One of the hardest concepts in middle school math is learning about ratios and proportions. Why is this? As a teacher, I think it is because it all comes down to…drum roll, please! The F WORD! Yep, it's the ol' fractions thing, once again. IF you are comfortable with fractions, then ratios and proportions are really quite simple and the ONLY thing you have to remember is this: READ and write the information down IN ORDER. Let's see what this looks like…beginning with vocabulary! 

Ratio…What is a ratio? A ratio is a comparison so understanding this particular vocabulary word is going to be KEY in figuring out proportions. Let's begin with ratios, then shall we? There are three ways to write a ratio. The thing to remember with ratios is that ORDER is important.


Look at this group of butterflies. How many are blue? How many are red? 

Let's make our comparisons now. What is the ratio of blue butterflies to red butterflies? (remember, ORDER is important) There are three ways to write the ratio:


IF we didn't keep the order, then, look at what we'd have.


Middle school standardized tests ALWAYS have lots and lots of word problems dealing with proportions. Well, guess what! IF you can set up the problem correctly, then YOU can solve 'em easily! Yaaaahooo! All it takes is being able to READ the problem and finding the information and putting it into the right order. Here's a typical word problem:


So, let's see the steps in how we can solve this particular problem. Don't be shocked to find it really isn't that hard at all! 

Step 1: Read the question. Find the numbers and labels of what you know. Underline them. From the problem we now have: 





Take this information and rewrite it as a ratio but in FRACTION form (remember, who is your BFF?) 

Step 2: Find the numbers and labels of what you need to know. Underline them. We now have: 





Take this information and rewrite it as a ratio but in FRACTION form 

Step 3: Set up your problem as an EQUATION. Solve it. (How? Think…Did you come up with 'crossmultiply?' Yaaahoo!) 





Step 4: Voila! Go back and put your solution back into the context of the question. 



Try a few problems on your own.


©2011–2017 Sherry Skipper Spurgeon. All rights reserved. 
