number cubes via the random number generator. They find sample means and standard deviations on spreadsheets and construct histograms of the sample distributions.

Tri This!

Airport Impact Study

Running Circles Around Quads

Quadrilaterals & General Polygons ... In this activity, students will explore various properties of cyclic quadrilaterals.

How Cool It Is!

Exponential Functions ... In this activity, students will use a temperature probe to generate a cooling curve and develop an appropriate regression equation to model collected data.

FTC Changed History

Introduction to the Central Limit Theorem

The Dirty Dawg Salon

Linear Systems ... In this activity, students will work through a scenario of a business venture involving washing dogs. They will translate fixed and variable costs to a cost function and make a decision about how much to charge to wash per dog. When the break-even point is found, students must interpret it to answer the question.

Count the Differences

Finite Differences ... In this activity, students are given data and asked to find the finite differences. They will use this to find a polynomial that models the data.

Rhombi, Kites, and Trapezoids

Quadrilaterals & General Polygons ... In this activity, students will discover properties of the diagonals of rhombi and kites and properties of angles in rhombi, kites, and trapezoids.

You Can�t Get There From Here

Asymptotes ... In this activity, students will explore rational functions graphically and algebraically to identify singularities and asymptotes, both vertical and horizontal.

Sum Rectangles

Riemann Sums ... In this activity, students will graphically and numerically explore Riemann sums and develop an understanding of summation notation for adding these rectangles.

Geometric Distributions

Random Distributions ... In this activity, students will simulate a geometric distribution of rolling a die unitl a 6 appears. They will determine experimental probabilities and draw conclusions about the number of rolls it takes for the first 6 to appear. Students will then calculate the theoretical probabilities and use a scatter plot to draw conclusions.

The Dirty Dawg Salon

Count the Differences

Finite Differences ... In this activity, students are given data and asked to find the finite differences. They will use this to find a polynomial that models the data.

Rhombi, Kites, and Trapezoids

Quadrilaterals & General Polygons ... In this activity, students will discover properties of the diagonals of rhombi and kites and properties of angles in rhombi, kites, and trapezoids.

You Can�t Get There From Here

Asymptotes ... In this activity, students will explore rational functions graphically and algebraically to identify singularities and asymptotes, both vertical and horizontal.

Sum Rectangles

Riemann Sums ... In this activity, students will graphically and numerically explore Riemann sums and develop an understanding of summation notation for adding these rectangles.

Geometric Distributions

All On The Line

Linear Systems ... In this activity, students will encounter the three different cases for linear systems: one point of intersection, no points of intersection, and infinitely many points of intersection. Then they will enter points into a spreadsheet and graph equation to help solve linear systems.

Transformers

Polynomials ... In this activity, students will explore the different transformations of polynomial functions. First they will use spreadsheet to investigate the changes of the y values as a value is added to or multiplied by the function. Then, students will confirm their conjectures using a minimized slider on a graph page.

Properties of Parallelograms

Quadrilaterals & General Polygons ... In this activity, students will explore the various properties of parallelograms. Students will also explore necessary and sufficient conditions that guarantee that a quadrilateral is a parallelogram.

Breaking Up Is Not Hard To Do

Rational Functions & Equations ... In this activity, students will split rational functions into sums of partial fractions. Graphing is utilized to verify accuracy of results and to support the understanding of functions being represented in multiple ways.

Exploring the Area Under a Curve

Fundamental Theorem of Calculus ... Students will explore Riemann sums to find the approximate area under the graph of a parabola on the interval [0, 1]. They will use the Rectangle tool to draw five left-endpoint, right-endpoint, and midpoint approximating rectangles. Additionally, students will learn to write formulas in expanded form and using summation notation.

Makin� It Through The Winter

Random Distributions ... In this teacher-led activity, students will simulate a binomial distribution. They will then calculate probabilities for a variety of situations involving binomial probability distributions.

All On The Line

Linear Systems ...

In this activity, students will encounter the three different cases for linear systems: one point of intersection, no points of intersection, and infinitely many points of intersection. Then they will enter points into a spreadsheet and graph equation to help solve linear systems.

Transformers

Properties of Parallelograms

Breaking Up Is Not Hard To Do

Exploring the Area Under a Curve

Makin� It Through The Winter

Shark Attack

Linear Functions & Equations ... In this activity, students will use sliders to separate what effect each change in the Point-Slope equation has on the graph. Then they will calculate the slope and write their own Point-Slope form of an equation using two data points and use the Graph Trace to make predictions.

One of the Many Ways

Polynomials ... In this activity, students will graph polynomials to determine the value and number of zeros for a given polynomial. Students will also use the rational root theorem to determine the value of zeros for a polynomial and connect the number of zeros to the degree of the polynomial.

Sine. It�s the Law.

Right Triangles & Trig Ratios ... In this activity, students will explore the Law of Sines. Students will derive the formula through exploration and solve some application problems. As an extension, students will prove the Law of Sines through guided questions.

Ride the Rollercoaster

Polynomial Functions ... In this activity, students will use polynomial regression to develop and assess the fit of equations modeling data. The equation models are then evaluated for reasonableness in their use for extrapolating beyond the given data sets.

Infestation to Extermination

Exponential Growth & Decay ... In this activity, students will investigate exponential growth and decay through the situation of infestation and extermination. Students review foundational understanding and learn the process of solving separable differential equations. Application questions are solved numerically and graphically.

It�s To Be Expected

Expected Value ... In this activity, students will use a tree diagram to find theoretical probabilities and use this information in a spreadsheet to find the expected value.

Shark Attack

One of the Many Ways

Sine. It�s the Law.

Ride the Rollercoaster

Infestation to Extermination

It�s To Be Expected

Expected Value ... In this activity, students will use a tree diagram to find theoretical probabilities and use this information in a spreadsheet to find the expected value.

Math Man On The Slopes

Linear Functions & Equations ... In this activity, students will practice identifying slopes with informal pictures, and can self-check their understanding with one of the measurement tools. The students will also identify the slope and intercept of a given graph and will choose the correct equation in a multiple choice format.

Area of the Missing Square

Quadratic Equations and Functions ... In this activity, students will be introduced to an area model for representing a quadratic equation. Students will explore the relationship between the value of b and c, in y = x2 + bx + c, form of the quadratic equation. The relationship will be examined with integer and non-integer values in order to help students recognize a pattern.

Triangle Inequalities

Right Triangles & Trig Ratios ... In this activity, students will discover the Triangle Inequality Theorem and explore the possible lengths of the third side of a triangle given the other two side lengths. Students will also classify the type of triangle as acute, obtuse, or right using the Pythagorean inequalities.

Going Back To Your Roots

Polynomial Functions ... In this activity, students apply the Fundamental Theorem of Algebra in determining the complex roots of polynomial functions. The theorem is applied both algebraically and graphically, utilizing features of TI-Nspire CAS technology to enhance student understanding.

Helicopter Bungee Jump

Derivatives ... In this activity, students will observe a simulation of a record breaking bungee jump, consider a mathematical model of the height as a function of time, and take the derivative to determine points of interest like the minimum height, maximum velocity, acceleration, and maximum jerk. Students will investigate higher order derivatives.

Too Many Choices!

Probability and Simulation ... In this activity, students will investigate the fundamental counting principle, permutations, and combinations. They will find the pattern in each situation and apply it to make

Math Man On The Slopes

Area of the Missing Square

Triangle Inequalities

Going Back To Your Roots

Helicopter Bungee Jump

Too Many Choices!

Dog Days or Dog Years?

Linear Functions & Equations ... In this activity, students will use order pairs, table of values, and a scatter plot to determine a function that represents real world data. Students will respond to questions about dog ages in human years, domain, range, and how the slope appears to be changing in the data/graph.

Around the Vertex in 80 Days

Quadratics ... In this activity, students will move a quadratic function in the coordinate plane to specific points to observe how the vertex form of the equation changes.

Gettin� the Swing

Derivatives ... In this activity, students will investigate sinusoidal functions, collect data from a swinging pendulum, model the data with a cosine function, and take the derivative to find the velocity and acceleration. Self-check multiple-choice questions help students review and build the foundation for their data collection and mathematical model activity.

That Area Is So Regular

General Polygons ... In this activity, students will investigate the formula for the area of regular polygons given the length of one side. Students will be asked inquiry questions to assist them in deriving the formula for a regular polygon with n = 3, 4, and 5 sides. They will then use the patterns they discovered to find the formula for the area of a regular polygon of n sides.

It�s a Rat Race for the Zero

Polynomial Functions ... In this introductory activity, students will use a program and graphing to help them explore the Rational Root Theorem. They will compare sets of functions that have at least one real zero or have no real roots and then determine how the factors of the first coefficient and the constant can produce a zero.

Independence Is The Word

Probability and Simulation ... In this activity, students will use a simulation to find the experimental probability of independent events. They will find the sample space and then compare the experimental and theoretical probabilities. Then students are introduced to dependent events and the formula for conditional probability.

Dog Days or Dog Years?

Around the Vertex in 80 Days

Quadratics ... In this activity, students will move a quadratic function in the coordinate plane to specific points to observe how the vertex form of the equation changes.

Gettin� the Swing

Derivatives ...

In this activity, students will investigate sinusoidal functions, collect data from a swinging pendulum, model the data with a cosine function, and take the derivative to find the velocity and acceleration. Self-check multiple-choice questions help students review and build the foundation for their data collection and mathematical model activity.

That Area Is So Regular

It�s a Rat Race for the Zero

Independence Is The Word

Order Pears

Functions and Relations ... In this activity, students will interactively investigate ordered pairs. They will graphically explore the coordinates of a point on a Cartesian plane, identifying characteristics of a point corresponding to the coordinate. Students will plot ordered pairs of a function, list these in a table of values, and graph them in a scatter plot.

Stretching the Quads

Quadratics ... In this activity, students will stretch and translate the parabola given by y = x2 and determine the effects on the equation. Students will also explore finding the vertex and zeros of a parabola and relate them to the equation.

From the Center of the Polygon

Quadrilaterals & General Polygons ... In this activity, students will explore the area of a regular polygon in terms of the apothem and the perimeter. Students will derive the formula for a regular pentagon and regular hexagon. Then, students will see how the formula relates to the formula for the area of triangles. Students will then be asked to apply what they have learned about the area of a regular polygon.

Relating Rates

Derivatives ... In this activity, students are introduced to the topic or related rates. The process is explained and dynamic visuals are provided. Self-check multiple choice questions help students build understanding and put what they learned into practice with homework or extension questions.

It�s a Parallelogram, You Say?

Complex Numbers ... In this interactive activity, students represent complex numbers in the complex plane as points or vectors and display the sum and difference of two complex numbers as diagonals of the parallelograms they define.

In It to Win It!

Probability and Simulations ... In this activity, students will calculate the experimental probability of winning a basketball game by shooting two free-throws using a random integer simulation. They will also calculate experimental probabilities for two people having a shared birthday and a batter in a baseball getting walked to first base.

Order Pears

Stretching the Quads

From the Center of the Polygon

Relating Rates

It�s a Parallelogram, You Say?

In It to Win It!

Cell Phone Range

Functions and Relations ... In this activity, students will learn to identify the domain and range of various real-world step functions. They will graphically explore numerical data points and observe step functions. Open and closed points on a graph are investigated and discussed. Students use self-check questions to check their understandings with immediate feedback.

Border Patrol

Linear Systems ... In this activity, students will graph one linear inequality and then graph a system of linear inequalities as they apply to an area of land. Students will practice graphing systems of inequalities and determining if a points lies in the solution. In the extension, students are challenged to write a system of inequalities that describe the area of Mississippi.

Pythagorean Proofs

Right Triangles & Trig Ratios ... In this activity, students will explore proofs of the Pythagorean Theorem. Students will explore the proof of the Pythagorean Theorem using area of squares, area of triangles and trapezoids, and by dissection. Students will then be asked to apply what they have learned about the Pythagorean Theorem.

Poly Want Some Division?

Polynomial Functions ... In this activity, students will use polynomial calculations to determine quotients and remainders when performing polynomial division using CAS commands. The Remainder Theorem is introduced and applied to identify roots or zeros and to determine function values. Graphs are incorporated to visually illustrate outcomes of polynomial division.

Exponentially Fast Derivative

Derivatives ... In this activity, students will investigate the derivative of exponential functions. For e^x, students will explore the slope of the tangent graphically and use CAS functionality to discover the chain rule for exponential functions. Similarly, a^x is explored graphically and CAS functionality is used to discover the rule.

To Toss or To Simulate?

Simulations ... In this introductory activity, students will use the RandInt() command to simulate the tossing of a coin and the rolling of a die. They will collect data for several trials and use the information to investigate the Law of Large Numbers.

Poly Want Some Division?

Cell Phone Range

Border Patrol

Pythagorean Proofs

Poly Want Some Division?

Exponentially Fast Derivative

To Toss or To Simulate?

Poly Want Some Division?

Back In Time?

Functions and Relations ... In this activity, students will explore the definition of a function through use of a graph, a set of ordered pairs, and an input-output diagram. This function machine dynamically allows students to discover the function by experimenting with input values that produce the desired output. Function notation is also reinforced.

Radical Transformations

Radical Functions ... In this activity, students will use sliders to examine how the square root function is transformed on the coordinate plane. As an extension, students will examine similar transformations on a cube root function.

Ratios of Right Triangles

Right Triangles & Trig Ratios ... In this activity, students will explore the ratios of right triangles. Students will discover that they can find the measure of the angles of a right triangle given the length of any two sides.

Extreme Punkin� Chunkin�

Polynomial Functions ... In this activity, students will explore extrema, zeros, and other key values of quadratic functions in real-world contexts.

What�s the Differential, Dr. Implicit?

Derivatives ... In this activity, students will be introduced to the concept of implicit differentiation. They will begin by solving a relation for y and use methods with which they are already familiar to find the derivative of the relation. Next, they will use the impDif command to find an alternate form of the derivative.

It�s A Two-Way Street

Categorical Data ... In this activity, students will be introduced to two-way tables. They will calculate marginal and conditional distributions using formulas in a spreadsheet. This activity is intended to be followed up with teacher discussion and student interpretation of the calculations. An additional data set is provided for students to use for homework.

Back In Time?

Radical Transformations

Ratios of Right Triangles

Extreme Punkin� Chunkin�

Polynomial Functions ... In this activity, students will explore extrema, zeros, and other key values of quadratic functions in real-world contexts.

What�s the Differential, Dr. Implicit?

It�s A Two-Way Street

Chirp, Jump, Scatter

Function and Relation ... In this activity, students will find a best fit line for data graphed as scatter plots. Applications of linear relationships provide motivation for students and improve their skills and understanding of finding the equation of a line from two known points. Movable lines make this activity approachable for Algebra 1 students. Students can put into practice what they have learned with extension/homework questions.

Discriminating Against the Zero

Polynomial Functions ... In this introductory activity, students explore when a graph has two zeros, one zero, and no zeros. They will also determine when a graph has real, rational, irrational, or imaginary roots. The teacher should then follow up with a formal discussion on the discriminant.

Intersecting the Solution

Linear Systems ... In this teacher-led activity, students will learn to solve systems of equations graphically. They will learn the relationship between the algebraic and graphical solutions and create equations that draw upon this connection.

The Euler Line and Its Ratios

Triangles & Their Centers ... In this activity, students will explore the Euler Line of a triangle. Students will discover that the centroid, circumcenter, and orthocenter are collinear. Students will also discover that if the triangle is isosceles, then the centroid, circumcenter, incenter, and orthocenter are all collinear. Students will also look at ratios involved in the Euler line.

Transforming Relationships

Two-Variable Statistics ... In this activity, students will assess the strength of a linear relationship using a residual plot. They will also calculate the correlation coefficient and coefficient of determination to assess the data set. Students will then learn to transform one or two variables in the relationship to create a linear relationship.

Somewhere in the Middle

Mean Value Theorem ... In this activity, students will explore the Mean Value Theorem. Students will find out when the slope of a tangent line is parallel to the secant line passing through the endpoints of an interval to help them find the values of c guaranteed to exist by the MVT. Students will also test functions where the hypotheses of the MVT are not met.

Chirp, Jump, Scatter

Discriminating Against the Zero

Intersecting the Solution

The Euler Line and Its Ratios

Transforming Relationships

Somewhere in the Middle

Can I Graph You, Too?

Absolute Value Inequalities ... In this activity, students will explore absolute value inequalities graphically, numerically, and algebraically. They will rewrite absolute value inequalities as compound inequalities without absolute value, then solve them.

Dilations with Matrices

Dilations ... In this activity, students will use matrices to perform dilations centered at the origin of triangles. Students will explore the effect of the scale factor on the size relationship between the preimage and image of a polygon.

Hey, Ortho! What�s Your Altitude?

Triangles & Their Centers ... In this activity, students will explore the altitudes of a triangle. Students will discover that the altitude can be inside, outside, or a side of the triangle. Students will discover that the altitudes are concurrent. The point of concurrency is the orthocenter. Students should discover the relationship between the type of triangle and the location of the point of concurrency. Students will discover properties of the orthocenter in equilateral triangles.

X-treme Calculus: Part 2

Derivative Applied to Motion ... In this activity, students will explore distance-time and velocity-time graphs to deepen their understanding of the application of the derivative. Students will investigate kinematic relationships—graphically, numerically, and algebraically—using animations, and with self-check multiple choice questions. A calculus lab using a CBR2 motion detector is also included to dynamically demonstrate the relationship between displacement, velocity, and acceleration.

Just Move It

Functions & Their Representations ... In this activity, students will explore translations, compressions, and stretches of the parent function graph f(x) = x2 and f(x) = x3.

One- and Two-Variable Statistics - Review

Review ... In this activity, students will review the concepts that they have learned up to this point in statistics. The first part of the activity includes one-variable topics such as graphing quantitative variables, calculating measures of central tendency and spread, and making comparisons. The second part includes two-variable topics, including linear regression, correlation, and interpolation. The coefficient of determination will be introduced.