Let’s Play Math!

Math games open an arena for strategic planning and reasoning, one of the NCTM Process Standards. Many games also provide practice in basic operations or problem solving, and all motivate the active participation we hope for in the classroom.

The Maths File Game Show
A collection of 12 interactive games that deal with basic concepts of mathematics: data handling, numbers, algebra, and measurement. Students can use order of operations to ensure that letters reach the right mailbox, compete in a test of fractions and percentages, and even guide a spaceship across Cartesian coordinates.

Towers of Hanoi: Algebra (Grades 6-8)
An online version of the ancient Towers of Hanoi puzzle, featuring three spindles and a graduated stack of two to eight discs, as decided by the player, with the largest disc on the bottom. The challenge is to move all discs from the original spindle to a new spindle in the smallest number of moves possible while never placing a larger disc on a smaller disc. By observing the pattern of number of discs to number of moves, students can generalize the relation and answer the question “What if you had 100 discs?”

Traffic Jam Activity
Why the jam? There are seven stepping stones and six people. Three stand on the left-hand stones and three on the right-hand; all face center. Everyone must move so that the people on the right and the people on the left pass each other, eventually standing on the side opposite from where they started. But no two people may stand on the same stone at the same time! This problem requires reasoning, but its solution also reveals a pattern that leads to an algebraic expression. A lesson plan is provided.

Clever Games for Clever People
Here are 16 strategy games from the book On Numbers and Games by mathematician John Conway. Each develops those critical thinking skills so valued in math. As for materials, only paper and pencil or, occasionally, crayons or a checkerboard, are needed. Game rules and setup are clearly described and illustrated for each game.


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 11/18/2011.

Venn Diagrams

Venn diagrams are one of many tools used in logic and reasoning. Their use is especially helpful in learning foundational notions of definition and set theory. One of the five Process Standards promoted by NCTM, Reasoning and Proof requires middle school students to sharpen such skills as they learn to develop mathematical argument.

Venn Diagram Shape Sorter
A good activity for introducing the concepts of definition and set! Students move various shapes, available in two sizes and three colors, into a circle. By seeing which figures are accepted into the circle, they determine the rule guiding the circle’s selection. In a more complicated example, a Venn diagram of two intersecting circles is used, requiring that two rules be stated.

Factor Tree (Grades 6-8)
Students first find the prime factors for two numbers. These are displayed in tree diagrams from which the student drags the factors to the appropriate areas of a Venn diagram. The Venn diagram offers a useful visual display showing unique factors and common factors for the original pair of numbers. Using the display, the learner must find the pair’s least common multiple (LCM) and greatest common factor (GCF).

Venn Diagrams
This virtual manipulative with an interactive three-circle Venn diagram can be used to model set operations for union, intersection, and subset. For each statement, the student highlights the region that is the solution, then clicks a button to find out if the solution is correct.

Who Played the Raptors?
In this online activity, students analyze predictions made by sportswriters about which basketball teams will win to determine which teams are playing each other. The solution illustrates and explains three different ways to successfully organize information, including using a Venn diagram.


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 10/18/2011.