More of the same...
In a certain group:
The ratio of males to females is 4:5.
The ratio of left-handed people to right-handed is 1:11 (assume no one is ambidextrous!).
64% of of the left-handed people are males.
(a) What % of the males are left-handed?
(b) What % of the females are left-handed?
- If students or any of us see enough variations of these, will they become almost mechanical or does one have to decide which method/model/representation is needed for each problem?
- How many models should students be shown for these? Usually students or our readers will find a method or model no one else imagined!
- Is algebra the most powerful method? The most efficient? How many variables? Is it usually best to use one variable and let it represent the total number of people in the group?
- Anyone ever use a matrix/spreadsheet/table/Punnett square model to represent the data for these kinds of relationship problems? Specifically, problems in which the entire group (the universe) is divided into either groups A and B or groups C and D. This will become less cryptic as the discussion unfolds.
- Do you think most students today would feel more comfortable working in %, decimal or fraction form? What about rest of us out there?
- Too challenging for middle schoolers or not? Math contest problem or just a challenge to develop facility with ratio thinking? How would most algebra students fare with this?