History to Enrich Mathematics Learning!

Although the NCTM Standards do not have student expectations for learning mathematics history, exposure to this history can help students see real-world connections in mathematics.

Approximating Pi
Mathematics and science owe a great deal to Archimedes, including a way to approximate pi. Here is historical information along with an applet to approximate pi using the perimeter lengths of polygons inscribed within and circumscribed around a circle.

The Beginnings of Probability
Teachers can share some of this mathematics history as they work with students to compute probabilities for simple compound events, an NCTM expectation for students in grades 6-8.

The Golden Ratio
This rich site connects linear measurement, ratio and proportion, art, and mathematics history.

Measuring the Circumference of the Earth
This Internet project is hands-on, real-world, and historical. Students join with classes around the world to repeat the experiment of Eratosthenes — measuring the shadow of a meter stick and making calculations to approximate the circumference of Earth.

Pythagorean Puzzle
The Pythagorean theorem is at the intersection of algebra and geometry. At this site, learn about the life of Pythagoras and the development of the Pythagorean theorem. And use an applet to explore the meaning of the most famous equation in algebra.

Manipula Math with Java: Pythagorean Theorem
Here is another applet offering a more sophisticated approach to affirm in a visual way the validity of the Pythagorean theorem.

Tortoise and Hare Race
Uing an applet, students can vary parameters for the race. There is information about Zeno’s paradox along with exploration questions for students that can lead to a discussion about infinity.


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We want and need your ideas, suggestions, and observations. What would you like to know more about? What questions have your students asked? We invite you to share with us and other readers by posting your comments. Please check back often for our newest posts or download the RSS feed for this blog. Let us know what you think and tell us how we can serve you better. We appreciate your feedback on all of our Middle School Portal 2 publications. You can also email us at msp@msteacher.org. Post updated 11/21/2011.

Making a Prediction

Middle school students need opportunities to examine how probability can be used to make predictions and sound decisions. These resources will engage students in real-world applications of probabilistic thinking.

Game of SKUNK
With this lesson, students examine choice versus chance and practice decision-making skills using the outcome probabilities when playing the game of SKUNK.

She Always Wins, It’s Not Fair!
This is the perfect activity to use when introducing the concept of fair and unfair games.

Lotto or Life: What Are the Chances?
Teachers interested in astronomy or in working with a science class will find this lesson offers an out-of-the-ordinary way to investigate outcomes based on probability.

A Statistical Study on the Letters of the Alphabet (CEC)
Students examine letter usage and make decisions based on data. This lesson can be developed as an interesting language arts connection.

Sticks and Stones
Students gather data when playing Sticks and Stones, an Apache game, to determine the average number of moves necessary to win the game.

Tree Diagrams and Probability
A tree diagram is a perfect way to make probability visual. In this lesson, students use tree diagrams and explore fair and unfair games based on the outcomes of car race trials.

What Are the Odds?
Use the navigation column to find background information, lesson plans, and student activities focused on the use of probability.


We Want Your Feedback
We want and need your ideas, suggestions, and observations. What
would you like to know more about? What questions have your
students asked? We invite you to share with us and other readers
by posting your comments. Please check back often for our newest
posts or download the RSS feed for this blog. Let us know what
you think and tell us how we can serve you better. We appreciate
your feedback on all of our Middle School Portal 2
publications. You can also email us at msp@msteacher.org. Post
updated 11/29/2011.

Theoretical and Experimental Probability

Middle school students need opportunities to think about probability to understand the meaning of taking a chance. These resources support the active development of the concept of probability and the appropriate use of related mathematics terminology.

Adjustable Spinner
This simulation demonstrates the difference between experimental and theoretical probabilities. It is easy to run a number of experiments.

Data Management: A Look at Leisure Activities
Use the navigation on this site to select appropriate class activities. Students collect and analyze data and can look at differences between experimental and theoretical data when rolling a die.

Introduction to the Concept of Probability
This lesson is a good way to build on students’ innate understanding of probability. It includes teacher information, student activities, and definitions of key terms.

Random Drawing Tool – Independent Trials
This applet enables students to run experiments to examine and better understand theoretical and experimental probabilities. See the related lesson Boxing Up at http://illuminations.nctm.org/LessonDetail.aspx?ID=L448.

The Smithville Families
This printable lesson uses Pascal’s triangle to build student understanding of theoretical probability. The lesson explores the probabilities for the births of boys and girls in a large family. The outcome of a coin toss is used to indicate the birth of a boy or a girl.


We Want Your Feedback
We want and need your ideas, suggestions, and observations. What would you like to know more about? What questions have your students asked? We invite you to share with us and other readers by posting your comments. Please check back often for our newest posts or download the RSS feed for this blog. Let us know what you think and tell us how we can serve you better. We appreciate your feedback on all of our Middle School Portal 2 publications. You can also email us at msp@msteacher.org. Post updated 11/07/2011.