How to Develop Proportional Thinking in Kids

Ever wonder how to develop Proportional Thinking in Kids? Here’s a WONDERFUL Exercise on how to do it, and specific techniques that you and your kids can use to better their skill set so they can master this difficult topic.

So, get your pencils sharpened and paper ready!


How to develop Proportional Thinking in Kids.

If 5 inches on a map represents 22 miles, how many miles are represented by 9 inches?


There are varying reactions when students or parents are presented with this problem, ranging from, “I was never good at math,” or, “I know we did that in school, but I don’t remember,” to, “Just set up a proportion.”


What does it mean to set up a proportion? What is proportional thinking?


Recently, a student taking a pre-assessment answered this question with 198 miles. Evidently, he multiplied 22 (miles) by 9 (inches). Often, students with limited number sense will simply choose numbers from a problem and manipulate them with a random mathematical operation.


Students versed in proportional thinking  would know almost instantly that 198 miles is much too large. The 20 Elements of the Mathnasium Program constitute a student’s number sense. A group of these elements that apply in this situation stipulate that the student:


#10…understands the nature and use of multiples

#15… develops a sense of scale

#19…(has) critical thinking skills


A student with good number sense might reason,”5 inches is 22 miles. 9 is close to 10, which is two 5’s, so 9 inches should represent a little less than 44 miles (two 22’s). Or, “22 is close to 20, so each inch represents a little more than 4 miles (there are four 5’s in 20), so 9 inches would represent a little more than 36 inches.” Obviously, by either reasoning pathway, 198 would not be a reasonable answer. If this question appeared on a multiple choice assessment, the ability to estimate, keeping in mind the scale given, might be all that is necessary to choose the correct answer.


If the answer was to be calculated, element 15 again comes into play:


#15 (The student) understands proportional thinking…and develops a sense of scale.


If the ration of inches to miles is 5:22 or 522, the scale is the same for a length of 9 inches. So, we can set up a proportion (two ratios that equal each other because they have the same scale):




Cross multiply:



Divide both sides by 5:






So, our student’s reasoning, that the answer is a little less than 44 and a little more than 36, would help him to see that not only is his answer correct, but that the initial answer of 198 just doesn’t make sense.


Most students who claim to hate math are just tired of being confused and frustrated. When math makes sense, students’ confidence soars as their problem-solving skills develop. If you’d like to check your number sense, go to Middle School Math Grade Level Check Up |

About Sam Thompson

I grew up in Fort Mitchell in a great family with and entrepreneurial hard working father, loving mother, and charismatic sister. Went to college and graduate school locally, and took my father's path and started my own business out of graduate school. Besides running my businesses, I love math, spending time with my wife, playing with my 2 sons, my daughter, and being out on the golf course, I love purchasing and rehabbing properties and dabbling in politics. I look forward to traveling someday when the kids grow up, but that wont be for sometime, so I'm enjoying the fast and busy life of little babies, toddlers, and growing businesses.