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Ratio is a mathematical concept dealing with a measurable relationship between variables of the same kind. These variables can be objects, people, places, things and concepts and are termed a/b, a to b, or a:b.
A ratio math problem example involving sports is when you are given odds of winning. For example, in a game of baseball with the Red Sox against the Braves there is an 8/4 odds against, meaning that if the Red Sox played the Braves 12 times, they would likely lose eight and win four. This can be reduced to 2 to 1. Another ratio math problem example would be to determine the ratio of people to animals in your home. In my home the ratio is 4:5. There are four people to five animals.
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Hands on Learning
Try some of these games to practice at home. For example, make a "football" out of paper which is usually shaped like a triangle and practice flipping it with your finger between the fingers of someone else. His or her fingers represent the goal. The person making the goal would hold his or her hands up palm facing your fingers folded down except for his or her index finger which points up or vertical and his or her thumbs touching horizontally. Record how many times you make the goal versus how many times you don't after trying 20 times and you have a ratio of hits to misses. Let the other person do the same. Determine who had the best ratio of hits to misses. Remember to reduce your numbers. You can make all types of variations to this game including making "baskets" into any object that would represent a basket and some kind of ball or using a real basketball and basketball net.
You may also create a matching game. Have someone write out equivalent ratios on index cards in fraction form then you would have to match each equivalent ratio. For example, 2/3 is equivalent to 6/9 because 6/9 is reduced to 2/3 by dividing 3 into 6 and then 3 into 9.
You can also practice ratios by working with recipes. Pick a recipe for your favorite food and practice changing the amount of each ingredient based on the number of people you plan to feed. For example, if a recipe requires 2 cups of sugar and prepares enough for 4 people the ratio is 2 to 4. If you want to make enough for 8 people, then double the sugar to 4 cups. Your 2/4 ratio is now a 4/8 ratio.
Use money to create ratios. For example, determine the ratio of pennies to a dime or nickels to a quarter or dimes to dollar. Then reduce all the ratios you come up with and determine if any are equivalent.
Finally, create a dice game which you can play by yourself or with others. Write down the following ratios on a sheet of paper for each player: 1/1, 1/2, 1/3, 1/4, 1/5, 1/6, 2/1, 2/3, 2/5, 3/1, 3/2, 3/4, 3/5, 4/1, 4/3, 4/5, 5/1, 5/2, 5/3, 5/4, 5/6, 6/1 and 6/5. Then each player rolls the dice twice and marks off each ratio as they are rolled. However, there are other combinations than the ones listed but they are reducible to the ones listed. Therefore, if you role 4/6, that reduces to 2/3 which means you can mark off 2/3. Whoever marks off all the ratios first is the winner. Don't tell your opponents if they missed a reducible number!
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There are various educational websites which have math ratio games that you can play for free in order to hone your skills and have fun! For example, 4Kids.org has many different games and activities. Ratio Blaster and Ratio Martian are two of the ratio games. Ratio Blaster involves shooting spaceships that have the corresponding equivalent ratio to the one listed. It goes pretty fast, so be ready! Ratio Martian involves a Martian that eats ratios that are notated properly. This is a simple game if you are just learning how to notate ratios.
Another website with math ratio games and instruction is Math.com. The work out section for each topic you learn about is the practice or hands-on learning section, but it is more like a practice test. However, they have other games that teach many math skills simultaneously, not just ratios. For example, you can manage a lemonade stand.
Another website with math ratio games is Skillswise from the BBC. Click on the number tab at the top and find games on ratios and proportions. This website will have instructions, quizzes, activities and games.
Finally, the site Internet4Classrooms contains links to various different fun games to play involving ratios, including links to Ratio Blaster and Ratio Martian mentioned above.
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BBC: SkillsWise, http://www.bbc.co.uk/skillswise/numbers/wholenumbers/ratioandproportion/ratio/factsheet.shtml