Link: Marriage problem
When I first read this problem, I thought that I knew exactly what to do. It had me thinking back to teaching fraction multiplication word problems to my grade eight students and telling them that of means multiply. So initially I thought that when 3/5 of the women married 2/3 of the men I wanted to multiply those fractions together. Boy was I ever wrong! I knew immediately that this was too easy of a solution and that I had to have been wrong. I then began my problem solving steps that I use every time I’m given a math word problem:
Step 1: Write down what I know
Step 2: Write down what I want to know
Step 3: Create a visual
Step 4: Make connections between what I know and what I want to know
Step 5: Perform any calculations
Step 6: State my answer
Step 7: Check my answer
Once I began thinking about what I knew from this problem I was able to write an algebraic equation to model the situation. If 3/5 of the women are married to 2/3 of the men, then that means that 3/5 of the women has to equal 2/3 of the men. This equality let me solve for one variable so that I can use it in a substitution when I have my next equation. When I wrote down what I wanted to know, I was easily able to create an expression that would give me the fraction of the population that’s married. It had to be the number of married people over the total population. From there I could substitute in from my equality and simplify, thus giving me my final answer of 12/19. While writing these steps out may seem simple, it took me quite a while to do.
To be honest, I kept trying to create another equation, thinking that the equality wouldn’t help me simplify my fraction at all. I played with so many different numbers and even invented a town with a population of women that I chose and went from there, in hopes that some solid numbers and data would help me figure out what to do. I got really frustrated because I knew that I had seen this question before, many times during my mathematical career. I had figured it out those times, why couldn’t I figure it out now? I was over-thinking. I am always over-thinking. What would my brain do if it wasn’t thinking? I don’t let it rest, I let it run into overdrive instead. I took a break and re-approached the question a few hours later and with a fresh mind I was able to play around with the algebra and set myself on the right path. I had reached out to some friends of mine that were always good at math and had them check over my ideas for me. I figured out what direction to go into before they responded, though.
When I think about how students would feel performing this problem, I am torn. Would they apply the same steps that I did? Has anyone ever actually taught them how to go about solving word problems? The frustration that I felt while trying this problem would probably be 1o times worse if I were a high school student. It really showed me the importance that I must put into my practice on how to solve math problems instead of simply just solving them. I was able to reach the solution with continued critical thinking; would my students be able to do the same thing?