
Analyzing Numeric and Geometric Patterns of Paper
Pool
The interactive paper pool game in this iMath investigation
provides an opportunity for students to further develop their
understanding of ratio, proportion and least common multiple.
Students develop rules for predicting the corner (pocket), number of
bounces and the length of the path for a cue ball on rectangular
pool tables of different sizes. 

Simulating Probability Situations Using Box Models
Investigations that allow students to explore the relationship
between theoretical and experimental probabilities are important in
the study of probability and statistics. A "box model" can help
students in such investigations. This iMath investigation contains
an interactive tool that simulates a statistical "box model" as well
as ideas for activities. 

Exploring Histograms
A histogram is a standard way of representing a
collection of data. The interactive tool contained in this iMath
investigation allows students to create their own sets of data and
examine how various statistical functions such as mean, median, and
standard deviation depend on the choice of data. 

Gathering Evidence About Students' Understanding of Volume
This iMath Investigation is coming soon. You can see the related
Reflection
on Teaching activity now. 

Learning about Multiplication Using
Dynamic Sketches of an Area Model
Students can learn to visualize the effects of multiplying a
fixed positive number by positive numbers greater than 1 and less
than 1 with this tool. Using interactive figures within this eexample,
students can investigate how changing the height of a rectangle with
a fixed width changes its area.


Learning about Rate of Change in
Linear Functions Using Interactive Graphs
In this twopart eexample,
users can drag a slider on an interactive graph to modify a rate of
change (cost per minute for phone use) and learn how modifications
in that rate affect the linear graph displaying accumulation (the
total cost of calls). The investigation explores the case when the
cost per minute for phone use remains constant over time and the
case when the cost per minute for phone use changes after the first
sixty minutes of calls. 

Learning about Length, Perimeter,
Area, and Volume of Similar Objects Using Interactive Figures
This twopart eexample
illustrates how students can learn about the length, perimeter,
area, and volume of similar objects using dynamic figures.


Understanding Congruence,
Similarity, and Symmetry Using Transformations and Interactive
Figures
The interactive figures in this fourpart eexample
allow a user to manipulate a shape and observe its behavior under a
particular transformation or composition of transformations.


Understanding the Pythagorean
Relationship Using Interactive Figures
The Pythagorean relationship, a^{2} +
b^{2} = c^{2} (where a and
b are the lengths of the legs of a right triangle and
c is the hypotenuse), can be demonstrated in many ways,
including with visual "proofs" that require little or no symbolism
or explanation. The activity in this eexample
presents one dynamic version of a demonstration of this
relationship. 

Comparing Properties of the Mean and
the Median through the use of Technology
Using interactive software in this eexample,
students can compare and contrast properties of measures of center,
specifically these tasks illustrate how changes in data values
influence the mean and median. When students change the data values,
the interactive figure immediately displays the mean and median of
the new data set. Experimenting with this software helps students
compare the utility of the mean and the median as measures of center
for different data sets. 