Before getting into the nuts and bolts of what ratios look like, explain just what ratios are: ratios are comparisons. They say you can’t compare apples to oranges, but when teaching ratios, not only can you do it, you absolutely should do it. For instance, if you have five fruits, of which three are apples and two are oranges, the comparison, or ratio, of apples to oranges is 3:2. The ratio of apples to the total number of fruits is 3:5. You can easily show this concept with actual apples and oranges.
By the time you introduce ratios to your students, they should already have a working familiarity with fractions. That’s perfect, because ratios and fractions are very closely related, allowing you to leverage your students’ understanding of fractions to introduce ratios. Using the same example, students should be able to tell you that 3/5 of the fruit you have are apples. The only difference in showing the ratio, then, is in using the colon instead instead of the fraction symbol. In this case, 3/5 as a ratio is 3:5.
After students have a command of ratios, they will be ready for proportions because proportions are nothing more than equations with ratios on each side. Sticking with our example, 3:5=9:15. The secret to figuring ratios is understanding that ratios are equal and will grow or shrink at equal rates. Because of this, simple division and multiplication will help you find the answer to any proportion question. For instance, if 3:5=n:10, we can divide our known values, 10/5=2. To figure for n, you multiply 3x2 to get 6.
One of the most common places students will encounter ratios and proportions is the supermarket. Candy bars that are 3/$1.00; bananas that are $.39/pound; shirts that are 2 for 1; these are all examples of ratios. For exercises, use practical examples from the supermarket. For instance, if candy bars are 3/$1.00, what is the ratio? The answer, of course, is 3:1. Now, if you have $4.00, how many candy bars could you buy? The proportion would be 3:1=n:4. Using the lesson from the previous section, students can figure out that $4.00 would get them 12 candy bars.