Introduction: Rational War is a game used to help students determine how to compare two rational numbers. The rational numbers will include: fractions, mixed fractions, improper fractions and decimals.

Timing: This game should take about 60 minutes to complete.

Group Size: Small groups

Learning Objectives: The objective of this game is to use the techniques developed in class to convert all rational numbers to decimal form and compare them.

Guiding Question: What are the different forms of rational numbers and how can they be compared?

Materials: Students will need pens and scrap paper. In my case I have mini-white boards for each student. Photocopy enough games sheets for students to work in pairs (or groups of three if there are an odd number of students).

There are four different decks of cards. Photocopy the playing cards onto colored card stock. Use one color for each different deck. There will be groups that have the same deck, but if they shuffle, I should not be a problem.


This game is similar to the classic playing card game, War. Each team lays down a single card and the highest card wins. The purpose of the game is to compare two rational numbers (fractions, mixed fractions, improper fractions and decimals) to determine which has the greater value. Students will be playing in teams of two. There may need to be groups of three if there are an odd number of students in the class.

Here are the rules of the game:

Students should shuffle the cards. Deal all of the cards, one at a time, into two stacks. Leaving the cards face down, each team plays from their own stack.

Play begins with both teams turning their top cards face up.

The team with the larger rational number value takes both cards.

Won cards are added to the bottom of the team’s stack.

In case of a “tie,” players continue turning up cards until the tie is broken. The winner of the tie takes all of the cards turned up since the beginning of the tie.

Play continues until a winner is declared. The winner is the player ending up with all of the cards or the player with the most cards at the end of a set period of time.

To prove the win, students must fill out the card play chart. Any illegal card captures will result in cancellation of the overall win.

Your team will alternate responsibilities from game to game. These responsibilities include:

Team Card Calculator – This person will convert the rational number on their team’s card into decimal form. This will be compared with the decimal value of other team’s card.

Opposition Card Checker– This person will convert the rational number on the other team’s card into decimal form. This will serve as check of the other team’s calculation and will help reduce error.

Double-checker (3 person team only) – This person will double-check their team member’s work separately.

This game is relatively easy to run. The only difficult part, is making sure one student is not doing all of the work. To succeed, students will need to work together and double check each others calculations. The instructor should wander and check for illegal card captures. I typically give points for the top five placing teams and points for the team that works best together.

Assessment: Students will complete questions throughout the game and receive immediate feedback on correctness and an overall grade after the entire assignment is complete.

Answer Key: The answer key is included.

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