Show students how ratios and proportions relate to their everyday lives. If they can ride a bike 10 miles per hour, which is a proportion, how far could they ride in two hours? In four hours? If gas costs $2 per gallon, how many gallons of gas could they buy with $10? Seeing how ratios and proportions relate to everyday life will help students to phrase them in more understandable terms. It will also help them to see ways to use the math skills that they are learning.
Use manipulatives such as counters to help students to understand proportions. Place two red counters and three blue counters on the table and ask: What is the ratio of red counters to blue ones? If there are four red counters on the table, how many blue ones should there be to maintain the ratio? Continue doing activities like this and have students use manipulatives to work with ratios until they understand the concept.
Once students understand the concept of working with ratios when they have manipulatives, have them practice filling in a table of ratios. Set up a table so that time is in one row and miles traveled is in another row. Label the time row with numbers 1 through 10 and fill in a number in the first row for miles. Then ask students to fill in the rest of the rows. For example, if your vehicle is traveling 30 miles in one hour, how far will it travel in two hours? In 10 hours? Filling in tables similar to these will help students to understand how ratios work.
When most of your students understand how to work with ratios in a table and with manipulatives, have them pair up to create and answer their own ratio equations. One student might create the ratio of three red dots to five blue ones and ask how many blue dots go with six red ones. The other student would, of course, answer that he needed 10 blue dots. Then it would be the other student’s turn to ask a question for his partner to answer. Having students work in pairs gives them a chance to teach each other while allowing you to monitor and make sure that all of the groups understand the concept.