Condominium Problem
In a particular condominium community 2/3 of all of the men are married to 3/5 of all of the women. What fraction of the entire condominium community are married?
When I first looked at the problem, I added the two fractions together and got 16/15. I knew that did not seem reasonable. I had to think about it for a moment. Then I realized this is a part to whole problem. The part represents married people and the whole represents everyone in the condominium community. Once this clicked in my mind, I just set the problem up using variables M and W. So this is how I solved it.
M = men 2/3M + 3/5W
W = women M + W
Assumptions: the number of men must equal the number of women; cannot marry yourself so I must have an even number of married people as a final answer
2/3M = 3/5W from this equation I solved for M and got: M = 9/10W
Then I substituted for M in my original equation:
2/3(9/10W) + 3/5W
9/10W + W
Next, I simplified and combined like terms on the top and like terms on the bottom:
6/5W
19/10W
Next, I cancelled out the W's and divided the fractions. My final answer is 12/19. There are 12 married people out of a total of 19 people.
I liked this problem because I had to think and process. I will share it with teachers!
Shannon-
ReplyDeleteI love the way you broke that problem down for my complete understanding. As you think back on this problem, what grade level would be most appropriate? What skills would be needed to work through this problem and how would you go about ensuring that your teachers could also break the problem down for student understanding?
Doresia,
DeleteThe condominium problem is a 7th grade math problem. The 7th grade Common Core standards has a ratio and proportional relationship domain and one of the standards include complex fractions. 7th grade students need to know how to divide fractions by fractions. This question maybe difficult for students the way I solved it. There are always several approaches to solving a problem.
I like to work out math problems with teachers to ensure understanding of how to assess standards and discuss different approaches to solving problems. I facilitate professional development during PLCs and work out math problems with teachers. I will share this problem next school year.
Wow! I never would have completed this with out your help. I am still sure I understand what you did and that is because I and I admit I can't connect my blue dots. What grade level would this represent? Since I teach third how would I go about helping teaching understand this problem even with your explanation?
ReplyDeletePat,
DeleteI think this is a 7th grade math problem. 7th grade Common Core standards has a standard that include complex fractions (fraction divided by a fraction). To help teachers understand you should scaffold like you would with students. I would start with simpler problems to make they understand part to whole and substitution. Then combine those two concepts with the condominium problem.
Thanks for sharing Shannon. I never thought to use substitution for this problem. I still got an answer of 12/19, but I listed the multiples of 3 and 5 and compared the common multiples to see which ones would yield a positive even integer. I have posted my method on my blog page if you want to check it out.
ReplyDelete