# Action with Fractions!

Really understanding what fractions are, how they fit on the number line, and how to operate with them – add, subtract, multiply, divide – is central to learning decimals and percentages. According to the NCTM Principles and Standards, students in the middle grades should be expected to acquire a deeper understanding of fractions, decimals, and percents and an increased flexibility in using them to solve problems. Yet students may reach even the higher grades of middle school without a firm grasp of fractions. Perhaps a change in strategy could help? Let’s offer compelling visuals and hands-on manipulation of those fractured numbers!

COUNTDOWN: Number and Operations – Fractions
COUNTDOWN is an interactive television math program broadcast on cable television in Chicago. This web site contains the archives of those broadcasts. The 4-7 minute math movies consist of direct instruction and are reinforced with literature, manipulatives, activities and related computer instruction. Topics include logic, perimeter, area, probability, graphing, congruence, integers and much more. Movies are organized according to content standards established by the National Council of Teachers of Mathematics. Many of the movies have associated worksheets that can be printed.

Visual Fractions
A thorough tutorial on the topic—from identifying and comparing fractions to operations with them! Students work through interactive exercises and games. A complete step-by-step, illustrated explanation of each subtopic is included. Don’t miss the game of Finding Grampy, where students practice finding a mixed number in lowest terms as they look for Grampy on the number line.

Fraction Sorter
Using this online manipulative, students represent two to four fractions—such as 7/13, 2/7, 8/9, and 2/3—by dividing and shading areas of squares or circles. They then order the fractions from smallest to largest on a number line. The visual representation here is powerful.

National Library of Virtual Manipulatives
Under the middle school offerings, you will find the activity Adding Fractions. Students must do the usual exercise of finding equivalent fractions with common denominators, but here the fractions are represented visually as portions of a square. Once the computer checks that the fractions are correct, the students can drag the representations into a third box and enter the sum of the fractions. This is a learning experience! There are other activities on fractions as well, all worth checking out.

The Maths File Game Show
This BBC site offers a game that requires players to match fractions with equivalent decimals or percentages, Go to Saloon Snap. When a question is answered correctly, the player can move his or her piece across the board. The goal is to be the first to create a path across a 10-by-10 grid. It’s a real math exercise and it’s motivating!

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
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.

# 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.

# 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.