MHEC Course Links

Regular font: multi-day activities
Italics: single-day activities

• Algebra/Geometry Connections

  • Understanding Ratios of Areas of Inscribed Figures Using Interactive Diagrams ¹
    (Illustrates connections between algebra and geometry)

  • Learning about Rate of Change in Linear Functions Using Interactive Graphs ¹

  • Exploring Linear Functions: Representational Relationships ¹
    (Investigates the effect of changing m and b on the graph of y=mx+b)

   

• Algebra

  • Using Graphs, Equations, and Tables to Investigate the Elimination of Medicine from the Body ¹
    (A three-part example that illustrates the use of iteration, recursion, and algebra)

  • Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond ^{1 a}

  • Whelk-Come to Mathematics: Using Rational Functions to Investigate the Behavior of Northwestern Crows
    (Includes a movie clip and an optional class experiment: a simulation of crows dropping whelks - requiring a meterstick and a cup of whole, blanched peanuts that have been removed from their shells)

  • Shedding Light on the Subject: Function Models of Light Decay
     

• Geometry

  • Symmetries and Their Properties ^{1 a}
    A series of four activities: 
    Rotational Symmetry; Reflections; Translations; Guide Reflections

  • Analyzing Numeric and Geometric Patterns of Paper Pool ¹

  • Spatial Reasoning using Cubes and Isometric Drawings ¹

  • Learning about Length, Perimeter, Area, and Volume of Similar Objects Using Interactive Figures ¹

  • Understanding Congruence, Similarity, and Symmetry Using Transformations and Interactive Figures ¹

  • Understanding the Pythagorean Relationship Using Interactive Figures ¹
     

• Data Analysis/Probability

  • Understanding the Least-Squares Regression Line with a Visual Model: Measuring Error in a Linear Model ¹
    (Explores three methods for measuring how well a linear model fits a set of data points.)

  • Investigating Linear Relationships: The Regression Line and Correlation ^{1 a}

  • Simulating Probability Situations Using Box Models ¹

  • Estimation Activities:
    Estimator ², Comparison Estimator ², More or Less Estimator ²
    Three activities which allow the student to explore the concept of estimation. The first activity asks students to estimate lengths, areas and numbers of objects. The other activities deal with similar types of estimates, but with a greater focus on comparison. 

  • Exploring Histograms ¹

  • Comparing Properties of the Mean and the Median through the use of Technology ¹
     

• Mathematical Modeling / Discrete Mathematics

  • Sound Wave - How do Computers Represent Sound? ^{1 a}

  • Using Algebra and Discrete Mathematics to Investigate Population Changes in a Trout Pond ^{1 a}

  • Put the Heart into Mathematics: Cardiac Output, Rates of Change and Accumulation ^{1 a}
    (Note: This activity includes an in-class experiment requiring: an aquarium pump, a temperature probe, a bucket tube with a port for injecting ice water, syringe and valve, and a data collection device such as a CBL. Movie clips available, demonstrating the activity in action in the classroom)

  • Shedding Light on the Subject: Function Models of Light Decay ^{1 a}
    (Movie clips available, demonstrating the activity in action in the classroom)

   

• Elementary Number Theory

  • Coloring Pascal's Triangle (compare to PascGalois!)
    Coloring Multiples ² , Coloring Remainders ²
    Note: These two activities - especially the second one - are sort of a "do-it-yourself" version of PascGalois. It appears that these activities might constitute a nice introduction to the notion of coloring in Pascal's Triangle before introducing the PascGalois package to a class.

  • The Factor Game ¹

  • The Product Game ¹

  • Fraction Pointer ² , Fraction Finder ²
    Fraction Pointer: Has user create graphical representations of two given fractions, then find a third fraction (first graphically, then numerically) between the two given fractions. Good activity for developing the concept of a fraction and for comparison of fractions.
    Fraction Finder: More challenging "sequel" to Fraction Pointer. In the first activity, the student has visual assistance in finding the fraction between the two given fractions; this assistance is taken away in the Fraction Finder activity.

  • Factorize ², Factorize2 ²
    Similar activities for practice with factorization, both numerically and graphically (with rectangular arrays). Main differences: "Factorize" is better for practicing numerical factoring; "Factorize2" is stronger for graphical representation of factoring. Note: "Factorize" (but not "Factorize2," as of 4/28/03) includes commentary on effective usage of the activity and NCTM Standards addressed.

  • Fraction Four ², Arithmetic Four ²
    Three games based on "Connect Four;" may want to show or explain this game to students who don't know it before using any of these activities. For each game, a student only gets to place a dot on the board (analogous to a playing piece in Connect Four) if s/he answers a question correctly. Types of questions in each game:

    • Fraction Four: Conversions among fractions, decimals and percents
    • Arithmetic Four: Arithmetic operations on the whole numbers and/or integers

    (Note: There is a third game, "Estimator Four," which I do not recommend, since what constitutes a "correct" answer in this game seems highly subjective at best...)

• Miscellaneous

  • Exploring Connections Between Mathematics and Art (Under Construction) ¹

  • Equivalence ^{1 a}
    Four-part activity illustrating how the concept of equivalence may be developed at all levels using technology

  • Learning about Properties of Vectors and Vector Sums Using Dynamic Software ¹
    Students learn about vectors and their properties in a game-like setting (as described in the Number and Operations standard) by controlling the velocity and direction vectors of a car or a plane. Fun activity for students!

  • Learning about Multiplication Using Dynamic Sketches of an Area Model ¹
    (Demonstrates effects of multiplying by numbers >1 and by numbers <1)

Last modified 4/28/03 --KEL

1 NCTM Illuminations i-Math Investigations (illuminations.nctm.org/imath)
a Student version available for download

2 Shodor Education Foundation, Inc.