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Information on Permutations and Combinations

 
 
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Information on Permutations and Combinations
by Candace Ketsa - Thursday, 30 May 2013, 2:59 PM
 

So when I was reevaluating my exams and assignments for permutations and combinations I came across a few that I could not find in our curriculum but were addressed inthe textbook. After further investigation, I found out that these questions are beyond the scope of the course.

I was also concerned about some pathway questions.  This was one that I expected my students to do, but again when looking curriculum I couldn't find a match because of the TWO rectangles.  I knew that one rectangle was a good question, but was not aware that two rectangles was appropriate.


 

So I investigated and this is what I understand to be correct.    Questions with complete rectangular networks (like p. 105, #9) are definitely appropriate because they can be solved by simply applying the permutations with repetitions formula. Questions that involve complete rectangular networks that meet at a vertex (like p. 105, #11c) or complete rectangular networks that overlap one another (like p. 105, #11a) might be appropriate, but would certainly be SE-type questions at the Math 30-2 level.
 

 
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Re: Information on Permutations and Combinations
by Scott Seland - Wednesday, 11 February 2015, 10:36 PM
 

I know this is quite a delayed reply, but this is my first time teaching Math 30-2. I was wondering about this too, so I've gone through all Assessment Standards and Exemplars, the Information Bulletins and the Released Items and came to the same conclusion as you regarding (n+2)! style questions.  BUT in the Program of Studies, the Achievement Indicators include:

5.3 Simplify a numeric or an algebraic fraction that contains factorials in both the numerator and denominator.

5.4 Solve an equation that involves factorials.

I know that achievement indicators only may be used, but the fact that they are in there makes me wonder if they are fair game for diploma questions. I'd rather not spend time on these if there is no chance they will be on the diploma because I don't think they add to students understanding of the concepts, but I also don't want to leave my students unprepared.

P.S. Thank you very much to everyone for all the great discussions and resources. It makes teaching the course for the first time much easier. 

 
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Re: Information on Permutations and Combinations
by James Smith - Thursday, 12 February 2015, 8:55 AM
 

In the 2014-15 standards document, in the general notes for the probability section there is the statement:

Teachers should be aware that specific outcomes 4, 5, and 6 do not require the simplification of factorial expressions (e.g. Simplify n! / (n - 2)! ).

This note was not included in the 2012-13 standards document.

I think solving equations like nP2=12 and nC2=45 are appropriate, but guessing and testing values is a satisfactory solution. I think the pathways problem is appropriate, but I don't think they'll see the case of overlapping rectangles

 
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